Axioms

10 pages, 277 KiB

Open AccessArticle

Analytical Solutions of Temperature Distribution in a Rectangular Parallelepiped

by Dinesh Kumar, Frédéric Yves Ayant and Clemente Cesarano

Axioms 2022, 11(9), 488; https://doi.org/10.3390/axioms11090488 - 19 Sep 2022

Cited by 1 | Viewed by 1907

In the present article, we give analytical solutions for temperature distribution in a rectangular parallelepiped with the help of a multivariable I-function. The results established in this paper are of a general character from which several known and new results can be [...] Read more.

In the present article, we give analytical solutions for temperature distribution in a rectangular parallelepiped with the help of a multivariable I-function. The results established in this paper are of a general character from which several known and new results can be deduced. We also give the special and particular cases of our main findings. Full article

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

12 pages, 275 KiB

Open AccessArticle

Neighborhood Versions of Geometric–Arithmetic and Atom Bond Connectivity Indices of Some Popular Graphs and Their Properties

by Muhammad Shafii Abubakar, Kazeem Olalekan Aremu and Maggie Aphane

Axioms 2022, 11(9), 487; https://doi.org/10.3390/axioms11090487 - 19 Sep 2022

Cited by 3 | Viewed by 1615

Abstract

In this article, we introduce the neighborhood versions of two classical topological indices, namely neighborhood geometric–arithmetic and neighborhood atom bond connectivity indices. We study the graph-theoretic properties of these new topological indices for some known graphs, e.g., complete graph

K_{n}

, regular [...] Read more.

In this article, we introduce the neighborhood versions of two classical topological indices, namely neighborhood geometric–arithmetic and neighborhood atom bond connectivity indices. We study the graph-theoretic properties of these new topological indices for some known graphs, e.g., complete graph

K_{n}

, regular graph

R_{n}

, cycle graph

C_{n}

, star graph

S_{n}

, pendant graph, and irregular graph and further establish their respective bounds. We note that the neighbourhood geometric–arithmetic index of

K_{n}

,

R_{n}

,

C_{n}

, and

S_{n}

is equal to the number of edges. The neighborhood atom bond connectivity index of an arbitrary simple graph

G

is strictly less than the number of edges. Our results contribute to the literature in this direction. Full article

(This article belongs to the Special Issue Advances in Discrete Mathematics and Theoretical Computer Science)

22 pages, 5497 KiB

Open AccessArticle

Object-Based Dynamics: Applying Forman–Ricci Flow on a Multigraph to Assess the Impact of an Object on The Network Structure

by Haim Cohen, Yinon Nachshon, Anat Maril, Paz M. Naim, Jürgen Jost and Emil Saucan

Axioms 2022, 11(9), 486; https://doi.org/10.3390/axioms11090486 - 19 Sep 2022

Cited by 4 | Viewed by 1928

Abstract

Temporal information plays a central role in shaping the structure of a network. In this paper, we consider the impact of an object on network structure over time. More specifically, we use a novel object-based dynamic measure to reflect the extent to which [...] Read more.

Temporal information plays a central role in shaping the structure of a network. In this paper, we consider the impact of an object on network structure over time. More specifically, we use a novel object-based dynamic measure to reflect the extent to which an object that is represented in the network by a vertex affects the topology of the network over time. By way of multigraph and Forman–Ricci flow, we assess the object’s impact on graph weights by comparing two graphs, one in which the object is present and one in which the object is absent. After using a case study to demonstrate the impact of Forman–Ricci flow on the network structure, we apply our measure in a semantic network to assess the effects of a word on the interactions between other words that follow it. In addition, we compare our novel measure to centrality and curvature measures so that we can ascertain the advantages of our measure over ones that already exist. Full article

(This article belongs to the Section Geometry and Topology)

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29 pages, 13638 KiB

Open AccessArticle

Interval Type-2 Fuzzy Approach for Dynamic Parameter Adaptation in the Bird Swarm Algorithm for the Optimization of Fuzzy Medical Classifier

by Ivette Miramontes and Patricia Melin

Axioms 2022, 11(9), 485; https://doi.org/10.3390/axioms11090485 - 19 Sep 2022

Cited by 7 | Viewed by 2004

Abstract

Optimization is essential for applications since it can improve the results provided in different areas; for this task, it is beneficial to use soft computing techniques, such as bio-inspired algorithms. In addition, it has been shown that if dynamic parameter adaptation is applied [...] Read more.

Optimization is essential for applications since it can improve the results provided in different areas; for this task, it is beneficial to use soft computing techniques, such as bio-inspired algorithms. In addition, it has been shown that if dynamic parameter adaptation is applied to these algorithms, they can provide a better result. For this work, the main contribution is to carry out the dynamic parameter adaptation to the bird swarm algorithm using interval type-2 fuzzy systems to realize a new fuzzy bio-inspired algorithm. The design of the proposed fuzzy system consists of two inputs corresponding to the iterations and diversity. As outputs, it takes the values of C and S, which are parameters to be adjusted by the algorithm. Once the design and the experimentation are realized, they are divided into two study cases. The first consists of a set of complex functions of the Congress of Evolutionary Competition 2017. The second case study consists of optimizing the membership functions in a fuzzy system designed to provide the nocturnal blood pressure profile, which corresponds to a neuro-fuzzy hybrid model to obtain the risk of hypertension. Analyzing the 30 experiments performed in both case studies, we can observe that the results obtained are improved when compared with the original method and other proposed methodologies, achieving good results in the complex functions. In addition, the optimized fuzzy system will reach an average of 97% correct classification. Statistically, it can be concluded that there is significant evidence to affirm that the proposed method provides good results. Full article

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

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17 pages, 8032 KiB

Open AccessArticle

Assessing Graph Robustness through Modified Zagreb Index

by Rui Chen, Jianping Li and Weihua He

Axioms 2022, 11(9), 484; https://doi.org/10.3390/axioms11090484 - 19 Sep 2022

Viewed by 1836

Abstract

Graph robustness or network robustness is the ability that a graph or a network preserves its connectivity or other properties after the loss of vertices and edges, which has been a central problem in the research of complex networks. In this paper, we [...] Read more.

