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Axioms, Volume 9, Issue 2 (June 2020) – 37 articles

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24 pages, 479 KiB  
Article
Revisiting Primordial Black Hole Evolution
by Maxim Khlopov, Biplab Paik and Saibal Ray
Axioms 2020, 9(2), 71; https://doi.org/10.3390/axioms9020071 - 25 Jun 2020
Cited by 3 | Viewed by 2431
Abstract
Primordial black holes (PBHs) are the sensitive probe for physics and cosmology of very early Universe. The observable effect of their existence depends on the PBH mass. Mini PBHs evaporate and do not survive to the present time, leaving only background effect of [...] Read more.
Primordial black holes (PBHs) are the sensitive probe for physics and cosmology of very early Universe. The observable effect of their existence depends on the PBH mass. Mini PBHs evaporate and do not survive to the present time, leaving only background effect of products of their evaporation, while PBHs evaporating now can be new exotic sources of energetic particles and gamma rays in the modern Universe. Here we revisit the history of evolution of mini PBHs. We follow the aspects associated with growth versus evaporation rate of “a mini PBH being trapped inside intense local cosmological matter inhomogeneity”. We show that the existence of baryon accretion forbidden black hole regime enables constraints on mini PBHs with the mass M ≤ 5.5 × 10 13 g. On the other hand, we propose the mechanism of delay of evaporation of primordial population of PBHs of primordial mass range 5.5 × 10 13 g ≤ M ≤ 5.1 × 10 14 g. It can provide their evaporation to be the main contributor to γ -ray flux distribution in the current Universe. At the final stage of evaporation these PBHs can be the source of ultrahigh energy cosmic rays and gamma radiation challenging probe for their existence in the LHAASO experiment. Full article
(This article belongs to the Special Issue Theory and Mathematical Aspects of Black Holes)
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21 pages, 384 KiB  
Article
Existence Results for Nonlocal Multi-Point and Multi-Term Fractional Order Boundary Value Problems
by Bashir Ahmad, Najla Alghamdi, Ahmed Alsaedi and Sotiris K. Ntouyas
Axioms 2020, 9(2), 70; https://doi.org/10.3390/axioms9020070 - 24 Jun 2020
Cited by 1 | Viewed by 2022
Abstract
In this paper, we discuss the existence and uniqueness of solutions for a new class of multi-point and integral boundary value problems of multi-term fractional differential equations by using standard fixed point theorems. We also demonstrate the application of the obtained results with [...] Read more.
In this paper, we discuss the existence and uniqueness of solutions for a new class of multi-point and integral boundary value problems of multi-term fractional differential equations by using standard fixed point theorems. We also demonstrate the application of the obtained results with the aid of examples. Full article
(This article belongs to the Special Issue Differential and Difference Equations: A Themed Issue Dedicated to Prof. Hari M. Srivastava on the Occasion of his 80th Birthday)
14 pages, 269 KiB  
Article
On a New Generalized Integral Operator and Certain Operating Properties
by Paulo M. Guzman, Luciano M. Lugo, Juan E. Nápoles Valdés and Miguel Vivas-Cortez
Axioms 2020, 9(2), 69; https://doi.org/10.3390/axioms9020069 - 20 Jun 2020
Cited by 21 | Viewed by 2551
Abstract
In this paper, we present a general definition of a generalized integral operator which contains as particular cases, many of the well-known, fractional and integer order integrals. Full article
(This article belongs to the Special Issue Fractional Calculus, Wavelets and Fractals)
19 pages, 350 KiB  
Article
Boundary Value Problem for Weak Nonlinear Partial Differential Equations of Mixed Type with Fractional Hilfer Operator
by Tursun K. Yuldashev and Bakhtiyor J. Kadirkulov
Axioms 2020, 9(2), 68; https://doi.org/10.3390/axioms9020068 - 17 Jun 2020
Cited by 35 | Viewed by 3372
Abstract
In this paper, we consider a boundary value problem for a nonlinear partial differential equation of mixed type with Hilfer operator of fractional integro-differentiation in a positive rectangular domain and with spectral parameter in a negative rectangular domain. With respect to the first [...] Read more.
