Axioms

13 pages, 330 KiB

Open AccessArticle

Some Implicational Semilinear Gaggle Logics: (Dual) Residuated-Connected Logics

by Eunsuk Yang

Axioms 2022, 11(4), 183; https://doi.org/10.3390/axioms11040183 - 18 Apr 2022

Viewed by 1374

Implicational partial Galois logics and some of their semilinear extensions, such as semilinear extensions satisfying abstract Galois and dual Galois connection properties, have been introduced together with their relational semantics. However, similar extensions satisfying residuated, dual residuated connection properties have not. This paper [...] Read more.

Implicational partial Galois logics and some of their semilinear extensions, such as semilinear extensions satisfying abstract Galois and dual Galois connection properties, have been introduced together with their relational semantics. However, similar extensions satisfying residuated, dual residuated connection properties have not. This paper fills the gaps by introducing those semilinear extensions and their relational semantics. To this end, the class of implicational (dual) residuated-connected prelinear gaggle logics is defined and it is verified that these logics are semilinear. In particular, associated with the contribution of this work, we note the following two: One is that implications can be introduced by residuated connection in semilinear logics. This shows that the residuated, dual residuated connection properties are important and so need to be investigated in semilinear logics. The other is that set-theoretic relational semantics can be provided for semilinear logics. Semilinear logics have been dealt with extensively in algebraic context, whereas they have not yet been performed in the set-theoretic one. Full article

(This article belongs to the Special Issue Algebra, Logic and Applications)

23 pages, 12249 KiB

Open AccessArticle

Application of the Multi-Criteria Optimization Method to Repair Landslides with Additional Soil Collapse

by Nikola Gvozdović, Kristina Božić-Tomić, Ljubo Marković, Ljiljana Milić Marković, Suzana Koprivica, Miljan Kovačević and Srdjan Jovic

Axioms 2022, 11(4), 182; https://doi.org/10.3390/axioms11040182 - 18 Apr 2022

Cited by 2 | Viewed by 1935

Abstract

In current practice, the remediation of landslides has shown that the biggest problem is the increase in the number of works, and therefore the price of the works. This is due to several factors, including characteristic of the soil, such as the collapse [...] Read more.

In current practice, the remediation of landslides has shown that the biggest problem is the increase in the number of works, and therefore the price of the works. This is due to several factors, including characteristic of the soil, such as the collapse (collapse) of the surrounding ground around the main slide during landslide remediation. Unless these soil erosion effects are taken into account, recovery costs will overrun, which can jeopardize the planned budget. This paper presents a multi-criteria optimization of landslide remediation using the PROMETHEE method and determines the optional number of walls for the additional soil erosion. In a case study on examples of real landslides in the Republic of Serbia, the application of the method is presented and appropriate conclusions are drawn. Full article

(This article belongs to the Special Issue Multiple-Criteria Decision Making II)

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20 pages, 1935 KiB

Open AccessArticle

Lexicon-Enhanced Multi-Task Convolutional Neural Network for Emotion Distribution Learning

by Yuchang Dong and Xueqiang Zeng

Axioms 2022, 11(4), 181; https://doi.org/10.3390/axioms11040181 - 17 Apr 2022

Cited by 2 | Viewed by 2010

Abstract

Emotion distribution learning (EDL) handles emotion fuzziness by means of the emotion distribution, which is an emotion vector that quantitatively represents a set of emotion categories with their intensity of a given instance. Despite successful applications of EDL in many practical emotion analysis [...] Read more.

Emotion distribution learning (EDL) handles emotion fuzziness by means of the emotion distribution, which is an emotion vector that quantitatively represents a set of emotion categories with their intensity of a given instance. Despite successful applications of EDL in many practical emotion analysis tasks, existing EDL methods have seldom considered the linguistic prior knowledge of affective words specific to the text mining task. To address the problem, this paper proposes a text emotion distribution learning model based on a lexicon-enhanced multi-task convolutional neural network (LMT-CNN) to jointly solve the tasks of text emotion distribution prediction and emotion label classification. The LMT-CNN model designs an end-to-end multi-module deep neural network to utilize both semantic information and linguistic knowledge. Specifically, the architecture of the LMT-CNN model consists of a semantic information module, an emotion knowledge module based on affective words, and a multi-task prediction module to predict emotion distributions and labels. Extensive comparative experiments on nine commonly used emotional text datasets showed that the proposed LMT-CNN model is superior to the compared EDL methods for both emotion distribution prediction and emotion recognition tasks. Full article

(This article belongs to the Special Issue Various Deep Learning Algorithms in Computational Intelligence)

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20 pages, 386 KiB

Open AccessArticle

Frame-Related Sequences in Chains and Scales of Hilbert Spaces

by Peter Balazs, Giorgia Bellomonte and Hessam Hosseinnezhad

Axioms 2022, 11(4), 180; https://doi.org/10.3390/axioms11040180 - 16 Apr 2022

Viewed by 1677

Abstract

Frames for Hilbert spaces are interesting for mathematicians but also important for applications in, e.g., signal analysis and physics. In both mathematics and physics, it is natural to consider a full scale of spaces, and not only a single one. In this paper, [...] Read more.

