Mathematics

35 pages, 10847 KiB

Open AccessArticle

A Novel Adaptive Manta-Ray Foraging Optimization for Stochastic ORPD Considering Uncertainties of Wind Power and Load Demand

by Sulaiman Z. Almutairi, Emad A. Mohamed and Fayez F. M. El-Sousy

Mathematics 2023, 11(11), 2591; https://doi.org/10.3390/math11112591 - 05 Jun 2023

Cited by 1 | Viewed by 1141

Abstract

The optimal control of reactive powers in electrical systems can improve a system’s performance and security; this can be provided by the optimal reactive power dispatch (ORPD). Under the high penetration of renewable energy resources (RERs) such as wind turbines (WTs), the ORPD [...] Read more.

The optimal control of reactive powers in electrical systems can improve a system’s performance and security; this can be provided by the optimal reactive power dispatch (ORPD). Under the high penetration of renewable energy resources (RERs) such as wind turbines (WTs), the ORPD problem solution has become a challenging and complex task due to the fluctuations and uncertainties of generated power from WTs. In this regard, this paper solved the conventional ORPD and the stochastic ORPD (SORPD) at uncertainties of the generated power from WTs and the load demand. An Adaptive Manta-Ray Foraging Optimization (AMRFO) was presented based on three modifications, including the fitness distance balance selection (FDB), Quasi Oppositional based learning (QOBL), and an adaptive Levy Flight (ALF). The ORPD and SORPD were solved to reduce the power loss (P_Loss) and the total expected P_Loss (TEPL), the voltage deviations (VD) and the total expected VD (TEVD). The normal and Weibull probability density functions (PDFs), along with the scenario reduction method and the Monte Carlo simulation (MCS), were utilized for uncertainty representations. The performance and validity of the suggested AMRFO were compared to other optimizers, including SCSO, WOA, DO, AHA, and the conventional MRFO on the IEEE 30-bus system and standard benchmark functions. These simulation results confirm the supremacy of the suggested AMRFO for the ORPD and SORPD solution compared to the other reported techniques. Full article

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24 pages, 481 KiB

Open AccessFeature PaperArticle

Ranking the Importance of Variables in a Nonparametric Frontier Analysis Using Unsupervised Machine Learning Techniques

by Raul Moragues, Juan Aparicio and Miriam Esteve

Mathematics 2023, 11(11), 2590; https://doi.org/10.3390/math11112590 - 05 Jun 2023

Cited by 1 | Viewed by 1060

Abstract

In this paper, we propose and compare new methodologies for ranking the importance of variables in productive processes via an adaptation of OneClass Support Vector Machines. In particular, we adapt two methodologies inspired by the machine learning literature: one involving the random shuffling [...] Read more.

In this paper, we propose and compare new methodologies for ranking the importance of variables in productive processes via an adaptation of OneClass Support Vector Machines. In particular, we adapt two methodologies inspired by the machine learning literature: one involving the random shuffling of values of a variable and another one using the objective value of the dual formulation of the model. Additionally, we motivate the use of these type of algorithms in the production context and compare their performance via a computational experiment. We observe that the methodology based on shuffling the values of a variable outperforms the methodology based on the dual formulation. We observe that the shuffling-based methodology correctly ranks the variables in 94% of the scenarios with one relevant input and one irrelevant input. Moreover, it correctly ranks each variable in at least 65% of replications of a scenario with three relevant inputs and one irrelevant input. Full article

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10 pages, 262 KiB

Open AccessArticle

On Reusing the Stages of a Rejected Runge-Kutta Step

by Vladislav N. Kovalnogov, Ruslan V. Fedorov, Tamara V. Karpukhina, Theodore E. Simos and Charalampos Tsitouras

Mathematics 2023, 11(11), 2589; https://doi.org/10.3390/math11112589 - 05 Jun 2023

Cited by 1 | Viewed by 1281

Abstract

Runge-Kutta (RK) pairs are amongst the most popular methods for numerically solving Initial Value Problems. While using an RK pair, we may experience rejection of some steps through the interval of integration. Traditionally, all of the evaluations are then dropped, and we proceed [...] Read more.

Runge-Kutta (RK) pairs are amongst the most popular methods for numerically solving Initial Value Problems. While using an RK pair, we may experience rejection of some steps through the interval of integration. Traditionally, all of the evaluations are then dropped, and we proceed with a completely new round of computations. In this work, we propose avoiding this waste and continuing by reusing the rejected RK stages. We focus especially on an RK pair of orders six and five. After step rejection, we reuse all the previously evaluated stages and only add three new stages. We proceed by evaluating the output using a smaller step. By this technique, we manage to significantly reduce the cost in a set of problems that are known to pose difficulties in RK algorithms with changing step sizes. Full article

(This article belongs to the Section Engineering Mathematics)

12 pages, 436 KiB

Open AccessArticle

A Markov Decision Process with Awareness and Present Bias in Decision-Making

by Federico Bizzarri, Chiara Mocenni and Silvia Tiezzi

Mathematics 2023, 11(11), 2588; https://doi.org/10.3390/math11112588 - 05 Jun 2023

Viewed by 1152

Abstract

We propose a Markov Decision Process Model that blends ideas from Psychological research and Economics to study decision-making in individuals with self-control problems. We have borrowed a dual-process of decision-making with self-awareness from Psychological research, and we introduce present bias in inter-temporal preferences, [...] Read more.