Graph robustness or network robustness is the ability that a graph or a network preserves its connectivity or other properties after the loss of vertices and edges, which has been a central problem in the research of complex networks. In this paper, we introduce the Modified Zagreb index and Modified Zagreb index centrality as novel measures to study graph robustness. We theoretically find some relationships between these novel measures and some other graph measures. Then, we use Modified Zagreb index centrality to analyze the robustness of BA scale-free networks, ER random graphs and WS small world networks under deliberate or random vertex attacks. We also study the correlations between this new measure and some other existed measures. Finally, we use Modified Zagreb index centrality to study the robustness of two real world networks. All these results demonstrate the efficiency of Modified Zagreb index centrality for assessing the graph robustness. Full article

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

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18 pages, 1030 KiB

Open AccessArticle

Efficient Modified Meta-Heuristic Technique for Unconstrained Optimization Problems

by Khalid Abdulaziz Alnowibet, Ahmad M. Alshamrani, Adel Fahad Alrasheedi, Salem Mahdi, Mahmoud El-Alem, Abdallah Aboutahoun and Ali Wagdy Mohamed

Axioms 2022, 11(9), 483; https://doi.org/10.3390/axioms11090483 - 19 Sep 2022

Cited by 4 | Viewed by 1950

Abstract

In this paper, a new Modified Meta-Heuristic algorithm is proposed. This method contains some modifications to improve the performance of the simulated-annealing algorithm (SA). Most authors who deal with improving the SA algorithm presented some improvements and modifications to one or more of [...] Read more.

In this paper, a new Modified Meta-Heuristic algorithm is proposed. This method contains some modifications to improve the performance of the simulated-annealing algorithm (SA). Most authors who deal with improving the SA algorithm presented some improvements and modifications to one or more of the five standard features of the SA algorithm. In this paper, we improve the SA algorithm by presenting some suggestions and modifications to all five standard features of the SA algorithm. Through these suggestions and modifications, we obtained a new algorithm that finds the approximate solution to the global minimum of a non-convex function. The new algorithm contains novel parameters, which are updated at each iteration. Therefore, the variety and alternatives in choosing these parameters demonstrated a noticeable impact on the performance of the proposed algorithm. Furthermore, it has multiple formulas by which the candidate solutions are generated. Diversity in these formulas helped the proposed algorithm to escape a local point while finding the global minimizer of a non-convex function. The efficiency of the proposed algorithm is reported through extensive numerical experiments on some well-known test problems. The performance profiles are used to evaluate and compare the performance of our proposed algorithm against the other five meta-heuristic algorithms. The comparison results between the performance of our suggested algorithm and the other five algorithms indicate that the proposed algorithm is competitive with, and in all cases superior to, the five algorithms in terms of the efficiency, reliability, and effectiveness for finding the global minimizers of non-convex functions. This superiority of the new proposed algorithm is due to those five modified standard features. Full article

(This article belongs to the Special Issue Optimization Algorithms and Applications)

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11 pages, 773 KiB

Open AccessArticle

Univariate and Multivariate Ostrowski-Type Inequalities Using Atangana–Baleanu Caputo Fractional Derivative

by Henok Desalegn Desta, Deepak B. Pachpatte, Jebessa B. Mijena and Tadesse Abdi

Axioms 2022, 11(9), 482; https://doi.org/10.3390/axioms11090482 - 19 Sep 2022

Cited by 4 | Viewed by 1504

Abstract

In this paper, we obtain some univariate and multivariate Ostrowski-type inequalities using the Atangana–Baleanu fractional derivative in the sense of Liouville–Caputo (ABC). The results obtained for both left and right ABC fractional derivatives can be applied to study further fractional inequalities and estimate [...] Read more.

In this paper, we obtain some univariate and multivariate Ostrowski-type inequalities using the Atangana–Baleanu fractional derivative in the sense of Liouville–Caputo (ABC). The results obtained for both left and right ABC fractional derivatives can be applied to study further fractional inequalities and estimate various non-local function problems since the operator consists of a non-singular kernel. The obtained results are more generalized in nature. Full article

(This article belongs to the Special Issue Current Research on Mathematical Inequalities)

25 pages, 2512 KiB

Open AccessArticle

Study on Comprehensive Evaluation Based on AHP-MADM Model for Patent Value of Balanced Vehicle

by Zhili Huang, Jinli Li and Hongge Yue

Axioms 2022, 11(9), 481; https://doi.org/10.3390/axioms11090481 - 18 Sep 2022

Cited by 8 | Viewed by 1982

Abstract

With the development of science and technology, people’s travel modes have become more diversified, and self-balancing vehicles have become a popular travel tool for young people. However, in recent years, due to its quality instability, many regions have issued relevant bans, affecting the [...] Read more.

