Search

This document is a preface to a special issue of the journal Mathematics titled "State-of-the-Art Mathematical Applications in Europe." The special issue features twelve original research papers and one review paper from European researchers and their collaborators in various fields of mathematics. The papers cover topics such as mathematical physics, applied mathematics, algebra, navigation algorithms, decision-making models, Lagrange interpolation polynomials, and nonlinear fractional differential equations. The preface provides a brief overview of each paper and expresses gratitude to the authors and reviewers. The special issue has received significant interest and demonstrates the importance of open access research in applied mathematics. [Extracted from the article]

Currently, digitalization and digital transformation are actively expanding into various areas of human activity, and researchers are identifying urgent problems and offering new solutions regarding digital environments in industry [[1]], economics [[3]], medicine [[5]], ecology [[7]], education [[9]], etc. Conclusions The purpose of this Special Issue was to attract high-quality new papers in the field of applied and computational mathematics for digital environments, offering original solutions to various problems that are relevant and in demand in various fields of human activity. 10.3390/math10224297 21 Demidova L.A. A Novel Approach to Decision-Making on Diagnosing Oncological Diseases Using Machine Learning Classifiers Based on Datasets Combining Known and/or New Generated Features of a Different Nature. I hope that these selected research papers are recognized as important and meaningful by the international scientific community and can form the basis for further research in the field of applied and computational mathematics for digital environments, solving complex problems in various disciplines and application areas. [Extracted from the article]

This review paper gives an overview of the method of multipliers for partial differential equations (PDEs). This method has made possible a lot of solutions to PDEs that are of interest in many areas such as applied mathematics, mathematical physics, engineering, etc. Looking at the history of the method and synthesizing the newest developments, we hope to give it the attention that it deserves to help develop the vast amount of work still needed to understand it and make the best use of it. It is also an interesting and a relevant method in itself that could possibly give interesting results in areas of mathematics such as modern algebra, group theory, topology, etc. The paper will be structured in such a manner that the last review known for this method will be presented to understand the theoretical framework of the method and then later work done will be presented. The information of four recent papers further developing the method will be synthesized and presented in such a manner that anyone interested in learning this method will have the most relevant information available and have all details cited for checking. [ABSTRACT FROM AUTHOR]

It is very meaningful and challenging to efficiently seek common solutions to operator systems (CSOSs), which are widespread in pure and applied mathematics, as well as some closely related optimization problems. The purpose of this paper is to introduce a novel class of multistep implicit iterative algorithms (MSIIAs) for solving general CSOSs. By using Xu's lemma and Maingé's fundamental and important results, we first obtain strong convergence theorems for both one-step and multistep implicit iterative schemes for CSOSs, involving asymptotically demicontractive operators. Finally, for the applications and profits of the main results presented in this paper, we give two numerical examples and present an iterative approximation to solve the general common solution to the variational inequalities and operator equations. [ABSTRACT FROM AUTHOR]

This paper addresses discontinuities in the solutions of mathematical physics that describe actual processes and are not observed in experiments. The appearance of discontinuities is associated in this paper with the classical differential calculus based on the analysis of infinitesimal quantities. Nonlocal functions and nonlocal derivatives, which are not specified, in contrast to the traditional approach to a point, but are the results of averaging over small but finite intervals of the independent variable are introduced. Classical equations of mathematical physics preserve the traditional form but include nonlocal functions. These equations are supplemented with additional equations that link nonlocal and traditional functions. The proposed approach results in continuous solutions of the classical singular problems of mathematical physics. The problems of a string and a circular membrane loaded with concentrated forces are used to demonstrate the procedure. Analytical results are supported with experimental data. [ABSTRACT FROM AUTHOR]

The processing of dielectric materials in the radio frequency field continues to be a concern in engineering. This procedure involves a rigorous analysis of the electromagnetic field based on specific numerical methods. This paper presents an original method for analysing the process of drying wooden boards in a radio frequency (RF) installation. The electromagnetic field and thermal field are calculated using the finite element method (FEM). The load capacity of the installation is also calculated, since the material being heated in the radio frequency heating installations is placed in a capacitor-type applicator. A specific method is created in order to solve the problem related to mass, a quantity which tends to change during the drying of the dielectric. In addition, special consideration is given to issues regarding the coupling of the electromagnetic field and the thermal field, along with aspects pertaining to mass. These are implemented numerically using a program written in the Fortran language, which takes the distribution of finite elements from the Flux2D program, the dielectric thermal module, intended only for the study of RF heating. The results obtained after running the program are satisfactory and they represent a support for future studies, especially if the movement of the dielectric is taken into account. [ABSTRACT FROM AUTHOR]

