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In order to solve the Sylvester equations more efficiently, a new four parameters positive and skew-Hermitian splitting (FPPSS) iterative method is proposed in this paper based on the previous research of the positive and skew-Hermitian splitting (PSS) iterative method. We prove that when coefficient matrix A and B satisfy certain conditions, the FPPSS iterative method is convergent in the parameter&rsquo, s value region. The numerical experiment results show that compared with previous iterative method, the FPPSS iterative method is more effective in terms of iteration number IT and runtime.

In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced reconstruction operator. Moreover, they introduced a procedure to modify any standard reconstruction operator, like MUSCL, ENO, CWENO, etc., in order to be well-balanced. This strategy involves a non-linear problem at every cell at every time step that consists in finding the stationary solution whose average is the given cell value. In a recent paper, a fully well-balanced method is presented where the non-linear problems to be solved in the reconstruction procedure are interpreted as control problems. The goal of this paper is to introduce a new technique to solve these local non-linear problems based on the application of the collocation RK methods. Special care is put to analyze the effects of computing the averages and the source terms using quadrature formulas. A general technique which allows us to deal with resonant problems is also introduced. To check the efficiency of the methods and their well-balance property, they have been applied to a number of tests, ranging from easy academic systems of balance laws consisting of Burgers equation with some non-linear source terms to the shallow water equations—without and with Manning friction—or Euler equations of gas dynamics with gravity effects.

The concept of an endpoint is a relatively new concept compared to the concept of a fixed point. The aim of this paper is to perform a convergence analysis of M—iteration involving α—Reich–Suzuki nonexpansive mappings. In this paper, we prove strong and Δ—convergence theorems in a hyperbolic metric space. Thus, our results generalize and improve many existing results.

In this paper, the existence of the solution and its stability to the fractional boundary value problem (FBVP) were investigated for an implicit nonlinear fractional differential equation (VOFDE) of variable order. All existence criteria of the solutions in our establishments were derived via Krasnoselskii’s fixed point theorem and in the sequel, and its Ulam–Hyers–Rassias (U-H-R) stability is checked. An illustrative example is presented at the end of this paper to validate our findings.

With the gradual popularity of online sales and the enhancement of consumers’ low-carbon awareness, the low-carbon e-commerce supply chain (LCECSC) has developed rapidly. However, most of the current research on LCECSC assumes that the decision-making body is rational, and there is less research on the irrational behavior of the e-platform altruistic preference. Therefore, aiming at the LCECSC composed of a single e-platform and a single manufacturer, this paper establishes two basic models with or without altruistic preference. Additionally, this paper combines the characteristics of online sales and assumes that altruistic preference is a proportional function of commission, then establishes a commission-based extended model with altruistic preference to further explore the influence of commission on its altruistic preference. The current literature does not consider this point, nor does it analyze the influence of other parameters on the degree of altruism preference. By comparing the optimal decisions and numerical analysis among the models, the following conclusions can be drawn that: (1) different from the traditional offline supply chain, the profit of the dominator e-platform is lower than the profit of the follower manufacturer, (2) when the consumers’ carbon emission reduction elasticity coefficient increases, service level, sales price, carbon emission reduction, sales, supply chain members profits, and system profit increase, ultimately improving economic and environmental performances, (3) the altruistic preference behavior of the e-platform is a behavior of ‘profit transferring’. The moderate altruistic preference is conducive to the stable operation and long-term development of LCECSC.

In this paper, we construct and study a new family of multi-point Ehrlich-type iterative methods for approximating all the zeros of a uni-variate polynomial simultaneously. The first member of this family is the two-point Ehrlich-type iterative method introduced and studied by Trićković and Petković in 1999. The main purpose of the paper is to provide local and semilocal convergence analysis of the multi-point Ehrlich-type methods. Our local convergence theorem is obtained by an approach that was introduced by the authors in 2020. Two numerical examples are presented to show the applicability of our semilocal convergence theorem.

The objective of this paper is to define one class of plane curves with arc-length parametrization. To accomplish this, we constructed a novel class of special polynomials and special functions. These functions form a basis of L2(R) space and some of their interesting properties are discussed. The developed curves are used for the linear static analysis of curved Bernoulli–Euler beam. Due to the parametrization with arc length, the exact analytical solution can be obtained. These closed-form solutions serve as the benchmark results for the development of numerical procedures. One such example is provided in this paper.

In this paper, we consider fractional ordinary differential equations and the fractional Euler–Poisson–Darboux equation with fractional derivatives in the form of a power of the Bessel differential operator. Using the technique of the Meijer integral transform and its modification, fundamental solutions to these equations are derived in terms of the Fox–Wright function, the Fox H-function, and their particular cases. We also provide some explicit formulas for the solutions to the corresponding initial-value problems in terms of the generalized convolutions introduced in this paper.