With the development of science and technology, people’s travel modes have become more diversified, and self-balancing vehicles have become a popular travel tool for young people. However, in recent years, due to its quality instability, many regions have issued relevant bans, affecting the development of the balanced vehicle industry. In order to better understand balancing vehicle technology, this paper starts with the balancing vehicle patent, and carries out the following research: This paper first introduces the background and current situation of balanced vehicles and the patent. Then, the principle and model of multi-attribute decision-making based on the analytic hierarchy process (AHP-MADM) are described. According to the three-dimensional patent valuation system issued by the State Intellectual Property Office, a core patent valuation system is established. Then, the weights of patent evaluation attributes are calculated by the improved AHP. After, the patent value of the self-balancing vehicle is evaluated using the established AHP-MADM model. On this basis, the status of patent research and the development of self-balancing vehicles is studied to provide a reference for relevant industry personnel, especially R & D personnel, in future product technology updates and patent layout. Full article

(This article belongs to the Special Issue Advances in Numerical Analysis and Scientific Computing)

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21 pages, 4101 KiB

Open AccessArticle

Corn Disease Recognition Based on Attention Mechanism Network

by Yingying Wang, Jin Tao and Haitao Gao

Axioms 2022, 11(9), 480; https://doi.org/10.3390/axioms11090480 - 18 Sep 2022

Cited by 10 | Viewed by 1981

Abstract

To extract more accurate and abundant features of corn disease and solve the problems of rough classification and low recognition accuracy, the attention mechanism is introduced into the field of corn disease recognition. The corn disease recognition model (AT-AlexNet) is proposed based on [...] Read more.

To extract more accurate and abundant features of corn disease and solve the problems of rough classification and low recognition accuracy, the attention mechanism is introduced into the field of corn disease recognition. The corn disease recognition model (AT-AlexNet) is proposed based on an attention mechanism. The network was based on AlexNet, and the new down-sampling attention module was constructed to enhance the foreground response of the disease; the Mish activation function was introduced to improve the nonlinear expression of the network; the new module of the full connection layer was designed to reduce the network parameters. In the experiment of the enhanced corn disease datasets, the average recognition accuracy of the attention-based network model AT-AlexNet is 99.35%. The recognition accuracy of using the Mish activation function is 0.65% higher than that of the ReLu activation function. The experiments show that compared with other identification methods, the proposed method has better classification performance for corn diseases. Full article

(This article belongs to the Special Issue A Hybrid Analysis of Information Technology and Decision Making)

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20 pages, 299 KiB

Open AccessArticle

Fixed-Point Theorems for ℒ_γ Contractions in Branciari Distance Spaces

by Seong-Hoon Cho

Axioms 2022, 11(9), 479; https://doi.org/10.3390/axioms11090479 - 18 Sep 2022

Cited by 2 | Viewed by 1292

Abstract

In this paper, the concepts of Suzuki-type ℒ_γ contractions and Suzuki–Berinde-type ℒ_γ contractions are introduced, and new fixed-point theorems for these two contractions are established. Full article

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

14 pages, 295 KiB

Open AccessArticle

Hadamard Compositions of Gelfond–Leont’ev Derivatives

by Myroslav Sheremeta

Axioms 2022, 11(9), 478; https://doi.org/10.3390/axioms11090478 - 18 Sep 2022

Cited by 1 | Viewed by 1266

Abstract

For analytic functions

f_{j} (z) = \sum_{n = 0}^{\infty} a_{n, j} z^{n}

,

1 \leq j \leq p

, the notion of a Hadamard composition [...] Read more.

For analytic functions

f_{j} (z) = \sum_{n = 0}^{\infty} a_{n, j} z^{n}

,

1 \leq j \leq p

, the notion of a Hadamard composition

{(f_{1} * \dots * f_{p})}_{m} = \sum_{n = 0}^{\infty} (\sum_{k_{1} + \dots + k_{p} = m} c_{k_{1} \dots k_{p}} a_{n, 1}^{k_{1}} \cdot \dots \cdot a_{n, p}^{k_{p}}) z^{n}

of genus m is introduced. The relationship between the growth of the Gelfond–Leont’ev derivative of the Hadamard composition of functions

f_{j}

and the growth Hadamard composition of Gelfond–Leont’ev derivatives of these functions is studied. We found conditions under which these derivatives and the composition have the same order and a lower order. For the maximal terms of the power expansion of these derivatives, I describe behavior of their ratios. Full article

(This article belongs to the Special Issue Honorary Special Issue Dedicated to Prof. Anatolii Asirovich Gol’dberg (1930–2008))

10 pages, 276 KiB

Open AccessArticle

Degenerate Fubini-Type Polynomials and Numbers, Degenerate Apostol–Bernoulli Polynomials and Numbers, and Degenerate Apostol–Euler Polynomials and Numbers

by Siqintuya Jin, Muhammet Cihat Dağli and Feng Qi

Axioms 2022, 11(9), 477; https://doi.org/10.3390/axioms11090477 - 17 Sep 2022

Cited by 2 | Viewed by 2191

Abstract

In this paper, by introducing degenerate Fubini-type polynomials, with the help of the Faà di Bruno formula and some properties of partial Bell polynomials, the authors provide several new explicit formulas and recurrence relations for Fubini-type polynomials and numbers, associate the newly defined [...] Read more.