Adequate mathematical description of magnetization curves is indispensable in engineering. The accuracy of the description has a significant impact on the design of electric machines and devices. The aim of this paper was to analyze the capability of Bézier curves systematically, to describe the nonlinear static magnetic properties of non-oriented electrical steels, and to compare this approach versus the established mathematical descriptions. First, analytic functions versus measurements were analyzed. The Bézier curves were then compared systematically with the most adequate analytic functions. Next, the most suitable orders of Bézier curves were determined for the approximation of nonlinear magnetic properties, where the influence of the range of the input measurement dataset on the approximation process was analyzed. Last, the extrapolation capabilities of the Bézier curves and analytic functions were evaluated. The general conclusion is that Bézier curves have adequate flexibility and significant potential for the approximation and extrapolation of nonlinear properties of non-oriented electrical steels. [ABSTRACT FROM AUTHOR]

Block matrices play an important role in all branches of pure and applied mathematics. In this paper, we study the two fundamental concepts: inverses and determinants of general n × n block matrices. In the first part, the inverses of 2 × 2 block matrices are given, where one of the blocks is a non-singular matrix, a result which can be generalised to a block matrix of any size, by splitting it into four blocks. The second part focuses on the determinants, which is covered in two different methods. In the first approach, we revise a formula for the determinant of a block matrix A, with blocks elements of R; a commutative subring of M n × n (F) . The determinants of tensor products of two matrices are also given in this part. In the second method for computing the determinant, we give the general formula, which would work for any block matrix, regardless of the ring or the field under consideration. The individual formulas for determinants of 2 × 2 and 3 × 3 block matrices are also produced here. [ABSTRACT FROM AUTHOR]

This article presents a study on singularly perturbed 1D parabolic Dirichlet's type differential equations with discontinuous source terms on an interior line. The time derivative is discretized using the Euler backward method, followed by the application of the streamline–diffusion finite element method (SDFEM) to solve locally one-dimensional stationary problems on a Shishkin mesh. Our proposed method is shown to achieve first-order convergence in time and second-order convergence in space. Our proposed method offers several advantages over existing techniques, including more accurate approximations of the solution on the boundary layer region, better efficiency, and robustness in dealing with discontinuous line source terms. The numerical examples presented in this paper demonstrate the effectiveness and efficiency of our method, which has practical applications in various fields, such as engineering and applied mathematics. Overall, our proposed method provides an effective and efficient solution to the challenging problem of solving singularly perturbed parabolic differential equations with discontinuous line source terms, making it a valuable tool for researchers and practitioners in various domains. [ABSTRACT FROM AUTHOR]

The topic of convex and nonconvex mapping has many applications in engineering and applied mathematics. The Aumann and fuzzy Aumann integrals are the most significant interval and fuzzy operators that allow the classical theory of integrals to be generalized. This paper considers the well-known fuzzy Hermite–Hadamard (HH) type and associated inequalities. With the help of fuzzy Aumann integrals and the newly introduced fuzzy number valued up and down convexity ( U D -convexity), we increase this mileage even further. Additionally, with the help of definitions of lower U D -concave (lower U D -concave) and upper U D -convex (concave) fuzzy number valued mappings ( F N V M s), we have gathered a sizable collection of both well-known and new extraordinary cases that act as applications of the main conclusions. We also offer a few examples of fuzzy number valued U D -convexity to further demonstrate the validity of the fuzzy inclusion relations presented in this study. [ABSTRACT FROM AUTHOR]