We propose a Markov Decision Process Model that blends ideas from Psychological research and Economics to study decision-making in individuals with self-control problems. We have borrowed a dual-process of decision-making with self-awareness from Psychological research, and we introduce present bias in inter-temporal preferences, a phenomenon widely explored in Economics. We allow for both an exogenous and endogenous, state-dependent, present bias in inter-temporal decision-making and explore, by means of numerical simulations, the consequences on well-being emerging from the solution of the model. We show that, over time, self-awareness may mitigate present bias and suboptimal choice behaviour. Full article

(This article belongs to the Special Issue Recent Advances in Mathematical Methods for Economics)

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14 pages, 308 KiB

Open AccessArticle

An Algorithm for the Numbers of Homomorphisms from Paths to Rectangular Grid Graphs

by Hatairat Yingtaweesittikul, Sayan Panma and Penying Rochanakul

Mathematics 2023, 11(11), 2587; https://doi.org/10.3390/math11112587 - 05 Jun 2023

Viewed by 904

Abstract

Let G and H be graphs. A mapping f from the vertices of G to the vertices of H is known as a

h o m o m o r p h i s m

from G to H if, for every pair [...] Read more.

Let G and H be graphs. A mapping f from the vertices of G to the vertices of H is known as a

h o m o m o r p h i s m

from G to H if, for every pair of adjacent vertices x and y in G, the vertices

f (x)

and

f (y)

are adjacent in H. A rectangular grid graph is the Cartesian product of two path graphs. In this paper, we provide a formula to determine the number of homomorphisms from paths to rectangular grid graphs. This formula gives the solution to the problem concerning the number of walks in the rectangular grid graphs. Full article

(This article belongs to the Special Issue Graph Theory: Advanced Algorithms and Applications)

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26 pages, 9573 KiB

Open AccessArticle

Mathematical Modeling the Performance of an Electric Vehicle Considering Various Driving Cycles

by Nikita V. Martyushev, Boris V. Malozyomov, Svetlana N. Sorokova, Egor A. Efremenkov and Mengxu Qi

Mathematics 2023, 11(11), 2586; https://doi.org/10.3390/math11112586 - 05 Jun 2023

Cited by 17 | Viewed by 6012

Abstract

Currently, the estimated range of an electric vehicle is a variable value. The assessment of this power reserve is possible by various methods, and the results of the assessment by these methods will be quite different. Thus, building a model based on these [...] Read more.

Currently, the estimated range of an electric vehicle is a variable value. The assessment of this power reserve is possible by various methods, and the results of the assessment by these methods will be quite different. Thus, building a model based on these cycles is an extremely important task for manufacturers of electric vehicles. In this paper, a simulation model was developed to determine the range of an electric vehicle by cycles of movement. A mathematical model was created to study the power reserve of an electric vehicle, taking into account four driving cycles, in which the lengths of cycles and the forces acting on the electric vehicle are determined; the calculation of the forces of resistance to movement was carried out taking into account the efficiency of the electric motor; thus, the energy consumption of an electric vehicle is determined. The modeling of the study of motion cycles on the presented model was carried out. The mathematical evaluation of battery life was based on simulation results. Simulation modeling of an electric vehicle in the MATLAB Simulink software environment was performed. An assessment of the power reserve of the developed electric vehicle was completed. The power reserve was estimated using the four most common driving cycles—NEDC, WLTC, JC08, US06. Studies have shown that the highest speed of the presented US06 cycle provides the shortest range of an electric vehicle. The JC08 and NEDC cycles have similar developed speeds in urban conditions, while in NEDC there is a phase of out-of-town traffic; therefore, due to the higher speed, the electric vehicle covers a greater distance in equal time compared to JC08. At the same time, the NEDC cycle is the least dynamic and the acceleration values do not exceed 1 m/s². Low dynamics allow for a longer range of an electric vehicle; however, the actual urban operation of an electric vehicle requires more dynamics. The cycles of movement presented in the article provide a sufficient variety and variability of the load of an electric vehicle and its battery over a wide range, which made it possible to conduct effective studies of the energy consumed, taking into account the recovery of electricity to the battery in a wide range of loads. It was determined that frequent braking, taking into account operation including in urban traffic, provides a significant return of electricity to the battery. Full article

(This article belongs to the Section Engineering Mathematics)

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39 pages, 2922 KiB

Open AccessReview

Chaos-Based Image Encryption: Review, Application, and Challenges

by Bowen Zhang and Lingfeng Liu

Mathematics 2023, 11(11), 2585; https://doi.org/10.3390/math11112585 - 05 Jun 2023

Cited by 18 | Viewed by 8509

Abstract

Chaos has been one of the most effective cryptographic sources since it was first used in image-encryption algorithms. This paper closely examines the development process of chaos-based image-encryption algorithms from various angles, including symmetric and asymmetric algorithms, block ciphers and stream ciphers, and [...] Read more.

Chaos has been one of the most effective cryptographic sources since it was first used in image-encryption algorithms. This paper closely examines the development process of chaos-based image-encryption algorithms from various angles, including symmetric and asymmetric algorithms, block ciphers and stream ciphers, and integration with other technologies. The unique attributes of chaos, such as sensitivity to initial conditions, topological transitivity, and pseudo-randomness, are conducive to cross-referencing with other disciplines and improving image-encryption methods. Additionally, this paper covers practical application scenarios and current challenges of chaotic image encryption, thereby encouraging researchers to continue developing and complementing existing situations, and may also serve as a basis of future development prospects for chaos-based image encryption. Full article

(This article belongs to the Special Issue Chaos-Based Secure Communication and Cryptography)

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13 pages, 1215 KiB

Open AccessArticle

Complementary Gamma Zero-Truncated Poisson Distribution and Its Application

by Ausaina Niyomdecha and Patchanok Srisuradetchai

Mathematics 2023, 11(11), 2584; https://doi.org/10.3390/math11112584 - 05 Jun 2023

Cited by 3 | Viewed by 1089

Abstract

Numerous lifetime distributions have been developed to assist researchers in various fields. This paper proposes a new continuous three-parameter lifetime distribution called the complementary gamma zero-truncated Poisson distribution (CGZTP), which combines the distribution of the maximum of a series of independently identical gamma-distributed [...] Read more.