In this paper, by introducing degenerate Fubini-type polynomials, with the help of the Faà di Bruno formula and some properties of partial Bell polynomials, the authors provide several new explicit formulas and recurrence relations for Fubini-type polynomials and numbers, associate the newly defined degenerate Fubini-type polynomials with degenerate Apostol–Bernoulli polynomials and degenerate Apostol–Euler polynomials of order

α

. These results enable one to present additional relations for some degenerate special polynomials and numbers. Full article

(This article belongs to the Special Issue Orthogonal Polynomials, Special Functions and Applications)

16 pages, 514 KiB

Open AccessArticle

A High-Order Approximate Solution for the Nonlinear 3D Volterra Integral Equations with Uniform Accuracy

by Zi-Qiang Wang, Ming-Dan Long and Jun-Ying Cao

Axioms 2022, 11(9), 476; https://doi.org/10.3390/axioms11090476 - 16 Sep 2022

Viewed by 1528

Abstract

In this paper, we present a high-order approximate solution with uniform accuracy for nonlinear 3D Volterra integral equations. This numerical scheme is constructed based on the three-dimensional block cubic Lagrangian interpolation method. At the same time, we give the local truncation error analysis [...] Read more.

In this paper, we present a high-order approximate solution with uniform accuracy for nonlinear 3D Volterra integral equations. This numerical scheme is constructed based on the three-dimensional block cubic Lagrangian interpolation method. At the same time, we give the local truncation error analysis of the numerical scheme based on Taylor’s theorem. Through theoretical analysis, we reach the conclusion that the optimal convergence order of this high-order numerical scheme is 4. Finally, we verify the effectiveness and applicability of the method through four numerical examples. Full article

(This article belongs to the Special Issue Numerical Methods for Fractional and Integer PDEs)

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16 pages, 327 KiB

Open AccessArticle

Stability for a Class of Differential Set-Valued Inverse Variational Inequalities in Finite Dimensional Spaces

by Xinyue Zhu, Wei Li and Xueping Luo

Axioms 2022, 11(9), 475; https://doi.org/10.3390/axioms11090475 - 16 Sep 2022

Cited by 2 | Viewed by 1679

Abstract

In this paper, we introduce and study a new class of differential set-valued inverse variational inequalities in finite dimensional spaces. By applying a result on differential inclusions involving an upper semicontinuous set-valued mapping with closed convex values, we first prove the existence of [...] Read more.

In this paper, we introduce and study a new class of differential set-valued inverse variational inequalities in finite dimensional spaces. By applying a result on differential inclusions involving an upper semicontinuous set-valued mapping with closed convex values, we first prove the existence of Carathéodory weak solutions for differential set-valued inverse variational inequalities. Then, by the existence result, we establish the stability for the differential set-valued inverse variational inequality problem when the constraint set and the mapping are perturbed by two different parameters. The closedness and continuity of Carathéodory weak solutions with respect to the two different parameters are obtained. Full article

(This article belongs to the Special Issue Nonlinear Dynamical Systems with Applications)

16 pages, 464 KiB

Open AccessArticle

A New Emergency-Risk-Evaluation Approach under Spherical Fuzzy-Information Environments

by Kuei-Hu Chang

Axioms 2022, 11(9), 474; https://doi.org/10.3390/axioms11090474 - 16 Sep 2022

Cited by 8 | Viewed by 1722

Abstract

When major emergencies or accidents occur, risk evaluation and prediction are the most important means to reduce their impact. Typical risk evaluation uses the failure mode and effects analysis (FMEA) method for failure-risk ranking and control. However, when faced with severe special infectious [...] Read more.

When major emergencies or accidents occur, risk evaluation and prediction are the most important means to reduce their impact. Typical risk evaluation uses the failure mode and effects analysis (FMEA) method for failure-risk ranking and control. However, when faced with severe special infectious diseases such as COVID-19, there are many cognitive and information uncertainties that the FMEA method is unable to effectively handle. To effectively deal with the issue of risk evaluation when major emergencies or accidents occur, this paper integrated the risk-priority number and spherical fuzzy-sets methods to propose a novel emergency-risk-evaluation method. In the numerical verification, this paper applied the example of preventing secondary COVID-19 transmissions in hospitals to explain the calculation procedure and validity of the proposed new emergency-risk-evaluation approach. The calculation results were also compared with the typical RPN, fuzzy-set, and intuitionistic fuzzy-set methods. The calculation results showed that the proposed new emergency-risk-evaluation approach could effectively handle the cognitive and informational uncertainties of emergency-risk-evaluation issues during the COVID-19 pandemic. Full article

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

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13 pages, 307 KiB

Open AccessArticle

Asymptotic Behavior of Solutions of the Cauchy Problem for a Hyperbolic Equation with Periodic Coefficients II

by Hovik A. Matevossian, Maria V. Korovina and Vladimir A. Vestyak

Axioms 2022, 11(9), 473; https://doi.org/10.3390/axioms11090473 - 16 Sep 2022

Cited by 6 | Viewed by 1652

Abstract

The paper is devoted to studying the behavior of solutions of the Cauchy problem for large values of time—more precisely, obtaining an asymptotic expansion characterizing the behavior of the solution of the Cauchy problem for a one-dimensional second-order hyperbolic equation with periodic coefficients [...] Read more.