Frames for Hilbert spaces are interesting for mathematicians but also important for applications in, e.g., signal analysis and physics. In both mathematics and physics, it is natural to consider a full scale of spaces, and not only a single one. In this paper, we study how certain frame-related properties of a certain sequence in one of the spaces, such as completeness or the property of being a (semi-) frame, propagate to the other ones in a scale of Hilbert spaces. We link that to the properties of the respective frame-related operators, such as analysis or synthesis. We start with a detailed survey of the theory of Hilbert chains. Using a canonical isomorphism, the properties of frame sequences are naturally preserved between different spaces. We also show that some results can be transferred if the original sequence is considered—in particular, that the upper semi-frame property is kept in larger spaces, while the lower one is kept in smaller ones. This leads to a negative result: a sequence can never be a frame for two Hilbert spaces of the scale if the scale is non-trivial, i.e., if the spaces are not equal. Full article

(This article belongs to the Special Issue Time-Frequency Analysis, Distributions, and Operators)

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14 pages, 4028 KiB

Open AccessArticle

A Comparative Study of Models for Heat Transfer in Bidisperse Gas–Solid Systems via CFD–DEM Simulations

by Zheqing Huang, Qi Huang, Yaxiong Yu, Yu Li and Qiang Zhou

Axioms 2022, 11(4), 179; https://doi.org/10.3390/axioms11040179 - 15 Apr 2022

Cited by 1 | Viewed by 1495

Abstract

In this study, flow and heat transfers in bidisperse gas–solid systems were numerically investigated using the computational fluid dynamics–discrete element method (CFD–DEM). Three different models to close the gas–solid heat transfer coefficient for each species of bidisperse systems were compared in the simulations. [...] Read more.

In this study, flow and heat transfers in bidisperse gas–solid systems were numerically investigated using the computational fluid dynamics–discrete element method (CFD–DEM). Three different models to close the gas–solid heat transfer coefficient for each species of bidisperse systems were compared in the simulations. The effect of the particle diameter ratio and particle number ratio between large and small particles on the particle mean temperature and temperature distribution of each species were systematically investigated. The simulation results show that differences in the particle mean temperature and temperature distribution profiles exist among the three heat transfer models at a higher particle number ratio. The differences between the effects of three heat transfer models on heat transfer properties in bidisperse systems with particle diameter ratios of up to 4 are marginal when the particle number ratio between small and large particles is 1. Full article

(This article belongs to the Special Issue Computational Heat Transfer and Fluid Dynamics)

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10 pages, 266 KiB

Open AccessArticle

Weighted Generalized Fractional Integration by Parts and the Euler–Lagrange Equation

by Houssine Zine, El Mehdi Lotfi, Delfim F. M. Torres and Noura Yousfi

Axioms 2022, 11(4), 178; https://doi.org/10.3390/axioms11040178 - 15 Apr 2022

Cited by 2 | Viewed by 1612

Abstract

Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control. Motivated by this fact, we construct a new, right-weighted generalized fractional derivative in the Riemann–Liouville sense with [...] Read more.

Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control. Motivated by this fact, we construct a new, right-weighted generalized fractional derivative in the Riemann–Liouville sense with its associated integral for the recently introduced weighted generalized fractional derivative with Mittag–Leffler kernel. We rewrite these operators equivalently in effective series, proving some interesting properties relating to the left and the right fractional operators. These results permit us to obtain the corresponding integration by parts formula. With the new general formula, we obtain an appropriate weighted Euler–Lagrange equation for dynamic optimization, extending those existing in the literature. We end with the application of an optimization variational problem to the quantum mechanics framework. Full article

(This article belongs to the Special Issue Calculus of Variations, Optimal Control, and Mathematical Biology: A Themed Issue Dedicated to Professor Delfim F. M. Torres on the Occasion of His 50th Birthday)

13 pages, 289 KiB

Open AccessArticle

Soft Rω-Open Sets and the Soft Topology of Soft δ_ω-Open Sets

by Samer Al Ghour

Axioms 2022, 11(4), 177; https://doi.org/10.3390/axioms11040177 - 15 Apr 2022

Cited by 7 | Viewed by 1649

Abstract

The author devotes this paper to defining a new class of soft open sets, namely soft

R ω

-open sets, and investigating their main features. With the help of examples, we show that the class of soft

R ω

-open sets lies strictly [...] Read more.