In this paper, an SIR-SI mathematical model in the form of a system of integral equations describing the transmission of dengue disease between human and mosquitoes is proposed and analyzed. Age-dependent functions are used to describe the survival of individuals in human and mosquito populations. The basic reproduction number is derived and its relationship to the equilibria is also explored. The results show that the existence of the positive endemic equilibrium is determined by a threshold number. This threshold number is also the same one that determines the global stability of the equilibrium. The threshold acts like the known basic reproduction number in the counterpart differential equations model and also follows the same rule for the critical level of intervention. Furthermore, as an application, the effect of wolbachia infection is explored, such as how this infection changes the resulting threshold and what the consequence of its presence is in the dynamics of the disease. In this case, the decrease of the mosquitoes' life expectancy and biting rate are used to reflect the effect of wolbachia bacterial infection on the mosquitoes. In other words, a mosquito which is infected by wolbachia has a lower life expectancy than a normal mosquito. The results, both from mathematical analysis and numerical examples, show that the presence of wolbachia has the potential as a biological control agent to eliminate the dengue in the human population. A comparison of the wolbachia introduction into the mosquito population with the existing strategy, such as vaccination, is also presented. [ABSTRACT FROM AUTHOR]

There is no doubt that convex and non-convex functions have a significant impact on optimization. Due to its behavior, convexity also plays a crucial role in the discussion of inequalities. The principles of convexity and symmetry go hand-in-hand. With a growing connection between the two in recent years, we can learn from one and apply it to the other. There have been significant studies on the generalization of Godunova–Levin interval-valued functions in the last few decades, as it has tremendous applications in both pure and applied mathematics. In this paper, we introduce the notion of interval- valued harmonical (h1, h2)-Godunova–Levin functions. Using the new concept, we establish a new interval Hermite–Hadamard and Jensen-type inequalities that generalize the ones that exist in the literature. Additionally, we provide some examples to prove the validity of our main results. [ABSTRACT FROM AUTHOR]

In this paper, the basic classification of asteroids and the history and current situation of asteroid exploration are introduced. Furthermore, some recent research progress on the orbital dynamics of asteroids, including models of the gravitational potential field, the dynamics near asteroids, hopping motion on the surface, and bifurcations under varying external parameters, is reviewed. In the meanwhile, the future research development such as the configuration and evolution of binary or triple asteroid systems and near-Earth asteroid defense is briefly discussed. [ABSTRACT FROM AUTHOR]

In this paper, one multidisciplinary-applicable aggregated model has been proposed and verified. This model uses traditional techniques, on the one hand, and algorithms of machine learning as modern techniques, on the other hand, throughout the determination process of the relevance of model attributes for solving any problems of multicriteria decision. The main goal of this model is to take advantage of both approaches and lead to better results than when the techniques are used alone. In addition, the proposed model uses feature selection methodology to reduce the number of attributes, thus increasing the accuracy of the model. We have used the traditional method of regression analysis combined with the well-known mathematical method Analytic Hierarchy Process (AHP). This approach has been combined with the application of the ReliefF classificatory modern ranking method of machine learning. Last but not least, the decision tree classifier J48 has been used for aggregation purposes. Information on grades of the first-year graduate students at the Criminalistics and Police University, Belgrade, after they chose and finished one of the three possible study modules, was used for the evaluation of the proposed model. To the best knowledge of the authors, this work is the first work when considering mining closed frequent trees in case of the streaming of time-varying data. [ABSTRACT FROM AUTHOR]

This development would have been impossible without the digitalization of communication systems, wherein mathematics played a vital supporting role. Mobile communication systems have a great importance in today's world. [Extracted from the article]

We study the asymptotic duration of optimal stopping problems involving a sequence of independent random variables that are drawn from a known continuous distribution. These variables are observed as a sequence, where no recall of previous observations is permitted, and the objective is to form an optimal strategy to maximise the expected reward. In our previous work, we presented a methodology, borrowing techniques from applied mathematics, for obtaining asymptotic expressions for the expectation duration of the optimal stopping time where one stop is permitted. In this study, we generalise further to the case where more than one stop is permitted, with an updated objective function of maximising the expected sum of the variables chosen. We formulate a complete generalisation for an exponential family as well as the uniform distribution by utilising an inductive approach in the formulation of the stopping rule. Explicit examples are shown for common probability functions as well as simulations to verify the asymptotic calculations. [ABSTRACT FROM AUTHOR]

