Showing papers in "Filomat in 2020"

Beetle swarm optimization algorithm: Theory and application

Abstract: In this paper, a new meta-heuristic algorithm, called beetle swarm optimization (BSO) algorithm, is proposed by enhancing the performance of swarm optimization through beetle foraging principles. The performance of 23 benchmark functions is tested and compared with widely used algorithms, including particle swarm optimization (PSO) algorithm, genetic algorithm (GA) and grasshopper optimization algorithm (GOA). Numerical experiments show that the BSO algorithm outperforms its counterparts. Besides, to demonstrate the practical impact of the proposed algorithm, two classic engineering design problems, namely, pressure vessel design problem and himmelblau’s optimization problem, are also considered and the proposed BSO algorithm is shown to be competitive in those applications.

A monotone Bregan projection algorithm for fixed point and equilibrium problems in a reflexive Banach space

Abstract: In this paper, a monotone Bregan projection algorithm is investigated for solving equilibrium problems and common fixed point problems of a family of closed multi-valued Bregman quasi-strict pseudocontractions. Strong convergence is guaranteed in the framework of reflexive Banach spaces.

Soft maps via soft somewhere dense sets

Abstract: The concept of soft sets was proposed as an effective tool to deal with uncertainty and vagueness. Topologists employed this concept to define and study soft topological spaces. In this paper, we introduce the concepts of soft SD-continuous, soft SD-open, soft SD-closed and soft SD-homeomorphism maps by using soft somewhere dense and soft cs-dense sets. We characterize them and discuss their main properties with the help of examples. In particular, we investigate under what conditions the restriction of soft SD-continuous, soft SD-open and soft SD-closed maps are respectively soft SD-continuous, soft SD-open and soft SD-closed maps. We logically explain the reasons of adding the null and absolute soft sets to the definitions of soft SD-continuous and soft SD-closed maps, respectively, and removing the null soft set from the definition of a soft SD-open map.

Beetle Antennae Search without Parameter Tuning (BAS-WPT) for Multi-objective Optimization

Abstract: Beetle antennae search (BAS) is an efficient meta-heuristic algorithm inspired by foraging behaviors of beetles. This algorithm includes several parameters for tuning and the existing results are limited to solve single objective optimization. This work pushes forward the research on BAS by providing one variant that releases the tuning parameters and is able to handle multi-objective optimization. This new approach applies normalization to simplify the original algorithm and uses a penalty function to exploit infeasible solutions with low constraint violation to solve the constraint optimization problem. Extensive experimental studies are carried out and the results reveal efficacy of the proposed approach to constraint handling.

Idealization of j-approximation spaces

Abstract: The current work concentrates on generating different topologies by using the concept of the ideal. These topologies are used to make more thorough studies on generalized rough set theory. The rough set theory was first proposed by Pawlak in 1982. Its core concept is upper and lower approximations. The principal goal of the rough set theory is reducing the vagueness of a concept to uncertainty areas at their borders by increasing the lower approximation and decreasing the upper approximation. For the mentioned goal, different methods based on ideals are proposed to achieve this aim. These methods are more accurate than the previous methods. Hence it is very interesting in rough set context for removing the vagueness (uncertainty).

Existence and stability results for Caputo fractional stochastic differential equations with Lévy noise

Abstract: In this paper, the existence of solution of stochastic fractional differential equations with Lévy noise is established by the Picard-Lindelöf successive approximation scheme. The stability of nonlinear stochastic fractional dynamical system with Lévy noise is obtained using Mittag Leffler function. Examples are provided to illustrate the theory.

Convergence theorems for generalized contractions and applications

Abstract: The principal results in this article deal with the existence of fixed points of a new class of generalized F-contraction. In our approach, by visualizing some non-trivial examples we will obtain better geometrical interpretation. Our main results substantially improve the theory of F-contraction mappings and the related fixed point theorems. In section-4, application to graph theory is entrusted and proved results are endorsed by an example through graph. The presented new techniques give the possibility to justify the existence problems of the solutions for some class of integral equations. For the future aspects of our study, an open problem is suggested regarding discretized population balance model, whose solution may be derived from the established techniques.

