Foundations doi: 10.3390/foundations3020023

Authors: Bernard A. Egwu Yubin Yan

We investigate the application of the Galerkin finite element method to approximate a stochastic semilinear space&ndash;time fractional wave equation. The equation is driven by integrated additive noise, and the time fractional order &alpha;&isin;(1,2). The existence of a unique solution of the problem is proved by using the Banach fixed point theorem, and the spatial and temporal regularities of the solution are established. The noise is approximated with the piecewise constant function in time in order to obtain a stochastic regularized semilinear space&ndash;time wave equation which is then approximated using the Galerkin finite element method. The optimal error estimates are proved based on the various smoothing properties of the Mittag&ndash;Leffler functions. Numerical examples are provided to demonstrate the consistency between the theoretical findings and the obtained numerical results.

]]>Foundations doi: 10.3390/foundations3020022

Authors: Bashir Ahmad Mokhtar Boumaaza Abdelkrim Salim Mouffak Benchohra

In this article, we present some results on the existence and uniqueness of random solutions to a non-linear implicit fractional differential equation involving the generalized Caputo fractional derivative operator and supplemented with non-local and periodic boundary conditions. We make use of the fixed point theorems due to Banach and Krasnoselskii to derive the desired results. Examples illustrating the obtained results are also presented.

]]>Foundations doi: 10.3390/foundations3020021

Authors: Zachary Denton Aghalaya S. Vatsala

One of the key applications of the Caputo fractional derivative is that the fractional order of the derivative can be utilized as a parameter to improve the mathematical model by comparing it to real data. To do so, we must first establish that the solution to the fractional dynamic equations exists and is unique on its interval of existence. The vast majority of existence and uniqueness results available in the literature, including Picard&rsquo;s method, for ordinary and/or fractional dynamic equations will result in only local existence results. In this work, we generalize Picard&rsquo;s method to obtain the existence and uniqueness of the solution of the nonlinear multi-order Caputo derivative system with initial conditions, on the interval where the solution is bounded. The challenge presented to establish our main result is in developing a generalized form of the Mittag&ndash;Leffler function that will cooperate with all the different fractional derivative orders involved in the multi-order nonlinear Caputo fractional differential system. In our work, we have developed the generalized Mittag&ndash;Leffler function that suffices to establish the generalized Picard&rsquo;s method for the nonlinear multi-order system. As a result, we have obtained the existence and uniqueness of the nonlinear multi-order Caputo derivative system with initial conditions in the large. In short, the solution exists and is unique on the interval where the norm of the solution is bounded. The generalized Picard&rsquo;s method we have developed is both a theoretical and a computational method of computing the unique solution on the interval of its existence.

]]>Foundations doi: 10.3390/foundations3020020

Authors: Sotiris K. Ntouyas Bashir Ahmad Jessada Tariboon

In this paper, we study a coupled system of nonlinear proportional fractional differential equations of the Hilfer-type with a new kind of multi-point and integro-multi-strip boundary conditions. Results on the existence and uniqueness of the solutions are achieved by using Banach&rsquo;s contraction principle, the Leray&ndash;Schauder alternative and the well-known fixed-point theorem of Krasnosel&rsquo;ski&#301;. Finally, the main results are illustrated by constructing numerical examples.

]]>Foundations doi: 10.3390/foundations3020019

Authors: Arno Keppens

Building on previous work that considered gravity to emerge from the collective behaviour of discrete, pre-geometric spacetime constituents, this work identifies these constituents with gravitons and rewrites their effective gravity-inducing interaction in terms of local variables for Schwarzschild&ndash;de Sitter scenarios. This formulation enables graviton-level simulations of entire emergent gravitational systems. A first simulation scenario confirms that the effective graviton interaction induces the emergence of spacetime curvature upon the insertion of a graviton condensate into a flat spacetime background. A second simulation scenario demonstrates that free fall can be considered to be fine-tuned towards a geodesic trajectory, for which the graviton flux, as experienced by a test mass, disappears.

]]>Foundations doi: 10.3390/foundations3020018

Authors: Stephen Baghdiguian Emilie Le Goff Laure Paradis Jean Vacelet Nelly Godefroy

The dynamic equilibrium between death and regeneration is well established at the cell level. Conversely, no study has investigated the homeostatic control of shape at the whole organism level through processes involving apoptosis. To address this fundamental biological question, we took advantage of the morphological and functional properties of the carnivorous sponge Lycopodina hypogea. During its feeding cycle, this sponge undergoes spectacular shape changes. Starved animals display many elongated filaments to capture prey. After capture, prey are digested in the absence of any centralized digestive structure. Strikingly, the elongated filaments actively regress and reform to maintain a constant, homeostatically controlled number and size of filaments in resting sponges. This unusual mode of nutrition provides a unique opportunity to better understand the processes involved in cell renewal and regeneration in adult tissues. Throughout these processes, cell proliferation and apoptosis are interconnected key actors. Therefore, L. hypogea is an ideal organism to study how molecular and cellular processes are mechanistically coupled to ensure global shape homeostasis.

]]>Foundations doi: 10.3390/foundations3020017

Authors: Espen Gaarder Haug

The discussion of what matter and mass are has been going on for more than 2500 years. Much has been discovered about mass in various areas, such as relativity theory and modern quantum mechanics. Still, quantum mechanics has not been unified with gravity. This indicates that there is perhaps something essential not understood about mass in relation to gravity. In relation to gravity, several new mass definitions have been suggested in recent years. We will provide here an overview of a series of potential mass definitions and how some of them appear likely preferable for a potential improved understanding of gravity at a quantum level. This also has implications for practical things such as getting gravity predictions with minimal uncertainty.

]]>Foundations doi: 10.3390/foundations3020016

Authors: Jagan Mohan Jonnalagadda

This article establishes a comparison principle for the nabla fractional difference operator &nabla;&rho;(a)&nu;, 1&lt;&nu;&lt;2. For this purpose, we consider a two-point nabla fractional boundary value problem with separated boundary conditions and derive the corresponding Green&rsquo;s function. I prove that this Green&rsquo;s function satisfies a positivity property. Then, I deduce a relatively general comparison result for the considered boundary value problem.

]]>Foundations doi: 10.3390/foundations3020015

Authors: Abhijith Ajayakumar Raju K. George

This paper examines the controllability of a class of heterogeneous networked systems where the nodes are linear time-invariant systems (LTI), and the network topology is triangularizable. The literature contains necessary and sufficient conditions for the controllability of such systems where the control input matrices are identical in each node. Here, we extend this result to a class of heterogeneous systems where the control input matrices are distinct in each node. Additionally, we discuss the controllability of a more general system with triangular network topology and obtain necessary and sufficient conditions for controllability. Theoretical results are supplemented with numerical examples.

]]>Foundations doi: 10.3390/foundations3020014

Authors: Samundra Regmi Ioannis K. Argyros Gagan Deep Laxmi Rathour

The present paper includes the local and semilocal convergence analysis of a fourth-order method based on the quadrature formula in Banach spaces. The weaker hypotheses used are based only on the first Fr&eacute;chet derivative. The new approach provides the residual errors, number of iterations, convergence radii, expected order of convergence, and estimates of the uniqueness of the solution. Such estimates are not provided in the approaches using Taylor expansions involving higher-order derivatives, which may not exist or may be very expensive or impossible to compute. Numerical examples, including a nonlinear integral equation and a partial differential equation, are provided to validate the theoretical results.

]]>Foundations doi: 10.3390/foundations3010013

Authors: Samundra Regmi Ioannis K. Argyros Jinny Ann John Jayakumar Jayaraman

Iterative methods which have high convergence order are crucial in computational mathematics since the iterates produce sequences converging to the root of a non-linear equation. A plethora of applications in chemistry and physics require the solution of non-linear equations in abstract spaces iteratively. The derivation of the order of the iterative methods requires expansions using Taylor series formula and higher-order derivatives not present in the method. Thus, these results cannot prove the convergence of the iterative method in these cases when such higher-order derivatives are non-existent. However, these methods may still converge. Our motivation originates from the need to handle these problems. No error estimates are given that are controlled by constants. The process introduced in this paper discusses both the local and the semi-local convergence analysis of two step fifth and multi-step 5+3r order iterative methods obtained using only information from the operators on these methods. Finally, the novelty of our process relates to the fact that the convergence conditions depend only on the functions and operators which are present in the methods. Thus, the applicability is extended to these methods. Numerical applications complement the theory.

]]>Foundations doi: 10.3390/foundations3010012

Authors: Ioannis K. Argyros Samundra Regmi Jinny Ann John Jayakumar Jayaraman

High-convergence order iterative methods play a major role in scientific, computational and engineering mathematics, as they produce sequences that converge and thereby provide solutions to nonlinear equations. The convergence order is calculated using Taylor Series extensions, which require the existence and computation of high-order derivatives that do not occur in the methodology. These results cannot, therefore, ensure that the method converges in cases where there are no such high-order derivatives. However, the method could converge. In this paper, we are developing a process in which both the local and semi-local convergence analyses of two related methods of the sixth order are obtained exclusively from information provided by the operators in the method. Numeric applications supplement the theory.

]]>Foundations doi: 10.3390/foundations3010011

Authors: Petri P. Kärenlampi

Multiannual growth systems are modeled in generic terms and investigated using partial derivatives and Lagrange multipliers. Grown stock density and temperature sum are used as independent variables. Estate capitalization increases continuously with grown stock and temperature sum, whereas capital return rate and gross profit rate reach a maximum with respect to grown stock. As two restrictions are applied simultaneously, the results mostly but not always follow intuition. The derivative of capital return rate with respect to gross profit rate is positive, and negative with respect to capitalization. The derivative of capitalization with respect to capital return rate shows some positive values, as well as that with respect to gross profit rate. The derivative of the gross profit rate is positive with respect to both capitalization and capital return rate. The results indicate a variety of alternative strategies, which may or may not be multiobjective.

]]>Foundations doi: 10.3390/foundations3010010

Authors: Iván Lechuga Karo Michaelian

Theories on life&rsquo;s origin generally acknowledge the advantage of a semi-permeable vesicle (protocell) for enhancing the chemical reaction&ndash;diffusion processes involved in abiogenesis. However, more and more evidence indicates that the origin of life is concerned with the photo-chemical dissipative structuring of the fundamental molecules under soft UV-C light (245&ndash;275 nm). In this paper, we analyze the Mie UV scattering properties of such a vesicle created with long-chain fatty acids. We find that the vesicle could have provided early life with a shield from the faint but destructive hard UV-C ionizing light (180&ndash;210 nm) that probably bathed Earth&rsquo;s surface from before the origin of life and at least until 1200 million years after, until the formation of a protective ozone layer as a result of the evolution of oxygenic photosynthesis.

]]>Foundations doi: 10.3390/foundations3010009

Authors: Ioannis K. Argyros Gagan Deep Samundra Regmi

In this study, we present a convergence analysis of a Newton-like midpoint method for solving nonlinear equations in a Banach space setting. The semilocal convergence is analyzed in two different ways. The first one is shown by replacing the existing conditions with weaker and tighter continuity conditions, thereby enhancing its applicability. The second one uses more general &omega;-continuity conditions and the majorizing principle. This approach includes only the first order Fr&eacute;chet derivative and is applicable for problems that were otherwise hard to solve by using approaches seen in the literature. Moreover, the local convergence is established along with the existence and uniqueness region of the solution. The method is useful for solving Engineering and Applied Science problems. The paper ends with numerical examples that show the applicability of our convergence theorems in cases not covered in earlier studies.