Numerous lifetime distributions have been developed to assist researchers in various fields. This paper proposes a new continuous three-parameter lifetime distribution called the complementary gamma zero-truncated Poisson distribution (CGZTP), which combines the distribution of the maximum of a series of independently identical gamma-distributed random variables with zero-truncated Poisson random variables. The proposed distribution’s properties, including proofs of the probability density function, cumulative distribution function, survival function, hazard function, and moments, are discussed. The unknown parameters are estimated using the maximum likelihood method, whose asymptotic properties are examined. In addition, Wald confidence intervals are constructed for the CGZTP parameters. Simulation studies are conducted to evaluate the efficacy of parameter estimation, and three real-world data applications demonstrate that CGZTP can be an alternative distribution for fitting data. Full article

(This article belongs to the Section Probability and Statistics)

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12 pages, 1214 KiB

Open AccessArticle

Traveling Wave Optical Solutions for the Generalized Fractional Kundu–Mukherjee–Naskar (gFKMN) Model

by Yong Tang

Mathematics 2023, 11(11), 2583; https://doi.org/10.3390/math11112583 - 05 Jun 2023

Cited by 2 | Viewed by 781

Abstract

The work considers traveling wave optical solutions for the nonlinear generalized fractional KMN equation. This equation is considered for describing pulse propagation in optical fibers and communication systems using two quite similar approaches, based on the expansion of these solutions in the exponential [...] Read more.

The work considers traveling wave optical solutions for the nonlinear generalized fractional KMN equation. This equation is considered for describing pulse propagation in optical fibers and communication systems using two quite similar approaches, based on the expansion of these solutions in the exponential or polynomial forms. Both approaches belong to the direct solving class of methods for PDEs and suppose the use of an auxiliary equation. The solutions acquired in this paper are obtained from first- and second-order differential equations that act as auxiliary equations. In addition, we generated 3D, contour, and 2D plots to illustrate the characteristics of the obtained soliton solutions. To create these plots, we carefully selected appropriate values for the relevant parameters. Full article

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15 pages, 1259 KiB

Open AccessArticle

Mathematical Modeling of Brain Swelling in Electroencephalography and Magnetoencephalography

by Athena Papargiri, George Fragoyiannis and Vasileios S. Kalantonis

Mathematics 2023, 11(11), 2582; https://doi.org/10.3390/math11112582 - 05 Jun 2023

Viewed by 1177

Abstract

In the present paper, the forward problem of EEG and MEG is discussed, where the head is modeled by a spherical two-shell piecewise-homogeneous conductor with a neuronal current source positioned in the exterior shell area representing the brain tissue, while the interior shell [...] Read more.

In the present paper, the forward problem of EEG and MEG is discussed, where the head is modeled by a spherical two-shell piecewise-homogeneous conductor with a neuronal current source positioned in the exterior shell area representing the brain tissue, while the interior shell portrays a cerebral edema. We consider constant conductivity, which assumes different values in each compartment, where the expansions of the electric potential and the magnetic field are represented via spherical harmonics. Furthermore, we demonstrate the reduction of our analytical results to the single-compartment model while it is shown that the magnetic field in the exterior of the conductor is a function only of the dipole moment and its position. Consequently, it does not depend on the inhomogeneity dictated by the interior shell, a fact that verifies the efficiency of the model. Full article

(This article belongs to the Special Issue Applications of Partial Differential Equations in Mathematical Physics, 1st Edition)

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12 pages, 606 KiB

Open AccessArticle

Super Spanning Connectivity of the Folded Divide-and-SwapCube

by Lantao You, Jianfeng Jiang and Yuejuan Han

Mathematics 2023, 11(11), 2581; https://doi.org/10.3390/math11112581 - 05 Jun 2023

Viewed by 772

Abstract

A

k^{*}

-container of a graph G is a set of k disjoint paths between any pair of nodes whose union covers all nodes of G. The spanning connectivity of G,

κ^{*} (G)

, is the largest [...] Read more.

A

k^{*}

-container of a graph G is a set of k disjoint paths between any pair of nodes whose union covers all nodes of G. The spanning connectivity of G,

κ^{*} (G)

, is the largest k, such that there exists a

j^{*}

-container between any pair of nodes of G for all

1 \leq j \leq k

. If

κ^{*} (G) = κ (G)

, then G is super spanning connected. Spanning connectivity is an important property to measure the fault tolerance of an interconnection network. The divide-and-swap cube

D S C_{n}

is a newly proposed hypercube variant, which reduces the network cost from

O (n^{2})

to

O (n {log}_{2} n)

compared with the hypercube and other hypercube variants. The folded divide-and-swap cube

F D S C_{n}

is proposed based on

D S C_{n}

to reduce the diameter of

D S C_{n}

. Both

D S C_{n}

and

F D S C_{n}

possess many better properties than hypercubes. In this paper, we investigate the super spanning connectivity of

F D S C_{n}

where

n = 2^{d}

and

d \geq 1

. We show that

κ^{*} (F D S C_{n}) = κ (F D S C_{n}) = d + 2

, which means there exists an m-DPC(node-disjoint path cover) between any pair of nodes in

F D S C_{n}

for all

1 \leq m \leq d + 2

. Full article

(This article belongs to the Special Issue Advances of Computer Algorithms and Data Structures)

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19 pages, 347 KiB

Open AccessArticle

Fixed Point Theorems of Almost Generalized Contractive Mappings in b-Metric Spaces and an Application to Integral Equation

by N. Seshagiri Rao, Zoran D. Mitrović, Dania Santina and Nabil Mlaiki

Mathematics 2023, 11(11), 2580; https://doi.org/10.3390/math11112580 - 05 Jun 2023

Cited by 1 | Viewed by 973

Abstract

In this study, we have new fixed point results for weak contraction mappings in complete and partially ordered b-metric spaces. Our findings expand and generalize the results of Jachymski and Mituku et al and many more results in the literature as well. [...] Read more.