In this paper, we consider a boundary value problem for a nonlinear partial differential equation of mixed type with Hilfer operator of fractional integro-differentiation in a positive rectangular domain and with spectral parameter in a negative rectangular domain. With respect to the first variable, this equation is a nonlinear fractional differential equation in the positive part of the considering segment and is a second-order nonlinear differential equation with spectral parameter in the negative part of this segment. Using the Fourier series method, the solutions of nonlinear boundary value problems are constructed in the form of a Fourier series. Theorems on the existence and uniqueness of the classical solution of the problem are proved for regular values of the spectral parameter. For irregular values of the spectral parameter, an infinite number of solutions of the mixed equation in the form of a Fourier series are constructed. Full article
(This article belongs to the Special Issue Nonlinear Differential Equations and Dynamical Systems: Theory and Applications)
28 pages, 338 KiB  
Article
Minimal Systems of Temporal Logic
by Dariusz Surowik
Axioms 2020, 9(2), 67; https://doi.org/10.3390/axioms9020067 - 16 Jun 2020
Cited by 1 | Viewed by 2264
Abstract
The article discusses minimal temporal logic systems built on the basis of classical logic as well as intuitionistic logic. The constructions of these systems are discussed as well as their basic properties. The K t system was discussed as the minimal temporal logic [...] Read more.
The article discusses minimal temporal logic systems built on the basis of classical logic as well as intuitionistic logic. The constructions of these systems are discussed as well as their basic properties. The K t system was discussed as the minimal temporal logic system built based on classical logic, while the IK t system and its modification were discussed as the minimal temporal logic system built based on intuitionistic logic. Full article
(This article belongs to the Special Issue Deductive Systems in Traditional and Modern Logic)
11 pages, 283 KiB  
Article
Structure and Functions of Topological Metagroups
by Sergey V. Ludkowski
Axioms 2020, 9(2), 66; https://doi.org/10.3390/axioms9020066 - 14 Jun 2020
Cited by 3 | Viewed by 1880
Abstract
In this article, the structure of topological metagroups was investigated. Relations between topological and algebraic properties of metagroups were scrutinized. A uniform continuity of functions on them was studied. Smashed products of topological metagroups were investigated. Full article
(This article belongs to the Collection Topological Groups)
23 pages, 840 KiB  
Article
Generalized Nabla Differentiability and Integrability for Fuzzy Functions on Time Scales
by R. Leelavathi, G. Suresh Kumar, Ravi P. Agarwal, Chao Wang and M.S.N. Murty
Axioms 2020, 9(2), 65; https://doi.org/10.3390/axioms9020065 - 08 Jun 2020
Cited by 3 | Viewed by 2179
Abstract
This paper mainly deals with introducing and studying the properties of generalized nabla differentiability for fuzzy functions on time scales via Hukuhara difference. Further, we obtain embedding results on E n for generalized nabla differentiable fuzzy functions. Finally, we prove a fundamental theorem [...] Read more.
This paper mainly deals with introducing and studying the properties of generalized nabla differentiability for fuzzy functions on time scales via Hukuhara difference. Further, we obtain embedding results on E n for generalized nabla differentiable fuzzy functions. Finally, we prove a fundamental theorem of a nabla integral calculus for fuzzy functions on time scales under generalized nabla differentiability. The obtained results are illustrated with suitable examples. Full article
(This article belongs to the Special Issue Differential and Difference Equations: A Themed Issue Dedicated to Prof. Hari M. Srivastava on the Occasion of his 80th Birthday)
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13 pages, 292 KiB  
Article
Conformally Flat Siklos Metrics Are Ricci Solitons
by Giovanni Calvaruso
Axioms 2020, 9(2), 64; https://doi.org/10.3390/axioms9020064 - 08 Jun 2020
Cited by 6 | Viewed by 1827
Abstract
We study and solve the Ricci soliton equation for an arbitrary locally conformally flat Siklos metric, proving that such spacetimes are always Ricci solitons. Full article
(This article belongs to the Special Issue Pseudo-Riemannian Metrics and Applications)
17 pages, 256 KiB  
Article
Functors among Relational Variants of Categories Related to L-Fuzzy Partitions, L-Fuzzy Pretopological Spaces and L-Fuzzy Closure Spaces
by Jiří Močkoř
Axioms 2020, 9(2), 63; https://doi.org/10.3390/axioms9020063 - 02 Jun 2020
Cited by 6 | Viewed by 1999
Abstract
Various types of topological and closure operators are significantly used in fuzzy theory and applications. Although they are different operators, in some cases it is possible to transform an operator of one type into another. This in turn makes it possible to transform [...] Read more.