Focusing first on the case HT ht , they determine bounds on the number of edges. Finally, the case of a fixed value HT ht is also discussed. They determine the graphs with largest HT ht -spectral radius with fixed vertex or edge connectivity. In addition, the corresponding extremal graphs are given and equations satisfying the HT ht -spectral radius are derived. [Extracted from the article]

The distribution of eigenvalues and the upper bounds for the spread of interval matrices are significant in various fields of mathematics and applied sciences, including linear algebra, numerical analysis, control theory, and combinatorial optimization. We present the distribution of eigenvalues within interval matrices and determine upper bounds for their spread using Geršgorin's theorem. Specifically, through an equality for the variance of a discrete random variable, we derive upper bounds for the spread of symmetric interval matrices. Finally, we give three numerical examples to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

It is difficult for wireless local area networks (WLANs), IEEE 802.11ax high-efficiency WLAN (HEW), to join next-generation innovations such as 5th generation (5G) and Internet of Things (IoT) because they still have their conventional channel access mechanism as their essential medium access control (MAC) protocol. The MAC protocol uses a traditional binary exponential backoff (BEB) algorithm to access channel resources that depend on the noncognitive increment of contention parameters for collision avoidance. In BEB, the collision issue increases with the increase in connected devices in the network due to a fixed contention window size. The larger the size of the network, the larger the collision in the network. To avoid such a circumstance, in this paper, we propose a sliding group window (sGW) mechanism dependent on collision-point assessment in order to improve the performance of MAC protocol for HEW. The proposed algorithm additionally presents a rebacking off for collision avoidance (ReBOCA) system for sGW, which combines the uniform dispersion of the contention parameters. This variation of an ordinary backoff algorithm permits the reasonable sliding of the user groups in the case of collision. The algorithm explicitly accounts for the peculiarities of dense environments and backward compatibility. Key aspects of the proposed solution include collision-point estimation, rebacking off for collision distribution convergence for fair treatment, and adaptive sliding of group windows to mitigate contention unfairness. We further formulated a closed-form Markov chain model for the performance analysis of our proposed sGW with ReBOCA scheme. Theoretical and practical results prove that our proposed scheme achieved maximal efficiency, even under dense environments. An increase in throughput with a lower packet collision probability was achieved with the proposed mechanism, and the efficiency increased as the number of contending stations increased than compared to traditional BEB performance. Our proposed ReBOCA mechanism enhanced network throughput by 38.18% than compared to the conventional BEB mechanism. [ABSTRACT FROM AUTHOR]

This paper considers the time continuum of Brouwer in terms of the complex system physics. It is based upon a processual definition of real numbers which concern the measurement problem. The multiresolution hierarchy of the measurement process is represented by the time operator acting on continuous signals. The wavelet domain hidden Markov model, which recapitulates statistical properties of the hierarchy, is verified experimentally on a wide range of signal ensembles. It indicates a novel method that has already been proved to be tremendously useful in applied mathematics. [ABSTRACT FROM AUTHOR]

This paper presents a long-term study of Preservice Mathematics Teachers (PMTs) at the Faculty of mathematics, physics and informatics, Comenius University in Bratislava (FMFI UK), focusing on the implementation of digital technologies (DT) into the teaching of theoretical and practical (or applied) subjects. We conducted parallel research into two aspects, one on Calculus lessons as a theoretical subject, another on the Financial Mathematics module as an applied subject. The implementation of DT and the way this was measured varied from year to year and also in the method of implementation into the aforementioned subjects. The methods of implementation and the results are briefly described, and a comparison of these two subjects in the PMTs' preparation is also discussed. [ABSTRACT FROM AUTHOR]

The question raised in the title of the article is not philosophical. We do not expect general answers of the form "to describe the reality surrounding us". The question should actually be formulated as a mathematical problem of applied mathematics, a task for new research. This question should be answered in mathematically rigorous statements about the interrelations between the properties of the operator's kernels and the types of phenomena. This article is devoted to a discussion of the question of what is fractional operator from the point of view of not pure mathematics, but applied mathematics. The imposed restrictions on the kernel of the fractional operator should actually be divided by types of phenomena, in addition to the principles of self-consistency of mathematical theory. In applications of fractional calculus, we have a fundamental question about conditions of kernels of fractional operator of non-integer orders that allow us to describe a particular type of phenomenon. It is necessary to obtain exact correspondences between sets of properties of kernel and type of phenomena. In this paper, we discuss the properties of kernels of fractional operators to distinguish the following types of phenomena: fading memory (forgetting) and power-law frequency dispersion, spatial non-locality and power-law spatial dispersion, distributed lag (time delay), distributed scaling (dilation), depreciation, and aging. [ABSTRACT FROM AUTHOR]