In this study, we have new fixed point results for weak contraction mappings in complete and partially ordered b-metric spaces. Our findings expand and generalize the results of Jachymski and Mituku et al and many more results in the literature as well. To illustrate our work, we present an application on the existence and uniqueness of a nonlinear quadratic integral problem solution. Moreover, an open problem is presented to enable the scope for future research in this area. Full article

(This article belongs to the Special Issue New Advances in Mathematical Analysis and Functional Analysis)

21 pages, 8511 KiB

Open AccessArticle

Regulating the Big Data-Based Discriminatory Pricing in Platform Retailing: A Tripartite Evolutionary Game Theory Analysis

by Shandong Mou, Kexin Zhong and Yamin Ma

Mathematics 2023, 11(11), 2579; https://doi.org/10.3390/math11112579 - 05 Jun 2023

Cited by 2 | Viewed by 1362

Abstract

Nowadays, with the rapid development of the platform economy, Big Data-based Discriminatory Pricing (BDDP) has become a common phenomenon in which big data and algorithms are applied to excessively seize consumer surplus and thus damage the rights and interests of consumers. This work [...] Read more.

Nowadays, with the rapid development of the platform economy, Big Data-based Discriminatory Pricing (BDDP) has become a common phenomenon in which big data and algorithms are applied to excessively seize consumer surplus and thus damage the rights and interests of consumers. This work aims to explore the equilibrium strategies of the consumers, the government, and the service platform and discuss factors affecting the BDDP practice of the service platforms. This study constructs a tripartite evolutionary game model among consumers, service platforms, and the government. Two evolutionary equilibrium strategies are derived and validated using simulation. Numerical experiments are conducted using MATLAB to reveal players’ evolutionary stability strategies under various settings. The study shows that (1) the strategies of the government and the platform always influence each other, (2) a reasonable adjustment of tax rate helps regulate the platform’s behavior, and (3) the proportion of consumers who switch the platform after they realize themselves suffering BDDP is an important factor influencing platform’s strategy. This study lastly summarizes the managerial insights for dealing with the platform’s BDDP behavior and safeguarding consumers’ rights from the perspectives of macro-regulation and privacy data protection. The conclusions of this study can help promote the high-quality development of the platform economy. Full article

(This article belongs to the Special Issue Application of Mathematical Methods to Economics, Management, Finance and Social Problems II)

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19 pages, 384 KiB

Open AccessArticle

Subclasses of p-Valent κ-Uniformly Convex and Starlike Functions Defined by the q-Derivative Operator

by Ekram E. Ali, Hari M. Srivastava and Abeer M. Albalahi

Mathematics 2023, 11(11), 2578; https://doi.org/10.3390/math11112578 - 04 Jun 2023

Cited by 3 | Viewed by 882

Abstract

The potential for widespread applications of the geometric and mapping properties of functions of a complex variable has motivated this article. On the other hand, the basic or quantum (or q-) derivatives and the basic or quantum (or q-) integrals are [...] Read more.

The potential for widespread applications of the geometric and mapping properties of functions of a complex variable has motivated this article. On the other hand, the basic or quantum (or q-) derivatives and the basic or quantum (or q-) integrals are extensively applied in many different areas of the mathematical, physical and engineering sciences. Here, in this article, we first apply the q-calculus in order to introduce the q-derivative operator

S_{η, p, q}^{n, m}

. Secondly, by means of this q-derivative operator, we define an interesting subclass

T ℵ_{λ, p}^{n, m} (η, α, κ)

of the class of normalized analytic and multivalent (or p-valent) functions in the open unit disk

U

. This p-valent analytic function class is associated with the class

κ

-

UCV

of

κ

-uniformly convex functions and the class

κ

-

UST

of

κ

-uniformly starlike functions in

U

. For functions belonging to the normalized analytic and multivalent (or p-valent) function class

T ℵ_{λ, p}^{n, m} (η, α, κ)

, we then investigate such properties as those involving (for example) the coefficient bounds, distortion results, convex linear combinations, and the radii of starlikeness, convexity and close-to-convexity. We also consider a number of corollaries and consequences of the main findings, which we derived herein. Full article

(This article belongs to the Special Issue New Trends in Complex Analysis Research, 2nd Edition)

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22 pages, 1275 KiB

Open AccessArticle

A Data-Driven Heuristic Method for Irregular Flight Recovery

by Nianyi Wang, Huiling Wang, Shan Pei and Boyu Zhang

Mathematics 2023, 11(11), 2577; https://doi.org/10.3390/math11112577 - 04 Jun 2023

Cited by 1 | Viewed by 1111

Abstract

In this study, we develop a data-driven heuristic method to solve the irregular flight recovery problem. Based on operational data from China South Airlines, Beijing, China, we evaluate the importance of a flight in the flight network and the influence of a delay [...] Read more.