Various types of topological and closure operators are significantly used in fuzzy theory and applications. Although they are different operators, in some cases it is possible to transform an operator of one type into another. This in turn makes it possible to transform results relating to an operator of one type into results relating to another operator. In the paper relationships among 15 categories of modifications of topological L-valued operators, including Čech closure or interior L-valued operators, L-fuzzy pretopological and L-fuzzy co-pretopological operators, L-valued fuzzy relations, upper and lower F-transforms and spaces with fuzzy partitions are investigated. The common feature of these categories is that their morphisms are various L-fuzzy relations and not only maps. We prove the existence of 23 functors among these categories, which represent transformation processes of one operator into another operator, and we show how these transformation processes can be mutually combined. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Applications)
9 pages, 263 KiB  
Article
On the Solvability of Nonlinear Third-Order Two-Point Boundary Value Problems
by Ravi P. Agarwal, Petio S. Kelevedjiev and Todor Z. Todorov
Axioms 2020, 9(2), 62; https://doi.org/10.3390/axioms9020062 - 31 May 2020
Cited by 1 | Viewed by 1792
Abstract
Under barrier strips type assumptions we study the existence of C 3 [ 0 , 1 ] —solutions to various two-point boundary value problems for the equation [...] Read more.
Under barrier strips type assumptions we study the existence of C 3 [ 0 , 1 ] —solutions to various two-point boundary value problems for the equation x ‴ = f ( t , x , x ′ , x ″ ) . We give also some results guaranteeing positive or non-negative, monotone, convex or concave solutions. Full article
(This article belongs to the Special Issue Nonlinear Differential Equations and Dynamical Systems: Theory and Applications)
12 pages, 608 KiB  
Article
On the Numerical Solution of Fractional Boundary Value Problems by a Spline Quasi-Interpolant Operator
by Francesca Pitolli
Axioms 2020, 9(2), 61; https://doi.org/10.3390/axioms9020061 - 25 May 2020
Cited by 8 | Viewed by 2250
Abstract
Boundary value problems having fractional derivative in space are used in several fields, like biology, mechanical engineering, control theory, just to cite a few. In this paper we present a new numerical method for the solution of boundary value problems having Caputo derivative [...] Read more.
Boundary value problems having fractional derivative in space are used in several fields, like biology, mechanical engineering, control theory, just to cite a few. In this paper we present a new numerical method for the solution of boundary value problems having Caputo derivative in space. We approximate the solution by the Schoenberg-Bernstein operator, which is a spline positive operator having shape-preserving properties. The unknown coefficients of the approximating operator are determined by a collocation method whose collocation matrices can be constructed efficiently by explicit formulas. The numerical experiments we conducted show that the proposed method is efficient and accurate. Full article
(This article belongs to the Special Issue Fractional Calculus, Wavelets and Fractals)
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21 pages, 324 KiB  
Article
Geometric Study of Marginally Trapped Surfaces in Space Forms and Robertson-Walker Spacetimes—An Overview
by Kristof Dekimpe and Joeri Van der Veken
Axioms 2020, 9(2), 60; https://doi.org/10.3390/axioms9020060 - 24 May 2020
Cited by 1 | Viewed by 1766
Abstract
A marginally trapped surface in a spacetime is a Riemannian surface whose mean curvature vector is lightlike at every point. In this paper we give an up-to-date overview of the differential geometric study of these surfaces in Minkowski, de Sitter, anti-de Sitter and [...] Read more.
A marginally trapped surface in a spacetime is a Riemannian surface whose mean curvature vector is lightlike at every point. In this paper we give an up-to-date overview of the differential geometric study of these surfaces in Minkowski, de Sitter, anti-de Sitter and Robertson-Walker spacetimes. We give the general local descriptions proven by Anciaux and his coworkers as well as the known classifications of marginally trapped surfaces satisfying one of the following additional geometric conditions: having positive relative nullity, having parallel mean curvature vector field, having finite type Gauss map, being invariant under a one-parameter group of ambient isometries, being isotropic, being pseudo-umbilical. Finally, we provide examples of constant Gaussian curvature marginally trapped surfaces and state some open questions. Full article
(This article belongs to the Special Issue Pseudo-Riemannian Metrics and Applications)
12 pages, 266 KiB  
Article
Measure of Noncompactness for Hybrid Langevin Fractional Differential Equations
by Ahmed Salem and Mohammad Alnegga
Axioms 2020, 9(2), 59; https://doi.org/10.3390/axioms9020059 - 23 May 2020
Cited by 21 | Viewed by 2675
Abstract
In this research article, we introduce a new class of hybrid Langevin equation involving two distinct fractional order derivatives in the Caputo sense and Riemann–Liouville fractional integral. Supported by three-point boundary conditions, we discuss the existence of a solution to this boundary value [...] Read more.