Distribution network reconfiguration (DNR) is the optimized change in the topological structure of distribution systems without violating its radial configuration. DNR has been of interest in applied mathematics and engineering because of its importance in modern power systems. In literature, various optimization techniques that constitute a large area of applied mathematics were proposed to obtain optimized radial configurations; however, most of them were tested in small distribution systems. In this paper, a novel graphically-based DNR is proposed to obtain the optimized radial configurations for power loss minimization. The proposed DNR is based on the graphical representation of the distribution system without any need for a radiality check. Case studies were conducted on 16-, 33-, 70-, 83-, 136-, 415-, 880-, 1760-, and 4400-node distribution systems in order to minimize the total power loss. Results have proven the ability of the proposed graphical DNR for power loss minimization by obtaining fast radial configurations in comparison with previous studies and also its ability to deal with large distribution systems efficiently. The proposed DNR succeeded in minimizing the total losses for large distribution systems as the 880-, 1760-, and 4400-node distribution systems by 69.45%, 72.51%, and 74.35%, respectively. [ABSTRACT FROM AUTHOR]

Let γ (D) denote the domination number of a digraph D and let C m □ C n denote the Cartesian product of C m and C n , the directed cycles of length n ≥ m ≥ 3 . Liu et al. obtained the exact values of γ (C m □ C n) for m up to 6 [Domination number of Cartesian products of directed cycles, Inform. Process. Lett. 111 (2010) 36–39]. Shao et al. determined the exact values of γ (C m □ C n) for m = 6 , 7 [On the domination number of Cartesian product of two directed cycles, Journal of Applied Mathematics, Volume 2013, Article ID 619695]. Mollard obtained the exact values of γ (C m □ C n) for m = 3 k + 2 [M. Mollard, On domination of Cartesian product of directed cycles: Results for certain equivalence classes of lengths, Discuss. Math. Graph Theory 33(2) (2013) 387–394.]. In this paper, we extend the current known results on C m □ C n with m up to 21. Moreover, the exact values of γ (C n □ C n) with n up to 31 are determined. [ABSTRACT FROM AUTHOR]

Problem-based learning (PBL) is a teaching method that appeared in the early 1960s and is widely applied in distinct areas nowadays. In the presented manuscript, we describe a PBL methodology use restricted to applied mathematics for problem solving among a group of engineering students in a Portuguese university. In the pandemic context, it was a huge challenge both for the students and for the teacher. Supported by the available literature, the experiment was defined. As it is well known, teachers are not only knowledge transmitters but also designers of teaching initiatives. Thus, teachers and students both have a large role in PBL methodologies, where collaboration, reflection and concepts discussion are essential. In the presented pedagogical challenge, students were devoted to integrating the previous knowledge acquired and the one acquired during the project. This process improved their new competences—both personal and team work. Despite being a recent pedagogical method, PBL is revealed to be an important teaching tool. [ABSTRACT FROM AUTHOR]

This work considers a multifactor linear mixed model under heteroscedasticity in random-effect factors and the skew-normal errors for modeling the correlated datasets. We implement an expectation–maximization (EM) algorithm to achieve the maximum likelihood estimates using conditional distributions of the skew-normal distribution. The EM algorithm is also implemented to extend the local influence approach under three model perturbation schemes in this model. Furthermore, a Monte Carlo simulation is conducted to evaluate the efficiency of the estimators. Finally, a real data set is used to make an illustrative comparison among the following four scenarios: normal/skew-normal errors and heteroscedasticity/homoscedasticity in random-effect factors. The empirical studies show our methodology can improve the estimates when the model errors follow from a skew-normal distribution. In addition, the local influence analysis indicates that our model can decrease the effects of anomalous observations in comparison to normal ones. [ABSTRACT FROM AUTHOR]