In this study, we develop a data-driven heuristic method to solve the irregular flight recovery problem. Based on operational data from China South Airlines, Beijing, China, we evaluate the importance of a flight in the flight network and the influence of a delay on a flight and its subsequent flights. Then, we classify historical states into three scenarios according to their delay reasons and investigate the recovery patterns for each scenario. Inspired by the results of the data analysis, we develop a heuristic algorithm that imitates dispatcher actions. The algorithm is based on two basic operations: swapping the tail numbers of two flights and resetting their flight departure times. The algorithm can provide multiple recovery plans in real time for different scenarios, and we continue to refine and validate the algorithm for more robust and general solutions through a cost analysis. Finally, we test the efficiency and effectiveness of the recovery method based on the flight schedule, with real and simulated delays, and compare it with two other methods and the recovery actions of dispatchers. Full article

(This article belongs to the Special Issue Optimization Theory and Applications in Engineering, Management and Other Fields)

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24 pages, 1304 KiB

Open AccessFeature PaperArticle

Challenges and Opportunities in Machine Learning for Geometry

by Rafael Magdalena-Benedicto, Sonia Pérez-Díaz and Adrià Costa-Roig

Mathematics 2023, 11(11), 2576; https://doi.org/10.3390/math11112576 - 04 Jun 2023

Cited by 1 | Viewed by 2319

Abstract

Over the past few decades, the mathematical community has accumulated a significant amount of pure mathematical data, which has been analyzed through supervised, semi-supervised, and unsupervised machine learning techniques with remarkable results, e.g., artificial neural networks, support vector machines, and principal component analysis. [...] Read more.

Over the past few decades, the mathematical community has accumulated a significant amount of pure mathematical data, which has been analyzed through supervised, semi-supervised, and unsupervised machine learning techniques with remarkable results, e.g., artificial neural networks, support vector machines, and principal component analysis. Therefore, we consider as disruptive the use of machine learning algorithms to study mathematical structures, enabling the formulation of conjectures via numerical algorithms. In this paper, we review the latest applications of machine learning in the field of geometry. Artificial intelligence can help in mathematical problem solving, and we predict a blossoming of machine learning applications during the next years in the field of geometry. As a contribution, we propose a new method for extracting geometric information from the point cloud and reconstruct a 2D or a 3D model, based on the novel concept of generalized asymptotes. Full article

(This article belongs to the Special Issue New Trends in Algebraic Geometry and Its Applications, 2nd Edition)

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23 pages, 635 KiB

Open AccessArticle

Optimizing Vehicle Repairs Scheduling Using Mixed Integer Linear Programming: A Case Study in the Portuguese Automobile Sector

by Fátima Pilar, Eliana Costa e Silva and Ana Borges

Mathematics 2023, 11(11), 2575; https://doi.org/10.3390/math11112575 - 04 Jun 2023

Cited by 1 | Viewed by 1341

Abstract

This study investigates the scheduling of mechanical repairs performed at a Portuguese firm in the automobile sector. The aim is to reduce the amount of time that vehicles spend inactive between interventions by developing a mathematical model that takes into account the available [...] Read more.

This study investigates the scheduling of mechanical repairs performed at a Portuguese firm in the automobile sector. The aim is to reduce the amount of time that vehicles spend inactive between interventions by developing a mathematical model that takes into account the available resources and mechanics, the necessary interventions, and the time required for each repair. To accomplish this, a mixed-integer linear programming (MILP) model was employed, incorporating various variables to schedule interventions, allocate resources, and determine start times for each vehicle. The problem was formulated using the AMPL modeling language, and real-world instances of the problem, derived from data provided by the company, were solved using the Gurobi solver. Results show that the developed model significantly improves the scheduling of the vehicles’ repairs at the firm, leading to a reduction of 67% on average in the downtime of the vehicles and allowing an automatic correct schedule of the mechanical interventions. Moreover, the comparison of the scheduling obtained from the developed model and the firm’s procedure shows that interventions on vehicles arriving at the repair shop are mostly repaired on the day of entry, allowing for quicker delivery to the customer. Full article

(This article belongs to the Special Issue Industrial Mathematics in Management and Engineering)

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35 pages, 3058 KiB

Open AccessArticle

The Analysis of Risk Measurement and Association in China’s Financial Sector Using the Tail Risk Spillover Network

by Can-Zhong Yao, Ze-Kun Zhang and Yan-Li Li

Mathematics 2023, 11(11), 2574; https://doi.org/10.3390/math11112574 - 04 Jun 2023

Viewed by 1322

Abstract

This study focused on analyzing the complexities and risk spillovers that arise among financial institutions due to the development of financial markets. The research employed the conditional value at risk (CoVaR) methodology to quantify the extent of tail risk spillover and constructed a [...] Read more.

This study focused on analyzing the complexities and risk spillovers that arise among financial institutions due to the development of financial markets. The research employed the conditional value at risk (CoVaR) methodology to quantify the extent of tail risk spillover and constructed a risk spillover network encompassing Chinese financial institutions. The study further investigated the characteristics, transmission paths, and dynamic evolution of this network under different risk conditions. The empirical findings of this research highlighted several important insights. First, financial institutions play distinct roles in the risk spillover process, with the securities and banking sectors as risk exporters and the insurance and diversified financial sectors as risk takers. The closest risk spillover relationships were observed between banking and insurance and between securities and diversified financial sectors. Second, in high-risk scenarios, there is significant intrasectoral risk transmission between banks and the diversified financial sector, as well as dual-sectoral risk contagion between banks and securities, with the most-common transmission occurring between diversified financial and securities sectors. Finally, the securities sector acts as the pivotal node for risk spillovers, being the main transmitter of intersectoral risks. The formation and evolution of risk spillover networks are influenced by endogenous mechanisms, in particular the convergence effect. Full article

(This article belongs to the Special Issue Advanced Research in Mathematical Economics and Financial Modelling)

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10 pages, 3408 KiB

Open AccessArticle

Spatial Effects of Phase Dynamics on Oscillators Close to Bifurcation

by Yihan Wang and Jinjie Zhu

Mathematics 2023, 11(11), 2573; https://doi.org/10.3390/math11112573 - 04 Jun 2023

Viewed by 707

Abstract

The phase reduction approach has manifested its efficacy in investigating synchronization behaviors in limit-cycle oscillators. However, spatial distributions of the phase value on the limit cycle may lead to illusions of synchronizations for oscillators close to bifurcations. In this paper, we compared the [...] Read more.

