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In this paper, we introduce a parametric type of Cauchy polynomials and study their characteristic and combinatorial properties. In particular, we show some determinant expressions. [ABSTRACT FROM AUTHOR]

T.Z. Mirkovic [14] obtained new inequalities of Wirtinger type by using some classical inequalities and special means for convex function. So in this paper, we obtain some inequalities of Wirtinger type for s-convex function, m-convex function, (α,m)-convex function, quasi-convex function and P-function. Also several special cases are discussed, which can be deduced from our main results. [ABSTRACT FROM AUTHOR]

Feature selection is one of the issues in machine learning as well as statistical pattern recognition. This is important in many fields (such as classification) because there are many features in these areas, many of which are either unused or have little information load. Not eliminating these features does not make a problem in terms of information, but it does increase the computational burden for the intended application. Besides, it causes to store of so much useless information along with useful data. A problem for machine learning research occurs when there are many possible features with few attributes of training data. One way is to first specify the best attributes for prediction and then to classify features based on a measure of their dependence. In this study, the Fuzzy-Rough subset evaluation has been used to take features in core of similar features. Fuzzy-rough set-based feature selection (FS) has been demonstrated to be extremely advantageous at reducing dataset size but has various problems that yield it unproductive for big datasets. Fuzzy-Rough subset evaluation algorithm indicates that the techniques greatly decrease dimensionality while keeping classification accuracy. This paper considers classifying attributes by using fuzzy set similarity measures as well as the dependency degree as a relatedness measure. Here we use Artificial Neural Network, Naive Bayes as classifiers, and the performance of these techniques are compared by accuracy, precision, recall, and F-measure metrics. [ABSTRACT FROM AUTHOR]

This paper is concerned with the asymptotic behavior of a p-Landau-Lifschitz type functional with radial structure as parameter goes to zero. We study the concentration compactness and give several global properties in the case of p > 2. [ABSTRACT FROM AUTHOR]

The main goal of our paper is to obtain sufficient conditions for the asymptotic equivalence of a linear differential system and a quasilinear system of impulsive differential equations with piecewise constant argument of generalized type, in short IDEPCAG. A deviating argument is of the advanced and delayed type. As an auxiliary result, the structure of the set of solutions of the quasilinear system is specified. Several examples are also given to show the feasibility of results. [ABSTRACT FROM AUTHOR]

This paper deals with join-semilattices whose sections, i.e. principal filters, are pseudocomplemented lattices. The pseudocomplement of a v b in the section [b,1] is denoted by a→b and can be considered as the connective implication in a certain kind of intuitionistic logic. Contrary to the case of Brouwerian semilattices, sections need not be distributive lattices. This essentially allows possible applications in non-classical logics. We present a connection of the semilattices mentioned in the beginning with the so-called non-classical implication semilattices which can be converted into I-algebras having everywhere defined operations. Moreover, we relate our structures to sectionally and relatively residuated semilattices which means that our logical structures are closely connected with substructural logics. We show that I-algebras form a congruence distributive, 3-permutable and weakly regular variety. [ABSTRACT FROM AUTHOR]

In this paper, we obtain sufficient conditions for existence of solutions of a third order m-point impulsive boundary value problem on time scales. To the best of our knowledge, there is hardly any work dealing with third order multi point dynamic impulsive BVPs. The reason may be the complex arguments caused by both impulsive perturbations and calculations on time scales. As an application, we give an example demonstrating our results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to improve some fixed point results given by I.A. Rus in (On a fixed point theorem of Maia, Studia Univ. Babes¸-Bolyai Math., 22(1977), 40-42), (Basic problem for Maia's theorem, Sem. on Fixed Point Theory, Preprint 3(1981), Babes¸-Bolyai Univ. Cluj- Napoca, 112-115) and (Data dependence of the fixed points in a set with two metrics, Fixed Point Theory, 8(2007), no. 1, 115-123), by applying, instead of contraction principle, some variants of Maia's fixed point theorem. 2010 Mathematics Subject Classification: 47H10, 47H09, 34K05, 34K12, 45D05, 45G10, [ABSTRACT FROM AUTHOR]