]]>Foundations doi: 10.3390/foundations3010008

Authors: Valentina Verdoliva Michele Saviano Stefania De Luca

Zeolites, both natural and synthetic, are certainly some of the most versatile minerals for their applications. Since the 1940s, they have been used in the chemical industry as catalysts, adsorbents and ion exchanger extensively, and the development of their practical usage is expected to continue upon years. Their versatility is the result of the combination of peculiar and indispensable properties, each of which can be found in other material as a single property, but seldom all of them are found in combination. However, despite the success of their employment, the mechanisms of many important catalytic processes involving zeolites remained elusive. In particular, the comprehension of the structure&ndash;property relationships for emerging applications are highly required. In this perspective article we focus on the role of zeolites as solid acid-base catalysts. We go deeply into the structural properties of the LTA kind (Zeolite-Na A 4 &Aring;ngstrom) that was successfully employed as basic catalyst for several nucleophilic substitution reactions.

]]>Foundations doi: 10.3390/foundations3010007

Authors: Eugene Oks

There exists the following paradigm: for interaction potentials U(r) that are negative and go to zero as r goes to infinity, bound states may exist only for the negative total energy E. For E &gt; 0 and for E = 0, bound states are considered to be impossible, both in classical and quantum mechanics. In the present paper we break this paradigm. Namely, we demonstrate the existence of bound states of E = 0 in neutron&ndash;neutron systems and in neutron&ndash;muon systems, specifically when the magnetic moments of the two particles in the pair are parallel to each other. As particular examples, we calculate the root-mean-square size of the bound states of these systems for the values of the lowest admissible values of the angular momentum, and show that it exceeds the neutron radius by an order of magnitude. We also estimate the average kinetic energy and demonstrate that it is nonrelativistic. The corresponding bound states of E = 0 may be called &ldquo;neutronium&rdquo; (for the neutron&ndash;neutron systems) and &ldquo;neutron&ndash;muonic atoms&rdquo; (for the neutron&ndash;muon systems). We also point out that this physical system possesses higher-than-geometric (i.e., algebraic) symmetry, leading to the approximate conservation of the square of the angular momentum, despite the geometric symmetry being axial. We use this fact for facilitating analytical and numerical calculations.

]]>Foundations doi: 10.3390/foundations3010006

Authors: Foundations Editorial Office Foundations Editorial Office

High-quality academic publishing is built on rigorous peer review [...]

]]>Foundations doi: 10.3390/foundations3010005

Authors: Henok Desalegn Desta Eze R. Nwaeze Tadesse Abdi Jebessa B. Mijena

In this paper, by using Jensen&ndash;Mercer&rsquo;s inequality we obtain Hermite&ndash;Hadamard&ndash;Mercer&rsquo;s type inequalities for a convex function employing left-sided (k,&nbsp;&psi;)-proportional fractional integral operators involving continuous strictly increasing function. Our findings are a generalization of some results that existed in the literature.

]]>Foundations doi: 10.3390/foundations3010004

Authors: Ahmed M. A. El-Sayed Yasmin M. Y. Omar Hind H. G. Hashem Shorouk M. Al-Issa

This article is devoted to the solvability and the asymptotic stability of a coupled system of a functional integral equation on the real half-axis. Our consideration is located in the space of bounded continuous functions on R+(BC(R+)). The main tool applied in this work is the technique associated with measures of noncompactness in BC(R+) by a given modulus of continuity. Next, we formulate and prove a sufficient condition for the solvability of that coupled system. We, additionally, provide an example and some particular cases to demonstrate the effectiveness and value of our results.

]]>Foundations doi: 10.3390/foundations3010003

Authors: Gagan Deep Ioannis K. Argyros

In the present study, two new compositions of convergence order six are presented for solving nonlinear equations. The first method is obtained from the third-order one given by Homeier using linear interpolation, and the second one is obtained from the third-order method given by Traub using divided differences. The first method requires three evaluations of the function and one evaluation of the first derivative, thereby enhancing the efficiency index. In the second method, the computation of a derivative is reduced by approximating it using divided differences. Various numerical experiments are performed which demonstrate the accuracy and efficacy of the proposed methods.

]]>Foundations doi: 10.3390/foundations3010002

Authors: László Nemes Christian G. Parigger

This work communicates cavity ring-down spectroscopy (CRDS) of methylidyne (CH) in a chemiluminescent plasma that is produced in a microwave cavity. Of interest are the rotational lines of the 0-0 vibrational transition for the A&ndash;X band and the 1-0 vibrational transition for the B&ndash;X band. The reported investigations originate from research on the CH radical in 1996, which constituted the first case of applying CRDS to the CH radical. The report also includes a recent analysis that shows excellent agreement of the measured and computed data, and it communicates CH line strength data. The CH radical is an important diatomic molecule in hydrocarbon combustion diagnosis and the analysis of stellar plasma emissions, to name just two examples of analytical plasma chemistry.

]]>Foundations doi: 10.3390/foundations3010001

Authors: Christian G. Parigger

This work communicates line-strength data and associated scripts for the computation and spectroscopic fitting of selected transitions of diatomic molecules. The scripts for data analysis are designed for inclusion in various software packages or program languages. Selected results demonstrate the applicability of the program for data analysis in laser-induced optical breakdown spectroscopy primarily at the University of Tennessee Space Institute, Center for Laser Applications. Representative spectra are calculated and referenced to measured data records. Comparisons of experiment data with predictions from other tabulated diatomic molecular databases confirm the accuracy of the communicated line-strength data.

]]>Foundations doi: 10.3390/foundations2040074

Authors: Aghalaya S. Vatsala Govinda Pageni V. Anthony Vijesh

It is known that, from a modeling point of view, fractional dynamic equations are more suitable compared to integer derivative models. In fact, a fractional dynamic equation is referred to as an equation with memory. To demonstrate that the fractional dynamic model is better than the corresponding integer model, we need to compute the solutions of the fractional differential equations and compare them with an integer model relative to the data available. In this work, we will illustrate that the linear nq-order sequential Caputo fractional differential equations, which are sequential of order q where q&lt;1 with fractional initial conditions and/or boundary conditions, can be solved. The reason for choosing sequential fractional dynamic equations is that linear non-sequential Caputo fractional dynamic equations with constant coefficients cannot be solved in general. We used the Laplace transform method to solve sequential Caputo fractional initial value problems. We used fractional boundary conditions to compute Green&rsquo;s function for sequential boundary value problems. In addition, the solution of the sequential dynamic equations yields the solution of the corresponding integer-order differential equations as a special case as q&rarr;1.

]]>Foundations doi: 10.3390/foundations2040073

Authors: Boris M. Smirnov

The evolution of the atmospheric temperature in the past, resulted from the EPICA project (European Project for Ice Coring in Antarctica) for the analysis of air bubbles in ice deposits near three weather stations in Antarctica, includes several glacial cycles. According to these studies, the glacial cycle consists of a slow cooling of the Earth&rsquo;s surface at a rate of about 10&minus;4&#8728;C per year for almost the entire time of a single cycle (about 100 thousand years) and of a fast process of heating the planet, similar to a thermal explosion. The observed cooling of the planet follows from the imbalance of energy fluxes absorbed by the Earth and going into its surrounding space, and this imbalance is four orders of magnitude less than the accuracy of determination of the fluxes themselves. The inconsistency of the popular Milankovich theory is shown, according to which glacial cycles in the evolution of the Earth&rsquo;s thermal state are associated with changes in the Earth&rsquo;s orbit relative to the Sun. In considering the glacial cycle as the transition between the warm (contemporary) and cold thermal states of the Earth with a difference in their temperatures of 12 &#8728;C according to measurements, we construct the energetic balance for each of Earth&rsquo;s states. The fast transition between the Earth&rsquo;s cold and warm states results from the change of the Earth&rsquo;s albedo due to the different volcano activity in these states. There is the feedback between the aggregate state of water covering the Earth&rsquo;s surface and volcanic eruptions, which become intense when ice covers approximately 40% of the Earth&rsquo;s surface. Dust measurements in ice deposits within the framework of the EPICA project confirms roughly a heightened volcano eruption during the cold phase of the glacial cycle. Numerical parameters of processes related to the glacial cycle are analyzed.

]]>Foundations doi: 10.3390/foundations2040072

Authors: Nita H. Shah Nisha Sheoran

It is well known that HIV (human immunodeficiency virus) weakens the immune system of individuals, resulting in risk of other infections, such as pneumonia. The most frequent viral pneumonia seen in individuals infected with HIV is cytomegalovirus (CMV). In this paper, pneumonia&ndash;HIV co-infection is modeled through the formulation of a mathematical compartmental model consisting of nine compartments. Some of the basic properties of the model are established, such as the positivity, boundedness of the system, equilibrium points, and computation of the basic reproduction number. After obtaining the solution, the homotopy perturbation method (HPM) is applied, as it is known for its convergence properties. It is observed that the HPM gives an accurate analytical solution that indicates various important factors that are responsible for the spread of cytomegalovirus pneumonia in HIV-infected populations, and this is justified through a plot made by using MATLAB 2020a.

]]>Foundations doi: 10.3390/foundations2040071

Authors: Kusal Rathnayake Alexander Lebedev Dimitri Volchenkov

A psychology experiment examining decision-making on a continuum of subjectively equivalent alternatives (directions) revealed that subjects follow a common pattern, giving preference to just a few directions over all others. When restricted experimental settings made the common pattern unfeasible, subjects demonstrated no common choice preferences. In the latter case, the observed distribution of choices made by a group of subjects was close to normal. We conclude that the abundance of subjectively equivalent alternatives may reduce the individual variability of choices, and vice versa. Choice overload paradoxically results in behavior patterning and eventually facilitates decision predictability, while restricting the range of available options fosters individual variability of choice, reflected in almost random behavior across the group.

]]>Foundations doi: 10.3390/foundations2040070

Authors: J. Gerard Wolff

This paper highlights 20 significant problems in AI research, with potential solutions via the SP Theory of Intelligence (SPTI) and its realisation in the SP Computer Model. With other evidence referenced in the paper, this is strong evidence in support of the SPTI as a promising foundation for the development of human-level broad AI, aka artificial general intelligence. The 20 problems include: the tendency of deep neural networks to make major errors in recognition; the need for a coherent account of generalisation, over- and under-generalisation, and minimising the corrupting effect of &lsquo;dirty data&rsquo;; how to achieve one-trial learning; how to achieve transfer learning; the need for transparency in the representation and processing of knowledge; and how to eliminate the problem of catastrophic forgetting. In addition to its promise as a foundation for the development of AGI, the SPTI has potential as a foundation for the study of human learning, perception, and cognition. And it has potential as a foundation for mathematics, logic, and computing.