Some topological structures of fractals and their related graphs

Abstract: The aim of this paper is to introduce a topological model of fractals. Self similar fractals will be approached as inverse limit of finite one dimensional topological spaces with alpha continuous bonding functions. The second approach is to investigate topological graphs in terms nano topological spaces for Lellis Thivagar. From these approximations, the dynamics of Julia sets as a special type of self similar fractals will be studied and some physical properties of fractals through their nano topological graphs will be applied.

Toric objects associated with the dodecahedron

Abstract: In this paper we illustrate a tight interplay between homotopy theory and combinatorics within toric topology by explicitly calculating homotopy and combinatorial invariants of toric objects associated with the dodecahedron. In particular, we calculate the cohomology ring of the (complex and real) moment-angle manifolds over the dodecahedron, and of a certain quasitoric manifold and of a related small cover. We finish by studying Massey products in the cohomology ring of moment-angle manifolds over the dodecahedron and how the existence of nontrivial Massey products influences the behaviour of the Poincaré series of the corresponding Pontryagin algebra.

Application of linear fractional programming problem with fuzzy nature in industry sector

Abstract: Several methods currently exist for solving fuzzy linear fractional programming problems under non negative fuzzy variables. However, due to the limitation of these methods, they cannot be applied for solving fully fuzzy linear fractional programming (FFLFP) problems where all the variables and parameters are fuzzy numbers. So, this paper is planning to fill in this gap and in order to obtain the fuzzy optimal solution we propose a new efficient method for FFLFP problems utilized in daily life circumstances. This proposed method is based on crisp linear fractional programming and has a simple structure. To show the efficiency of our proposed method some numerical and real life problems have been illustrated.

Sequences of topological near open and near closed sets with rough applications

Abstract: In this paper, we initiated new types of near open and closed sets called higher order sets. These sets generated by much iteration of topological interior and closure operations for a given set. These new sets are the terms of many sequences of topological near open and near closed sets. We studied many generalizations of the classical near open sets to these sequences. This paper is the starting point of a new way for researchers to study the high order topology.

Generalized Simpson type inequalities involving Riemann-Liouville fractional integrals and their applications

Abstract: We establish a Simpson type identity and several Simpson type inequalities for Riemann– Liouville fractional integrals. As applications, we apply the obtained results to special means of real numbers, an error estimate for Simpson type quadrature formula, and q-digamma function, respectively.

Study of matrix transformation of uniformly almost surely convergent complex uncertain sequences

Abstract: In this paper, we introduce the concept of convergence of complex uncertain series. We initiate matrix transformation of complex uncertain sequence and extend the study via linearity and boundedness. In this context, we prove Silverman-Toeplitz theorem and Kojima-Schur theorem considering complex uncertain sequences. Finally, we establish some results on co-regular matrices .

On asymptotically λ-statistical equivalent sequences of order α in probability

Abstract: In this study, we introduce and examine the concepts of asymptotically λ−statistical equivalent sequences of order α in probability and strong asymptotically λ−equivalent sequences of order α in probability. We give some relations connected to these concepts.

Complete convergence and complete moment convergence for negatively dependent random variables under sub-linear expectations

Abstract: This paper we study and establish the complete convergence and complete moment convergence theorems under a sub-linear expectation space. As applications, the complete convergence and complete moment convergence for negatively dependent random variables with CV (exp (ln? |X|)) < ?, ? > 1 have been generalized to the sub-linear expectation space context. We extend some complete convergence and complete moment convergence theorems for the traditional probability space to the sub-linear expectation space. Our results generalize corresponding results obtained by Gut and Stadtm?ller (2011), Qiu and Chen (2014) and Wu and Jiang (2016). There is no report on the complete moment convergence under sub-linear expectation, and we provide the method to study this subject.