The aim of the present paper is to analyze sharp type inequalities including the scalar and Ricci curvatures of anti-invariant Riemannian submersions in complex space forms. [ABSTRACT FROM AUTHOR]

In this paper the Decomposition Theorem for functional equations is shown. As an application of this Theorem the two times continuously differentiable solution of the functional equation G1(x(x+y))+F1(y) = G2(y(x+y))+F2(y) can be given with unknown functions ... where the Equation is fulfilled for all ... . [ABSTRACT FROM AUTHOR]

Inspired by the paper of Fazli and Nieto in [Open Math. 17 (2019) 499--512], we establish new existence and uniqueness result for a type of fractional Bagley--Torvik differential equation. Reported result not only generalizes previous results but also adopts different technique. We finish this study by concluding remarks which discuss the preference of our theorem compared to previous results. An example is constructed with specific parameters that requires weaker conditions for the existence of a unique solution. Meanwhile, we construct an iterative sequence that converges to the unique solution and can not be commented via the results of Fazli and Nieto. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some new results on radicals of an ideal in BL-algebras. Further, we introduce I-balls in BL-algebras and prove that I-balls constitutes a basis for a topology on BL-algebras. We also derive some new relations of sequences in BL-algebras. [ABSTRACT FROM AUTHOR]

In this paper, we solve a new Jensen type m-dimensional multiplicative inverse functional equation and then its various stability problems in the setting of non-negative real numbers and non-Archimedean spaces via fixed point method. The functional equation dealt in this study is linked with the famous relationship between arithmetic and harmonic mean of m values. The role of harmonic mean is very significant in many other fields such as traffic flow theory, industrial engineering, communication system, etc. By inversing the arithmetic mean of reciprocal values, we attain the harmonic mean. This property could be analyzed as an inverse problem via the functional equation dealt in this investigation. [ABSTRACT FROM AUTHOR]

This paper deals with the initial boundary value problem for a higher-order parabolic equation with logarithmic source term ... . By employing the potential wells technique we show the global existence of the weak solution. Also, we obtain the exponential decay for the weak solutions. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider a system of N -fixed point equations in metric spaces. The existence and uniqueness of solution and an iterative algorithm for approximating the solution are studied. This system of N -fixed point equations is an extension of the classical of fixed point equation x = T x. The results of this paper improve several important works recently published in the literature. [ABSTRACT FROM AUTHOR]

In this paper, a new class of nonconvex nonsmooth multiobjective programming problems with both inequality and equality constraints defined in a real Banach space is considered. Under the nondifferentiable vectorial (Φρ)w-invexity notion introduced in the paper, optimality conditions and duality results in Mond-Weir sense are established for the considered nonsmooth vector optimization problem. It turns out that the results developed here under (Φρ)w-invexity are applicable for a larger class of nonconvex nondifferentiable multiobjective programming problems than under several generalized convexity notions existing in the literature. [ABSTRACT FROM AUTHOR]

In this paper, new types of k-Fibonacci numbers are described, with respect to the definition of the distance between numbers using a recurrence relation. However, these sequences differ not only by the value of the natural number k but also according to the value of a new parameter r which is used in defining this distance. Furthermore, various properties of these new numbers are discussed. In the second part of this paper, we apply the binomial transform to these generalized k-Fibonacci sequences. [ABSTRACT FROM AUTHOR]