The phase reduction approach has manifested its efficacy in investigating synchronization behaviors in limit-cycle oscillators. However, spatial distributions of the phase value on the limit cycle may lead to illusions of synchronizations for oscillators close to bifurcations. In this paper, we compared the phase sensitivity function in the spatial domain and time domain for oscillators close to saddle-node homoclinic (SNH) bifurcation, also known as saddle-node bifurcation on an invariant circle. It was found that the phase sensitivity function in the spatial domain can show the phase accumulation feature on the limit cycle, which can be ignored in the phase sensitivity function in the time domain. As an example, the synchronization distributions of uncoupled SNH oscillators driven by common and independent noises were investigated, where the space-dependent coupling function was considered on common noise. These results shed some light on the phase dynamics of oscillators close to bifurcations. Full article

(This article belongs to the Section Dynamical Systems)

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11 pages, 595 KiB

Open AccessArticle

Scrambling Reports: New Estimators for Estimating the Population Mean of Sensitive Variables

by Pablo O. Juárez-Moreno, Agustín Santiago-Moreno, José M. Sautto-Vallejo and Carlos N. Bouza-Herrera

Mathematics 2023, 11(11), 2572; https://doi.org/10.3390/math11112572 - 04 Jun 2023

Cited by 1 | Viewed by 892

Abstract

Warner proposed a methodology called randomized response techniques, which, through the random scrambling of sensitive variables, allows the non-response rate to be reduced and the response bias to be diminished. In this document, we present a randomized response technique using simple random sampling. [...] Read more.

Warner proposed a methodology called randomized response techniques, which, through the random scrambling of sensitive variables, allows the non-response rate to be reduced and the response bias to be diminished. In this document, we present a randomized response technique using simple random sampling. The scrambling of the sensitive variable is performed through the selection of a report R_i, i = 1,2,3. In order to evaluate the accuracy and efficiency of the proposed estimators, a simulation was carried out with two databases, where the sensitive variables are the destruction of poppy crops in Guerrero, Mexico, and the age at first sexual intercourse. The results show that more accurate estimates are obtained with the proposed model. Full article

(This article belongs to the Special Issue Current Research in Biostatistics)

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14 pages, 298 KiB

Open AccessArticle

Percolation Problems on N-Ary Trees

by Tianxiang Ren and Jinwen Wu

Mathematics 2023, 11(11), 2571; https://doi.org/10.3390/math11112571 - 04 Jun 2023

Viewed by 717

Abstract

Percolation theory is a subject that has been flourishing in recent decades. Because of its simple expression and rich connotation, it is widely used in chemistry, ecology, physics, materials science, infectious diseases, and complex networks. Consider an infinite-rooted N-ary tree where each [...] Read more.

Percolation theory is a subject that has been flourishing in recent decades. Because of its simple expression and rich connotation, it is widely used in chemistry, ecology, physics, materials science, infectious diseases, and complex networks. Consider an infinite-rooted N-ary tree where each vertex is assigned an i.i.d. random variable. When the random variable follows a Bernoulli distribution, a path is called head run if all the random variables that are assigned on the path are 1. We obtain the weak law of large numbers for the length of the longest head run. In addition, when the random variable follows a continuous distribution, a path is called an increasing path if the sequence of random variables on the path is increasing. By Stein’s method and other probabilistic methods, we prove that the length of the longest increasing path with a probability of one focuses on three points. We also consider limiting behaviours for the longest increasing path in a special tree. Full article

(This article belongs to the Special Issue Probability Distributions and Their Applications)

10 pages, 278 KiB

Open AccessArticle

Linear Algebraic Relations among Cardinalities of Sets of Matroid Functions

by Martin Kochol

Mathematics 2023, 11(11), 2570; https://doi.org/10.3390/math11112570 - 03 Jun 2023

Cited by 1 | Viewed by 580

Abstract

We introduce a unifying approach for invariants of finite matroids that count mappings to a finite set. The aim of this paper is to show that if the cardinalities of mappings with fixed values on a restricted set satisfy contraction–deletion rules, then there [...] Read more.

We introduce a unifying approach for invariants of finite matroids that count mappings to a finite set. The aim of this paper is to show that if the cardinalities of mappings with fixed values on a restricted set satisfy contraction–deletion rules, then there is a relation among them that can be expressed in terms of linear algebra. In this way, we study regular chain groups, nowhere-zero flows and tensions on graphs, and acyclic and totally cyclic orientations of oriented matroids and graphs. Full article

(This article belongs to the Special Issue The Matrix Theory of Graphs)

10 pages, 275 KiB

Open AccessArticle

Stabilization of n-Order Function Differential Equations by Parametric Distributed Control Function with Palindromic Parameters Set

by Irina Volinsky and Roman Shklyar

Mathematics 2023, 11(11), 2569; https://doi.org/10.3390/math11112569 - 03 Jun 2023

Viewed by 683

Abstract

Stabilization by a parametric distributed control function plays a very important role in aeronautics, aerospace and physics. Choosing the right parameters is necessary for handling the distributed control. In the current paper, we introduce stabilization criteria for an n-order functional-differential equation with [...] Read more.