The paper presents k-version of the finite element method for boundary value problems (BVPs) and initial value problems (IVPs) in which global differentiability of approximations is always the result of the union of local approximations. The higher order global differentiability approximations (HGDA/DG) are always p-version hierarchical that permit use of any desired p-level without effecting global differentiability. HGDA/DG are true Ci, Cij, Cijk, hence the dofs at the nonhierarchical nodes of the elements are transformable between natural and physical coordinate spaces using calculus. This is not the case with tensor product higher order continuity elements discussed in this paper, thus confirming that the tensor product approximations are not true Ci, Cijk, Cijk approximations. It is shown that isogeometric analysis for a domain with more than one patch can only yield solutions of class C0. This method has no concept of finite elements and local approximations, just patches. It is shown that compariso of this method with k-version of the finite element method is meaningless. Model problem studies in R2 establish accuracy and superior convergence characteristics of true Cijp-version hierarchical local approximations presented in this paper over tensor product approximations. Convergence characteristics of p-convergence, k-convergence and pk-convergence are illustrated for self adjoint, non-self adjoint and non-linear differential operators in BVPs. It is demonstrated that h, p and k are three independent parameters in all finite element computations. Tensor product local approximations and other published works on k-version and their limitations are discussed in the paper and are compared with present work.

The present paper deals with a class of second-order PDE constrained controlled optimization problems with application in Lagrange–Hamilton dynamics. Concretely, we formulate and prove necessary conditions of optimality for the considered class of control problems driven by multiple integral cost functionals involving second-order partial derivatives. Moreover, an illustrative example is provided to highlight the effectiveness of the results derived in the paper. In the final part of the paper, we present an algorithm to summarize the steps for solving a control problem such as the one investigated here.

Since Gottlieb introduced and investigated the so-called Gottlieb polynomials in 1938, which are discrete orthogonal polynomials, many researchers have investigated these polynomials from diverse angles. In this paper, we aimed to investigate the q-extensions of these polynomials to provide certain q-generating functions for three sequences associated with a finite power series whose coefficients are products of the known q-extended multivariable and multiparameter Gottlieb polynomials and another non-vanishing multivariable function. Furthermore, numerous possible particular cases of our main identities are considered. Finally, we return to Khan and Asif’s q-Gottlieb polynomials to highlight certain connections with several other known q-polynomials, and provide its q-integral representation. Furthermore, we conclude this paper by disclosing our future investigation plan.

This paper provides several error estimations for total variation (TV) type regularization, which arises in a series of areas, for instance, signal and imaging processing, machine learning, etc. In this paper, some basic properties of the minimizer for the TV regularization problem such as stability, consistency and convergence rate are fully investigated. Both a priori and a posteriori rules are considered in this paper. Furthermore, an improved convergence rate is given based on the sparsity assumption. The problem under the condition of non-sparsity, which is common in practice, is also discussed, the results of the corresponding convergence rate are also presented under certain mild conditions.

After the death of Peter Wynn in December 2017, manuscript documents he left came to our knowledge. They concern continued fractions, rational (Padé) approximation, Thiele interpolation, orthogonal polynomials, moment problems, series, and abstract algebra. The purpose of this paper is to analyze them and to make them available to the mathematical community. Some of them are in quite good shape, almost finished, and ready to be published by anyone willing to check and complete them. Others are rough notes, and need to be reworked. Anyway, we think that these works are valuable additions to the literature on these topics and that they cannot be left unknown since they contain ideas that were never exploited. They can lead to new research and results. Two unpublished papers are also mentioned here for the first time.

Power electronic converters are mathematically represented by a system of ordinary differential equations discontinuous right-hand side that does not verify the conditions of the Cauchy-Lipschitz Theorem. More generally, for the properties that characterize their discontinuous behavior, they represent a particular class of systems on which little has been investigated over the years. The purpose of the paper is to prove the existence of at least one global solution in Filippov’s sense to the Cauchy problem related to the mathematical model of a power converter and also to calculate the error in norm between this solution and the integral of its averaged approximation. The main results are the proof of this theorem and the analytical formulation that provides to calculate the cited error. The demonstration starts by a proof of local existence provided by Filippov himself and already present in the literature for a particular class of systems and this demonstration is generalized to the class of electronic power converters, exploiting the non-chattering property of this class of systems. The obtained results are extremely useful for estimating the accuracy of the averaged model used for analysis or control of the effective system. In the paper, the goodness of the analytical proof is supported by experimental tests carried out on a converter prototype representing the class of power electronics converter.