The author devotes this paper to defining a new class of soft open sets, namely soft

R ω

-open sets, and investigating their main features. With the help of examples, we show that the class of soft

R ω

-open sets lies strictly between the classes of soft regular open sets and soft open sets. We show that soft

R ω

-open subsets of a soft locally countable soft topological space coincide with the soft open sets. Moreover, we show that soft

R ω

-open subsets of a soft anti-locally countable coincide with the soft regular open sets. Moreover, we show that the class of soft

R ω

-open sets is closed under finite soft intersection, and as a conclusion, we show that this class forms a soft base for some soft topology. In addition, we define the soft

δ_{ω}

-closure operator as a new operator in soft topological spaces. Moreover, via the soft

δ_{ω}

-closure operator, we introduce soft

δ_{ω}

-open sets as a new class of soft open sets which form a soft topology. Moreover, we study the correspondence between soft

δ_{ω}

-open in soft topological spaces and

δ_{ω}

-open in topological spaces. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application)

22 pages, 1468 KiB

Open AccessArticle

Fuzzy Multi Criteria Decision Making Model for Agritourism Location Selection: A Case Study in Vietnam

by Chihkang Kenny Wu, Chia-Nan Wang and Thi Kim Trang Le

Axioms 2022, 11(4), 176; https://doi.org/10.3390/axioms11040176 - 14 Apr 2022

Cited by 7 | Viewed by 2614

Abstract

Agritourism is an increasing new trend in the global tourism industry. Vietnam has a long tradition of agricultural production combined with diverse natural resources stretching from the north to the south, bringing advantages in the development of agritourism. The study aims to choose [...] Read more.

Agritourism is an increasing new trend in the global tourism industry. Vietnam has a long tradition of agricultural production combined with diverse natural resources stretching from the north to the south, bringing advantages in the development of agritourism. The study aims to choose the most appropriate agritourism location in Vietnam for long-term investment. A hybrid fuzzy multi-criteria decision model (FMCDM) is proposed to find the optimal location based on eco-nomic, social, and environmental factors. In the first stage, the fuzzy analytic hierarchy process (FAHP) is used to estimate the relative criteria rating through the evaluation process. In the second stage, the fuzzy technique for order preference using similarities to ideal solution (FTOPSIS) is applied to rank the potential alternative locations. Finally, the best alternative to tourist site investment is Can Tho (A8), which maximizes resources and enhances the local benefits. Future research can also be used to support similar site-selection processes in other regions or could be applied to other types of tourism. Full article

(This article belongs to the Special Issue Soft Computing with Applications to Decision Making and Data Mining)

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10 pages, 281 KiB

Open AccessArticle

Approximate Optimal Control for a Parabolic System with Perturbations in the Coefficients on the Half-Axis

by Olena A. Kapustian, Oleksiy V. Kapustyan, Anton Ryzhov and Valentyn Sobchuk

Axioms 2022, 11(4), 175; https://doi.org/10.3390/axioms11040175 - 14 Apr 2022

Cited by 9 | Viewed by 1352

Abstract

In this paper, we use the averaging method to find an approximate solution in the optimal control problem of a parabolic system with non-linearity of the form

f (t / ε, y)

on an infinite time interval. Full article

(This article belongs to the Special Issue Approximation Theory and Related Applications)

14 pages, 286 KiB

Open AccessArticle

Various Series Related to the Polylogarithmic Function

by Vuk Stojiljković, Nicola Fabiano, Mirjana Pantović, Slobodan Radojević, Stojan Radenović and Vesna Šešum Ćavić

Axioms 2022, 11(4), 174; https://doi.org/10.3390/axioms11040174 - 13 Apr 2022

Cited by 2 | Viewed by 1483

Abstract

We derive some series related to the polylogarithmic function, and we also give a new proof to the existing series. Our approach is based on using the summation and integral representation methods. We obtain various interesting series as a consequence. Full article

(This article belongs to the Section Mathematical Analysis)

25 pages, 2132 KiB

Open AccessArticle

On the Generalized Bilal Distribution: Some Properties and Estimation under Ranked Set Sampling

by Zuber Akhter, Ehab M. Almetwally and Christophe Chesneau

Axioms 2022, 11(4), 173; https://doi.org/10.3390/axioms11040173 - 13 Apr 2022

Cited by 6 | Viewed by 1718

Abstract

The generalized Bilal (GB) distribution can be defined as the distribution of the median of three independent random variables drawn from the Weibull distribution. Its failure rate function can be monotonic (decreasing or increasing) or upside-down bathtub-shaped. In this study, we aim to [...] Read more.

The generalized Bilal (GB) distribution can be defined as the distribution of the median of three independent random variables drawn from the Weibull distribution. Its failure rate function can be monotonic (decreasing or increasing) or upside-down bathtub-shaped. In this study, we aim to reveal some important properties of the GB distribution that have not been considered before. The findings are both theoretical and practical. From the theoretical viewpoint, we present explicit expressions for both single and product moments of order statistics from the GB distribution. The L-moments are derived as well. From the practical viewpoint, the parameter estimations are accomplished using the maximum likelihood (ML) method, which is based on two different sampling schemes: simple random sampling (SRS) and ranked set sampling (RSS) schemes. Furthermore, the asymptotic confidence intervals for the SRS and RSS estimators are discussed. For the sake of comparison and illustration, a simulation study and a real data example are presented. Concluding remarks are given at the end. Full article

(This article belongs to the Special Issue Communications in Industrial Statistics—Theory and Methods)

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11 pages, 294 KiB

Open AccessArticle

Hadamard Product Properties for Certain Subclasses of p-Valent Meromorphic Functions

by Alaa H. El-Qadeem and Ibrahim S. Elshazly

Axioms 2022, 11(4), 172; https://doi.org/10.3390/axioms11040172 - 13 Apr 2022

Cited by 3 | Viewed by 1456

Abstract

We study the Hadamard product features of certain subclasses of p-valent meromorphic functions defined in the punctured open-unit disc using the q-difference operator. For functions belonging to these subclasses, we obtained certain coefficient estimates and inclusion characteristics. Furthermore, linkages between the results [...] Read more.