Stabilization by a parametric distributed control function plays a very important role in aeronautics, aerospace and physics. Choosing the right parameters is necessary for handling the distributed control. In the current paper, we introduce stabilization criteria for an n-order functional-differential equation with a parametric distributed control function in n-term integrals and

2 n

parameter sets. In our article, we use properties of unimodal and log-concave polynomials. Full article

29 pages, 2667 KiB

Open AccessArticle

Solving Nonlinear Transcendental Equations by Iterative Methods with Conformable Derivatives: A General Approach

by Giro Candelario, Alicia Cordero, Juan R. Torregrosa and María P. Vassileva

Mathematics 2023, 11(11), 2568; https://doi.org/10.3390/math11112568 - 03 Jun 2023

Cited by 2 | Viewed by 869

Abstract

In recent years, some Newton-type schemes with noninteger derivatives have been proposed for solving nonlinear transcendental equations by using fractional derivatives (Caputo and Riemann–Liouville) and conformable derivatives. It has also been shown that the methods with conformable derivatives improve the performance of classical [...] Read more.

In recent years, some Newton-type schemes with noninteger derivatives have been proposed for solving nonlinear transcendental equations by using fractional derivatives (Caputo and Riemann–Liouville) and conformable derivatives. It has also been shown that the methods with conformable derivatives improve the performance of classical schemes. In this manuscript, we design point-to-point higher-order conformable Newton-type and multipoint procedures for solving nonlinear equations and propose a general technique to deduce the conformable version of any classical iterative method with integer derivatives. A convergence analysis is given and the expected orders of convergence are obtained. As far as we know, these are the first optimal conformable schemes, beyond the conformable Newton procedure, that have been developed. The numerical results support the theory and show that the new schemes improve the performance of the original methods in some aspects. Additionally, the dependence on initial guesses is analyzed, and these schemes show good stability properties. Full article

(This article belongs to the Section Computational and Applied Mathematics)

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26 pages, 6077 KiB

Open AccessArticle

Violation of Neumann Problem’s Solvability Condition for Poisson Equation, Involved in the Non-Linear PDEs, Containing the Reaction-Diffusion-Convection-Type Equation, at Numerical Solution by Direct Method

by Vyacheslav Trofimov, Maria Loginova, Vladimir Egorenkov, Yongqiang Yang and Zhongwei Yan

Mathematics 2023, 11(11), 2567; https://doi.org/10.3390/math11112567 - 03 Jun 2023

Viewed by 971

Abstract

In this paper, we consider the 3D problem of laser-induced semiconductor plasma generation under the action of the optical pulse, which is governed by the set of coupled time-dependent non-linear PDEs involving the Poisson equation with Neumann boundary conditions. The main feature of [...] Read more.

In this paper, we consider the 3D problem of laser-induced semiconductor plasma generation under the action of the optical pulse, which is governed by the set of coupled time-dependent non-linear PDEs involving the Poisson equation with Neumann boundary conditions. The main feature of this problem is the non-linear feedback between the Poisson equation with respect to induced electric field potential and the reaction-diffusion-convection-type equation with respect to free electron concentration and accounting for electron mobility (convection’s term). Herein, we focus on the choice of the numerical method for the Poisson equation solution with inhomogeneous Neumann boundary conditions. Despite the ubiquitous application of such a direct method as the Fast Fourier Transform for solving an elliptic problem in simple spatial domains, we demonstrate that applying a direct method for solving the problem under consideration results in a solution distortion. The reason for the Neumann problem’s solvability condition violation is the computational error’s accumulation. In contrast, applying an iterative method allows us to provide finite-difference scheme conservativeness, asymptotic stability, and high computation accuracy. For the iteration technique, we apply both an implicit alternating direction method and a new three-stage iteration process. The presented computer simulation results confirm the advantages of using iterative methods. Full article

(This article belongs to the Special Issue Mathematical Modelling, Nonlinear Optimization, Nondimensionalization and Engineering Applications)

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19 pages, 339 KiB

Open AccessArticle

Fractional Equations for the Scaling Limits of Lévy Walks with Position-Dependent Jump Distributions

by Vassili N. Kolokoltsov

Mathematics 2023, 11(11), 2566; https://doi.org/10.3390/math11112566 - 03 Jun 2023

Viewed by 771

Abstract

Lévy walks represent important modeling tools for a variety of real-life processes. Their natural scaling limits are known to be described by the so-called material fractional derivatives. So far, these scaling limits have been derived for spatially homogeneous walks, where Fourier and Laplace [...] Read more.

Lévy walks represent important modeling tools for a variety of real-life processes. Their natural scaling limits are known to be described by the so-called material fractional derivatives. So far, these scaling limits have been derived for spatially homogeneous walks, where Fourier and Laplace transforms represent natural tools of analysis. Here, we derive the corresponding limiting equations in the case of position-depending times and velocities of walks, where Fourier transforms cannot be effectively applied. In fact, we derive three different limits (specified by the way the process is stopped at an attempt to cross the boundary), leading to three different multi-dimensional versions of Caputo–Dzherbashian derivatives, which correspond to different boundary conditions for the generators of the related Feller semigroups and processes. Some other extensions and generalizations are analyzed. Full article

(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications)

23 pages, 668 KiB

Open AccessArticle

Ordinal Time Series Analysis with the R Package otsfeatures

by Ángel López-Oriona and José A. Vilar

Mathematics 2023, 11(11), 2565; https://doi.org/10.3390/math11112565 - 03 Jun 2023

Cited by 2 | Viewed by 1262

Abstract

The 21st century has witnessed a growing interest in the analysis of time series data. While most of the literature on the topic deals with real-valued time series, ordinal time series have typically received much less attention. However, the development of specific analytical [...] Read more.