In this research article, we introduce a new class of hybrid Langevin equation involving two distinct fractional order derivatives in the Caputo sense and Riemann–Liouville fractional integral. Supported by three-point boundary conditions, we discuss the existence of a solution to this boundary value problem. Because of the important role of the measure of noncompactness in fixed point theory, we use the technique of measure of noncompactness as an essential tool in order to get the existence result. The modern analysis technique is used by applying a generalized version of Darbo’s fixed point theorem. A numerical example is presented to clarify our outcomes. Full article
(This article belongs to the Special Issue Fractional Calculus, Wavelets and Fractals)
8 pages, 251 KiB  
Article
On the Stability of the Generalized Psi Functional Equation
by Gwang Hui Kim and Themistocles M. Rassias
Axioms 2020, 9(2), 58; https://doi.org/10.3390/axioms9020058 - 23 May 2020
Cited by 1 | Viewed by 1739
Abstract
In this paper, we investigate the generalized Hyers–Ulam stability for the generalized psi functional equation f ( x + p ) = f ( x ) + φ ( x ) by the direct method in the sense of P. Gǎvruta and the [...] Read more.
In this paper, we investigate the generalized Hyers–Ulam stability for the generalized psi functional equation f ( x + p ) = f ( x ) + φ ( x ) by the direct method in the sense of P. Gǎvruta and the Hyers–Ulam–Rassias stability. Full article
(This article belongs to the Special Issue Stability and Solution of Functional Equations)
13 pages, 346 KiB  
Article
Initial Value Problem For Nonlinear Fractional Differential Equations With ψ-Caputo Derivative Via Monotone Iterative Technique
by Choukri Derbazi, Zidane Baitiche, Mouffak Benchohra and Alberto Cabada
Axioms 2020, 9(2), 57; https://doi.org/10.3390/axioms9020057 - 21 May 2020
Cited by 34 | Viewed by 3405
Abstract
In this article, we discuss the existence and uniqueness of extremal solutions for nonlinear initial value problems of fractional differential equations involving the ψ -Caputo derivative. Moreover, some uniqueness results are obtained. Our results rely on the standard tools of functional analysis. More [...] Read more.
In this article, we discuss the existence and uniqueness of extremal solutions for nonlinear initial value problems of fractional differential equations involving the ψ -Caputo derivative. Moreover, some uniqueness results are obtained. Our results rely on the standard tools of functional analysis. More precisely we apply the monotone iterative technique combined with the method of upper and lower solutions to establish sufficient conditions for existence as well as the uniqueness of extremal solutions to the initial value problem. An illustrative example is presented to point out the applicability of our main results. Full article
(This article belongs to the Special Issue Nonlinear Differential Equations and Dynamical Systems: Theory and Applications)
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16 pages, 291 KiB  
Article
Aristotle’s Syllogistic as a Deductive System
by Piotr Kulicki
Axioms 2020, 9(2), 56; https://doi.org/10.3390/axioms9020056 - 19 May 2020
Cited by 2 | Viewed by 6255
Abstract
Aristotle’s syllogistic is the first ever deductive system. After centuries, Aristotle’s ideas are still interesting for logicians who develop Aristotle’s work and draw inspiration from his results and even more from his methods. In the paper we discuss the essential elements of the [...] Read more.
Aristotle’s syllogistic is the first ever deductive system. After centuries, Aristotle’s ideas are still interesting for logicians who develop Aristotle’s work and draw inspiration from his results and even more from his methods. In the paper we discuss the essential elements of the Aristotelian system of syllogistic and Łukasiewicz’s reconstruction of it based on the tools of modern formal logic. We pay special attention to the notion of completeness of a deductive system as discussed by both authors. We describe in detail how completeness can be defined and proved with the use of an axiomatic refutation system. Finally, we apply this methodology to different axiomatizations of syllogistic presented by Łukasiewicz, Lemmon and Shepherdson. Full article
(This article belongs to the Special Issue Deductive Systems in Traditional and Modern Logic)
6 pages, 216 KiB  
Article
On the Product Rule for the Hyperbolic Scator Algebra
by Jan L. Cieśliński and Artur Kobus
Axioms 2020, 9(2), 55; https://doi.org/10.3390/axioms9020055 - 19 May 2020
Cited by 5 | Viewed by 1792
Abstract
Scator set, introduced by Fernández-Guasti and Zaldívar, is endowed with a very peculiar non-distributive product. In this paper we consider the scator space of dimension 1 + 2 and the so called fundamental embedding which maps the subset of scators with non-zero scalar [...] Read more.
Scator set, introduced by Fernández-Guasti and Zaldívar, is endowed with a very peculiar non-distributive product. In this paper we consider the scator space of dimension 1 + 2 and the so called fundamental embedding which maps the subset of scators with non-zero scalar component into 4-dimensional space endowed with a natural distributive product. The original definition of the scator product is induced in a straightforward way. Moreover, we propose an extension of the scator product on the whole scator space, including all scators with vanishing scalar component. Full article
(This article belongs to the Special Issue Non-associative Structures, Yang–Baxter Equations and Related Topics)
33 pages, 429 KiB  
Review
The Generalized Hypergeometric Structure of the Ward Identities of CFT’s in Momentum Space in d > 2
by Claudio Corianò and Matteo Maria Maglio
Axioms 2020, 9(2), 54; https://doi.org/10.3390/axioms9020054 - 14 May 2020
Cited by 5 | Viewed by 2477
Abstract
We review the emergence of hypergeometric structures (of F4 Appell functions) from the conformal Ward identities (CWIs) in conformal field theories (CFTs) in dimensions d > 2. We illustrate the case of scalar 3- and 4-point functions. 3-point functions are associated to [...] Read more.