]]>Foundations doi: 10.3390/foundations2040069

Authors: Ioannis K. Argyros Samundra Regmi Christopher I. Argyros Debasis Sharma

We compare the convergence balls and the dynamical behaviors of two efficient weighted-Newton-like equation solvers by Sharma and Arora, and Grau-S&aacute;nchez et al. First of all, the results of ball convergence for these algorithms are established by employing generalized Lipschitz constants and assumptions on the first derivative only. Consequently, outcomes for the radii of convergence, measurable error distances and the existence&ndash;uniqueness areas for the solution are discussed. Then, the complex dynamical behaviors of these solvers are compared by applying the attraction basin tool. It is observed that the solver suggested by Grau-S&aacute;nchez et al. has bigger basins than the method described by Sharma and Arora. Lastly, our ball analysis findings are verified on application problems and the convergence balls are compared. It is found that the method given by Grau-S&aacute;nchez et al. has larger convergence balls than the solver of Sharma and Arora. Hence, the solver presented by Grau-S&aacute;nchez et al. is more suitable for practical application. The convergence analysis uses the first derivative in contrast to the aforementioned studies, utilizing the seventh derivative not on these methods. The developed process can be used on other methods in order to increase their applicability.

]]>Foundations doi: 10.3390/foundations2040068

Authors: Ioannis K. Argyros Christopher I. Argyros Jinny Ann John Jayakumar Jayaraman

We propose the semi-local convergence of two derivative-free, competing methods of order six to address non-linear equations. The sufficient convergence criteria are the same, making a direct comparison between them possible. The existing convergence technique uses the standard Taylor series approach, which requires derivatives up to order seven. The novelty and originality of our work lies in the fact that in contrast to previous research works, our convergence theorems only demand the first derivative. In addition, formulas for determining the region of uniqueness for solution, convergence radii, and error estimations are suggested. Such results cannot be found in works relying on the seventh derivatives. As a consequence, we are able to broaden the utility of these productive methods. The confirmation of our convergence findings through application problems brings this research to a close.

]]>Foundations doi: 10.3390/foundations2040067

Authors: Sebastián Michel-Mata Mónica Gómez-Salazar Víctor Castaño Iván Santamaría-Holek

An innovative and integrative modeling strategy for assessing the sustainability and resilience of social-ecological systems (SES) is presented by introducing a social-ecological entropy production (SEEP) method. In analogy to the thermodynamic entropy production of irreversible processes, we discuss a theoretical model that relates energy and information flow with the cultural and epistemological peculiarities of different communities that exploit the same natural resource. One of the innovative aspects of our approach comes from the fact that sustainability is assessed by a single parameter (SEEP) incorporating the simulation outcomes of all the populations participating in the dynamics, and not only on the fate of the resource. This is significant as far as the non-linearities introduced by the coupling of the different dynamics considered may lead to high sensitivity to small perturbations. Specifically, by assuming two possible types of technical and environmental knowledge-transfer methods [direct (D) and phase-in (P)] within each one of the two communities that exploit and restore a resource, we generate four mathematical models to explore the long-term sustainability scenario due to the intervention, by a new epistemological community, of an initially sustainable resource-community SES. By exploring the space of four key parameters characterizing the degree of technical and environmental knowledge, as well as the rates of social inclusion and knowledge transfer, our simulations show that, from 400 scenarios studied in each case, the P-P model predicts 100% sustainable cases in the use of the resource after the intervention by the second community. The mixed scenarios P-D and D-P predict about 29%, and the D-D scenario only predicts 23% of sustainable cases. Catastrophic outcomes are predicted at about 71% in P-D and D-P scenarios, and about 77% of extinction of the system by exhaustion of the resource and community populations in the D-D scenario. In this form, our theoretical strategy and the knowledge-transfer scenarios studied may help policymakers to find a priori science-based criteria to solve possible controversies arising from social-ecological interventions.

]]>Foundations doi: 10.3390/foundations2040066

Authors: Tejmani Kumar Prashant K. Rai Abhishek K. Rai Nilesh K. Rai Awadhesh K. Rai Christian G. Parigger Geeta Watal Suman Yadav

This interdisciplinary work communicates the identification and quantification of elements responsible for the bioactive potency of leaves from pointed gourd, trichosanthes dioica, using laser-induced breakdown spectroscopy (LIBS). Calibration-free LIBS determines the presence of various trace and major elements, their concentrations, and ratios in which they are present in the leaves. The presence of specific elemental ratios of magnesium/sodium and magnesium/potassium could be promising for managing diabetes mellitus. Variable doses of aqueous extract from trichosanthes dioica leaves are administered for determination of the most effective one. Based on encouraging results, the extract could be harvested to serve as anti-diabetic medication for diabetes and associated symptoms.

]]>Foundations doi: 10.3390/foundations2040065

Authors: Christof Baumgärtel Simon Maher

This article reviews the electrodynamic force law of Wilhelm Weber and its importance in electromagnetic theory. An introduction is given to Weber&rsquo;s force and it is shown how it has been utilised in the literature to explain electromagnetism as well as phenomena in other disciplines of physics, where the force law has connections to the nuclear force, gravity, cosmology, inertia and quantum mechanics. Further, criticism of Weber&rsquo;s force is reviewed and common misconceptions addressed and rectified. It is found that, while the theory is not without criticism and has much room for improvement, within the limitations of its validity, it is equally as successful as Maxwell&rsquo;s theory in predicting certain phenomena. Moreover, it is discussed how Weber offers a valid alternative explanation of electromagnetic phenomena which can enrich and complement the field perspective of electromagnetism through a particle based approach.

]]>Foundations doi: 10.3390/foundations2040064

Authors: Christian G. Parigger

This work investigates spatial and temporal distributions of hydroxyl, OH, in laser-plasma in laboratory air at standard ambient temperature and pressure. Of interest are determination of temperature and density of OH and establishment of a correlation of molecular OH emission spectra with shadow graphs for time delays of 50 to 100 &mu;s, analogous to previous work on shadow graph and emission spectroscopy correlation for cyanide, CN, in gas mixtures and for time delays of the order of 1 &mu;s. Wavelength- and sensitivity-corrected spatiotemporal data analysis focuses on temperature inferences using molecular OH emission spectroscopy. Near-IR radiation from a Q-switched laser device initiates optical breakdown in laboratory air. The laser device provides 6 ns, up to 850 milli Joule, pulses at a wavelength of 1064 nm, and focal irradiance in the range of 1 to 10 terawatt per centimeter-squared. Frequency doubled beams are utilized for capturing shadow graphs for visualization of the breakdown kernel at time delays in the range of 0.1 to 100 &mu;s. OH emission spectra of the laser plasma, spatially resolved along the slit dimension, are recorded in the wavelength range of 298 nm to 321 nm, and with gate widths adjusted to 10 &mu;s for the intensified charge-coupled device that is mounted at the exit plane of a 0.64 m Czerny-Turner configuration spectrometer. Diatomic OH signals occur due to recombination of the plasma and are clearly distinguishable for time delays larger than 50 &mu;s, but are masked by spectra of N2 early in the plasma decay.

]]>Foundations doi: 10.3390/foundations2040063

Authors: Ayub Samadi Sotiris K. Ntouyas Bashir Ahmad Jessada Tariboon

This paper is concerned with the existence of solutions for a new boundary value problem of nonlinear coupled (k,&psi;)&ndash;Hilfer fractional differential equations subject to coupled (k,&psi;)&ndash;Riemann&ndash;Liouville fractional integral boundary conditions. We prove two existence results by applying the Leray&ndash;Schauder alternative, and Krasnosel&rsquo;ski&#301;&rsquo;s fixed-point theorem under different criteria, while the third result, concerning the uniqueness of solutions for the given problem, relies on the Banach&rsquo;s contraction mapping principle. Examples are included for illustrating the abstract results.

]]>Foundations doi: 10.3390/foundations2040062

Authors: Eugene Oks

The proton radius puzzle is one of the most fundamental challenges of modern physics. Before the year 2010, the proton charge radius rp was determined by the spectroscopic method, relying on the electron energy levels in hydrogen atoms, and by the elastic scattering of electrons on protons. In 2010, and then in 2013, two research teams determined rp from the experiment on muonic hydrogen atoms and they claimed rp to be by about 4% smaller than it was found from the experiments with electronic hydrogen atoms. Since then, several research groups performed corresponding experiments with electronic hydrogen atoms and obtained contradictory results: some of them claimed that they found the same value of rp as from the muonic hydrogen experiments, while others reconfirmed the larger value of rp. The conclusion of the latest papers (including reviews) is that the puzzle is not resolved yet. In the present paper, we bring to the attention of the research community, dealing with the proton radius puzzle, the contributing factor never taken into account in any previous calculations. This factor has to do with the hydrogen atoms of the second flavor, whose existence is confirmed in four different types of atomic experiments. We present a relatively simple model illustrating the role of this factor. We showed that disregarding the effect of even a relatively small admixture of the second flavor of muonic hydrogen atoms to the experimental gas of muonic hydrogen atoms could produce the erroneous result that the proton charge radius is by about 4% smaller than its actual value, so that the larger out of the two disputed values of the proton charge radius could be, in fact, correct.

]]>Foundations doi: 10.3390/foundations2040061

Authors: Jeet Amrit Pattnaik Joshua T. Majekodunmi Mrutunjaya Bhuyan Suresh Kumar Patra

The present study is focused on revealing a characteristic kink of the neutron shell closure N = 126 across the Hg-isotopic chain within the relativistic mean-field (RMF) approach with the IOPB-I, DD-ME2, DD-PC1 and NL3 parameter sets. The RMF densities are converted to their spherical equivalence via the Wood&ndash;Saxon approximation and used as input within the parametrization procedure of the coherent density fluctuation model (CDFM). The nuclear matter symmetry energy is calculated using the Br&uuml;ckner energy density functional, and its surface, as well as volume components, are evaluated within Danielwicz&rsquo;s liquid drop prescription. In addition, a comparison between Br&uuml;ckner and relativistic energy density functionals using the NL3 parameter set is shown as a representative case. The binding energy, charge distribution radius and symmetry energy are used as indicators of the isotopic shift in both ground and isomeric states. We have found the presence of a kink at the shell/sub-shell closure at N = 126 for neutron-rich 206Hg. The formation of the kink is traceable to the early filling of the 1i11/2 orbitals rather than 2g9/2, due to the large spin-orbit splitting. As such, the link between the occupational probability and the magicity of nuclei over the Hg-isotopic chain is established.

]]>Foundations doi: 10.3390/foundations2040060

Authors: Paul W. Eloe Jeffrey T. Neugebauer

We construct a Green&rsquo;s function for the three-term fractional differential equation &minus;D0+&alpha;u+aD0+&mu;u+f(t)u=h(t), 0&lt;t&lt;b, where &alpha;&isin;(2,3], &mu;&isin;(1,2], and f is continuous, satisfying the boundary conditions u(0)=u&prime;(0)=0, D0+&beta;u(b)=0, where &beta;&isin;[0,2]. To accomplish this, we first construct a Green&rsquo;s function for the two-term problem &minus;D0+&alpha;u+aD0+&mu;u=h(t), 0&lt;t&lt;b, satisfying the same boundary conditions. A lemma from spectral theory is integral to our construction. Some limiting properties of the Green&rsquo;s function for the two-term problem are also studied. Finally, existence results are given for a nonlinear problem.