In this paper we are addressing a counting problem of discrete mathematics, more precisely of digital geometry. In the Euclidean plane the shortest path between any two points is given by the straight line segment connecting the points. In discrete mathematics, the shortest path is usually not unique, e.g., in graphs there could be several shortest paths between two vertices. In this paper, a special infinite graph, the square grid, (i.e., the usual digital plane) is used. In digital geometry there are various digital, i.e., path based distance functions. A neighborhood sequence B gives the condition for each step of a B-path separately what type of neighborhood is used in that step. Therefore, the length and also the number of the shortest paths between two points depend not only on the respective positions (coordinate differences) of the points but also on the neighborhood sequence B. We give an algorithm and also closed formulae to compute the number of shortest B-paths. [ABSTRACT FROM AUTHOR]

In this paper, we will prove some fixed point results using a Pompeiu type metric on Pcl(X), for multi-valued operators satisfying two conditions: contractivity and monotonicity. The approach is based on a fixed point theorem for a multi-valued operator in the setting of a b-metric space. Several qualitative properties(well-posedness, Ulam-Hyers stability) are also obtained. In the second part of this paper, we will consider the extended coupled fixed point problem for a multi-valued operator. We will consider the problem of the existence of the solutions. Data dependence and well-posedness of the extended coupled fixed point problem are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, all normal extensions of the minimal operator associated with the singular degenerate linear differential expressions for first order in the Hilbert space of vector-functions are investigated in terms of boundary values. As well, it analyses the spectrum parts of any normal extension. [ABSTRACT FROM AUTHOR]

In induction heating process, there is a problem of uniform heating. In this paper, an optimal applied electric field control problem for induction heating process of conductive materials is considered. The cost function is defined such that the temperature profile at the final stage has a relative uniform distribution in the field. The controlled system is a coupled by Maxwell's equations with nonlinear heat equation. The existence of solutions for weakly coupled system is proved. We show that there exists an optimal applied electric field which minimizes the cost functional. Moreover, a fist-order necessary condition is derived. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and study the concepts of statistical convergence and statistical summability for martingale sequences of random variables via deferred Cesaro ` mean. We then establish an inclusion theorem concerning the relation between these two beautiful and potentially useful concepts. Also, based upon our proposed notions, we state and prove new Korovkin-type approximation theorems with algebraic test functions for a martingale sequence over a Banach space. Moreover, we demonstrate that our theorems effectively extend and improve most (if not all) of the previously existing results (in statistical and classical versions). Finally, by using the generalized Bernstein polynomials, we present an illustrative example of a martingale sequence in order to demonstrate that our established theorems are stronger than their traditional and statistical versions. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to deal with the dynamics of following higher order difference equation xn+1 = A+B xn-m x 2 n where A,B > 0, and initial values are positive, and m = {1,2....}. Furthermore, we discuss the periodicity, boundedness, semi-cycles, global asymptotic stability of solutions of these equations. We also handle the rate of convergence of solutions of these difference equations. [ABSTRACT FROM AUTHOR]

Consider a simple connected graph G = (V(G),E(G)), where V(G) represents the vertex set and E(G) represents the edge set respectively. A subset W of V(G) is called a resolving set for a graph G if for every two distinct vertices x, y ∈V(G), there exist some vertex w ∈W such that d(x,w) 6= d(y,w), where d(u, v) denotes the distance between vertices u and v. A resolving set of minimal cardinality is called a metric basis for G and its cardinality is called the metric dimension of G, which is denoted by β(G). A subset D of V(G) is called a doubly resolving set of G if for every two distinct vertices x, y of G, there are two vertices u, v ∈ D such that d(u, x) - d(u, y) 6= d(v, x) - d(v, y). A doubly resolving set with minimum cardinality is called minimal doubly resolving set. This minimum cardinality is denoted by ψ(G). In this paper, we determine the minimal doubly resolving sets for antiprism graphs denoted by An with n ≥ 3 and for Mobius ladders denoted by Mn, for every even positive integer n ≥ 8. It has been proved that ψ(An) = 3 for n ≥ 3 and ψ(Mn) = ( 3, if n ≡ 0 or 4 (mod 8) 4, if n ≡ 2 or 6 (mod 8) for every even positive integer n ≥ 8. [ABSTRACT FROM AUTHOR]