We review the emergence of hypergeometric structures (of F4 Appell functions) from the conformal Ward identities (CWIs) in conformal field theories (CFTs) in dimensions d > 2. We illustrate the case of scalar 3- and 4-point functions. 3-point functions are associated to hypergeometric systems with four independent solutions. For symmetric correlators, they can be expressed in terms of a single 3K integral—functions of quadratic ratios of momenta—which is a parametric integral of three modified Bessel K functions. In the case of scalar 4-point functions, by requiring the correlator to be conformal invariant in coordinate space as well as in some dual variables (i.e., dual conformal invariant), its explicit expression is also given by a 3K integral, or as a linear combination of Appell functions which are now quartic ratios of momenta. Similar expressions have been obtained in the past in the computation of an infinite class of planar ladder (Feynman) diagrams in perturbation theory, which, however, do not share the same (dual conformal/conformal) symmetry of our solutions. We then discuss some hypergeometric functions of 3 variables, which define 8 particular solutions of the CWIs and correspond to Lauricella functions. They can also be combined in terms of 4K integral and appear in an asymptotic description of the scalar 4-point function, in special kinematical limits. Full article
(This article belongs to the Special Issue Geometric Analysis and Mathematical Physics)
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14 pages, 1011 KiB  
Article
Optimization of the Time-Dependent Traveling Salesman Problem Using Interval-Valued Intuitionistic Fuzzy Sets
by Ruba Almahasneh, Boldizsár Tüű-Szabó, László T. Kóczy and Péter Földesi
Axioms 2020, 9(2), 53; https://doi.org/10.3390/axioms9020053 - 13 May 2020
Cited by 13 | Viewed by 2685
Abstract
This study proposes a new model and approach for solving a realistic extension of the Time-Dependent Traveling Salesman Problem, by using the concept of distance between interval-valued intuitionistic fuzzy sets. For this purpose, we developed an interval-valued fuzzy degree repository based on the [...] Read more.
This study proposes a new model and approach for solving a realistic extension of the Time-Dependent Traveling Salesman Problem, by using the concept of distance between interval-valued intuitionistic fuzzy sets. For this purpose, we developed an interval-valued fuzzy degree repository based on the relations between rush hour periods and traffic regions in the “city center areas”, and then we utilized the interval-valued intuitionistic fuzzy weighted arithmetic average to aggregate fuzzy information to be able to quantify the delay in any given trip between two nodes (cities). The proposed method is illustrated by a simple numerical example. Full article
(This article belongs to the Special Issue Type-2 Fuzzy Logic: Theory, Algorithms and Applications)
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8 pages, 329 KiB  
Article
Vaidya Collapse with Nonzero Radial Pressure and Charge
by Aroonkumar Beesham
Axioms 2020, 9(2), 52; https://doi.org/10.3390/axioms9020052 - 13 May 2020
Cited by 1 | Viewed by 2015
Abstract
The cosmic censorship hypothesis is regarded as one of the most important unsolved problems in classical general relativity; viz., will generic gravitational collapse of a star after it has exhausted its nuclear fuel lead to black holes only, under reasonable physical conditions. We [...] Read more.
The cosmic censorship hypothesis is regarded as one of the most important unsolved problems in classical general relativity; viz., will generic gravitational collapse of a star after it has exhausted its nuclear fuel lead to black holes only, under reasonable physical conditions. We discuss the collapse of a fluid with nonzero radial pressure within the context of the Vaidya spacetime considering a decaying cosmological parameter as well as nonzero charge. Previously, a similar analysis was done, but without considering charge. A decaying cosmological parameter may also be associated with dark energy. We found that both black holes and naked singularities can form, depending upon the initial conditions. Hence, charge does not restore the validity of the hypothesis. This provides another example of the violation of the cosmic censorship hypothesis. We also discuss some radiating rotating solutions, arriving at the same conclusion. Full article
(This article belongs to the Special Issue Theory and Mathematical Aspects of Black Holes)
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24 pages, 411 KiB  
Article
Inertial Subgradient Extragradient Methods for Solving Variational Inequality Problems and Fixed Point Problems
by Godwin Amechi Okeke, Mujahid Abbas and Manuel de la Sen
Axioms 2020, 9(2), 51; https://doi.org/10.3390/axioms9020051 - 11 May 2020
Cited by 3 | Viewed by 2473
Abstract
We propose two new iterative algorithms for solving K-pseudomonotone variational inequality problems in the framework of real Hilbert spaces. These newly proposed methods are obtained by combining the viscosity approximation algorithm, the Picard Mann algorithm and the inertial subgradient extragradient method. We establish [...] Read more.