]]>Foundations doi: 10.3390/foundations2040059

Authors: Alejandro Mahillo Pedro J. Miana

In this paper, we treat some fractional differential equations on the sequence Lebesgue spaces &#8467;p(N0) with p&ge;1. The Caputo fractional calculus extends the usual derivation. The operator, associated to the Cauchy problem, is defined by a convolution with a sequence of compact support and belongs to the Banach algebra &#8467;1(Z). We treat in detail some of these compact support sequences. We use techniques from Banach algebras and a Functional Analysis to explicity check the solution of the problem.

]]>Foundations doi: 10.3390/foundations2040058

Authors: Leonardo Chiatti

The double nature of material particles, i.e., their wave and corpuscular characteristics, is usually considered incomprehensible, as it cannot be represented visually. It is proposed to the student, in introductory courses, as a fact justified by quantum interference experiments for which, however, no further analysis is possible. On this note, we propose a description of the wave function in terms of a simple electrical analogy, which reproduces at least some of its essential properties. Our aim is to provide a cognitive representation of an analogical type: starting from a classical context (electrical circuits) and introducing in an appropriate way the notions of &ldquo;wave&rdquo; and &ldquo;particle&rdquo;, we show how typically quantum properties such as delocalization and entanglement emerge in a natural, understandable, and intuitive way.

]]>Foundations doi: 10.3390/foundations2040057

Authors: Charles Wing Ho Green Yubin Yan

We consider a predictor&ndash;corrector numerical method for solving Caputo&ndash;Hadamard fractional differential equation over the uniform mesh logtj=loga+logtNajN,j=0,1,2,&hellip;,N with a&ge;1, where loga=logt0&lt;logt1&lt;&hellip;&lt;logtN=logT is a partition of [loga,logT]. The error estimates under the different smoothness properties of the solution y and the nonlinear function f are studied. Numerical examples are given to verify that the numerical results are consistent with the theoretical results.

]]>Foundations doi: 10.3390/foundations2040056

Authors: Christopher I. Argyros Ioannis K. Argyros Samundra Regmi Jinny Ann John Jayakumar Jayaraman

The semi-local convergence is presented for a one parameter seventh order method to obtain solutions of Banach space valued nonlinear models. Existing works utilized hypotheses up to the eighth derivative to prove the local convergence. But these high order derivatives are not on the method and they may not exist. Hence, the earlier results can only apply to solve equations containing operators that are at least eight times differentiable although this method may converge. That is why, we only apply the first derivative in our convergence result. Therefore, the results on calculable error estimates, convergence radius and uniqueness region for the solution are derived in contrast to the earlier proposals dealing with the less challenging local convergence case. Hence, we enlarge the applicability of these methods. The methodology used does not depend on the method and it is very general. Therefore, it can be used to extend other methods in an analogous way. Finally, some numerical tests are performed at the end of the text, where the convergence conditions are fulfilled.

]]>Foundations doi: 10.3390/foundations2030055

Authors: Ravi P. Agarwal Asif R. Khan Sumayyah Saadi

In this work, we use similarly separable vectors in separable Hilbert spaces to provide generalized integral results related to majorization, Niezgoda, and &#262;ebys&eacute;v type inequalities. Next, we furnish some refinements of these inequalities. Theorems obtained in this work extend and improve several known results in the literature. An important aspect of our work is that these inequalities are directly related to Arithmetic, Geometric, Harmonic, and Power means. These means have played an important role in many branches of arts and sciences since the last 2600 years.

]]>Foundations doi: 10.3390/foundations2030054

Authors: Victor Dmitrievich Borisov

The work is devoted to the results of processing electromagnetic radiation signals obtained during laboratory loading of marble and diabase samples using a technique for determining the parameters of microcracks, developed and published by the author earlier. As a result of such processing, certain patterns were found in the nature of the evolution of the oscillatory process ensemble of microcracks. For example, solitary non-linear waves almost always preceded a sequence of High Frequency traces. Equations for straight lines approximating High Frequency traces in logarithmic coordinates, close to the equation of the Gutenberg&ndash;Richter law. Due to the similarity of seismic processes at different scale levels, the results of modeling at the microscale level can be used to describe seismic processes at the macroscale level, for example, to study the processes occurring immediately before destruction and at the time of destruction in order to search for repeatability and regularities. The regularities obtained can be used in the development of a predictive criterion that makes it possible to predict the time of one or another geophysical (seismic) event.

]]>Foundations doi: 10.3390/foundations2030053

Authors: Lorentz Jäntschi

Polyynes are alternations of single and triple bonds between carbon atoms, while cumulenes are successions of double bonds. Since the triple bond is the strongest bond between two carbon atoms, recent preoccupations included synthesizing and condensing cyclic polyynes and cumulenes and their clusters. Density functional theory calculations predicted stable monocyclic rings formation for a number of C atoms equal to or higher than 16. Alternative to the series of Carbon atoms are alternations of Boron and Nitrogen. Large rings (such as those of 24 atoms) can be crossed and thus small clusters can be formed. Patterns of three crosses seem to further stabilize the atomic ensemble. Clusters of 4C24 and 4B12N12 (96 atoms) as well as 4C26 (104 atoms) have been designed, and their conformation has been studied here.

]]>Foundations doi: 10.3390/foundations2030052

Authors: Zhonghui Li Yueyu Lei Enyuan Wang Vladimir Frid Dexing Li Xiaofei Liu Xuekun Ren

In order to explore the evolution characteristics of multi-scale rock-like material failure, we studied the acoustic emission (AE) and electromagnetic radiation (EMR) characteristics of different scale rock-like materials by using the AE-EMR experimental system of coal and rock failure, and the AE and EMR response law of rockburst in mining sites was analyzed. The results show that under uniaxial loading, the stress&ndash;strain curve of the specimen has a compaction stage, linear elastic stage, elastic&ndash;plastic stage and failure stage. The cumulative AE count, AE energy and stress level of the specimen have an exponential relationship during loading and compression. The cumulative EMR counts of loading and unloading showed a trend of first decreasing and then increasing with the increase in stress level. Electromagnetic radiation and microseismic hypocentral distance show an abnormal change trend when rockburst occurs, and this abnormal phenomenon can be used as a precursor feature signal for rockburst monitoring and early warning.

]]>Foundations doi: 10.3390/foundations2030051

Authors: Yingjie Zhao Dazhao Song Menghan Wei Majid Khan Zhenlei Li Liming Qiu Shan Yin

The accurate monitoring and early warning of coal and rock dynamic disasters become challenging in complex geological environments. Mostly, the signal information contains interferences, which misguides the technician, and thus leads to inaccurate monitoring results. To reduce the influence of interference signals, the synchronous response of the acoustic emission (AE) and electromagnetic emission (EME) signals before the failure of coal specimens during uniaxial loading was investigated in this study. Additionally, the coupling relationship between M value, AE energy/AE ringing count per unit time, and the damage of coal is established, and the early warning index of AE and EME (R value) was computed and verified through the field investigations. The results show that a strong synchronization of the acoustoelectric signals occurs only after the specimen enters the strain strengthening area. The analysis of the obtained results showed that the M value of the AE-EME synchronous response signal represents a strong degree of damage occurring in the coal body, however, this is still subject to false alarms. In contrast, the analysis of the R value accurately helped in determining the damage evaluation, thus, it can be regarded as one of the precursors of the imminent failure of coal. With R &gt; 1, the specimen is closed to the failure state, thereby dangerous regions are identified with a dense concentration of R &gt; 1 events. The obtained R value index through on-site AE and EME monitoring corresponds closely with the stress distribution cloud map of the roadway. It is inferred that the anti-interference ability and the reliability of the R value index are stronger than the routine early warning indicators of the single-AE or EME energy.

]]>Foundations doi: 10.3390/foundations2030050

Authors: Konstantinos A. Lazopoulos

&Lambda;-fractional differential equations are discussed since they exhibit non-locality and accuracy. Fractional derivatives form fractional differential equations, considered as describing better various physical phenomena. Nevertheless, fractional derivatives fail to satisfy the prerequisites of differential topology for generating differentials. Hence, all the sources of generating fractional differential equations, such as fractional differential geometry, the fractional calculus of variations, and the fractional field theory, are not mathematically accurate. Nevertheless, the &Lambda;-fractional derivative conforms to all prerequisites demanded by differential topology. Hence, the various mathematical forms, including those derivatives, do not lack the mathematical accuracy or defects of the well-known fractional derivatives. A summary of the &Lambda;-fractional analysis is presented with its influence on the sources of differential equations, such as fractional differential geometry, field theorems, and calculus of variations. &Lambda;-fractional ordinary and partial differential equations will be discussed.

]]>Foundations doi: 10.3390/foundations2030049

Authors: Hamza Tabti Mohammed Belmekki

In this paper, we consider the existence of multiple positive solutions to boundary value problems of nonlinear fractional differential equation with integral boundary conditions and parameter dependence. To obtain our results, we used a functional-type cone expansion-compression fixed point theorem and the Leggett&ndash;Williams fixed point theorem. Examples are included to illustrate the main results.

]]>Foundations doi: 10.3390/foundations2030048

Authors: Ravi P. Agarwal Hana Al-Hutami Bashir Ahmad Boshra Alharbi

This article is concerned with the study of a new class of hybrid fractional q-integro-difference equations involving Caputo type q-derivatives and Riemann-Liouville q-integrals of different orders with a nonlocal q-integro-initial condition. An existence result for the given problem is obtained by means of Krasnoselskii&rsquo;s fixed point theorem, whereas the uniqueness of its solutions is shown by applying the Banach contraction mapping principle. We also discuss the stability of solutions of the problem at hand and find that it depends on the nonlocal parameter in contrast to the initial position of the domain. To demonstrate the application of the obtained results, examples are constructed.

]]>Foundations doi: 10.3390/foundations2030047

Authors: Eugene Oks

In one of our previous papers, we performed a comparative analysis of the experimental and theoretical cross-sections for the excitation of atomic hydrogen by electrons. We found that the theoretical ratio of the cross-section &sigma;2s of the excitation of the state 2s to the cross-section &sigma;2p of the excitation of the state 2p was systematically higher than the corresponding experimental ratio by about 20% (far beyond the experimental error margins). We showed that this discrepancy can be due to the presence of the Second Flavor of Hydrogen Atoms (SFHA) in the experimental gas and that the share of the SFHA in the mixture, required for removing this discrepancy, was about the same as the share of the usual hydrogen atoms. The theory behind the SFHA was based on the standard quantum mechanics&mdash;on the second solution of the Dirac equation for hydrogen atoms&mdash;and on the experimental fact that the charge distribution inside the proton has the peak at the center of the proton; the term &ldquo;flavor&rdquo; was used by the analogy with flavors of quarks. In the present paper, we used the same guiding principles, as employed in that previous study, for the comparative analysis of the experimental and theoretical cross-sections for the excitation of molecular hydrogen by electrons. We found that presumably the most sophisticated calculations, using the convergent close-coupling method involving 491 states, very significantly underestimate the corresponding experimental cross-sections for the two lowest stable triplet states. We showed that if in some hydrogen molecules one or both atoms would be the SFHA, then the above very significant discrepancy could be eliminated. We estimated that it would take such unusual hydrogen molecules to be represented in the experimental gas by the share of about 0.26. This is just by about 40% smaller than the share 0.45 of the SFHA deduced in our previous analysis of the experiment on the electron impact excitation of hydrogen atoms (rather than hydrogen molecules). It should be emphasized that from the theoretical point of view, the share of the unusual hydrogen molecules in any experimental gas and the share of the unusual hydrogen atoms (SFHA) in any experimental gas should not be expected to coincide (it would be the comparison of &ldquo;apples to oranges&rdquo;, rather than &ldquo;apples to apples&rdquo;). In addition, given the roughness of the above estimates, we can state that the results of the present paper reinforce the main conclusion of our previous papers of the very significant share of the SFHA in the experimental hydrogen gases. Thus, the experiments on the electron impact excitation of hydrogen molecules are the fourth type of atomic experiments that proved the existence of the SFHA.