We study the Hadamard product features of certain subclasses of p-valent meromorphic functions defined in the punctured open-unit disc using the q-difference operator. For functions belonging to these subclasses, we obtained certain coefficient estimates and inclusion characteristics. Furthermore, linkages between the results given here and those found in previous publications are highlighted. Full article

(This article belongs to the Special Issue New Developments in Geometric Function Theory)

28 pages, 423 KiB

Open AccessArticle

BMO and Asymptotic Homogeneity

by Vladimir Gutlyanskii, Vladimir Ryazanov, Evgeny Sevost’yanov and Eduard Yakubov

Axioms 2022, 11(4), 171; https://doi.org/10.3390/axioms11040171 - 12 Apr 2022

Cited by 3 | Viewed by 1325

Abstract

First, we prove that the BMO condition by John–Nirenberg leads in the natural way to the asymptotic homogeneity at the origin of regular homeomorphic solutions of the degenerate Beltrami equations. Then, on this basis we establish a series of criteria for the existence [...] Read more.

First, we prove that the BMO condition by John–Nirenberg leads in the natural way to the asymptotic homogeneity at the origin of regular homeomorphic solutions of the degenerate Beltrami equations. Then, on this basis we establish a series of criteria for the existence of regular homeomorphic solutions of the degenerate Beltrami equations in the whole complex plane with asymptotic homogeneity at infinity. These results can be applied to the fluid mechanics in strongly anisotropic and inhomogeneous media because the Beltrami equation is a complex form of the main equation of hydromechanics. Full article

(This article belongs to the Special Issue Approximation Theory and Related Applications)

15 pages, 614 KiB

Open AccessArticle

Fractional Modelling and Optimal Control of COVID-19 Transmission in Portugal

by Silvério Rosa and Delfim F. M. Torres

Axioms 2022, 11(4), 170; https://doi.org/10.3390/axioms11040170 - 11 Apr 2022

Cited by 9 | Viewed by 2050

Abstract

A fractional-order compartmental model was recently used to describe real data of the first wave of the COVID-19 pandemic in Portugal [Chaos Solitons Fractals 144 (2021), Art. 110652]. Here, we modify that model in order to correct time dimensions and use it to [...] Read more.

A fractional-order compartmental model was recently used to describe real data of the first wave of the COVID-19 pandemic in Portugal [Chaos Solitons Fractals 144 (2021), Art. 110652]. Here, we modify that model in order to correct time dimensions and use it to investigate the third wave of COVID-19 that occurred in Portugal from December 2020 to February 2021, and that has surpassed all previous waves, both in number and consequences. A new fractional optimal control problem is then formulated and solved, with vaccination and preventive measures as controls. A cost-effectiveness analysis is carried out, and the obtained results are discussed. Full article

(This article belongs to the Special Issue Mathematics of the COVID-19)

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20 pages, 366 KiB

Open AccessArticle

Two Open Problems on CA-Groupoids and Cancellativities of T2CA-Groupoids

by Xiaogang An, Xiaohong Zhang and Zhirou Ma

Axioms 2022, 11(4), 169; https://doi.org/10.3390/axioms11040169 - 08 Apr 2022

Cited by 3 | Viewed by 1716

Abstract

Cyclic associative groupoids (CA-groupoids) and Type-2 cyclic associative groupoids (T2CA-groupoids) are two types of non-associative groupoids which satisfy cyclic associative law and type-2 cyclic associative law, respectively. In this paper, we prove two theorems that weak cancellativity is cancellativity and right quasi-cancellativity is [...] Read more.

Cyclic associative groupoids (CA-groupoids) and Type-2 cyclic associative groupoids (T2CA-groupoids) are two types of non-associative groupoids which satisfy cyclic associative law and type-2 cyclic associative law, respectively. In this paper, we prove two theorems that weak cancellativity is cancellativity and right quasi-cancellativity is left quasi-cancellativity in a CA-groupoid, thus successfully solving two open problems. Moreover, the relationships among separativity, quasi-cancellativity and commutativity in a CA-groupoid are discussed. Finally, we study the various cancellativities of T2CA-groupoids such as power cancellativity, quasi-cancellativity and cancellativity. By determining the relationships between them, we can illuminate the structure of T2CA-groupoids. Full article

(This article belongs to the Special Issue Algebra, Logic and Applications)

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7 pages, 277 KiB

Open AccessArticle

Strong Chromatic Index of Outerplanar Graphs

by Ying Wang, Yiqiao Wang, Weifan Wang and Shuyu Cui

Axioms 2022, 11(4), 168; https://doi.org/10.3390/axioms11040168 - 08 Apr 2022

Cited by 1 | Viewed by 1624

Abstract

The strong chromatic index

χ_{s}^{'} (G)

of a graph G is the minimum number of colors needed in a proper edge-coloring so that every color class induces a matching in G. It was proved In 2013, that every [...] Read more.