In this paper, we introduce the concept of n-dimensional Diamond-Alpha integral on time scales. In particular, it transforms into multiple Delta, Nabla and mixed integrals by taking different values of alpha. Some of its properties are explored, and the relationship between it and the multiple mixed integral is provided. As an application, we establish some weighted Ostrowski type inequalities through the new integral. These new inequalities expand some known inequalities in the monographs and papers, and in addition, furnish some other interesting inequalities. Examples of Ostrowski type inequalities are posed in detail at the end of the paper.

The present paper introduces new classes of Stancu–Kantorovich operators constructed in the King sense. For these classes of operators, we establish some convergence results, error estimations theorems and graphical properties of approximation for the classes considered, namely, operators that preserve the test functions e0(x)=1 and e1(x)=x, e0(x)=1 and e2(x)=x2, as well as e1(x)=x and e2(x)=x2. The class of operators that preserve the test functions e1(x)=x and e2(x)=x2 is a genuine generalization of the class introduced by Indrea et al. in their paper “A New Class of Kantorovich-Type Operators”, published in Constr. Math. Anal.

In tokamak nuclear fusion reactors, one of the main issues is to know the total emission of radiation, which is mandatory to understand the plasma physics and is very useful to monitor and control the plasma evolution. This radiation can be measured by means of a bolometer system that consists in a certain number of elements sensitive to the integral of the radiation along straight lines crossing the plasma. By placing the sensors in such a way to have families of crossing lines, sophisticated tomographic inversion algorithms allow to reconstruct the radiation tomography in the 2D poloidal cross-section of the plasma. In tokamaks, the number of projection cameras is often quite limited resulting in an inversion mathematic problem very ill conditioned so that, usually, it is solved by means of a grid-based, iterative constrained optimization procedure, whose convergence time is not suitable for the real time requirements. In this paper, to illustrate the method, an assumption not valid in general is made on the correlation among the grid elements, based on the statistical distribution of the radiation emissivity over a set of tomographic reconstructions, performed off-line. Then, a regularization procedure is carried out, which merge highly correlated grid elements providing a squared coefficients matrix with an enough low condition number. This matrix, which is inverted offline once for all, can be multiplied by the actual bolometer measures returning the tomographic reconstruction, with calculations suitable for real time application. The proposed algorithm is applied, in this paper, to a synthetic case study.

The paper is devoted to the guaranteeing estimation of parameters in the uncertain stochastic nonlinear regression. The loss function is the conditional mean square of the estimation error given the available observations. The distribution of regression parameters is partially unknown, and the uncertainty is described by a subset of probability distributions with a known compact domain. The essential feature is the usage of some additional constraints describing the conformity of the uncertain distribution to the realized observation sample. The paper contains various examples of the conformity indices. The estimation task is formulated as the minimax optimization problem, which, in turn, is solved in terms of saddle points. The paper presents the characterization of both the optimal estimator and the set of least favorable distributions. The saddle points are found via the solution to a dual finite-dimensional optimization problem, which is simpler than the initial minimax problem. The paper proposes a numerical mesh procedure of the solution to the dual optimization problem. The interconnection between the least favorable distributions under the conformity constraint, and their Pareto efficiency in the sense of a vector criterion is also indicated. The influence of various conformity constraints on the estimation performance is demonstrated by the illustrative numerical examples.

In this paper, we use integral equations of non-integer orders to derive discrete maps with memory. Note that discrete maps with memory were not previously derived from fractional integral equations of non-integer orders. Such a derivation of discrete maps with memory is proposed for the first time in this work. In this paper, we derived discrete maps with nonlocality in time and memory from exact solutions of fractional integral equations with the Riemann–Liouville and Hadamard type fractional integrals of non-integer orders and periodic sequence of kicks that are described by Dirac delta-functions. The suggested discrete maps with nonlocality in time are derived from these fractional integral equations without any approximation and can be considered as exact discrete analogs of these equations. The discrete maps with memory, which are derived from integral equations with the Hadamard type fractional integrals, do not depend on the period of kicks.

Previous works were dedicated to the functional k-Nearest Neighbors (kNN) and the local linearity method estimations of a regression operator. In this paper, a sequence pair of (Xi,Yi)i=1,…,n of functional mixing observations are considered. We treat the local linear estimation of the cumulative function of Yi given functional input variable Xi. Precisely, we combine the kNN method with the local linear algorithm to construct a new and fast efficiency estimator of the conditional distribution function. The main purpose of this paper is to prove the strong convergence of the constructed estimator under mixing conditions. An application to the functional times series prediction is used to compare our proposed estimator with the existing competitive estimators, and show its efficiency and superiority.