Some new results on (s,q)-Dass-Gupta-Jaggi type contractive mappings in b-metric-like spaces

Abstract: In this paper we consider cyclic (s-q)-Dass-Gupta-Jaggi type contractive mapping in b-metric like spaces. By using our new approach for the proof that one Picard’s sequence is Cauchy in the context of b-metric-like space, our results generalize, improve and complement several results in the existing literature. Moreover, we showed that the cyclic type results of Kirk et al. are equivalent with the corresponding usual fixed point ones for Dass-Gupta-Jaggi type contractive mappings. Finally, some examples are presented here to illustrate the usability of the obtained theoretical results.

Connecting quantum calculus and harmonic starlike functions

Abstract: Quantum calculus or q−calculus plays an important role in hypergeometric series, quantum physics, operator theory, approximation theory, sobolev spaces, geometric functions theory and others. But role of q−calculus in the theory of harmonic univalent functions is quite new. In this paper, we make an attempt to connect quantum calculus and harmonic univalent starlike functions. In particular, we introduce and investigate the properties of q−harmonic functions and q−harmonic starlike functions of order α.

Topological approach for rough sets by using J-nearly concepts via ideals

Abstract: Topological concepts and methods have been applied as useful tools to study computer science, information systems and rough set. Rough set was introduced by Pawlak. Its core concept is upper and lower approximation operations, which are the operations induced by an equivalent relation on a domain. They can also be seen as a closure operator and a interior operator of the topology induced by an equivalent relation on a domain. This paper explores rough set theory from the point of view of topology. I generalize the notions of rough sets based on the topological space. The set approximations are defined by using the new topological notions namely I-J-nearly open sets. The topological properties of the present approximations are introduced and compared to the previous one and shown to be more general.

Quantitative estimates for the tensor product (p,q)-Balázs-Szabados operators and associated generalized Boolean sum operators

Abstract: In this study, we give some approximation results for the tensor product of (p,q)-Bal?zs-Szabados operators associated generalized Boolean sum (GBS) operators. Firstly, we introduce tensor product (p,q)-Bal?zs-Szabados operators and give an uniform convergence theorem of these operators on compact rectangular regions with an illustrative example. Then we estimate the approximation for the tensor product (p,q)-Bal?zs-Szabados operators in terms of the complete modulus of continuity, the partial modulus of continuity, Lipschitz functions and Petree?s K-functional corresponding to the second modulus of continuity. After that, we introduce the GBS operators associated the tensor product (p,q)-Bal?zs-Szabados operators. Finally, we improve the rate of smoothness by the mixed modulus of smoothness and Lipschitz class of B?gel continuous functions for the GBS operators.

Analytical solutions of some general classes of differential and integral equations by using the Laplace and Fourier transforms

Abstract: This article deals with a general class of differential equations and two general classes of integral equations. By using the Laplace transform and the Fourier transform, analytical solutions are derived for each of these classes of differential and integral equations. Some illustrative examples and particular cases are also considered. The various analytical solutions presented in this article are potentially useful in solving the corresponding simpler differential and integral equations.

On statistical and strong convergence with respect to a modulus function and a power series method

Abstract: This paper introduces and focuses on two pairs of concepts in two main sections. The first section aims to examine the relation between the concepts of strong Jp-convergence with respect to a modulus function f and Jp-statistical convergence, where Jp is a power series method. The second section introduces the notions of f -Jp-statistical convergence and f -strong Jp-convergence and discusses some possible relations among them.

A decomposition of signed graphs with two eigenvalues

Abstract: In this study we consider connected signed graphs with 2 eigenvalues that admit a vertex set partition such that the induced signed graphs also have 2 eigenvalues, each. We derive some spectral characterizations, along with examples supported by additional theoretical results. We also prove an inequality that is a fundamental ingredient for the resolution of the Sensitivity Conjecture.

Riesz potential, Marcinkiewicz integral and their commutators on mixed Morrey spaces

Abstract: This paper deals with the boundedness of integral operators and their commutators in the framework of mixed Morrey spaces. Precisely, we study the mixed boundedness of the commutator [b,Iα], where Iα denotes the fractional integral operator of order α and b belongs to a suitable homogeneous Lipschitz class. Some results related to the higher order commutator [b,Iα]k are also shown. Furthermore, we examine some boundedness properties of the Marcinkiewicz-type integral μΩ and the commutator [b,μΩ] when b belongs to the BMO class.