The strong chromatic index

χ_{s}^{'} (G)

of a graph G is the minimum number of colors needed in a proper edge-coloring so that every color class induces a matching in G. It was proved In 2013, that every outerplanar graph G with

Δ \geq 3

has

χ_{s}^{'} (G) \leq 3 Δ - 3

. In this paper, we give a characterization for an outerplanar graph G to have

χ_{s}^{'} (G) = 3 Δ - 3

. We also show that if G is a bipartite outerplanar graph, then

χ_{s}^{'} (G) \leq 2 Δ

; and

χ_{s}^{'} (G) = 2 Δ

if and only if G contains a particular subgraph. Full article

(This article belongs to the Special Issue Graph Theory with Applications)

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26 pages, 379 KiB

Open AccessArticle

Note on the Higher-Order Derivatives of the Hyperharmonic Polynomials and the r-Stirling Polynomials of the First Kind

by José L. Cereceda

Axioms 2022, 11(4), 167; https://doi.org/10.3390/axioms11040167 - 08 Apr 2022

Viewed by 1467

Abstract

In this paper, we focus on the higher-order derivatives of the hyperharmonic polynomials, which are a generalization of the ordinary harmonic numbers. We determine the hyperharmonic polynomials and their successive derivatives in terms of the r-Stirling polynomials of the first kind and [...] Read more.

In this paper, we focus on the higher-order derivatives of the hyperharmonic polynomials, which are a generalization of the ordinary harmonic numbers. We determine the hyperharmonic polynomials and their successive derivatives in terms of the r-Stirling polynomials of the first kind and show the relationship between the (exponential) complete Bell polynomials and the r-Stirling numbers of the first kind. Furthermore, we provide a new formula for obtaining the generalized Bernoulli polynomials by exploiting their link with the higher-order derivatives of the hyperharmonic polynomials. In addition, we obtain various identities involving the r-Stirling numbers of the first kind, the Bernoulli numbers and polynomials, the Stirling numbers of the first and second kind, and the harmonic numbers. Full article

(This article belongs to the Section Mathematical Analysis)

12 pages, 282 KiB

Open AccessArticle

On an Integral Equation with the Riemann Function Kernel

by Sergei Sitnik and Abdul Ahad Arian

Axioms 2022, 11(4), 166; https://doi.org/10.3390/axioms11040166 - 07 Apr 2022

Viewed by 1462

Abstract

This paper is concerned with a study of a special integral equation. This integral equation arises in many applied problems, including transmutation theory, inverse scattering problems, the solution of singular Sturm–Liouville and Shrödinger equations, and the representation of solutions of singular Sturm–Liouville and [...] Read more.

This paper is concerned with a study of a special integral equation. This integral equation arises in many applied problems, including transmutation theory, inverse scattering problems, the solution of singular Sturm–Liouville and Shrödinger equations, and the representation of solutions of singular Sturm–Liouville and Shrödinger equations. A special integral equation is derived and formulated using the Riemann function of a singular hyperbolic equation. In the paper, the existence of a unique solution to this equation is proven by the method of successive approximations. The results can be applied, for example, to representations of solutions to Sturm–Liouville equations with singular potentials, such as Bargmann and Miura potentials, and similiar. The treatment of problems with such potentials are very important in mathematical physics, and inverse, scattering and related problems. The estimates received do not contain any undefined constants, and for transmutation kernels all estimates are explicitly written. Full article

(This article belongs to the Special Issue Advances in Nonlinear Boundary Value Problems: Theory and Applications)

14 pages, 290 KiB

Open AccessArticle

On a Family of Infinite Series with Reciprocal Catalan Numbers

by Kunle Adegoke, Robert Frontczak and Taras Goy

Axioms 2022, 11(4), 165; https://doi.org/10.3390/axioms11040165 - 07 Apr 2022

Cited by 2 | Viewed by 1691

Abstract

We study a certain family of infinite series with reciprocal Catalan numbers. We first evaluate two special candidates of the family in closed form, where we also present some Catalan–Fibonacci relations. Then, we focus on the general properties of the family and prove [...] Read more.

We study a certain family of infinite series with reciprocal Catalan numbers. We first evaluate two special candidates of the family in closed form, where we also present some Catalan–Fibonacci relations. Then, we focus on the general properties of the family and prove explicit formulas, including two types of integral representations. Full article

(This article belongs to the Section Mathematical Analysis)

11 pages, 305 KiB

Open AccessArticle

Positive Solutions for a System of Fractional Boundary Value Problems with r-Laplacian Operators, Uncoupled Nonlocal Conditions and Positive Parameters

by Alexandru Tudorache and Rodica Luca

Axioms 2022, 11(4), 164; https://doi.org/10.3390/axioms11040164 - 06 Apr 2022

Cited by 4 | Viewed by 1645

Abstract

In this paper, we investigate the existence and nonexistence of positive solutions for a system of Riemann–Liouville fractional differential equations with r-Laplacian operators, subject to nonlocal uncoupled boundary conditions that contain Riemann–Stieltjes integrals, various fractional derivatives and positive parameters. We first change [...] Read more.