In this study, we conduct a bibliometric review of the Mathematics journal to map its thematic structure, and to identify major research trends for future research to build on. Our review focuses primarily on the bibliometric clusters derived from an application of a bibliographic coupling algorithm and offers insights into how studies included in the review sample relate to one another to form coherent research streams. We combine this analysis with keyword frequency and topic modeling analyses to reveal the discourse that is taking place in the journal more recently. We believe that a systematic/computer-assisted review of the Mathematics journal can open a path for new developments and discoveries in research and help editors assess the performance and historic evolution of the journal and predict future developments. In so doing, the findings should advance our cumulative understanding in those areas consistent with the scope of the Mathematics journal, such as applied mathematics, analytics, and computational sciences. [ABSTRACT FROM AUTHOR]

Developing new and efficient numerical integration techniques is of great importance in applied mathematics and computer science. Among the variety of available methods, multistep ODE solvers are broadly used in simulation software. Recently, semi-implicit integration proved to be an efficient compromise between implicit and explicit ODE solvers, and multiple high-performance semi-implicit methods were proposed. However, the computational efficiency of any ODE solver can be significantly increased through the introduction of an adaptive integration stepsize, but it requires the estimation of local truncation error. It is known that recently proposed extrapolation semi-implicit multistep methods (ESIMM) cannot operate with existing local truncation error (LTE) estimators, e.g., embedded methods approach, due to their specific right-hand side calculation algorithm. In this paper, we propose two different techniques for local truncation error estimation and study the performance of ESIMM methods with adaptive stepsize control. The first considered approach is based on two parallel semi-implicit solutions with different commutation orders. The second estimator, called the "double extrapolation" method, is a modification of the embedded method approach. The introduction of the double extrapolation LTE estimator allowed us to additionally increase the precision of the ESIMM solver. Using several known nonlinear systems, including stiff van der Pol oscillator, as the testbench, we explicitly show that ESIMM solvers can outperform both implicit and explicit linear multistep methods when implemented with an adaptive stepsize. [ABSTRACT FROM AUTHOR]

10.3390/math7020181 5 Meng S., Cui Y. The Extremal Solution To Conformable Fractional Differential Equations Involving Integral Boundary Condition. 10.3390/math7030224 8 Ilhan O.A., Kasimov S.G., Otaev S.Q., Baskonus H.M. On the Solvability of a Mixed Problem for a High-Order Partial Differential Equation with Fractional Derivatives with Respect to Time, with Laplace Operators with Spatial Variables and Nonlocal Boundary Conditions in Sobolev Classes. 10.3390/math7030285 10 Zhang S., Hu L. Unique Existence Result of Approximate Solution to Initial Value Problem for Fractional Differential Equation of Variable Order Involving the Derivative Arguments on the Half-Axis. [Extracted from the article]

Several phenomena in nature are subjected to the interaction of various physical parameters, which, if these latter are well known, allow us to predict the behavior of such phenomena. In most cases, these physical parameters are not exactly known, or even more these are unknown, so identification techniques could be employed in order to estimate their values. Systems for which their inputs and outputs vary both temporally and spatially are the so-called distributed parameter systems (DPSs) modeled through partial differential equations (PDEs). The way in which their parameters evolve with respect to time may not always be known and may also induce undesired behavior of the dynamics of the system. To reverse the above, the well-known adaptive boundary control technique can be used to estimate the unknown parameters assuring a stable behavior of the dynamics of the system. In this work, we focus our attention on the design of an adaptive boundary control for a parabolic type reaction–advection–diffusion PDE under the assumption of unknown parameters for both advection and reaction terms and Robin and Neumann boundary conditions. An identifier PDE system is established and parameter update laws are designed following the certainty equivalence approach with a passive identifier. The performance of the adaptive Neumann stabilizing controller is validated via numerical simulation. [ABSTRACT FROM AUTHOR]