In previous papers, a technique has been suggested to avoid order reduction when integrating initial boundary value problems with several kinds of exponential methods. The technique implies in principle to calculate additional terms at each step from those already necessary without avoiding order reduction. The aim of the present paper is to explain the surprising result that, many times, in spite of having to calculate more terms at each step, the computational cost of doing it through Krylov methods decreases instead of increases. This is very interesting since, in that way, the methods improve not only in terms of accuracy, but also in terms of computational cost.

Here, we review some results of fractional volatility models, where the volatility is driven by fractional Brownian motion (fBm). In these models, the future average volatility is not a process adapted to the underlying filtration, and fBm is not a semimartingale in general. So, we cannot use the classical Itô’s calculus to explain how the memory properties of fBm allow us to describe some empirical findings of the implied volatility surface through Hull and White type formulas. Thus, Malliavin calculus provides a natural approach to deal with the implied volatility without assuming any particular structure of the volatility. The aim of this paper is to provides the basic tools of Malliavin calculus for the study of fractional volatility models. That is, we explain how the long and short memory of fBm improves the description of the implied volatility. In particular, we consider in detail a model that combines the long and short memory properties of fBm as an example of the approach introduced in this paper. The theoretical results are tested with numerical experiments.

In this paper we give some common fixed point theorems for Ćirić type operators in complex valued b-metric spaces. Also, some corollaries under this contraction condition are obtained. Our results extend and generalize the results of Hammad et al. In the second part of the paper, in order to strengthen our main results, an illustrative example and some applications are given.

This paper describes a number of simple but quite effective methods for constructing exact solutions of nonlinear partial differential equations that involve a relatively small amount of intermediate calculations. The methods employ two main ideas: (i) simple exact solutions can serve to construct more complex solutions of the equations under consideration and (ii) exact solutions of some equations can serve to construct solutions of other, more complex equations. In particular, we propose a method for constructing complex solutions from simple solutions using translation and scaling. We show that in some cases, rather complex solutions can be obtained by adding one or more terms to simpler solutions. There are situations where nonlinear superposition allows us to construct a complex composite solution using similar simple solutions. We also propose a few methods for constructing complex exact solutions to linear and nonlinear PDEs by introducing complex-valued parameters into simpler solutions. The effectiveness of the methods is illustrated by a large number of specific examples (over 30 in total). These include nonlinear heat equations, reaction–diffusion equations, wave type equations, Klein–Gordon type equations, equations of motion through porous media, hydrodynamic boundary layer equations, equations of motion of a liquid film, equations of gas dynamics, Navier–Stokes equations, and some other PDEs. Apart from exact solutions to `ordinary’ partial differential equations, we also describe some exact solutions to more complex nonlinear delay PDEs. Along with the unknown function at the current time, u=u(x,t), these equations contain the same function at a past time, w=u(x,t−τ), where τ&gt, 0 is the delay time. Furthermore, we look at nonlinear partial functional-differential equations of the pantograph type, which, in addition to the unknown u=u(x,t), also contain the same functions with dilated or contracted arguments, w=u(px,qt), where p and q are scaling parameters. We propose an efficient approach to construct exact solutions to such functional-differential equations. Some new exact solutions of nonlinear pantograph-type PDEs are presented. The methods and examples in this paper are presented according to the principle “from simple to complex”.

Recently Panda et al. obtained some identities for the reciprocal sums of balancing and Lucas-balancing numbers. In this paper, we derive general identities related to reciprocal sums of products of two balancing numbers, products of two Lucas-balancing numbers and products of balancing and Lucas-balancing numbers. The method of this paper can also be applied to even-indexed and odd-indexed Fibonacci, Lucas, Pell and Pell–Lucas numbers.

In this paper, we present some new refinements of Hermite–Hadamard inequalities for continuous convex functions by using (p,q)-calculus. Moreover, we study some new (p,q)-Hermite–Hadamard inequalities for multiple integrals. Many results given in this paper provide extensions of others given in previous research.