]]>Foundations doi: 10.3390/foundations2030046

Authors: Sotiris K. Ntouyas Bashir Ahmad Jessada Tariboon

In the present research, single and multi-valued (k,&psi;)-Hilfer type fractional boundary value problems of order in (1,2] involving nonlocal integral boundary conditions were studied. In the single-valued case, the Banach and Krasnosel&rsquo;ski&#301; fixed point theorems as well as the Leray&ndash;Schauder nonlinear alternative were used to establish the existence and uniqueness results. In the multi-valued case, when the right-hand side of the inclusion has convex values, we established an existence result via the Leray&ndash;Schauder nonlinear alternative method for multi-valued maps, while the second existence result, dealing with the non-convex valued right-hand side of the inclusion, was obtained by applying Covitz-Nadler fixed point theorem for multi-valued contractions. The obtained theoretical results are well illustrated by the numerical examples provided.

]]>Foundations doi: 10.3390/foundations2030045

Authors: J. M. Nieto-Villar R. Mansilla

From the perspectives of the thermodynamics of irreversible processes and the theory of complex systems, a characterization of longevity and aging and their relationships with the emergence and evolution of cancer was carried out. It was found that: (1) the rate of entropy production could be used as an index of the robustness, plasticity, and aggressiveness of cancer, as well as a measure of biological age; (2) the aging process, as well as the evolution of cancer, goes through what we call a &ldquo;biological phase transition&rdquo;; (3) the process of metastasis, which occurs during the epithelial&ndash;mesenchymal transition (EMT), appears to be a phase transition that is far from thermodynamic equilibrium and exhibits Shilnikov chaos-like dynamic behavior, which guarantees the robustness of the process and, in turn, its unpredictability; (4) as the ferroptosis process progresses, the complexity of the dynamics that are associated with the emergence and evolution of cancer decreases. The theoretical framework that was developed in this study could contribute to a better understanding of the biophysical and chemical phenomena of longevity and aging and their relationships with cancer.

]]>Foundations doi: 10.3390/foundations2030044

Authors: Filopimin Malkotsis Dimitrios Z. Politis Dionisis Dimakos Stelios M. Potirakis

The ground-based monitoring of the lower ionosphere by studying the perturbations of the subionospheric propagation of very-low-frequency/low-frequency (VLF/LF) signals is important in the research of a wide variety of geophysical and Sun/space extreme phenomena. Such perturbations are identified as anomalies in the signal received from the VLF/LF transmitters operating worldwide for military purposes, time code broadcasting, etc. Especially for the study of local ionosphere-influencing phenomena, such as earthquakes, volcanoes, typhoons, etc., the monitoring of several subionospheric propagation paths is necessary. However, it is very difficult to find in the market (or reproduce) hardware (HW) for wide-band VLF/LF receivers that could receive many different transmitters, while the involved software (SW) is mainly proprietary. Aiming to provide a low-cost and easy-to-build alternative for the scientists involved in this research field, we suggest a VLF/LF receiver setup based on amateur radio open-source HW and SW. Its key components are the so-called &ldquo;mini-whip&rdquo; active antenna and the freeware &ldquo;SpectrumLab&rdquo; and &ldquo;GPS2Time&rdquo;. The full HW schematics and all settings of the employed SW configuration for the proposed VLF/LF receiver setup are provided in the article. To check the reliability of the proposed receiver setup, two almost identical VLF/LF radio receivers were installed in the prefecture of Attica in Greece, in June and September of 2021, respectively. Examples of ionospheric perturbations due to different phenomena (solar flares, earthquakes, and a magnetic storm) are provided to show the ability of the proposed receiver setup to provide reliable data for ionosphere-related research.

]]>Foundations doi: 10.3390/foundations2030043

Authors: Juan Núñez Valdés Fernando de Pablos Pons Antonio Ramos Carrillo

It is assumed that the history of modern science in Africa began between the last two decades of the 19th century and the first two or three of the 20th century [...]

]]>Foundations doi: 10.3390/foundations2030042

Authors: Santhosh George Ioannis K. Argyros Christopher I. Argyros Kedarnath Senapati

The Traub iterates generate a sequence that converges to a solution of a nonlinear equation given certain conditions. The order of convergence has been shown provided that the fifth Fr&eacute;chet-derivative exists. Notice that this derivative does not appear on the Traub method. Therefore, according to the earlier results, there is no guarantee that the Traub method converges if the operator is not five times Fr&eacute;chet-differentiable or more. However, the Traub method can converge, since these assumptions are only sufficient. The novelty of our new technique is the fact that only the Fr&eacute;chet-derivative on the method is assumed to exist to prove convergence. Moreover, the new results does not depend on the Traub method. Consequently, the same technique can be applied on other methods. The dynamics of this method are also studied. Examples further explain the theoretical results.

]]>Foundations doi: 10.3390/foundations2030041

Authors: Henok Desalegn Jebessa B. Mijena Eze R. Nwaeze Tadesse Abdi

In this paper, we give new Simpson&rsquo;s type integral inequalities for the class of functions whose derivatives of absolute values are s-convex via generalized proportional fractional integrals. Some results in the literature are particular cases of our results.

]]>Foundations doi: 10.3390/foundations2030040

Authors: Dimos Triantis Andronikos Loukidis Ilias Stavrakas Ermioni D. Pasiou Stavros K. Kourkoulis

The acoustic activity in beam-shaped specimens made of cement is studied, assuming that the beams are loaded in three-point bending under a step-wise loading scheme. Attention is focused to the attenuation of the acoustic activity during the constant-load stage of each specific loading step. The experimental data are analyzed in terms of the interevent time intervals between any two successive acoustic hits (using the F-function concept) and, further, in terms of the power of the acoustic hits (in terms of the recently introduced P-function). It is indicated that while the mechanical load is kept constant, the acoustic activity attenuates steadily, and during the early steps of this attenuation phase, the temporal evolution of both the F- and P-functions is excellently described by an exponential law. Moreover, it is proven that for both the F- and P-functions, the relaxation exponents decrease monotonically with increasing load. This decrease becomes quite abrupt for loads exceeding about 80% of the fracture load, providing an interesting and promising pre-failure indicator, i.e., a warning signal that the specimen is entering into the stage of impending macroscopic fracture. The specific conclusions are in very satisfactory agreement, both qualitatively and quantitatively, with similar ones drawn by considering the temporal evolution of the respective b-value.

]]>Foundations doi: 10.3390/foundations2030039

Authors: Vladimir Pletser

In the first part of this paper, we considered several theoretical models, a static and four dynamic models without rebounds, of the throw of a fair coin landing on its edge, to demonstrate that the probability of heads or tails is less than 50%, depending on the initial toss conditions, the coin geometry and conditions of the coin and landing surfaces. For the dynamic model with rebounds that is the subject of this second part of the paper, it is found that the probability that a 50 Euro cent coin thrown from a normal height with common initial velocity conditions and appropriate surface conditions will end up on its edge is in the order of one against several thousand.

]]>Foundations doi: 10.3390/foundations2030038

Authors: Kirill V. Romanevich Mikhail O. Lebedev Semen V. Andrianov Sergey N. Mulev

Electromagnetic radiation (EMR) technology makes it possible to evaluate changes in the stress-strain state (SSS) in the &ldquo;tunnel lining-enclosing rock mass&rdquo; system at a high level of interference, and to create schemes of long-term EMR control in tunnels (geotechnical monitoring systems). The issues of the variations in EMR signals are extremely important for monitoring systems: based on anomalous deviations from the normal regime one can draw conclusions about changes in the SSS, leading to geodynamic phenomena (e.g., rock bursts). This article presents data obtained during laboratory studies on samples and field studies in transport tunnels. Also, some results of long-term geotechnical monitoring by a set of methods is presented: EMR and tensometry of the tunnel lining, both methods are in the automatic mode. The ability of an EMR control system to respond to earthquakes affecting tunnel structures is shown. An analysis of long-term EMR studies was conducted, which showed the periodic oscillation of the &ldquo;tunnel lining-enclosing rock mass&rdquo; system. In a stable compressed state, minima of EMR pulses are recorded; when the rock mass and lining material are stretched, charges are separated on the edges of micro-defects and EMR increases; complete separation of the edges of micro-defects leads to the termination of intense EMR. The same occurs in the opposite direction during the compression of micro-defects and micro-fractures in the rock mass and concrete lining. The periods of compression and expansion are closely related to temperature fluctuations. The results differ in detail and, therefore, in to be more confident, additional studies are needed in various host rock massifs and types of tunnel lining.

]]>Foundations doi: 10.3390/foundations2030037

Authors: Vladimir Pletser

Considering that a fair coin has two sides and a cylindrical edge, the probability that it would fall on its edge is calculated, yielding the probability of heads or tails of less than 50%. In this first part, the theoretical models for a static case and for five dynamic cases, without rebounds, show that there is a small probability that the coin does not fall on its head or tail, depending on the initial toss conditions, the coin geometry and conditions of the coin and landing surfaces. It is found that the probability that a 50 Eurocent coin thrown from a normal height with common initial velocity conditions and appropriate surface conditions will end up on its edge is in the order of one against several thousand. In the second part of the paper, the dynamic model with rebounds is investigated.

]]>Foundations doi: 10.3390/foundations2030036

Authors: Eugene Oks

For the excitation of the n = 2 states of hydrogen atoms due to electron impact, we compared the experimental and theoretical ratios of the cross-sections &sigma;2s/&sigma;2p. We found this theoretical ratio to be systematically higher than the corresponding experimental ratio by about 20%&mdash;far beyond the experimental error margins. We suggest that this discrepancy can be explained by the presence of the Second Flavor of Hydrogen Atoms (SFHA) in the experimental hydrogen gas. The explanation is based on the fact that, in the experiments, the cross-section &sigma;2s was determined by using the quenching technique&mdash;by applying an electric field that mixed the 2s and 2p states, followed by the emission of the Lyman-alpha line from the 2p state. However, the SFHA only had the s-states, so the quenching technique would not count the excitation of the SFHA in the 2s state and, thus, lead to the underestimation of the cross-section &sigma;2s. We estimates the share of the SFHA in the experimental hydrogen gas required for eliminating the above discrepancy and found this share to be about the same as the share of the usual hydrogen atoms. Thus, our results constitute the third proof from atomic experiments that the SFHA does exist, the first proof being related to the experimental distribution of the linear momentum in the ground state of hydrogen atoms, and the second proof being related to the experimental cross-section of charge exchange between hydrogen atoms and low-energy protons.