We propose two new iterative algorithms for solving K-pseudomonotone variational inequality problems in the framework of real Hilbert spaces. These newly proposed methods are obtained by combining the viscosity approximation algorithm, the Picard Mann algorithm and the inertial subgradient extragradient method. We establish some strong convergence theorems for our newly developed methods under certain restriction. Our results extend and improve several recently announced results. Furthermore, we give several numerical experiments to show that our proposed algorithms performs better in comparison with several existing methods. Full article
(This article belongs to the Special Issue Fixed Point Theory and Its Related Topics II)
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16 pages, 819 KiB  
Article
Nonlocal Fractional Boundary Value Problems Involving Mixed Right and Left Fractional Derivatives and Integrals
by Ahmed Alsaedi, Abrar Broom, Sotiris K. Ntouyas and Bashir Ahmad
Axioms 2020, 9(2), 50; https://doi.org/10.3390/axioms9020050 - 01 May 2020
Cited by 4 | Viewed by 2042
Abstract
In this paper, we study the existence of solutions for nonlocal single and multi-valued boundary value problems involving right-Caputo and left-Riemann–Liouville fractional derivatives of different orders and right-left Riemann–Liouville fractional integrals. The existence of solutions for the single-valued case relies on Sadovskii’s fixed [...] Read more.
In this paper, we study the existence of solutions for nonlocal single and multi-valued boundary value problems involving right-Caputo and left-Riemann–Liouville fractional derivatives of different orders and right-left Riemann–Liouville fractional integrals. The existence of solutions for the single-valued case relies on Sadovskii’s fixed point theorem. The first existence results for the multi-valued case are proved by applying Bohnenblust-Karlin’s fixed point theorem, while the second one is based on Martelli’s fixed point theorem. We also demonstrate the applications of the obtained results. Full article
(This article belongs to the Special Issue Differential and Difference Equations: A Themed Issue Dedicated to Prof. Hari M. Srivastava on the Occasion of his 80th Birthday)
37 pages, 1841 KiB  
Article
Discrete and Fuzzy Models of Time Series in the Tasks of Forecasting and Diagnostics
by Anton Romanov, Valeria Voronina, Gleb Guskov, Irina Moshkina and Nadezhda Yarushkina
Axioms 2020, 9(2), 49; https://doi.org/10.3390/axioms9020049 - 30 Apr 2020
Cited by 6 | Viewed by 2343
Abstract
The development of the economy and the transition to industry 4.0 creates new challenges for artificial intelligence methods. Such challenges include the processing of large volumes of data, the analysis of various dynamic indicators, the discovery of complex dependencies in the accumulated data, [...] Read more.
The development of the economy and the transition to industry 4.0 creates new challenges for artificial intelligence methods. Such challenges include the processing of large volumes of data, the analysis of various dynamic indicators, the discovery of complex dependencies in the accumulated data, and the forecasting of the state of processes. The main point of this study is the development of a set of analytical and prognostic methods. The methods described in this article based on fuzzy logic, statistic, and time series data mining, because data extracted from dynamic systems are initially incomplete and have a high degree of uncertainty. The ultimate goal of the study is to improve the quality of data analysis in industrial and economic systems. The advantages of the proposed methods are flexibility and orientation to the high interpretability of dynamic data. The high level of the interpretability and interoperability of dynamic data is achieved due to a combination of time series data mining and knowledge base engineering methods. The merging of a set of rules extracted from the time series and knowledge base rules allow for making a forecast in case of insufficiency of the length and nature of the time series. The proposed methods are also based on the summarization of the results of processes modeling for diagnosing technical systems, forecasting of the economic condition of enterprises, and approaches to the technological preparation of production in a multi-productive production program with the application of type 2 fuzzy sets for time series modeling. Intelligent systems based on the proposed methods demonstrate an increase in the quality and stability of their functioning. This article contains a set of experiments to approve this statement. Full article
(This article belongs to the Special Issue Fuzzy Systems for Data Managing in Business, Society, and Economics)
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42 pages, 569 KiB  
Review
Weighted Bergman Kernels and Mathematical Physics
by Elisabetta Barletta, Sorin Dragomir and Francesco Esposito
Axioms 2020, 9(2), 48; https://doi.org/10.3390/axioms9020048 - 29 Apr 2020
Cited by 1 | Viewed by 2846
Abstract
We review several results in the theory of weighted Bergman kernels. Weighted Bergman kernels generalize ordinary Bergman kernels of domains Ω ⊂ C n but also appear locally in the attempt to quantize classical states of mechanical systems whose classical phase space is [...] Read more.