The paper is devoted to studying the behavior of solutions of the Cauchy problem for large values of time—more precisely, obtaining an asymptotic expansion characterizing the behavior of the solution of the Cauchy problem for a one-dimensional second-order hyperbolic equation with periodic coefficients for large values of the time parameter t. To obtain this asymptotic expansion as t→∞, methods of the spectral theory of differential operators are used, as well as the properties of the spectrum of a non-positive Hill operator with periodic coefficients. Full article

(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)

29 pages, 8435 KiB

Open AccessArticle

Rational and Semi-Rational Solutions to the (2 + 1)-Dimensional Maccari System

by Yong Zhang, Huan-He Dong and Yong Fang

Axioms 2022, 11(9), 472; https://doi.org/10.3390/axioms11090472 - 15 Sep 2022

Cited by 1 | Viewed by 1960

Abstract

The KP hierarchy reduction method is one of the most reliable and efficient techniques for determining exact solitary wave solutions to nonlinear partial differential equations. In this paper, according to the KP hierarchy reduction technique, rational and some other semi-rational solutions to the [...] Read more.

The KP hierarchy reduction method is one of the most reliable and efficient techniques for determining exact solitary wave solutions to nonlinear partial differential equations. In this paper, according to the KP hierarchy reduction technique, rational and some other semi-rational solutions to the (2 + 1)-dimensional Maccari system are investigated. It is shown that two different types of breathers can be derived, and under appropriate parameter constraints, they can be reduced to some well known solutions, involving the homoclinic orbits, dark soliton or anti-dark soliton solution. For the dark and anti-dark solution, its interaction is similar to a resonance soliton. Furthermore, by using a limiting technique, we derive two kinds of rational solutions, one is the lump and the other one is the rogue wave. After constructing these solutions, we further discuss the interactions between the obtained solutions. It is interesting that we obtain a parallel breather and a intersectional breather, which seems very surprising. Finally, we also provide a new three-state interaction, which is composed by the dark-soliton, rogue wave and breather and has never been provided for the Maccari system. Full article

(This article belongs to the Topic Advances in Nonlinear Dynamics: Methods and Applications)

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24 pages, 319 KiB

Open AccessArticle

Controllability Results for First Order Impulsive Fuzzy Differential Systems

by Rui Liu, Michal Fečkan, Donal O’Regan and Jinrong Wang

Axioms 2022, 11(9), 471; https://doi.org/10.3390/axioms11090471 - 14 Sep 2022

Cited by 1 | Viewed by 1571

Abstract

In this paper, we investigate the controllability of first-order impulsive fuzzy differential equations. Using the direct construction method, the controllability of first-order linear impulsive fuzzy differential equations is considered with

a < 0

, the (c1) solution, and

a < 0

[...] Read more.

In this paper, we investigate the controllability of first-order impulsive fuzzy differential equations. Using the direct construction method, the controllability of first-order linear impulsive fuzzy differential equations is considered with

a < 0

, the (c1) solution, and

a < 0

, the (c2) solution, respectively.In addition, by employing the Banach fixed-point theorem, the controllability of first-order nonlinear impulsive fuzzy differential equations is studied. Finally, examples are presented to illustrate our theoretical results. Full article

(This article belongs to the Special Issue Nonautonomous and Random Dynamical Systems)

18 pages, 350 KiB

Open AccessArticle

Solving Fractional Volterra–Fredholm Integro-Differential Equations via A** Iteration Method

by Austine Efut Ofem, Aftab Hussain, Oboyi Joseph, Mfon Okon Udo, Umar Ishtiaq, Hamed Al Sulami and Chukwuka Fernando Chikwe

Axioms 2022, 11(9), 470; https://doi.org/10.3390/axioms11090470 - 14 Sep 2022

Cited by 11 | Viewed by 1942

Abstract

In this article, we develop a faster iteration method, called the

A^{* *}

iteration method, for approximating the fixed points of almost contraction mappings and generalized

α

-nonexpansive mappings. We establish some weak and strong convergence results of the

A^{* *}

[...] Read more.

In this article, we develop a faster iteration method, called the

A^{* *}

iteration method, for approximating the fixed points of almost contraction mappings and generalized

α

-nonexpansive mappings. We establish some weak and strong convergence results of the

A^{* *}

iteration method for fixed points of generalized

α

-nonexpansive mappings in uniformly convex Banach spaces. We provide a numerical example to illustrate the efficiency of our new iteration method. The weak

w^{2}

-stability result of the new iteration method is also studied. As an application of our main results, we approximate the solution of a fractional Volterra–Fredholm integro-differential equation. Our results improve and generalize several well-known results in the current literature. Full article

(This article belongs to the Special Issue Advances in Nonlinear Analysis and Related Fixed Point Problems)

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20 pages, 971 KiB

Open AccessArticle

PTG-PLM: Predicting Post-Translational Glycosylation and Glycation Sites Using Protein Language Models and Deep Learning

by Alhasan Alkuhlani, Walaa Gad, Mohamed Roushdy, Michael Gr. Voskoglou and Abdel-badeeh M. Salem

Axioms 2022, 11(9), 469; https://doi.org/10.3390/axioms11090469 - 14 Sep 2022

Cited by 6 | Viewed by 3859

Abstract

Post-translational glycosylation and glycation are common types of protein post-translational modifications (PTMs) in which glycan binds to protein enzymatically or nonenzymatically, respectively. They are associated with various diseases such as coronavirus, Alzheimer’s, cancer, and diabetes diseases. Identifying glycosylation and glycation sites is significant [...] Read more.