This paper presents new geometric viewpoints to Chen chaotic system. Firstly, the existence of two nontransverse homoclinic orbits in Chen system is rigorously proved beyond the classical parameters. Secondly, combined with the theory of tangent bundle, a new geometric viewpoint is given to explore chaos mechanism of Chen system. The fundamental geometric definition of tangent bundle and the essential role of nonlinear connection between the tangent space and the base space are described. By introducing the geometrical viewpoints of second order system governed by Lie-Poisson equation, some geometric invariants of Chen system can be obtained. Furthermore, the torsion tensor as one of the geometric invariants is obtained, and it gives the geometrical interpretation to the chaotic behaviour of Chen system. Finally, the torsion tensor of Chen system and Lorenz system are also compared. The obtaining results show that torsion tensor change will lead the Chen system from periodic to chaotic, which is not found in Lorenz system. [ABSTRACT FROM AUTHOR]

For a ∈ (0,1) and r ∈ (0,1), let Ea(r) be the generalized elliptic integral of the second kind and R(a) be Ramanujan's constant. In this paper, we prove the following inequalities sin(πa) 2(1-a) +r'2 (1-a)sin(πa)log e R(a)/2 r ! -σ ! < Ea(r) < sin(πa) 2(1-a) +r 2 (1-a)sin(πa)log e R(a)/2 r ! -δ ! with the best possible constants σ = 1 4 sin(πa) and δ = sin(πa) 2(1-a) + (1-a)sin(πa) R(a) 2 - π 2. [ABSTRACT FROM AUTHOR]

In this paper we study the regular prism tilings and construct ball packings by geodesic balls related to the above tilings in the projective model of Nil geometry. Packings are generated by action of the discrete prism groups pq21. We prove that these groups are realized by prism tilings in Nil space if (p,q) = (3,6),(4,4),(6,3) and determine packing density formulae for geodesic ball packings generated by the above prism groups. Moreover, studying these formulae we determine the conjectured maximal dense packing arrangements and their densities and visualize them in the projective model of Nil geometry. We get a dense (conjectured locally densest) geodesic ball arrangement related to the parameters (p,q) = (6,3) where the kissing number of the packing is 14, similarly to the densest lattice-like Nil geodesic ball arrangement investigated by the second author in [11]. [ABSTRACT FROM AUTHOR]

In this paper, we establish new weighted integral inequalities for differentiable hconvex and quasi-convex functions. Applications of our findings to continuous random variables and approximation of integrals are given. [ABSTRACT FROM AUTHOR]

In this paper, we establish the stability of n-cubic functional equations in Lipschitz spaces and as a consequence we give the stability of cubic functional equations. [ABSTRACT FROM AUTHOR]

This paper includes four finite element methods which are based on quadratic, cubic, quartic and quintic trigonometric B-spline functions for space discretization and Crank-Nicolson method for time discretization, to be achieved the numerical solution of the Schrodinger equation (SE). The algorithms obtained by different degrees trigonometric B-spline Galerkin methods are new for getting numerical solution of the SE. To see the accuracy of the proposed methods, two numerical experiments are investigated and the comparison of the methods are given in the test problem section. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of (p,ϕh)-convex functions and present some properties and representation of such functions. Finally, a version of Hermite Hadamard-type inequalities for (p,ϕh)-convex functions are established. [ABSTRACT FROM AUTHOR]

In this paper, some new weighted Simpson's type integral inequalities are presented for the class of harmonically-preinvex functions by using power-mean integral inequality and Holder's integral inequality. [ABSTRACT FROM AUTHOR]

In this paper, we study the complex dynamical behaviors of a discrete-time SIR epidemic model. Analysis of the model demonstrates that the Diseases Free Equilibrium (DFE) point is globally asymptotically stable if the basic reproduction number is less than one while the Endemic Equilibrium (EE) point is globally asymptotically stable if the basic reproduction number is greater than one. The results are further substantiated visually with numerical simulations. Furthermore, numerical results demonstrate that the discrete model has more complex dynamical behaviors including multiple periodic orbits, quasi-periodic orbits and chaotic behaviors. The maximum Lyapunov exponent and chaotic attractors also confirm the chaotic dynamical behaviors of the model. [ABSTRACT FROM AUTHOR]