In this paper, we investigate the existence and nonexistence of positive solutions for a system of Riemann–Liouville fractional differential equations with r-Laplacian operators, subject to nonlocal uncoupled boundary conditions that contain Riemann–Stieltjes integrals, various fractional derivatives and positive parameters. We first change the unknown functions such that the new boundary conditions have no positive parameters, and then, by using the corresponding Green functions, we equivalently write this new problem as a system of nonlinear integral equations. By constructing an appropriate operator

A

, the solutions of the integral system are the fixed points of

A

. Following some assumptions regarding the nonlinearities of the system, we show (by applying the Schauder fixed-point theorem) that operator

A

has at least one fixed point, which is a positive solution of our problem, when the positive parameters belong to some intervals. Then, we present intervals for the parameters for which our problem has no positive solution. Full article

(This article belongs to the Special Issue 10th Anniversary of Axioms: Mathematical Physics)

11 pages, 4783 KiB

Open AccessArticle

Analysis and Prediction of Flow-Induced Vibration of Convection Pipe for 200 t/h D Type Gas Boiler

by Shouguang Yao, Xinyu Huang, Linglong Zhang, Huiyi Mao and Xiaofei Sun

Axioms 2022, 11(4), 163; https://doi.org/10.3390/axioms11040163 - 05 Apr 2022

Cited by 1 | Viewed by 1946

Abstract

This paper is aimed at the analysis and prediction of the fluid-induced vibration phenomenon in the convection tube bundle area caused by Karman vortex street shedding in the background of a 200 t/h large-capacity D-type gas boiler. Based on the numerical simulation of [...] Read more.

This paper is aimed at the analysis and prediction of the fluid-induced vibration phenomenon in the convection tube bundle area caused by Karman vortex street shedding in the background of a 200 t/h large-capacity D-type gas boiler. Based on the numerical simulation of flue heat state flow field and fast Fourier transform, the lift coefficient curve of different monitoring areas and the corresponding Karman vortex street shedding frequency are obtained. The accuracy of the analysis model is validated by comparing Karman vortex shedding frequency with acoustic equipment standing wave frequency. In order to meet the design requirements of the 200 t/h D-type gas boiler for reliable and stable operation, the vibration characteristics and variation rules of a convection tube bundle in a D-type boiler under different working conditions are predicted. Full article

(This article belongs to the Special Issue Computational Heat Transfer and Fluid Dynamics)

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16 pages, 322 KiB

Open AccessFeature PaperArticle

On the Bias in Confirmatory Factor Analysis When Treating Discrete Variables as Ordinal Instead of Continuous

by Alexander Robitzsch

Axioms 2022, 11(4), 162; https://doi.org/10.3390/axioms11040162 - 01 Apr 2022

Cited by 6 | Viewed by 2453

Abstract

Confirmatory factor analysis is some of the most widely used statistical techniques in the social sciences. Frequently, variables (i.e., items) stemming from questionnaires are analyzed. Two competing approaches for estimating confirmatory factor analysis can be distinguished. First, ordinal variables could be treated as [...] Read more.

Confirmatory factor analysis is some of the most widely used statistical techniques in the social sciences. Frequently, variables (i.e., items) stemming from questionnaires are analyzed. Two competing approaches for estimating confirmatory factor analysis can be distinguished. First, ordinal variables could be treated as in the case of continuous variables using Pearson correlations, and maximum likelihood estimation method would be applied. Second, an ordinal factor analysis based on polychoric correlations can be fitted. In the majority of the psychometric literature, there is a preference for the ordinal factor analysis based on polychoric correlations because the continuous treatment of variables results in biased factor loadings and biased factor correlations. This article argues that it is not legitimate to speak about bias when comparing the two competing factor analytic approaches because it depends on how true model parameters are defined. This decision can be made individually by a researcher. It is shown in simulation studies and analytical derivations that treating variables ordinally using polychoric correlations instead of continuous using Pearson correlations can also lead to biased estimates of factor loadings and factor correlations. Consequently, it should only be stated that different model parameters are defined in a continuous and an ordinal treatment, and one approach should not generally be preferred over the other. Full article

(This article belongs to the Collection Mathematical Analysis and Applications)

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12 pages, 280 KiB

Open AccessArticle

Approximation Properties of the Generalized Abel-Poisson Integrals on the Weyl-Nagy Classes

by Inna Kal’chuk and Yurii Kharkevych

Axioms 2022, 11(4), 161; https://doi.org/10.3390/axioms11040161 - 01 Apr 2022

Cited by 26 | Viewed by 1625

Abstract

Asymptotic equalities are obtained for the least upper bounds of approximations of functions from the classes

W_{β, \infty}^{r}

by the generalized Abel-Poisson integrals

P_{γ} (δ), 0 < γ \leq 2,

for the case [...] Read more.