Asphalt production plants play an important role in the field of civil engineering, but also in the entire economic system since the construction of roads enables uninterrupted functioning within it. In this paper, the ranking of asphalt production plants on the territory of the Autonomous Province of Vojvodina has been performed. The modern economy needs contemporary models and methods to solve complicated MCDM problems and, for these purposes, it has been developed an original Interval Rough Number (IRN) Multi-criteria decision-making (MCDM) model that implies an extension of two methods belonging to the field with interval rough numbers. After forming a list of eight most significant criteria for assessing the efficiency of asphalt production plants, the Interval Rough Number PIvot Pairwise RElative Criteria Importance Assessment (IRN PIPRECIA) method was developed to determine the significance of the criteria. A total of 21 locations with asphalt mixture installation were considered. For that purpose, seven asphalt production plants were included, and for their ranking, the IRN EDAS (Evaluation based on Distance from Average Solution) method was created. The aim of this paper is to develop a novel interval rough model that can be useful for determining the efficiency of asphalt production plants. Averaging in group decision-making (GDM) for both methods was performed using an IRN Dombi weighted geometric averaging (IRNDWGA) aggregator. The obtained results show that (A15) Ruma (SP)–Mačvanska Mitrovica–Zasavica has the best characteristics out of the set of locations considered in this study. However, Alternatives A6 and A19 are also variants with remarkably good characteristics since there is very little difference in values compared to the first-ranked alternative. Also, the obtained results have shown that the developed model is applicable, which is proven through a comparative analysis.

In this paper, we present a numerical solution of a two-phase fractional Stefan problem with time derivative described in the Caputo sense. In the proposed algorithm, we use a special case of front-fixing method supplemented by the iterative procedure, which allows us to determine the position of the moving boundary. The presented method is an extension of a front-fixing method for the one-phase problem to the two-phase case. The novelty of the method is a new discretization of the partial differential equation dedicated to the second phase, which is carried out by introducing a new spatial variable immobilizing the moving boundary. Then, the partial differential equation is transformed to an equivalent integro-differential equation, which is discretized on a homogeneous mesh of nodes with a constant spatial and time step. A new convergence criterion is also proposed in the iterative algorithm determining the location of the moving boundary. The motivation for the development of the method is that the analytical solution of the considered problem is impossible to calculate in some cases, as can be seen in the figures in the paper. Moreover, the change of the boundary conditions makes obtaining a closed analytical solution very problematic. Therefore, creating new numerical methods is very valuable. In the final part, we also present some examples illustrating the comparison of the analytical solution with the results received by the proposed numerical method.

This paper is concerned with the orthogonal polynomials. Upper and lower bounds of Legendre polynomials are obtained. Furthermore, entropies associated with discrete probability distributions is a topic considered in this paper. Bounds of the entropies which improve some previously known results are obtained in terms of inequalities. In order to illustrate the results obtained in this paper and to compare them with other results from the literature some graphs are provided.

This paper described a method to design a limit-cycle suppressor. The dithering technique was used to eliminate self-sustained oscillations or limit cycles. Otherwise, the Dual Input Describing Function (DIDF) method was applied to design dither parameters and analyze the existence of limit cycles. This method was done in a nonlinear system with relay nonlinearity using three standard dither signals, namely sine, triangle, and square waves. The aim of choosing varying dithers was to investigate the effect of dither shapes and the minimum amplitude required for the quenching strategy. First, the possibility and amplitude of limit cycles were determined graphically on the DIDF curve. Then, the minimum amplitude of dither was calculated based on the DIDF analysis. Finally, a simulation was built to verify the analytical work using a digital computer. The simulation results were related to the analysis results. It was evident that the dithering technique is a simple way to suppress limit cycles in a nonlinear system. This paper also presented that dither is an amplitude function, and square-wave dither has the minimum amplitude to quench limit cycles.

In 2006, A. Stakhov introduced a new coding/decoding process based on generating matrices of the Fibonacci p-numbers, which he called the Fibonacci coding/decoding method. Stakhov&rsquo, s papers have motivated many other scientists to seek certain generalizations by introducing new additional coefficients into recurrence of Fibonacci p-numbers. In 2013, I. Włoch et al. studied (2,q)-distance Fibonacci numbers F2(q,n) and found some of their combinatorial properties. In this paper, we state a new coding theory based on the sequence (Tq(n))n=&minus, &infin, which is an extension of Włoch&rsquo, s sequence (F2(q,n))n=0&infin

In this paper, we investigate the CUSUM-type estimator of mean change-point models based on m-asymptotically almost negatively associated (m-AANA) sequences. The family of m-AANA sequences contains AANA, NA, m-NA, and independent sequences as special cases. Under some weak conditions, some convergence rates are obtained such as OP(n1/p&minus, 1), OP(n1/p&minus, 1log1/pn) and OP(n&alpha, &minus, 1), where 0&le, &alpha, &lt, 1 and 1&lt, p&le, 2. Our rates are better than the ones obtained by Kokoszka and Leipus (Stat. Probab. Lett., 1998, 40, 385&ndash, 393). In order to illustrate our results, we do perform simulations based on m-AANA sequences. As important applications, we use the CUSUM-type estimator to do the change-point analysis based on three real data such as Quebec temperature, Nile flow, and stock returns for Tesla. Some potential applications to change-point models in finance and economics are also discussed in this paper.