]]>Foundations doi: 10.3390/foundations2030035

Authors: Te Ma Laurence Schimleck Joseph Dahlen Seung-Chul Yoon Tetsuya Inagaki Satoru Tsuchikawa Anna Sandak Jakub Sandak

Near-infrared spectroscopy (NIRS) allows for the rapid estimation of a wide range of wood properties. Typically, NIRS studies on wood have utilized benchtop spectrometers, but efforts to utilize NIR hyperspectral imaging to examine wood and wood products have increased. Compared to benchtop NIR systems, hyperspectral imaging has several advantages (speed, visualization of spatial variability), but the data typically have a lower signal-to-noise ratio as well as fewer wavelengths saved; thus, hyperspectral imaging systems have a larger spectral sampling interval (SSI). Furthermore, the SSI and wavelength range varies considerably among different HSI cameras. NIR-HSI systems based on indium gallium arsenide (InGaAs) detectors have a wavelength range typically from 900 to 1700 nm, while short-wave infrared hyperspectral imaging (SWIR-HSI) systems based on mercury cadmium telluride (MCT) detectors have the &lsquo;full&rsquo; NIR wavelength range from 1000 to 2500 nm. These factors may influence the performance of wood property calibrations. We compared one NIR-HSI (900&ndash;1700 nm) and three SWIR-HSI (1000&ndash;2500 nm) commercially available cameras with an NIRS benchtop spectrometer (1100&ndash;2500 nm). The performance of specific gravity (SG) and stiffness (MOE) calibration models was compared with one-hundred Douglas-fir (Pseudotsuga menziesii) samples. The limited wavelength range of an NIR-HSI camera provided the best models for MOE, whereas the NIR-HSI and two SWIR-HSI cameras provided similar SG results. SWIR-HSI models heavily favored wavelengths greater than 1900 nm.

]]>Foundations doi: 10.3390/foundations2020034

Authors: Ioannis K. Argyros Jai Prakash Jaiswal Akanksha Saxena Michael I. Argyros

The significant feature of this paper is that the semi-local convergence of high order methods for solving nonlinear equations defined on abstract spaces has not been studied extensively as done for the local convergence by a plethora of authors which is certainly a more interesting case. A process is developed based on majorizing sequences and the notion of restricted Lipschitz condition to provide a semi-local convergence analysis for the third convergent order Noor&ndash;Waseem method. Due to the generality of our technique, it can be used on other high order methods. The convergence analysis is enhanced. Numerical applications complete are used to test the convergence criteria.

]]>Foundations doi: 10.3390/foundations2020033

Authors: Samundra Regmi Ioannis K. Argyros Santhosh George Christopher I. Argyros

The Newton&ndash;Kantorovich theorem for solving Banach space-valued equations is a very important tool in nonlinear functional analysis. Several versions of this theorem have been given by Adley, Argyros, Ciarlet, Ezquerro, Kantorovich, Potra, Proinov, Wang, et al. This result, e.g., establishes the existence and uniqueness of the solution. Moreover, the Newton sequence converges to the solution under certain conditions of the initial data. However, the convergence region in all of these approaches is small in general; the error bounds on the distances involved are pessimistic, and information about the location of the solutions appears improvable. The novelty of our study lies in the fact that, motivated by optimization concerns, we address all of these. In particular, we introduce a technique that extends the convergence region; provides weaker sufficient semi-local convergence criteria; offers tighter error bounds on the distances involved and more precise information on the location of the solution. These advantages are achieved without additional conditions. This technique can be used to extend other iterative methods along the same lines. Numerical experiments illustrate the theoretical results.

]]>Foundations doi: 10.3390/foundations2020032

Authors: Alexander Robitzsch

In this article, statistical properties of the root mean square deviation (RMSD) item fit statistic in item response models are studied. It is shown that RMSD estimates will indicate even misfit for items whose parametric assumption of the item response function is correct (i.e., fitting items) if some item response functions in the test are misspecified. Moreover, it is demonstrated that the RMSD values of misfitting and fitting items depend on the proportion of misfitting items. We propose three alternative bias-corrected RMSD estimators that reduce the bias for fitting items. However, these alternative estimators provide slightly negatively biased estimates for misfitting items compared to the originally proposed RMSD statistic. In the numerical experiments, we study the case of a misspecified one-parameter logistic item response model and the behavior of the RMSD statistic if differential item functioning occurs.

]]>Foundations doi: 10.3390/foundations2020031

Authors: Juan Núñez Valdés Fernando de Pablos Pons Antonio Ramos Carrillo

At present, several countries on the Asian continent are still very closed off to the idea of allowing not only the work of women, but also even the fact that they can study university degrees and, after finishing them, go on to practice their professions. In addition, if we go back to the beginning of the 20th century, this situation was even more serious. However, this was not an impediment for some women from these countries to achieve their goals of pursuing higher education and then serving society with their work. This article is dedicated to showing the biographies of three of them, the Indian chemist Asima Chatterjee and Philippine pharmacists Matilde S. Arquiza and Filomena Francisco. The most relevant features of their personal and professional lives are presented and previous biographies about them are completed. The main objective of this work is to show these figures to society and hold them up as references to other people, and the methodology followed has been the search for data about their lives and work that would allow us to complete the previous existing biographies about them. A brief biography on Janaki Ammal, the first Indian woman to obtain a doctorate, is also included.

]]>Foundations doi: 10.3390/foundations2020030

Authors: Miguel Á. Hernández-Verón Natalia Romero

In this work, we focus on analyzing the location and separation of the solutions of the simplest quadratic matrix equation. For this, we use the qualitative properties that we can deduce of the study of the convergence of iterative processes. This study allow us to determine domains of existence and uniqueness of solutions, and therefore to locate and separate the solutions. Another goal is to approximate a solution of the quadratic matrix equation. For this, we consider iterative processes of fixed point type. So, analyzing the convergence of these iterative processes of fixed point type, we locate, separate and approximate solutions of quadratic matrix equations.

]]>Foundations doi: 10.3390/foundations2020029

Authors: Juan Núñez Valdés Fernando de Pablos Pons Antonio Ramos Carrillo

Gertrude Belle Elion was a woman who had to overcome many difficulties to achieve her dream of studying to be able to cure illnesses, especially those of the heart. These difficulties were imposed both by the limited economic resources of herself and her family, which did not allow her to pay the academic fees of the university in which she wanted to enroll, as well as gender, since she also had to fight against inequalities of that type prevalent in the society of her time. However, and despite these obstacles, she managed to graduate in Chemistry, based on interest, effort and tenacity, and later began a research career full of successes, which led her to discover relevant active substances which allow her to be awarded the Nobel Prize in Physiology or Medicine in 1988. This article presents the most relevant features of her personal and professional life and completes previous biographies about her life. Its main objective is to reintroduce her to society and put her as a reference to other people. The methodology followed has been the search for those data about her life and work that would allow completing the previous existing biographies about her.

]]>Foundations doi: 10.3390/foundations2020028

Authors: Emilio Santos

We characterize the electromagnetic vacuum as a stochastic field. Some consequences, like the particle behaviour of light, are studied. The stochastic approach is connected with the standard Hilbert space formalism via the Weyl transform. Several experiments involving spontaneous parametric down conversion are studied comparing Hilbert space and Weyl&ndash;Wigner formalisms. This allows an intuitive picture of entanglement to be obtained as a correlation between field fluctuations in distant places, involving the vacuum fields. The analysis shows that the Bell definition of local realism is not general enough, whence the reported violation of Bell inequalities does not refute local realism.

]]>Foundations doi: 10.3390/foundations2020027

Authors: Carla Pires

Background: Lack of access to patients&rsquo; digital health records by community pharmacists can negatively impact pharmaceutical care. Access to these records by community pharmacists is only available in some countries. Thus, the study aim was to compare and discuss the shared patients&rsquo; health records between the National Health Systems and Community Pharmacies in UK and Australia. Methods: Two platforms were selected: Summary Care Records (SCR) (UK) and My Health Record (MyHR) (Australia). A qualitative and descriptive study was carried out. The type of shared health records was collected in public/official websites. Qualitative classifiers/descriptors were created to classify the shared health records. Results: The common classifiers/descriptors between both SCR and MyHR were medicines, medicines/immunization, and medical history. However, MyHR seems to comprise more details/information, such as patient&rsquo;s discharge summaries, specialist letters, or documents to communicate significant patient information from one healthcare provider to another. Conclusion: Community pharmacists can update or consult SCR and MyHR to provide direct patient care in UK and Australia, respectively. The profile of shared health records with community pharmacies was not equal between SCR (UK) and MyHR (Australia). More studies are recommended to evaluate the benefits and risks of using these platforms on patients&rsquo; outcomes.

]]>Foundations doi: 10.3390/foundations2020026

Authors: Sotiris Ntouyas Bashir Ahmad Jessada Tariboon

In this paper, we establish existence and uniqueness results for a new class of boundary value problems involving the ψ-Hilfer generalized proportional fractional derivative operator, supplemented with mixed nonlocal boundary conditions including multipoint, fractional integral multiorder and derivative multiorder operators. The given problem is first converted into an equivalent fixed point problem, which is then solved by means of the standard fixed point theorems. The Banach contraction mapping principle is used to establish the existence of a unique solution, while the Krasnosel’skiĭ and Schaefer fixed point theorems as well as the Leray–Schauder nonlinear alternative are applied for obtaining the existence results. We also discuss the multivalued analogue of the problem at hand. The existence results for convex- and nonconvex-valued multifunctions are respectively proved by means of the Leray–Schauder nonlinear alternative for multivalued maps and Covitz–Nadler’s fixed point theorem for contractive multivalued maps. Numerical examples illustrating the obtained results are also presented.

]]>Foundations doi: 10.3390/foundations2020025

Authors: Frank Nielsen

The informational energy of Onicescu is a positive quantity that measures the amount of uncertainty of a random variable. However, contrary to Shannon&rsquo;s entropy, the informational energy is strictly convex and increases when randomness decreases. We report a closed-form formula for Onicescu&rsquo;s informational energy and its associated correlation coefficient when the probability distributions belong to an exponential family. We show how to instantiate the generic formula for several common exponential families. Finally, we discuss the characterization of valid thermodynamic process trajectories on a statistical manifold by enforcing that the entropy and the informational energy shall vary in opposite directions.

]]>Foundations doi: 10.3390/foundations2020024

Authors: Samundra Regmi Ioannis K. Argyros Santhosh George Christopher I. Argyros

King&rsquo;s method applies to solve scalar equations. The local analysis is established under conditions including the fifth derivative. However, the only derivative in this method is the first. Earlier studies apply to equations containing at least five times differentiable functions. Consequently, these articles provide no information that can be used to solve equations involving functions that are less than five times differentiable, although King&rsquo;s method may converge. That is why the new analysis uses only the operators and their first derivatives which appear in King&rsquo;s method. The article contains the semi-local analysis for complex plane-valued functions not presented before. Numerical applications complement the theory.