Asymptotic equalities are obtained for the least upper bounds of approximations of functions from the classes

W_{β, \infty}^{r}

by the generalized Abel-Poisson integrals

P_{γ} (δ), 0 < γ \leq 2,

for the case

r > γ

in the uniform metric, which provide the solution to the Kolmogorov–Nikol’skii problem for the given method of approximation on the Weyl-Nagy classes. Full article

(This article belongs to the Special Issue Approximation Theory and Related Applications)

17 pages, 1720 KiB

Open AccessFeature PaperArticle

Data Analysis Using a Coupled System of Ornstein–Uhlenbeck Equations Driven by Lévy Processes

by Maria C. Mariani, Peter K. Asante, William Kubin and Osei K. Tweneboah

Axioms 2022, 11(4), 160; https://doi.org/10.3390/axioms11040160 - 01 Apr 2022

Viewed by 1960

Abstract

In this work, we have analyzed data sets from various fields using a coupled Ornstein–Uhlenbeck (OU) system of equations driven by Lévy processes. The Ornstein–Uhlenbeck model is well known for its ability to capture stochastic behaviors when used as a predictive model. There’s [...] Read more.

In this work, we have analyzed data sets from various fields using a coupled Ornstein–Uhlenbeck (OU) system of equations driven by Lévy processes. The Ornstein–Uhlenbeck model is well known for its ability to capture stochastic behaviors when used as a predictive model. There’s empirical evidence showing that there exist dependencies or correlations between events; thus, we may be able to model them together. Here we show such correlation between data from finance, geophysics and health as well as show the predictive performance when they are modeled with a coupled Ornstein–Uhlenbeck system of equations. The results show that the solution to the stochastic system provides a good fit to the data sets analyzed. In addition by comparing the results obtained when the BDLP is a

Γ (a, b)

process or an IG(a,b) process, we are able to deduce the best choice out of the two to model our data sets. Full article

(This article belongs to the Special Issue Financial Mathematics and Econophysics)

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7 pages, 258 KiB

Open AccessArticle

Statistically Convergent Sequences in Intuitionistic Fuzzy Metric Spaces

by Banu Pazar Varol

Axioms 2022, 11(4), 159; https://doi.org/10.3390/axioms11040159 - 01 Apr 2022

Cited by 3 | Viewed by 1740

Abstract

In this paper, we introduce the concepts of statistical convergence and statistical Cauchy sequences with respect to the intuitionistic fuzzy metric spaces inspired by the idea of statistical convergence in fuzzy metric spaces. Then, we give useful characterizations for statistically convergent sequences and [...] Read more.

In this paper, we introduce the concepts of statistical convergence and statistical Cauchy sequences with respect to the intuitionistic fuzzy metric spaces inspired by the idea of statistical convergence in fuzzy metric spaces. Then, we give useful characterizations for statistically convergent sequences and statistically Cauchy sequences. Full article

(This article belongs to the Special Issue Advances in Mathematics and Its Applications)

10 pages, 274 KiB

Open AccessFeature PaperArticle

Homomorphic Encoders of Profinite Abelian Groups II

by María V. Ferrer and Salvador Hernández

Axioms 2022, 11(4), 158; https://doi.org/10.3390/axioms11040158 - 29 Mar 2022

Cited by 1 | Viewed by 1426

Abstract

Let

{G_{i} : i \in N}

be a family of finite Abelian groups. We say that a subgroup

G \leq \prod_{i \in N} G_{i}

is order controllable if for every

i \in N

, there is [...] Read more.

Let

{G_{i} : i \in N}

be a family of finite Abelian groups. We say that a subgroup

G \leq \prod_{i \in N} G_{i}

is order controllable if for every

i \in N

, there is

n_{i} \in N

such that for each

c \in G

, there exists

c_{1} \in G

satisfying

c_{1 | [1, i]} = c_{| [1, i]}

,

s u p p (c_{1}) \subseteq [1, n_{i}]

, and order

(c_{1})

divides order

(c_{| [1, n_{i}]})

. In this paper, we investigate the structure of order-controllable group codes. It is proved that if G is an order controllable, shift invariant, group code over a finite abelian group H, then G possesses a finite canonical generating set. Furthermore, our construction also yields that G is algebraically conjugate to a full group shift. Full article

(This article belongs to the Special Issue Topological Groups and Dynamics)

17 pages, 4381 KiB

Open AccessArticle

Control of String Vibrations by Displacement of One End with the Other End Fixed, Given the Deflection Form at an Intermediate Moment of Time

by Vanya Barseghyan and Svetlana Solodusha

Axioms 2022, 11(4), 157; https://doi.org/10.3390/axioms11040157 - 28 Mar 2022

Cited by 3 | Viewed by 1603

Abstract

We consider a boundary control problem for the equation of string vibration with given initial and final conditions, given the deflection form at an intermediate moment of time. The control is carried out by displacement of one end with the other end fixed. [...] Read more.