Post-translational glycosylation and glycation are common types of protein post-translational modifications (PTMs) in which glycan binds to protein enzymatically or nonenzymatically, respectively. They are associated with various diseases such as coronavirus, Alzheimer’s, cancer, and diabetes diseases. Identifying glycosylation and glycation sites is significant to understanding their biological mechanisms. However, utilizing experimental laboratory tools to identify PTM sites is time-consuming and costly. In contrast, computational methods based on machine learning are becoming increasingly essential for PTM site prediction due to their higher performance and lower cost. In recent years, advances in Transformer-based Language Models based on deep learning have been transferred from Natural Language Processing (NLP) into the proteomics field by developing language models for protein sequence representation known as Protein Language Models (PLMs). In this work, we proposed a novel method, PTG-PLM, for improving the performance of PTM glycosylation and glycation site prediction. PTG-PLM is based on convolutional neural networks (CNNs) and embedding extracted from six recent PLMs including ProtBert-BFD, ProtBert, ProtAlbert, ProtXlnet, ESM-1b, and TAPE. The model is trained and evaluated on two public datasets for glycosylation and glycation site prediction. The results show that PTG-PLM based on ESM-1b and ProtBert-BFD has better performance than PTG-PLM based on the other PLMs. Comparison results with the existing tools and representative supervised learning methods show that PTG-PLM surpasses the other models for glycosylation and glycation site prediction. The outstanding performance results of PTG-PLM indicate that it can be used to predict the sites of the other types of PTMs. Full article

(This article belongs to the Special Issue Mathematical Modeling)

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6 pages, 234 KiB

Open AccessArticle

Equivalence between the Existence of Best Proximity Points and Fixed Points for Some Classes of Proximal Contractions

by Sumit Som, Moosa Gabeleh and Manuel De la Sen

Axioms 2022, 11(9), 468; https://doi.org/10.3390/axioms11090468 - 13 Sep 2022

Viewed by 1467

Abstract

In the year 2014, Almeida et al. introduced a new class of mappings, namely, contractions of Geraghty type. Additionally, in the year 2021, Beg et al. introduced the concept of generalized F-proximal contraction of the first kind and generalized F-proximal contraction [...] Read more.

In the year 2014, Almeida et al. introduced a new class of mappings, namely, contractions of Geraghty type. Additionally, in the year 2021, Beg et al. introduced the concept of generalized F-proximal contraction of the first kind and generalized F-proximal contraction of the second kind, respectively. After developing these concepts, authors mainly studied the best proximity points for these classes of mappings. In this short note, we prove that the problem of the existence of the best proximity points for the said classes of proximal contractions is equivalent to the corresponding fixed points problems. Full article

(This article belongs to the Special Issue Fixed Point Theory and Its Related Topics III)

20 pages, 533 KiB

Open AccessArticle

Green Financing Efficiency and Influencing Factors of Chinese Listed Construction Companies against the Background of Carbon Neutralization: A Study Based on Three-Stage DEA and System GMM

by Yaguai Yu, Yina Yan, Panyi Shen, Yuting Li and Taohan Ni

Axioms 2022, 11(9), 467; https://doi.org/10.3390/axioms11090467 - 13 Sep 2022

Cited by 7 | Viewed by 2188

Abstract

This paper combines the green industrial strategy and green financial policies for the construction industry implemented in China in the context of carbon neutrality. A total of 67 listed companies in the construction industry from 2017 to 2020 were taken as the research [...] Read more.

This paper combines the green industrial strategy and green financial policies for the construction industry implemented in China in the context of carbon neutrality. A total of 67 listed companies in the construction industry from 2017 to 2020 were taken as the research sample, the green financing efficiency was measured, and its influencing factors were identified based on the three-stage DEA and systematic GMM method. The findings show that the green financing efficiency of listed companies in the construction industry is not high overall, although it is increasing. There are obvious differences in subsectors, among which, the efficiency of architectural design and service industries is relatively high. Overall, the financial environment, and the interaction between the government and the financial market, significantly and positively influence the green financing efficiency. In addition, the macroeconomic environment and the government–enterprise relationship has a complex impact on the green financing efficiency. The ownership concentration and having corporate executives with a financial background have a significant positive impact on the green financing efficiency, and the enterprise size, the debt maturity structure, and the R&D and innovation capability have a significant negative impact. The findings of this paper have implications for the improvement of the policy system that supports green development in the construction industry, and provide guidance for the strategic adjustment of the construction industry itself. Full article

(This article belongs to the Special Issue Information Theory in Economics, Finance, and Management)

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13 pages, 295 KiB

Open AccessArticle

Pointwise Wavelet Estimations for a Regression Model in Local Hölder Space

by Junke Kou, Qinmei Huang and Huijun Guo

Axioms 2022, 11(9), 466; https://doi.org/10.3390/axioms11090466 - 10 Sep 2022

Cited by 2 | Viewed by 1338

Abstract

This paper considers an unknown functional estimation problem in a regression model with multiplicative and additive noise. A linear wavelet estimator is first constructed by a wavelet projection operator. The convergence rate under the pointwise error of linear wavelet estimators is studied in [...] Read more.