We review several results in the theory of weighted Bergman kernels. Weighted Bergman kernels generalize ordinary Bergman kernels of domains Ω ⊂ C n but also appear locally in the attempt to quantize classical states of mechanical systems whose classical phase space is a complex manifold, and turn out to be an efficient computational tool that is useful for the calculation of transition probability amplitudes from a classical state (identified to a coherent state) to another. We review the weighted version (for weights of the form γ = | φ | m on strictly pseudoconvex domains Ω = { φ < 0 } ⊂ C n ) of Fefferman’s asymptotic expansion of the Bergman kernel and discuss its possible extensions (to more general classes of weights) and implications, e.g., such as related to the construction and use of Fefferman’s metric (a Lorentzian metric on ∂ Ω × S 1 ). Several open problems are indicated throughout the survey. Full article
(This article belongs to the Special Issue Geometric Analysis and Mathematical Physics)
12 pages, 279 KiB  
Article
Lyapunov Type Theorems for Exponential Stability of Linear Skew-Product Three-Parameter Semiflows with Discrete Time
by Davor Dragičević and Ciprian Preda
Axioms 2020, 9(2), 47; https://doi.org/10.3390/axioms9020047 - 27 Apr 2020
Cited by 5 | Viewed by 2035
Abstract
For linear skew-product three-parameter semiflows with discrete time acting on an arbitrary Hilbert space, we obtain a complete characterization of exponential stability in terms of the existence of appropriate Lyapunov functions. As a nontrivial application of our work, we prove that the notion [...] Read more.
For linear skew-product three-parameter semiflows with discrete time acting on an arbitrary Hilbert space, we obtain a complete characterization of exponential stability in terms of the existence of appropriate Lyapunov functions. As a nontrivial application of our work, we prove that the notion of an exponential stability persists under sufficiently small linear perturbations. Full article
(This article belongs to the Special Issue Differential and Difference Equations: A Themed Issue Dedicated to Prof. Hari M. Srivastava on the Occasion of his 80th Birthday)
13 pages, 1249 KiB  
Article
Can the SOM Analysis Predict Business Failure Using Capital Structure Theory? Evidence from the Subprime Crisis in Spain
by Juan Pedro Lucanera, Laura Fabregat-Aibar, Valeria Scherger and Hernán Vigier
Axioms 2020, 9(2), 46; https://doi.org/10.3390/axioms9020046 - 27 Apr 2020
Cited by 5 | Viewed by 2551
Abstract
The paper aims to identify which variables related to capital structure theory predict business failure in the Spanish construction sector during the subprime crisis. An artificial neural network (ANN) approach based on Self-Organizing Maps (SOM) is proposed, which allows one to cluster between [...] Read more.
The paper aims to identify which variables related to capital structure theory predict business failure in the Spanish construction sector during the subprime crisis. An artificial neural network (ANN) approach based on Self-Organizing Maps (SOM) is proposed, which allows one to cluster between default and active firms’ groups. The similarities and differences between the main features in each group determine the variables that explain the capacities of failure of the analyzed firms. The network tests whether the factors that explain leverage, such as profitability, growth opportunities, size of the company, risk, asset structure, and age of the firm, can be suitable to predict business failure. The sample is formed by 152 construction firms (76 default and 76 active) in the Spanish market. The results show that the SOM correctly predicts 97.4% of firms in the construction sector and classifies the firms in five groups with clear similarities inside the clusters. The study proves the suitability of the SOM for predicting business bankruptcy situations using variables related to capital structure theory and financial crises. Full article
(This article belongs to the Special Issue Soft Computing in Economics, Finance and Management)
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21 pages, 290 KiB  
Article
Nonlocal Inverse Problem for a Pseudohyperbolic- Pseudoelliptic Type Integro-Differential Equations
by Tursun K. Yuldashev
Axioms 2020, 9(2), 45; https://doi.org/10.3390/axioms9020045 - 27 Apr 2020
Cited by 29 | Viewed by 2997
Abstract
The questions of solvability of a nonlocal inverse boundary value problem for a mixed pseudohyperbolic-pseudoelliptic integro-differential equation with spectral parameters are considered. Using the method of the Fourier series, a system of countable systems of ordinary integro-differential equations is obtained. To determine arbitrary [...] Read more.