We consider a boundary control problem for the equation of string vibration with given initial and final conditions, given the deflection form at an intermediate moment of time. The control is carried out by displacement of one end with the other end fixed. The problem is reduced to the problem of a distributed action control with zero boundary conditions. We propose a constructive approach to constructing a boundary control action by the separation of variables and methods of the theory of control of finite-dimensional systems. The approach is applied to given functions. A computational experiment was carried out with the construction of the corresponding graphs and their comparative analysis. They confirm the obtained results. Full article

(This article belongs to the Special Issue 10th Anniversary of Axioms: Mathematical Physics)

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20 pages, 662 KiB

Open AccessArticle

Deterministic and Stochastic Prey–Predator Model for Three Predators and a Single Prey

by Yousef Alnafisah and Moustafa El-Shahed

Axioms 2022, 11(4), 156; https://doi.org/10.3390/axioms11040156 - 28 Mar 2022

Cited by 4 | Viewed by 2158

Abstract

In this paper, a deterministic prey–predator model is proposed and analyzed. The interaction between three predators and a single prey was investigated. The impact of harvesting on the three predators was studied, and we concluded that the dynamics of the population can be [...] Read more.

In this paper, a deterministic prey–predator model is proposed and analyzed. The interaction between three predators and a single prey was investigated. The impact of harvesting on the three predators was studied, and we concluded that the dynamics of the population can be controlled by harvesting. Some sufficient conditions were obtained to ensure the local and global stability of equilibrium points. The transcritical bifurcation was investigated using Sotomayor’s theorem. We performed a stochastic extension of the deterministic model to study the fluctuation environmental factors. The existence of a unique global positive solution for the stochastic model was investigated. The exponential–mean–squared stability of the resulting stochastic differential equation model was examined, and it was found to be dependent on the harvesting effort. Theoretical results are illustrated using numerical simulations. Full article

(This article belongs to the Special Issue Differential Equations and Asymptotic Analysis: Recent Advances and Applications)

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9 pages, 263 KiB

Open AccessArticle

Application of Fractional Grey Forecasting Model in Economic Growth of the Group of Seven

by Yumei Liao, Xu Wang and Jinrong Wang

Axioms 2022, 11(4), 155; https://doi.org/10.3390/axioms11040155 - 28 Mar 2022

Cited by 1 | Viewed by 2015

Abstract

This paper uses the idea of fractional order accumulation instead of the form of grey index, and applies the fractional order accumulation prediction model to the economic growth prediction of the member states of the Group of Seven from 1973 to 2016. By [...] Read more.

This paper uses the idea of fractional order accumulation instead of the form of grey index, and applies the fractional order accumulation prediction model to the economic growth prediction of the member states of the Group of Seven from 1973 to 2016. By comparing different evaluation indexes such as

R^{2}

, MAD and BIC, it is found that the prediction performance of fractional order cumulative grey prediction model (GM(

α

,1)) is significantly improved in the medium and long term compared with the traditional grey prediction model (GM(1,1)). Full article

(This article belongs to the Special Issue Mathematical Analysis Is the Theoretical Basis of a Number of Mathematical Disciplines)

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24 pages, 2043 KiB

Open AccessArticle

Selection of Cold Chain Logistics Service Providers Based on a Grey AHP and Grey COPRAS Framework: A Case Study in Vietnam

by Ngoc-Ai-Thy Nguyen, Chia-Nan Wang, Le-Thanh-Hieu Dang, Le-Thanh-Tuyen Dang and Thanh-Tuan Dang

Axioms 2022, 11(4), 154; https://doi.org/10.3390/axioms11040154 - 27 Mar 2022

Cited by 18 | Viewed by 5059

Abstract

Choosing the most suitable cold chain logistics service providers (CLPs) is a vital strategic decision for businesses aiming to achieve an effective and sustainable cold supply chain. A sustainable CLP is one that integrates sustainable practices across its whole operation cycle to achieve [...] Read more.

Choosing the most suitable cold chain logistics service providers (CLPs) is a vital strategic decision for businesses aiming to achieve an effective and sustainable cold supply chain. A sustainable CLP is one that integrates sustainable practices across its whole operation cycle to achieve product quality, on-time deliveries, and satisfied customer requirements, while preventing products from going to waste, which is especially important in the context of a developing country. This study aims to evaluate and select the best CLP regarding their sustainability performance. For this evaluation, a multi-criteria decision making (MCDM)-based framework is proposed that integrates the grey analytic hierarchy process (G-AHP) and grey complex proportional assessment (G-COPRAS) methodologies, in which grey numbers are used to express the linguistic evaluation statements of experts. Initially, the evaluation criteria based on service level, economic, environmental, and social dimensions were determined by means of a literature review and experts’ opinions to employ the MCDM approach. The G-AHP was utilized to identify the criteria weights, and then, G-COPRAS was used to select the best CLP among the alternatives. A case illustration in Vietnam is presented to exhibit the presented approach’s applicability. From the G-AHP findings, product quality, logistics costs, innovation, and effectiveness of cold chain processes, customer experience, and CO emissions of refrigerated vehicle were ranked as the five most important criteria. From the G-COPRAS analysis, Yoshida Saigon Cold Logistic (CPL-05) is the best CLP. The robustness of the applied integrated MCDM approach was also tested by conducting a comparative analysis, in which the priority rankings of the best CLPs were very similar. The assessment in this study is directed towards enabling managers, practitioners, and stakeholders of cold chain businesses to assess the most efficient CLP in the supply chain in the market and also to devise suitable strategies toward sustainable development. Full article

(This article belongs to the Special Issue Multiple-Criteria Decision-Making and Computational Intelligence: Recent Applications)

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