This paper considers an unknown functional estimation problem in a regression model with multiplicative and additive noise. A linear wavelet estimator is first constructed by a wavelet projection operator. The convergence rate under the pointwise error of linear wavelet estimators is studied in local Hölder space. A nonlinear wavelet estimator is provided by the hard thresholding method in order to obtain an adaptive estimator. The convergence rate of the nonlinear estimator is the same as the linear estimator up to a logarithmic term. Finally, it should be pointed out that the convergence rates of two wavelet estimators are consistent with the optimal convergence rate on pointwise nonparametric estimation. Full article

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

16 pages, 337 KiB

Open AccessArticle

A Study of Team Recommended Generalized Assignment Methods

by Fachao Li, Ruya Fan and Chenxia Jin

Axioms 2022, 11(9), 465; https://doi.org/10.3390/axioms11090465 - 9 Sep 2022

Cited by 1 | Viewed by 1379

Abstract

This study considers the team recommendation problem as a generalized assignment problem. Firstly, a formal description of the team recommendation problem is given; secondly, a team-recommended generalized assignment model (TRGAM) is established based on the work ability value of alternative members, the comprehensive [...] Read more.

This study considers the team recommendation problem as a generalized assignment problem. Firstly, a formal description of the team recommendation problem is given; secondly, a team-recommended generalized assignment model (TRGAM) is established based on the work ability value of alternative members, the comprehensive work ability value of the team as the core concern index, the importance weight of team tasks and the energy allocation weight of team members as the fusion strategy of the data; thirdly, a solution method for the standard case of TRGAM is designed using the enumeration method and Hungarian algorithms (BEM⊕HM–TRGAMs) as local computational tools; fourthly, the alternative member set refinement methods and standardization measures for TRGAM are given; finally, BEM⊕HM–TRGAMs are analyzed using specific arithmetic examples. The theoretical analysis and experimental results show that TRGAM has good structural features and interpretability and BEM⊕HM–TRGAMs can effectively solve the TRGAM solving problem. Full article

19 pages, 1462 KiB

Open AccessArticle

Political Signed Temporal Networks: A Deep Learning Approach

by Alejandro Chinea Manrique de Lara and Elka Korutcheva

Axioms 2022, 11(9), 464; https://doi.org/10.3390/axioms11090464 - 8 Sep 2022

Viewed by 1815

Abstract

The evolution analysis of networks whose links are either positive or negative, representing opposite relationships such as friendship and enmity, has been revealed to be particularly useful in sociological contexts. Using a large relational dataset containing the last two centuries of state-wise geopolitical [...] Read more.

The evolution analysis of networks whose links are either positive or negative, representing opposite relationships such as friendship and enmity, has been revealed to be particularly useful in sociological contexts. Using a large relational dataset containing the last two centuries of state-wise geopolitical information (the correlates of war–alliance conflicts), a machine learning approach is presented to predict network dynamics. The combination of geometric as well as information–theoretic measures to characterize the resulting discrete time series together with the power of deep learning machines is used to generate a model whose predictions are even accurate on the few days in two centuries of international relations when the typical value (i.e., Alliance or Neutral) changed to a war or a conflict. In other words, the model can predict the next state of the network with a probability of error close to zero. Full article

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10 pages, 2758 KiB

Open AccessCommunication

Selection of Appropriate Symbolic Regression Models Using Statistical and Dynamic System Criteria: Example of Waste Gasification

by Pavel Praks, Marek Lampart, Renáta Praksová, Dejan Brkić, Tomáš Kozubek and Jan Najser

Axioms 2022, 11(9), 463; https://doi.org/10.3390/axioms11090463 - 8 Sep 2022

Cited by 5 | Viewed by 2256

Abstract

In this paper, we analyze the interpretable models from real gasification datasets of the project “Centre for Energy and Environmental Technologies” (CEET) discovered by symbolic regression. To evaluate CEET models based on input data, two different statistical metrics to quantify their accuracy are [...] Read more.

In this paper, we analyze the interpretable models from real gasification datasets of the project “Centre for Energy and Environmental Technologies” (CEET) discovered by symbolic regression. To evaluate CEET models based on input data, two different statistical metrics to quantify their accuracy are usually used: Mean Square Error (MSE) and the Pearson Correlation Coefficient (PCC). However, if the testing points and the points used to construct the models are not chosen randomly from the continuum of the input variable, but instead from the limited number of discrete input points, the behavior of the model between such points very possibly will not fit well the physical essence of the modelled phenomenon. For example, the developed model can have unexpected oscillatory tendencies between the used points, while the usually used statistical metrics cannot detect these anomalies. However, using dynamic system criteria in addition to statistical metrics, such suspicious models that do fit well-expected behavior can be automatically detected and abandoned. This communication will show the universal method based on dynamic system criteria which can detect suitable models among all those which have good properties following statistical metrics. The dynamic system criteria measure the complexity of the candidate models using approximate and sample entropy. The examples are given for waste gasification where the output data (percentage of each particular gas in the produced mixture) is given only for six values of the input data (temperature in the chamber in which the process takes place). In such cases instead, to produce expected simple spline-like curves, artificial intelligence tools can produce inappropriate oscillatory curves with sharp picks due to the known tendency of symbolic regression to produce overfitted and relatively more complex models if the nature of the physical model is simple. Full article

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

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16 pages, 663 KiB

Open AccessEditor’s ChoiceArticle

The Use of a Log-Normal Prior for the Student t-Distribution

by Se Yoon Lee

Axioms 2022, 11(9), 462; https://doi.org/10.3390/axioms11090462 - 8 Sep 2022

Cited by 7 | Viewed by 3719

Abstract

It is typically difficult to estimate the number of degrees of freedom due to the leptokurtic nature of the Student t-distribution. Particularly in studies with small sample sizes, special care is needed concerning prior choice in order to ensure that the analysis [...] Read more.