]]>Foundations doi: 10.3390/foundations2020023

Authors: Ioannis K. Argyros Debasis Sharma Christopher I. Argyros Sanjaya Kumar Parhi

For the purpose of obtaining solutions to Banach-space-valued nonlinear models, we offer a new extended analysis of the local convergence result for a seventh-order iterative approach without derivatives. Existing studies have used assumptions up to the eighth derivative to demonstrate its convergence. However, in our convergence theory, we only use the first derivative. Thus, in contrast to previously derived results, we obtain conclusions on calculable error estimates, convergence radius, and uniqueness region for the solution. As a result, we are able to broaden the utility of this efficient method. In addition, the convergence regions of this scheme for solving polynomial equations with complex coefficients are illustrated using the attraction basin approach. This study is concluded with the validation of our convergence result on application problems.

]]>Foundations doi: 10.3390/foundations2010022

Authors: Karo Michaelian

There is little doubt that life&rsquo;s origin followed from the known physical and chemical laws of Nature. The most general scientific framework incorporating the laws of Nature and applicable to most known processes to good approximation, is that of thermodynamics and its extensions to treat out-of-equilibrium phenomena. The event of the origin of life should therefore also be amenable to such an analysis. In this review paper, I describe the non-equilibrium thermodynamic foundations of the origin of life for the non-expert from the perspective of the &ldquo;Thermodynamic Dissipation Theory for the Origin of Life&rdquo; which is founded on Classical Irreversible Thermodynamic theory developed by Lars Onsager, Ilya Prigogine, and coworkers. A Glossary of Thermodynamic Terms can be found at the end of the article to aid the reader.

]]>Foundations doi: 10.3390/foundations2010021

Authors: Prakash Singh Shilpi Jain Praveen Agarwal

The objective of this research is to obtain some fractional integral formulas concerning products of the generalized Mittag&ndash;Leffler function and two H-functions. The resulting integral formulas are described in terms of the H-function of several variables. Moreover, we give some illustrative examples for the efficiency of the general approach of our results.

]]>Foundations doi: 10.3390/foundations2010020

Authors: Aurelian Cernea

A coupled system of Hilfer fractional differential inclusions with nonlocal integral boundary conditions is considered. An existence result is established when the set-valued maps have non-convex values. We treat the case when the set-valued maps are Lipschitz in the state variables and we avoid the applications of fixed point theorems as usual. An illustration of the results is given by a suitable example.

]]>Foundations doi: 10.3390/foundations2010019

Authors: Said Mikki

We utilize relativistic quantum mechanics to develop general quantum field-theoretic foundations suitable for understanding, analyzing, and designing generic quantum antennas for potential use in secure quantum communication systems and other applications. Quantum antennas are approached here as abstract source systems capable of producing what we dub &ldquo;quantum radiation.&rdquo; We work from within a generic relativistic framework, whereby the quantum antenna system is modeled in terms of a fundamental quantum spacetime field. After developing a framework explaining how quantum radiation can be understood using the methods of perturbative relativistic quantum field theory (QFT), we investigate in depth the problem of quantum radiation by a controlled abstract source functions. We illustrate the theory in the case of the neutral Klein-Gordon linear quantum antenna, outlining general methods for the construction of the Green&rsquo;s function of a source&mdash;receiver quantum antenna system, the latter being useful for the computation of various candidate angular quantum radiation directivity and gain patterns analogous to the corresponding concepts in classical antenna theory. We anticipate that the proposed formalism may be extended to deal with a large spectrum of other possible controlled emission types for quantum communications applications, including, for example, the production of scalar, fermionic, and bosonic particles, where each could be massless or massive. Therefore, our goal is to extend the idea of antenna beyond electromagnetic waves, where now our proposed QFT-based concept of a quantum antenna system could be used to explore scenarios of controlled radiation of any type of relativistic particles, i.e., effectively transcending the well-known case of photonic systems through the deployment of novel non-standard quantum information transmission carriers such as massive photons, spin-1/2 particles, gravitons, antiparticles, higher spin particles, and so on.

]]>Foundations doi: 10.3390/foundations2010018

Authors: Janak Raj Sharma Ioannis K. Argyros Harmandeep Singh Michael I. Argyros

The local convergence of a generalized (p+1)-step iterative method of order 2p+1 is established in order to estimate the locally unique solutions of nonlinear equations in the Banach spaces. In earlier studies, convergence analysis for the given iterative method was carried out while assuming the existence of certain higher-order derivatives. In contrast to this approach, the convergence analysis is carried out in the present study by considering the hypothesis only on the first-order Fr&eacute;chet derivatives. This study further provides an estimate of convergence radius and bounds of the error for the considered method. Such estimates were not provided in earlier studies. In view of this, the applicability of the given method clearly seems to be extended over the wider class of functions or problems. Moreover, the numerical applications are presented to verify the theoretical deductions.

]]>Foundations doi: 10.3390/foundations2010017

Authors: Christopher I. Argyros Ioannis K. Argyros Stepan Shakhno Halyna Yarmola

We study semi-local convergence of two-step Jarratt-type method for solving nonlinear equations under the classical Lipschitz conditions for first-order derivatives. To develop a convergence analysis we use the approach of restricted convergence regions in combination to majorizing scalar sequences and our technique of recurrent functions. Finally, the numerical example is given.

]]>Foundations doi: 10.3390/foundations2010016

Authors: Eugene Oks

We analyze Molecular Hydrogen Ions (MHIs) formed by collisions of low-energy protons with the Second Flavor of Hydrogen Atoms SFHA, whose existence was previously proven by two kinds of atomic experiments and also evidenced by two kinds of astrophysical observations. We find that the resulting MHIs would lack a significant number of terms compared to the MHIs formed by collisions of low-energy protons with the usual hydrogen atoms. We show that, in this situation, the radiative transition between the terms of such MHIs of the lowest quantum numbers would be between the terms 5f&sigma; and 4d&sigma;. We calculate the position of the edge of the corresponding molecular band and find it to be at the frequency 14,700 cm&minus;1 or equivalently at the wavelength of 680 nm, which belongs to the visible range. It should be easier to observe this band compared to the spectral bands that are completely beyond the visible range. We emphasize that these results open up another avenue for finding an additional experimental proof of the existence of the SFHA. Namely, if the SFHA is present in gas (in addition to the usual hydrogen atoms), on which a beam of low-energy protons is incident, then the relative intensity of the band, corresponding to the radiative transitions between the terms 5f&sigma; and 4d&sigma; of the MHIs, would be enhanced compared to the absence of the SFHA.

]]>Foundations doi: 10.3390/foundations2010015

Authors: David B. Hayrapetyan

In the framework of the effective mass approximation, negative and positive trions, exciton, and biexciton states are investigated in strongly prolate ellipsoidal quantum dots by the variational method. Since the ellipsoidal quantum dot has a prolate character, all excitonic complexes are considered quasi-one-dimensional. As in such a system, the analytical solution does not exist for the many-particle problem, it is solved by the variational method. The trial variation functions based on the one-particle wave functions are used to construct the wavefunctions for the excitonic complexes. The energy spectrum, binding, and recombination energies dependent on the geometrical parameters of the ellipsoidal quantum dots are calculated for the excitons, negative and positive trions, and biexcitons. The radiative lifetime of exciton complexes in ellipsoid is estimated.

]]>Foundations doi: 10.3390/foundations2010014

Authors: Foundations Editorial Office Foundations Editorial Office

Rigorous peer-reviews are the basis of high-quality academic publishing [...]

]]>Foundations doi: 10.3390/foundations2010013

Authors: Attiq ul Rehman Ram Singh Praveen Agarwal

In this paper, fractional Lyapunov functions for epidemic models are introduced and the concept of Mittag-Leffler stability is applied. The global stability of the epidemic model at an equilibrium state is established.

]]>Foundations doi: 10.3390/foundations2010012

Authors: Peeter Saari Ioannis M. Besieris

Vector-valued electromagnetic waves for which the integral of the electric field over time is zero at every location in space were characterized as &ldquo;usual&rdquo; by Bessonov several decades ago. Otherwise, they were called &ldquo;strange&rdquo;. Recently, Popov and Vinogradov studied conditions leading to usual waves using a spectral representation. Their main result is that pulses of finite energy in free space are usual and, consequently, bipolar. However, they do not exclude the possibility of the existence of finite-energy strange pulses, although quite exotic, in a vacuum. Our emphasis in this article is to examine what the relevant necessary and sufficient conditions are for usual and strange waves, particularly for scalar pulses. Illustrative examples are provided, including spherical symmetric collapsing pulses, propagation-invariant, and the so-called almost undistorted spatiotemporally localized waves. Finally, source-generated strange electromagnetic fields are reported.

]]>Foundations doi: 10.3390/foundations2010011

Authors: Valeriy Evgenjevich Ogluzdin

In the review, based on the analysis of the results published in the works of domestic and foreign researchers, a variant of an unconventional interpretation of the photoluminescence of dispersive media in the energy range of 0.5&ndash;3 eV is proposed. The interpretation meets the requirements of the energy conservation law for photons and axions participating in the photoluminescence process. The participation of axions in the process is consistent with Primakov&rsquo;s hypothesis. The role of nonradiative relaxation at the stage of axion decay is noted. The axion lifetimes are estimated for a number of dispersive media.

]]>Foundations doi: 10.3390/foundations2010010

Authors: Ahmed M. A. El-Sayed Hind H. G. Hashem Shorouk M. Al-Issa

Quadratic integral equations of fractional order have been studied from different views. Here we shall study the existence of continuous solutions of a &#981;&minus; fractional-orders quadratic functional integral equation, establish some properties of these solutions and prove the existence of maximal and minimal solutions of that quadratic integral equation. Moreover, we introduce some particular cases to illustrate our results.

]]>Foundations doi: 10.3390/foundations2010009

Authors: Nandhihalli Srinivas Gopal Jagan Mohan Jonnalagadda

In this paper, we look at the two-point boundary value problem for a finite nabla fractional difference equation with dual non-local boundary conditions. First, we derive the associated Green&rsquo;s function and some of its properties. Using the Guo&ndash;Krasnoselkii fixed point theorem on a suitable cone and under appropriate conditions on the non-linear part of the difference equation, we establish sufficient requirements for at least one and at least two positive solutions of the boundary value problem. Next, we discuss the existence and uniqueness of solutions to the considered problem. For this purpose, we use Brouwer and Banach fixed point theorem, respectively. Finally, we provide a few examples to illustrate the applicability of established results.

]]>Foundations doi: 10.3390/foundations2010008

Authors: Christopher I. Argyros Ioannis K. Argyros Stepan Shakhno Halyna Yarmola

We study the semi-local convergence of a three-step Newton-type method for solving nonlinear equations under the classical Lipschitz conditions for first-order derivatives. To develop a convergence analysis, we use the approach of restricted convergence regions in combination with majorizing scalar sequences and our technique of recurrent functions. Finally, a numerical example is given.