Optimal control problems governed by stochastic partial differential equations have become an important field in applied mathematics. In this article, we investigate one such important optimization problem, that is, the stochastic Stokes control problem with forcing term perturbed by noise. A multigrid scheme with three-factor coarsening to solve the corresponding discretized control problem is presented. On staggered grids, a three-factor coarsening strategy helps in simplifying the inter-grid transfer operators and reduction in computation (CPU time). For smoothing, a distributive Gauss–Seidel scheme with a line search strategy is employed. To validate the proposed multigrid staggered grid framework, numerical results are presented with white noise at the end. [ABSTRACT FROM AUTHOR]

For a graph G, its k-rainbow independent domination number, written as γ rik (G) , is defined as the cardinality of a minimum set consisting of k vertex-disjoint independent sets V 1 , V 2 , ... , V k such that every vertex in V 0 = V (G) \ (∪ i = 1 k V i) has a neighbor in V i for all i ∈ { 1 , 2 , ... , k } . This domination invariant was proposed by Kraner Šumenjak, Rall and Tepeh (in Applied Mathematics and Computation 333(15), 2018: 353–361), which aims to compute the independent domination number of G □ K k (the generalized prism) via studying the problem of integer labeling on G. They proved a Nordhaus–Gaddum-type theorem: 5 ≤ γ ri 2 (G) + γ ri 2 (G ¯) ≤ n + 3 for any n-order graph G with n ≥ 3 , in which G ¯ denotes the complement of G. This work improves their result and shows that if G ≇ C 5 , then 5 ≤ γ ri 2 (G) + γ ri 2 (G ¯) ≤ n + 2 . [ABSTRACT FROM AUTHOR]

Recently, Special Function Theory (SPFT) and Operator Theory (OPT) have acquired a lot of concern due to their considerable applications in disciplines of pure and applied mathematics. The Hurwitz-Lerch Zeta type functions, as a part of Special Function Theory (SPFT), are significant in developing and providing further new studies. In complex domain, the convolution tool is a salutary technique for systematic analytical characterization of geometric functions. The analytic functions in the punctured unit disk are the so-called meromorphic functions. In this present analysis, a new convolution complex operator defined on meromorphic functions related with the Hurwitz-Lerch Zeta type functions and Kummer functions is considered. Certain sufficient stipulations are stated for several formulas of this defining operator to attain subordination. Indeed, these outcomes are an extension of known outcomes of starlikeness, convexity, and close to convexity. [ABSTRACT FROM AUTHOR]

The aim of this study is to evaluate students' achievements in mathematics using three machine learning regression methods: classification and regression trees (CART), CART ensembles and bagging (CART-EB) and multivariate adaptive regression splines (MARS). A novel ensemble methodology is proposed based on the combination of CART and CART-EB models in a new ensemble to regress the actual data using MARS. Results of a final exam test, control and home assignments, and other learning activities to assess students' knowledge and competencies in applied mathematics are examined. The exam test combines problems on elements of mathematical analysis, statistics and a small practical project. The project is the new competence-oriented element, which requires students to formulate problems themselves, to choose different solutions and to use or not use specialized software. Initially, empirical data are statistically modeled using six CART and six CART-EB competing models. The models achieve a goodness-of-fit up to 96% to actual data. The impact of the examined factors on the students' success at the final exam is determined. Using the best of these models and proposed novel ensemble procedure, final MARS models are built that outperform the other models for predicting the achievements of students in applied mathematics. [ABSTRACT FROM AUTHOR]

There are physical phenomena, involving diffusion and structural vibrations, modeled by partial differential equations (PDEs) whose solution reflects their spatial distribution. Systems whose dynamics evolve on an infinite-dimensional Hilbert space, i.e., infinite-dimensional systems, are modeled by PDEs. The aim when designing a controller for infinite-dimensional systems is similar to that for finite-dimensional systems, i.e., the control system must be stable. Another common goal is to design the controller in such a way that the response of the system does not be affected by external disturbances. The controller design for finite-dimensional systems is not an easy task, so, the controller design for infinite-dimensional systems is even more challenging. The backstepping control approach is a dominant methodology for boundary feedback design. In this work, we try with the backstepping design for the boundary control of a reaction-advection-diffusion (R-A-D) equation, namely, a type parabolic PDE, but with constant coefficients and Neumann boundary conditions, with actuation in one of these latter. The heat equation with Neumann boundary conditions is considered as the target system. Dynamics of the open- and closed-loop solution of the PDE system are validated via numerical simulation. The MATLAB ® -based numerical algorithm related with the implementation of the control scheme is here included. [ABSTRACT FROM AUTHOR]