The questions of solvability of a nonlocal inverse boundary value problem for a mixed pseudohyperbolic-pseudoelliptic integro-differential equation with spectral parameters are considered. Using the method of the Fourier series, a system of countable systems of ordinary integro-differential equations is obtained. To determine arbitrary integration constants, a system of algebraic equations is obtained. From this system regular and irregular values of the spectral parameters were calculated. The unique solvability of the inverse boundary value problem for regular values of spectral parameters is proved. For irregular values of spectral parameters is established a criterion of existence of an infinite set of solutions of the inverse boundary value problem. The results are formulated as a theorem. Full article
(This article belongs to the Special Issue Differential and Difference Equations: A Themed Issue Dedicated to Prof. Hari M. Srivastava on the Occasion of his 80th Birthday)
17 pages, 314 KiB  
Article
Existence of Solutions for Nonlinear Fractional Differential Equations and Inclusions Depending on Lower-Order Fractional Derivatives
by Subramanian Muthaiah and Dumitru Baleanu
Axioms 2020, 9(2), 44; https://doi.org/10.3390/axioms9020044 - 25 Apr 2020
Cited by 14 | Viewed by 2156
Abstract
This article deals with the solutions of the existence and uniqueness for a new class of boundary value problems (BVPs) involving nonlinear fractional differential equations (FDEs), inclusions, and boundary conditions involving the generalized fractional integral. The nonlinearity relies on the unknown function and [...] Read more.
This article deals with the solutions of the existence and uniqueness for a new class of boundary value problems (BVPs) involving nonlinear fractional differential equations (FDEs), inclusions, and boundary conditions involving the generalized fractional integral. The nonlinearity relies on the unknown function and its fractional derivatives in the lower order. We use fixed-point theorems with single-valued and multi-valued maps to obtain the desired results, through the support of illustrations, the main results are well explained. We also address some variants of the problem. Full article
(This article belongs to the Special Issue Fractional Calculus, Wavelets and Fractals)
13 pages, 272 KiB  
Article
Integral Representation of Coherent Lower Previsions by Super-Additive Integrals
by Serena Doria, Radko Mesiar and Adam Šeliga
Axioms 2020, 9(2), 43; https://doi.org/10.3390/axioms9020043 - 23 Apr 2020
Cited by 8 | Viewed by 2302
Abstract
Coherent lower previsions generalize the expected values and they are defined on the class of all real random variables on a finite non-empty set. Well known construction of coherent lower previsions by means of lower probabilities, or by means of super-modular capacities-based Choquet [...] Read more.
Coherent lower previsions generalize the expected values and they are defined on the class of all real random variables on a finite non-empty set. Well known construction of coherent lower previsions by means of lower probabilities, or by means of super-modular capacities-based Choquet integrals, do not cover this important class of functionals on real random variables. In this paper, a new approach to the construction of coherent lower previsions acting on a finite space is proposed, exemplified and studied. It is based on special decomposition integrals recently introduced by Even and Lehrer, in our case the considered decomposition systems being single collections and thus called collection integrals. In special case when these integrals, defined for non-negative random variables only, are shift-invariant, we extend them to the class of all real random variables, thus obtaining so called super-additive integrals. Our proposed construction can be seen then as a normalized super-additive integral. We discuss and exemplify several particular cases, for example, when collections determine a coherent lower prevision for any monotone set function. For some particular collections, only particular set functions can be considered for our construction. Conjugated coherent upper previsions are also considered. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Applications)
13 pages, 318 KiB  
Article
Generalized Briot-Bouquet Differential Equation Based on New Differential Operator with Complex Connections
by Rabha W. Ibrahim, Rafida M. Elobaid and Suzan J. Obaiys
Axioms 2020, 9(2), 42; https://doi.org/10.3390/axioms9020042 - 21 Apr 2020
Cited by 8 | Viewed by 2217
Abstract
A class of Briot–Bouquet differential equations is a magnificent part of investigating the geometric behaviors of analytic functions, using the subordination and superordination concepts. In this work, we aim to formulate a new differential operator with complex connections (coefficients) in the open unit [...] Read more.
A class of Briot–Bouquet differential equations is a magnificent part of investigating the geometric behaviors of analytic functions, using the subordination and superordination concepts. In this work, we aim to formulate a new differential operator with complex connections (coefficients) in the open unit disk and generalize a class of Briot–Bouquet differential equations (BBDEs). We study and generalize new classes of analytic functions based on the new differential operator. Consequently, we define a linear operator with applications. Full article
(This article belongs to the Special Issue Differential and Difference Equations: A Themed Issue Dedicated to Prof. Hari M. Srivastava on the Occasion of his 80th Birthday)
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