It is typically difficult to estimate the number of degrees of freedom due to the leptokurtic nature of the Student t-distribution. Particularly in studies with small sample sizes, special care is needed concerning prior choice in order to ensure that the analysis is not overly dominated by any prior distribution. In this article, popular priors used in the existing literature are examined by characterizing their distributional properties on an effective support where it is desirable to concentrate on most of the prior probability mass. Additionally, we suggest a log-normal prior as a viable prior option. We show that the Bayesian estimator based on a log-normal prior compares favorably to other Bayesian estimators based on the priors previously proposed via simulation studies and financial applications. Full article

(This article belongs to the Special Issue Statistical Methods and Applications)

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13 pages, 334 KiB

Open AccessArticle

Geometry of Indefinite Kenmotsu Manifolds as *η-Ricci-Yamabe Solitons

by Abdul Haseeb, Mohd Bilal, Sudhakar K. Chaubey and Mohammad Nazrul Islam Khan

Axioms 2022, 11(9), 461; https://doi.org/10.3390/axioms11090461 - 7 Sep 2022

Cited by 8 | Viewed by 1583

Abstract

In this paper, we study the properties of

ϵ

-Kenmotsu manifolds if its metrics are

* η

-Ricci-Yamabe solitons. It is proven that an

ϵ

-Kenmotsu manifold endowed with a

* η

-Ricci-Yamabe soliton is

η

-Einstein. The necessary conditions for an

ϵ

[...] Read more.

In this paper, we study the properties of

ϵ

-Kenmotsu manifolds if its metrics are

* η

-Ricci-Yamabe solitons. It is proven that an

ϵ

-Kenmotsu manifold endowed with a

* η

-Ricci-Yamabe soliton is

η

-Einstein. The necessary conditions for an

ϵ

-Kenmotsu manifold, whose metric is a

* η

-Ricci-Yamabe soliton, to be an Einstein manifold are derived. Finally, we model an indefinite Kenmotsu manifold example of dimension 5 to examine the existence

* η

-Ricci-Yamabe solitons. Full article

(This article belongs to the Section Geometry and Topology)

20 pages, 349 KiB

Open AccessArticle

Entire Symmetric Functions on the Space of Essentially Bounded Integrable Functions on the Union of Lebesgue-Rohlin Spaces

by Taras Vasylyshyn and Kostiantyn Zhyhallo

Axioms 2022, 11(9), 460; https://doi.org/10.3390/axioms11090460 - 7 Sep 2022

Cited by 7 | Viewed by 1453

Abstract

The class of measure spaces which can be represented as unions of Lebesgue-Rohlin spaces with continuous measures contains a lot of important examples, such as

R^{n}

for any

n \in N

with the Lebesgue measure. In this work we consider symmetric functions [...] Read more.

The class of measure spaces which can be represented as unions of Lebesgue-Rohlin spaces with continuous measures contains a lot of important examples, such as

R^{n}

for any

n \in N

with the Lebesgue measure. In this work we consider symmetric functions on Banach spaces of all complex-valued integrable essentially bounded functions on such unions. We construct countable algebraic bases of algebras of continuous symmetric polynomials on these Banach spaces. The completions of such algebras of polynomials are Fréchet algebras of all complex-valued entire symmetric functions of bounded type on the abovementioned Banach spaces. We show that each such Fréchet algebra is isomorphic to the Fréchet algebra of all complex-valued entire symmetric functions of bounded type on the complex Banach space of all complex-valued essentially bounded functions on

[0, 1]

. Full article

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

27 pages, 1890 KiB

Open AccessArticle

Inferences of a Mixture Bivariate Alpha Power Exponential Model with Engineering Application

by Refah Alotaibi, Mazen Nassar, Indranil Ghosh, Hoda Rezk and Ahmed Elshahhat

Axioms 2022, 11(9), 459; https://doi.org/10.3390/axioms11090459 - 7 Sep 2022

Cited by 4 | Viewed by 1692

Abstract

The univariate alpha power exponential (APE) distribution has several appealing characteristics. It behaves similarly to Weibull, Gamma, and generalized exponential distributions with two parameters. In this paper, we consider different bivariate mixture models starting with two independent univariate APE models, and, in the [...] Read more.

The univariate alpha power exponential (APE) distribution has several appealing characteristics. It behaves similarly to Weibull, Gamma, and generalized exponential distributions with two parameters. In this paper, we consider different bivariate mixture models starting with two independent univariate APE models, and, in the latter case, starting from two dependent APE models. Several useful structural properties of such a mixture model (under the assumption of two independent APE distribution) are discussed. Bivariate APE (BAPE), in short, modelled under the dependent set up are also discussed in the context of a copula-based construction. Inferential aspects under the classical and under the Bayesian paradigm are considered to estimate the model parameters, and a simulation study is conducted for this purpose. For illustrative purposes, a well-known motor data is re-analyzed to exhibit the flexibility of the proposed bivariate mixture model. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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Axioms, Volume 11, Issue 9 (September 2022) – 66 articles

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