The present paper aims to construct an inequality for bi-warped product submanifolds in a special class of almost metric manifolds, namely nearly Kenmotsu manifolds. As geometric applications, some exceptional cases that generalized several other inequalities are discussed. We also deliberate some applications in the context of mathematical physics and derive a new relation between the Dirichlet energy and the second fundamental form. Finally, we present a constructive remark at the end of this paper which shows the motive of the study.

In this paper, we extend our previous study regarding a Riemannian manifold endowed with a singular (or regular) distribution, generalizing Bochner&rsquo, s technique and a statistical structure. Following the construction of an almost Lie algebroid, we define the central concept of the paper: The Weitzenb&ouml, ck type curvature operator on tensors, prove the Bochner&ndash, Weitzenb&ouml, ck type formula and obtain some vanishing results about the null space of the Hodge type Laplacian on a distribution.

Let Ckn,l be a simple closed k-curves with l elements in Zn and W:=Ckn,l&or, ⋯&or, Ckn,l︷m-times be an m-iterated digital wedges of Ckn,l, and F(Conk(W)) be an alignment of fixed point sets of W. Then, the aim of the paper is devoted to investigating various properties of F(Conk(W)). Furthermore, when proceeding with this work, this paper addresses several unsolved problems. To be specific, we firstly formulate an alignment of fixed point sets of Ckn,l, denoted by F(Conk(Ckn,l)), where l(&ge, 7) is an odd natural number and k&ne, 2n. Secondly, given a digital image (X,k) with X♯=n, we find a certain condition that supports n&minus, 1,n&minus, 2&isin, F(Conk(X)). Thirdly, after finding some features of F(Conk(W)), we develop a method of making F(Conk(W)) perfect according to the (even or odd) number l of Ckn,l. Finally, we prove that the perfectness of F(Conk(W)) is equivalent to that of F(Conk(Ckn,l)). This can play an important role in studying fixed point theory and digital curve theory. This paper only deals with k-connected digital images (X,k) such that X♯&ge, 2.

This paper deals with the oscillation of the first-order differential equation with several delay arguments x′t+∑i=1mpitxτit=0,t≥t0, where the functions pi,τi∈Ct0,∞,R+, for every i=1,2,…,m,τit≤t for t≥t0 and limt→∞τit=∞. In this paper, the state-of-the-art on the sharp oscillation conditions are presented. In particular, several sufficient oscillation conditions are presented and it is shown that, under additional hypotheses dealing with slowly varying at infinity functions, some of the “liminf” oscillation conditions can be essentially improved replacing “liminf” by “limsup”. The importance of the slowly varying hypothesis and the essential improvement of the sufficient oscillation conditions are illustrated by examples.

The Łukasiewicz conjunction (sometimes also considered to be a logic of absolute comparison), which is used in multivalued logic and in fuzzy set theory, is one of the most important t-norms. In combination with the binary operation ‘maximum’, the Łukasiewicz t-norm forms the basis for the so-called max-Łuk algebra, with applications to the investigation of systems working in discrete steps (discrete events systems; DES, in short). Similar algebras describing the work of DES’s are based on other pairs of operations, such as max-min algebra, max-plus algebra, or max-T algebra (with a given t-norm, T). The investigation of the steady states in a DES leads to the study of the eigenvectors of the transition matrix in the corresponding max-algebra. In real systems, the input values are usually taken to be in some interval. Various types of interval eigenvectors of interval matrices in max-min and max-plus algebras have been described. This paper is oriented to the investigation of strong, strongly tolerable, and strongly universal interval eigenvectors in a max-Łuk algebra. The main method used in this paper is based on max-Ł linear combinations of matrices and vectors. Necessary and sufficient conditions for the recognition of strong, strongly tolerable, and strongly universal eigenvectors have been found. The theoretical results are illustrated by numerical examples.

In this paper a new method called the least squares differential quadrature method (LSDQM) is introduced as a straightforward and efficient method to compute analytical approximate polynomial solutions for nonlinear partial differential equations with fractional time derivatives. LSDQM is a combination of the differential quadrature method and the least squares method and in this paper it is employed to find approximate solutions for a very general class of nonlinear partial differential equations, wherein the fractional derivatives are described in the Caputo sense. The paper contains a clear, step-by-step presentation of the method and a convergence theorem. In order to emphasize the accuracy of LSDQM we included two test problems previously solved by means of other, well-known methods, and observed that our solutions present not only a smaller error but also a much simpler expression. We also included a problem with no known exact solution and the solutions computed by LSDQM are in good agreement with previous ones.