The 21st century has witnessed a growing interest in the analysis of time series data. While most of the literature on the topic deals with real-valued time series, ordinal time series have typically received much less attention. However, the development of specific analytical tools for the latter objects has substantially increased in recent years. The R package otsfeatures attempts to provide a set of simple functions for analyzing ordinal time series. In particular, several commands allowing the extraction of well-known statistical features and the execution of inferential tasks are available for the user. The output of several functions can be employed to perform traditional machine learning tasks including clustering, classification, or outlier detection. otsfeatures also incorporates two datasets of financial time series which were used in the literature for clustering purposes, as well as three interesting synthetic databases. The main properties of the package are described and its use is illustrated through several examples. Researchers from a broad variety of disciplines could benefit from the powerful tools provided by otsfeatures. Full article

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

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16 pages, 4269 KiB

Open AccessArticle

On Consequences of Carreau Nanofluid Model with Dufour–Soret Effects and Activation Energy Subject to New Mass Flux Condition: A Numerical Study

by Usman Ali and Mawia Osman

Mathematics 2023, 11(11), 2564; https://doi.org/10.3390/math11112564 - 03 Jun 2023

Cited by 1 | Viewed by 1011

Abstract

Activation energy can be elaborated as the minimal energy required to start a certain chemical reaction. The concept of this energy was first presented by Arrhenius in the year 1889 and was later used in the oil reservoir industry, emulsion of water, geothermal [...] Read more.

Activation energy can be elaborated as the minimal energy required to start a certain chemical reaction. The concept of this energy was first presented by Arrhenius in the year 1889 and was later used in the oil reservoir industry, emulsion of water, geothermal as well as chemical engineering and food processing. This study relates to the impacts of mass transfer caused by temperature differences (Soret) and heat transport due to concentration gradient (Dufour) in a Carreau model with nanofluids (NFs), mixed convection and a magnetic field past a stretched sheet. Moreover, thermal radiation and activation energy with new mass flux constraints are presumed. All chemical science specifications of nanofluid are measured as constant. As a result of the motion of nanofluid particles, the fluid temperature and concentration are inspected, with some physical description. A system of coupled partial differential frameworks is used mathematically to formulate the physical model. A numerical scheme named the Runge–Kutta (R-K) approach along with the shooting technique are used to solve the obtained equations to a high degree of accuracy. The MATLAB R2022b software is used for the graphical presentation of the solution. The temperature of the nanofluid encompasses a quicker rate within the efficiency of a Dufour number. An intensifying thermal trend is observed for thermophoresis and the Brownian motion parameter. The Soret effect causes a decline in the fluid concentration, and the opposite trend is observed for rising activation energy. In addition, the local Nusselt number increases with the Prandtl number. Further, the comparative outcomes for drag force are established, with satisfying agreement with the existing literature. The results acquired here are anticipated to be applied to improving heat exchanger thermal efficiency to maintain thermal balancing control in compact heat density equipment and devices. Full article

(This article belongs to the Special Issue Advances in Computational and Applied Fluid Dynamics)

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22 pages, 375 KiB

Open AccessArticle

Bifurcation of Limit Cycles and Center in 3D Cubic Systems with Z₃-Equivariant Symmetry

by Ting Huang, Jieping Gu, Yuting Ouyang and Wentao Huang

Mathematics 2023, 11(11), 2563; https://doi.org/10.3390/math11112563 - 03 Jun 2023

Viewed by 1065

Abstract

This paper focuses on investigating the bifurcation of limit cycles and centers within a specific class of three-dimensional cubic systems possessing

Z_{3}

-equivariant symmetry. By calculating the singular point values of the systems, we obtain a necessary condition for a singular point [...] Read more.

This paper focuses on investigating the bifurcation of limit cycles and centers within a specific class of three-dimensional cubic systems possessing

Z_{3}

-equivariant symmetry. By calculating the singular point values of the systems, we obtain a necessary condition for a singular point to be a center. Subsequently, the Darboux integral method is employed to demonstrate that this condition is also sufficient. Additionally, we demonstrate that the system can bifurcate 15 small amplitude limit cycles with a distribution pattern of

5 - 5 - 5

originating from the singular points after proper perturbation. This finding represents a novel contribution to the understanding of the number of limit cycles present in three-dimensional cubic systems with

Z_{3}

-equivariant symmetry. Full article

(This article belongs to the Section Dynamical Systems)

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9 pages, 707 KiB

Open AccessArticle

Exploration of New Solitons for the Fractional Perturbed Radhakrishnan–Kundu–Lakshmanan Model

by Melike Kaplan and Rubayyi T. Alqahtani

Mathematics 2023, 11(11), 2562; https://doi.org/10.3390/math11112562 - 03 Jun 2023

Cited by 10 | Viewed by 1060

Abstract

The key objective of the current manuscript was to investigate the exact solutions of the fractional perturbed Radhakrishnan–Kundu–Lakshmanan model. For this purpose, we applied two reliable and efficient approaches; specifically, the modified simple equation (MSE) and exponential rational function (ERF) techniques. The methods [...] Read more.

The key objective of the current manuscript was to investigate the exact solutions of the fractional perturbed Radhakrishnan–Kundu–Lakshmanan model. For this purpose, we applied two reliable and efficient approaches; specifically, the modified simple equation (MSE) and exponential rational function (ERF) techniques. The methods considered in this paper offer solutions for problems in nonlinear theory and mathematical physics practice. We also present solutions obtained graphically with the Maple package program. Full article

(This article belongs to the Special Issue Advances in Differential and Difference Equations with Applications 2023)

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Mathematics, Volume 11, Issue 11 (June-1 2023) – 183 articles

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