The many technical and computational problems that appear to be constantly emerging in various branches of physics and engineering beg for a more detailed understanding of the fundamental mathematics that serves as the cornerstone of our way of understanding natural phenomena. Specifically, it starts with the work [[3]], by Emilia Bazhlekova and Ivan Bazhlekov, concerning a subordination approach to the multi-dimensional space-time fractional diffusion equation. It is then followed by an interesting note [[6]] on a generalization of the time-fractional relativistic diffusion equation based on the application of Caputo fractional derivatives of a function with respect to another function, by Luisa Beghin and Roberto Garra. [Extracted from the article]

The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied mathematics and mathematical physics, based on a special transformation with an integral term and the generalized splitting principle. The effectiveness of this approach is illustrated by nonlinear diffusion-type equations that contain reaction and convective terms with variable coefficients. The focus is on equations of a fairly general form that depend on one, two or three arbitrary functions (such nonlinear PDEs are most difficult to analyze and find exact solutions). A lot of new functional separable solutions and generalized traveling wave solutions are described (more than 30 exact solutions have been presented in total). It is shown that the method of functional separation of variables can, in certain cases, be more effective than (i) the nonclassical method of symmetry reductions based on an invariant surface condition, and (ii) the method of differential constraints based on a single differential constraint. The exact solutions obtained can be used to test various numerical and approximate analytical methods of mathematical physics and mechanics. [ABSTRACT FROM AUTHOR]

In this article, we introduce the notions of maximal products of fuzzy graph structures, regular fuzzy graph structures, and describe these notions with examples and properties. Further, we present the degree and total degree of a vertex in maximal product of fuzzy graph structures and explain some of their properties. Furthermore, we develop a flowchart to show general procedure of application of fuzzy graph structure, regarding identification of most controversial issues among countries. [ABSTRACT FROM AUTHOR]

With advanced manufacturing technology, organizations like to cut their operational cost and improve product quality, yet the importance of human labor is still alive in some manufacturing industries. The performance of human-based systems depends much on the skill of labor that varies person to person within available manpower. Much work has been done on human resource and management, however, allocation of manpower based on their skill yet not investigated. For this purpose, this study considered offline inspection system where inspection is performed by the human labor of varying skill levels. A multi-objective optimization model is proposed based on Time-Varying factors; inspection skill, operation time and learning behavior. Min-max goal programming technique was used to determine the efficient combination of inspectors of each skill level at different time intervals of a running order. The optimized results ensured the achievement of all objectives of inspection station: the cost associated with inspectors, outgoing quality and inspected quantity. The obtained results proved that inspection performance of inspectors improves significantly with learning and revision of allocation of inspectors with the proposed model ensure better utilization of available manpower, maintain good quality and reduce cost as well. [ABSTRACT FROM AUTHOR]

Higher-order derivatives are used to determine the convergence order of iterative methods. However, such derivatives are not present in the formulas. Therefore, the assumptions on the higher-order derivatives of the function restrict the applicability of methods. Our convergence analysis of an eighth-order method uses only the derivative of order one. The convergence results so obtained are applied to some real problems, which arise in science and engineering. Finally, stability of the method is checked through complex geometry shown by drawing basins of attraction of the solutions. [ABSTRACT FROM AUTHOR]

The aim of this study is to view the role of Bézier curves in both the Euclidean plane E 2 and Euclidean space E 3 with the help of the fundamental algorithm which is commonly used in Computer Science and Applied Mathematics and without this algorithm. The Serret-Frenet elements of non-unit speed curves in the Euclidean plane E 2 and Euclidean space E 3 are given by Gray et al. in 2016. We used these formulas to find Serret-Frenet elements of planar Bézier curve at the end points and for every parameter t. Moreover, we reconstruct these elements for a planar Bézier curve, which is defined by the help of the algorithm based on intermediate points. Finally, in the literature, the spatial Bézier curve only mentioned at the end points, so we improve these elements for all parameters t. Additionally, we calculate these elements for all parameters t using algorithm above mentioned for spatial Bézier curve. [ABSTRACT FROM AUTHOR]