Using the recently introduced Sălăgean integro-differential operator, three new classes of bi-univalent functions are introduced in this paper. In the study of bi-univalent functions, estimates on the first two Taylor&ndash, Maclaurin coefficients are usually given. We go further in the present paper and bounds of the first three coefficients a 2 , a 3 and a 4 of the functions in the newly defined classes are given. Obtaining Fekete&ndash, Szego inequalities for different classes of functions is a topic of interest at this time as it will be shown later by citing recent papers. So, continuing the study on the coefficients of those classes, the well-known Fekete&ndash, Szego functional is obtained for each of the three classes.

In this paper, a localized boundary knot method is proposed, based on the local concept in the localized method of fundamental solutions. The localized boundary knot method is formed by combining the classical boundary knot method and the localization approach. The localized boundary knot method is truly free from mesh and numerical quadrature, so it has great potential for solving complicated engineering applications, such as multiply connected problems. In the proposed localized boundary knot method, both of the boundary nodes and interior nodes are required, and the algebraic equations at each node represent the satisfaction of the boundary condition or governing equation, which can be derived by using the boundary knot method at every subdomain. A sparse system of linear algebraic equations can be yielded using the proposed localized boundary knot method, which can greatly reduce the computer time and memory required in computer calculations. In this paper, several cases of simply connected domains and multi-connected domains of the Laplace equation and bi-harmonic equation are demonstrated to evidently verify the accuracy, convergence and stability of this proposed meshless method.

This paper analyzes the diagnostic of near-multicollinearity in a multiple linear regression from auxiliary centered (with intercept) and noncentered (without intercept) regressions. From these auxiliary regressions, the centered and noncentered variance inflation factors (VIFs) are calculated. An expression is also presented that relates both of them. In addition, this paper analyzes why the VIF is not able to detect the relation between the intercept and the rest of the independent variables of an econometric model. At the same time, an analysis is also provided to determine how the auxiliary regression applied to calculate the VIF can be useful to detect this kind of multicollinearity., University of Almeria

In this paper, we study the oscillatory behavior of solutions for a type of generalized proportional fractional differential equations with forcing and damping terms. Several oscillation criteria are established for the proposed equations in terms of Riemann-Liouville and Caputo settings. The results of this paper generalize some existing theorems in the literature. Indeed, it is shown that for particular choices of parameters, the obtained conditions in this paper reduce our theorems to some known results. Numerical examples are constructed to demonstrate the effectiveness of the our main theorems. Furthermore, we present and illustrate an example which does not satisfy the assumptions of our theorem and whose solution demonstrates nonoscillatory behavior.

The authors acknowledge with thanks DSR for financial support. A.F. Roldán López de Hierro is grateful to Junta de Andalucía by project FQM-365 of the Andalusian CICYE and Project TIN2017-89517-P of the Ministerio de Economía, Industria y Competitividad., In this paper we present some novel fixed point theorems for a family of contractions depending on two functions (that are not defined on t = 0) and on some parameters that we have called multiparametric contractions. We develop our study in the setting of b-metric spaces because they allow to consider some families of functions endowed with b-metrics deriving from similarity measures that are more general than norms. Taking into account that the contractivity condition we will employ is very general (of Hardy-Rogers type), we will discuss the validation and usage of this novel condition. After that, we introduce the main results of this paper and, finally, we deduce some consequences of them which illustrates the wide applicability of the main results., Junta de Andalucia FQM-365, Ministerio de Economia, Industria y Competitividad TIN2017-89517-P, DSR

In this survey paper, we present both some basic properties of the four-parameters Wright function and its applications in Fractional Calculus. For applications in Fractional Calculus, the four-parameters Wright function of the second kind is especially important. In the paper, three case studies illustrating a wide spectrum of its applications are presented. The first case study deals with the scale-invariant solutions to a one-dimensional time-fractional diffusion-wave equation that can be represented in terms of the Wright function of the second kind and the four-parameters Wright function of the second kind. In the second case study, we consider a subordination formula for the solutions to a multi-dimensional space-time-fractional diffusion equation with different orders of the fractional derivatives. The kernel of the subordination integral is a special case of the four-parameters Wright function of the second kind. Finally, in the third case study, we shortly present an application of an operational calculus for a composed Erdélyi-Kober fractional operator for solving some initial-value problems for the fractional differential equations with the left- and right-hand sided Erdélyi-Kober fractional derivatives. In particular, we present an example with an explicit solution in terms of the four-parameters Wright function of the second kind.