Applications of (M,N)-Lucas polynomials for holomorphic and bi-univalent functions

Abstract: In this article, we use the (M,N)-Lucas polynomials to define a new family HΣ(λ; x) of normalized holomorphic and bi-univalent functions and to establish the bounds for |a2| and |a3|, where a2, a3 are the initial Taylor-Maclaurin coefficients. Further we investigate Fekete-Szegö inequality for functions in the family HΣ(λ; x) which we have introduced here.

Regression analysis and statistical examination of Knoop Hardness on abrasion resistance in Lyca Beige Marbles

Abstract: Marbles are secondary decomposition products formed by metamorphism of limestone. Effective classification of marble quarries in terms of quality enables the selection of a sustainable production method and safety application. This evaluation is based on physico-mechanical properties of the samples. Obtained results of physico-mechanical properties of the marbles were statistically analyzed using Stata 14 and SPSS 21 software. The marbles indicated mostly normal physical and mechanical properties. A strong inverse relationship exists between Abrasion Value and Knoop Hardness Determination that indicates a significant nonlinear relationship. Samples were distinguished into 3 groups of close similarity and related properties. The estimated value of the parameters is in the 95 % confidence interval. The equation obtained by regression analysis was used for the determination of resistance to abrasion.

On the solvability of a self-reference functional and quadratic functional integral equations

Abstract: In this paper we study the existence of solutions of a self-reference functional integral equation and functional quadratic integral equation. Some examples will be given.

On a solvable three-dimensional system of difference equations

Abstract: In this paper, we show that the following three-dimensional system of difference equations xn = zn-2xn-3/axn-3 + byn-1, yn = xn-2yn-3/cyn-3 + dzn-1, zn = yn-2zn-3/ezn-3+ fxn-1, n ∈ N0, where the parameters a, b, c, d, e, f and the initial values x-i, y-i, z-i, i ∈ {1, 2, 3}, are real numbers, can be solved, extending further some results in literature. Also, we determine the asymptotic behavior of solutions and the forbidden set of the initial values by using the obtained formulas.

A new compact alternating direction implicit method for solving two dimensional time fractional diffusion equation with Caputo-Fabrizio derivative

Abstract: In this paper, a new compact alternating direction implicit (ADI) difference scheme is proposed for the solution of two dimensional time fractional diffusion equation. Theoretical considerations are discussed. We show that the proposed method is fourth order accurate in space and two order accurate in time. The stability and convergence of the compact ADI method are presented by the Fourier analysis method. Numerical examples confirm the theoretical results and high accuracy of the proposed scheme.

On pseudo H-symmetric Lorentzian manifolds with applications to relativity

Abstract: In this paper, we introduce a new type of curvature tensor named H-curvature tensor of type (1, 3) which is a linear combination of conformal and projective curvature tensors. First we deduce some basic geometric properties of H-curvature tensor. It is shown that a H-flat Lorentzian manifold is an almost product manifold. Then we study pseudo H-symmetric manifolds (PHS)n (n > 3) which recovers some known structures on Lorentzian manifolds. Also, we provide several interesting results. Among others, we prove that if an Einstein (PHS)n is a pseudosymmetric (PS)n, then the scalar curvature of the manifold vanishes and conversely. Moreover, we deal with pseudo H-symmetric perfect fluid spacetimes and obtain several interesting results. Also, we present some results of the spacetime satisfying divergence free H-curvature tensor. Finally, we construct a non-trivial Lorentzian metric of (PHS)4.

Bitopological approximation space with application to data reduction in multi-valued information systems

Abstract: We presented bitopological approximation space as a generalization of classical approximation space. This generalization is based on a topological space that have a subbases generated by a family of binary relations defined on the universe of discourse. We studied some properties of rough sets on bitopological approximation spaces. Many new membership functions and inclusion functions are defined and are used for redefining the rough approximations. Finally, some real life application examples are given to illustrate the benefit of our approach.