]]>Foundations doi: 10.3390/foundations2010007

Authors: Sasmita Kumari Pradhan Sunil Kumar Tripathy Zashmir Naik Dipanjali Behera Mrutunjaya Bhuyan

In this work, we present a Big Rip scenario within the framework of the generalized Brans-Dicke (GBD) theory. In the GBD theory, we consider an evolving BD parameter along with a self-interacting potential. An anisotropic background is considered to have a more general view of the cosmic expansion. The GBD theory with a cosmological constant is presented as an effective cosmic fluid within general relativity which favours a phantom field dominated phase. The model parameters are constrained so that the model provides reasonable estimates of the Hubble parameter and other recent observational aspects at the present epoch. The dynamical aspects of the BD parameter and the BD scalar field have been analysed. It is found that the present model witnesses a finite time doomsday at a time of tBR&#8771;16.14Gyr, and for this scenario, the model requires a large negative value of the Brans-Dicke parameter.

]]>Foundations doi: 10.3390/foundations2010006

Authors: Samundra Regmi Christopher I. Argyros Ioannis K. Argyros Santhosh George

The celebrated Traub&rsquo;s method involving Banach space-defined operators is extended. The main feature in this study involves the determination of a subset of the original domain that also contains the Traub iterates. In the smaller domain, the Lipschitz constants are smaller too. Hence, a finer analysis is developed without the usage of additional conditions. This methodology applies to other methods. The examples justify the theoretical results.

]]>Foundations doi: 10.3390/foundations2010005

Authors: Nikolay Kryukov Eugene Oks

Previously published analytical results for the effects of a high-frequency laser field on hydrogen Rydberg atoms demonstrated that the unperturbed elliptical orbit of the Rydberg electron, generally is engaged simultaneously in the precession of the orbital plane about the direction of the laser field and in the precession within the orbital plane. These results were obtained while disregarding relativistic effects. In the present paper, we analyze the relativistic effect for hydrogenic Rydberg atoms or ions in a high-frequency linearly- or circularly-polarized laser field, the effect being an additional precession of the electron orbit in its own plane. For the linearly-polarized laser field, the general case, where the electron orbit is not perpendicular to the direction of the laser field, we showed that the precession of the electron orbit within its plane can vanish at some critical polar angle &theta;c of the orbital plane. We calculated analytically the dependence of the critical angle on the angular momentum of the electron and on the parameters of the laser field. Finally, for the particular situation, where the electron orbit is perpendicular to the direction of the laser field, we demonstrated that the relativistic precession and the precession due to the laser field occur in the opposite directions. As a result, the combined effect of these two kinds of the precession is smaller than the absolute value of each of them. We showed that by varying the ratio of the laser field strength F to the square of the laser field frequency &omega;, one can control the precession frequency of the electron orbit and even make the precession vanish, so that the elliptical orbit of the electron would become stationary. This is a counterintuitive result.

]]>Foundations doi: 10.3390/foundations2010004

Authors: Tolulope Majekodunmi Joshua Nishu Jain Raj Kumar Khairul Anwar Nooraihan Abdullah Mrutunjaya Bhuyan

A new &alpha;-emitting 214U has been recently observed experimentally. This opens the window to theoretically investigate the ground-state properties of the lightest known even&ndash;even neutron deficient 214,216,218U isotopes and to examine &alpha;-particle clustering around the shell closure. The decay half-lives are calculated within the preformed cluster-decay model (PCM). To obtain the &alpha;-daughter interaction potential, the RMF densities are folded with the newly developed R3Y and the well-known M3Y NN potentials for comparison. The alpha preformation probability (P&alpha;) is calculated from the analytic formula of Deng and Zhang. The WKB approximation is employed for the calculation of the transmission probability. The individual binding energies (BE) for the participating nuclei are estimated from the relativistic mean-field (RMF) formalism and those from the finite range droplet model (FRDM) as well as WS3 mass tables. In addition to Z=84, the so-called abnormal enhancement region, i.e., 84&le;Z&le;90 and N&lt;126, is normalised by an appropriately fitted neck-parameter &Delta;R. On the other hand, the discrepancy sets in due to the shell effect at (and around) the proton magic number Z=82 and 84, and thus a higher scaling factor ranging from 10&minus;8&ndash;10&minus;5 is required. Additionally, in contrast with the experimental binding energy data, large deviations of about 5&ndash;10 MeV are evident in the RMF formalism despite the use of different parameter sets. An accurate prediction of &alpha;-decay half-lives requires a Q-value that is in proximity with the experimental data. In addition, other microscopic frameworks besides RMF could be more reliable for the mass region under study. &alpha;-particle clustering is largely influenced by the shell effect.

]]>Foundations doi: 10.3390/foundations2010003

Authors: Said Mikki

An alternative to conventional spacetime is proposed and rigorously formulated for nonlocal continuum field theories through the deployment of a fiber bundle-based superspace extension method. We develop, in increasing complexity, the concept of nonlocality starting from general considerations, going through spatial dispersion, and ending up with a broad formulation that unveils the link between general topology and nonlocality in generic material media. It is shown that nonlocality naturally leads to a Banach (vector) bundle structure serving as an enlarged space (superspace) inside which physical processes, such as the electromagnetic ones, take place. The added structures, essentially fibered spaces, model the topological microdomains of physics-based nonlocality and provide a fine-grained geometrical picture of field&ndash;matter interactions in nonlocal metamaterials. We utilize standard techniques in the theory of smooth manifolds to construct the Banach bundle structure by paying careful attention to the relevant physics. The electromagnetic response tensor is then reformulated as a superspace bundle homomorphism and the various tools needed to proceed from the local topology of microdomains to global domains are developed. For concreteness and simplicity, our presentations of both the fundamental theory and the examples given to illustrate the mathematics all emphasize the case of electromagnetic field theory, but the superspace formalism developed here is quite general and can be easily extended to other types of nonlocal continuum field theories. An application to fundamental theory is given, which consists of utilizing the proposed superspace theory of nonlocal metamaterials in order to explain why nonlocal electromagnetic materials often require additional boundary conditions or extra input from microscopic theory relative to local electromagnetism, where in the latter case such extra input is not needed. Real-life case studies quantitatively illustrating the microdomain structure in nonlocal semiconductors are provided. Moreover, in a series of connected appendices, we outline a new broad view of the emerging field of nonlocal electromagnetism in material domains, which, together with the main superspace formalism introduced in the main text, may be considered a new unified general introduction to the physics and methods of nonlocal metamaterials.

]]>Foundations doi: 10.3390/foundations2010002

Authors: Neelma Eiman Kamal Shah

This current work is devoted to develop qualitative theory of existence of solution to some families of fractional order differential equations (FODEs). For this purposes we utilize fixed point theory due to Banach and Schauder. Further using differential transform method (DTM), we also compute analytical or semi-analytical results to the proposed problems. Also by some proper examples we demonstrate the results.

]]>Foundations doi: 10.3390/foundations2010001

Authors: Eugene Oks

Many totally different kinds of astrophysical observations demonstrated that, in our universe, there exists a preferred direction. Specifically, from observations in a wide range of frequencies, the alignment of various preferred directions in different data sets was found. Moreover, the observed Cosmic Microwave Background (CMB) quadrupole, CMB octopole, radio and optical polarizations from distant sources also indicate the same preferred direction. While this hints at a gravitational pull from the &ldquo;outside&rdquo;, the observational data from the Plank satellite showed that the bulk flow velocity was relatively small: much smaller than was initially thought. In the present paper we propose a configuration where two three-dimensional universes (one of which is ours) are embedded in a four-dimensional space and rotate about their barycenter in such a way that the centrifugal force nearly (but not exactly) compensates their mutual gravitational pull. This would explain not only the existence of a preferred direction for each of the three-dimensional universes (the direction to the other universe), but also the fact that the bulk flow velocity, observed in our universe, is relatively small. We point out that this configuration could also explain the perplexing features of the Unidentified Aerial Phenomena (UAP), previously called Unidentified Flying Objects (UFOs), recorded by various detection systems&mdash;the features presented in the latest official report by the US Office of the Director of National Intelligence. Thus, the proposed configuration of the two rotating, parallel three-dimensional universes seems to explain both the variety of astrophysical observations and (perhaps) the observed features of the UAP.

]]>Foundations doi: 10.3390/foundations1020022

Authors: Samar Elaraby Sherif M. Abuelenin Adel Moussa Yasser M. Sabry

Miniaturized Fourier transform infrared spectrometers serve emerging market needs in many applications such as gas analysis. The miniaturization comes at the cost of lower performance than bench-top instrumentation, especially for the spectral resolution. However, higher spectral resolution is needed for better identification of the composition of materials. This article presents a convolutional neural network (CNN) for 3X resolution enhancement of the measured infrared gas spectra using a Fourier transform infrared (FTIR) spectrometer beyond the transform limit. The proposed network extracts a set of high-dimensional features from the input spectra and constructs high-resolution outputs by nonlinear mapping. The network is trained using synthetic transmission spectra of complex gas mixtures and simulated sensor non-idealities such as baseline drifts and non-uniform signal-to-noise ratio. Ten gases that are relevant to the natural and bio gas industry are considered whose mixtures suffer from overlapped features in the mid-infrared spectral range of 2000&ndash;4000 cm&minus;1. The network results are presented for both synthetic and experimentally measured spectra using both bench-top and miniaturized MEMS spectrometers, improving the resolution from 60 cm&minus;1 to 20 cm&minus;1 with a mean square error down to 2.4&times;10&minus;3 in the transmission spectra. The technique supports selective spectral analysis based on miniaturized MEMS spectrometers.

]]>Foundations doi: 10.3390/foundations1020021

Authors: Vishal Nikam Dhananjay Gopal Rabha W. Ibrahim

The existence of a parametric fractional integral equation and its numerical solution is a big challenge in the field of applied mathematics. For this purpose, we generalize a special type of fixed-point theorems. The intention of this work is to prove fixed-point theorems for the class of &beta;&minus;G, &psi;&minus;G contractible operators of Darbo type and demonstrate the usability of obtaining results for solvability of fractional integral equations satisfying some local conditions in Banach space. In this process, some recent results have been generalized. As an application, we establish a set of conditions for the existence of a class of fractional integrals taking the parametric Riemann&ndash;Liouville formula. Moreover, we introduce numerical solutions of the class by using the set of fixed points.

]]>Foundations doi: 10.3390/foundations1020020

Authors: Giacomo Ortali Ioannis G. Tollis

In a dominance drawing &Gamma; of a directed acyclic graph (DAG) G, a vertex v is reachable from a vertex u if, and only if all the coordinates of v are greater than or equal to the coordinates of u in &Gamma;. Dominance drawings of DAGs are very important in many areas of research. They combine the aspect of drawing a DAG on the grid with the fact that the transitive closure of the DAG is apparently obvious by the dominance relation between grid points associated with the vertices. The smallest number d for which a given DAG G has a d-dimensional dominance drawing is called dominance drawing dimension, and it is NP-hard to compute. In this paper, we present efficient algorithms for computing dominance drawings of G with a number of dimensions respecting theoretical bounds. We first describe a simple algorithm that shows how to compute a dominance drawing of G from its compressed transitive closure. Next, we describe a more complicated algorithm, which is based on the concept of modular decomposition of G, and obtaining dominance drawings with a lower number of dimensions. Finally, we consider the concept of weak dominance, a relaxed version of the dominance, and we discuss interesting experimental results.

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