In this paper, a new method for determining weight coefficients by forming a non-decreasing series at criteria significance levels (the NDSL method) is presented. The NDLS method includes the identification of the best criterion (i.e., the most significant and most influential criterion) and the ranking of criteria in a decreasing series from the most significant to the least significant criterion. Criteria are then grouped as per the levels of significance within the framework of which experts express their preferences in compliance with the significance of such criteria. By employing this procedure, fully consistent results are obtained. In this paper, the advantages of the NDSL model are singled out through a comparison with the Best Worst Method (BWM) and Analytic Hierarchy Process (AHP) models. The advantages include the following: (1) the NDSL model requires a significantly smaller number of pairwise comparisons of criteria, only involving an n &minus, 1 comparison, whereas the AHP requires an n(n &minus, 1)/2 comparison and the BWM a 2n &minus, 3 comparison, (2) it enables us to obtain reliable (consistent) results, even in the case of a larger number of criteria (more than nine criteria), (3) the NDSL model applies an original algorithm for grouping criteria according to the levels of significance, through which the deficiencies of the 9-degree scale applied in the BWM and AHP models are eliminated. By doing so, the small range and inconsistency of the 9-degree scale are eliminated, (4) while the BWM includes the defining of one unique best/worst criterion, the NDSL model eliminates this limitation and gives decision-makers the freedom to express the relationships between criteria in accordance with their preferences. In order to demonstrate the performance of the developed model, it was tested on a real-world problem and the results were validated through a comparison with the BWM and AHP models.

In this present paper we study the non-local Hadmard proportional integrals recently proposed by Rahman et al. (Advances in Difference Equations, (2019) 2019:454) which containing exponential functions in their kernels. Then we establish certain new weighted fractional integral inequalities involving a family of n ( n &isin, N ) positive functions by utilizing Hadamard proportional fractional integral operator. The inequalities presented in this paper are more general than the inequalities existing in the literature.

This paper is devoted to the study of the stability of finite-dimensional distribution of time-inhomogeneous, discrete-time Markov chains on a general state space. The main result of the paper provides an estimate for the absolute difference of finite-dimensional distributions of a given time-inhomogeneous Markov chain and its perturbed version. By perturbation, we mean here small changes in the transition probabilities. Stability estimates are obtained using the coupling method.

We have studied the k-rainbow domination number of C n □ C m for k &ge, 4 (Gao et al. 2019), in which we present the 3-rainbow domination number of C n □ C m , which should be bounded above by the four-rainbow domination number of C n □ C m . Therefore, we give a rough bound on the 3-rainbow domination number of C n □ C m . In this paper, we focus on the 3-rainbow domination number of the Cartesian product of cycles, C n □ C m . A 3-rainbow dominating function (3RDF) f on a given graph G is a mapping from the vertex set to the power set of three colors { 1 , 2 , 3 } in such a way that every vertex that is assigned to the empty set has all three colors in its neighborhood. The weight of a 3RDF on G is the value &omega, ( f ) = &sum, v &isin, V ( G ) | f ( v ) | . The 3-rainbow domination number, &gamma, r 3 ( G ) , is the minimum weight among all weights of 3RDFs on G. In this paper, we determine exact values of the 3-rainbow domination number of C 3 □ C m and C 4 □ C m and present a tighter bound on the 3-rainbow domination number of C n □ C m for n &ge, 5 .

Semi-Markov processes generalize the Markov chains framework by utilizing abstract sojourn time distributions. They are widely known for offering enhanced accuracy in modeling stochastic phenomena. The aim of this paper is to provide closed analytic forms for three types of probabilities which describe attributes of considerable research interest in semi-Markov modeling: (a) the number of transitions to a state through time (Occupancy), (b) the number of transitions or the amount of time required to observe the first passage to a state (First passage time) and (c) the number of transitions or the amount of time required after a state is entered before the first real transition is made to another state (Duration). The non-homogeneous in time recursive relations of the above probabilities are developed and a description of the corresponding geometric transforms is produced. By applying appropriate properties, the closed analytic forms of the above probabilities are provided. Finally, data from human DNA sequences are used to illustrate the theoretical results of the paper.

This paper considers a variant of the relocation problem, which is formulated from an urban renewal project. There is a set of jobs to be processed in a two-machine flow shop subject to a given initial resource level. Each job consumes some units of the resource to start its processing on machine 1 and will return some amount of the resource when it is completed on machine 2. The amount of resource released by a job is not necessarily equal to the amount of resource acquired by the job for starting the process. Subject to the resource constraint, the problem is to find a feasible schedule whose makespan is minimum. In this paper, we first prove the NP-hardness of two special cases. Two heuristic algorithms with different processing characteristics, permutation and non-permutation, are designed to construct feasible schedules. Ant colony optimization (ACO) algorithms are also proposed to produce approximate solutions. We design and conduct computational experiments to appraise the performances of the proposed algorithms.