The aim of this paper is to improve some fixed point results given by I. A. Rus in (On a fixed point theorem of Maia, Studia Univ. Babeş-Bolyai Math., 22(1977), 40-42), (Basic problem for Maia's theorem, Sem. on Fixed Point Theory, Preprint 3(1981), Babeş-Bolyai Univ. ClujNapoca, 112-115) and (Data dependence of the fixed points in a set with two metrics, Fixed Point Theory, 8(2007), no. 1, 115-123), by applying, instead of contraction principle, some variants of Maia's fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of nonlinear operators-the class of general historydependent operators. These are the operators defined on spaces of functions endowed with a structure of Banach space (the case of bounded interval of time) or Frechet space (the case of unbounded interval of time). We state and prove various properties of such operators, including fixed point properties. Moreover, we also study several classes of differential equations in Banach spaces, for which we our previous results can be applied. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of positive solutions of second-order impulsive differential equations with integral boundary conditions on an infinite interval. As an application, an example is given to demonstrate our main results. [ABSTRACT FROM AUTHOR]

This paper deals with a problem of a wave equation with p-Laplacian and logarithmic nonlinearity term. Firstly, local existence of weak solutions have been obtained by applying Banach fixed theorem. Later, the finite-time blow up of the solutions have been obtained for negative initial energy. [ABSTRACT FROM AUTHOR]

Matrix factorizations have been widely used in recent years, especially in engineering problems, to facilitate performance-requiring computations. In this paper, we investigate some interesting relationships between some combinatorial matrices such as Pascal matrix, Stirling matrices and k-order Fibonacci matrices. We give factorizations and inverse factorizations of the Pascal and Stirling matrices via k-order Fibonacci matrices. Moreover, we derive various combinatorial properties by using relationships between these matrices. Finally, compared to previous studies, we present more general results for specific values of k. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analysis of the following linear 2m-th order parabolic equation ∂tu+(-1) m ∑ N k=1 ∂ 2m xk u = f, subject to Dirichlet type condition ∂ l νu = 0, l = 0,1,...,m-1, on the lateral boundary, where m is a positive integer. The right-hand side f of the equation is taken in the Lebesgue space L p, 1 < p < +∞. The problem is set in a domain of the form Q = (t, x1,..., xN) ∈ R N+1 : 0 ≤ q x 2 1 +...+x 2 N < t α with α > 1/2m. [ABSTRACT FROM AUTHOR]

In this paper we find all involutive solutions X ∈ Cn×n of the Yang-Baxter matrix equation AXA = XAX, where A ∈ Cn×n is a given involutory matrix. The construction is algorithmic. It is based on the concept of quadratic matrices. Algorithms for generating concrete involutive solutions of the Yang-Baxter matrix equation AXA = XAX are also presented along with several examples. [ABSTRACT FROM AUTHOR]

Assume that Tn is the nth term of Tribonacci sequence and Rm is the mth term of Perrin sequence. In this paper, we solve the equation Tn = Rm completely. [ABSTRACT FROM AUTHOR]

In this paper, we examine a generalized convexity type inequality, called e-convexity. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the existence of positive solutions for the semipositone fractional boundary value problem with n point fractional integral boundary conditions. The existence of positive solutions is established using the five functionals fixed point theorem. An example is given to ratify that our main result is theoretically feasible. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of a non-trivial solution in W 1,p(x) 0 (Ω) for the problem ( ∆p(x)u = f(x,u,∇u) in Ω, u = 0 in Ω. The proof is based on Schaefer's fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we extend the relation-theoretic contraction principle due to Alam and Imdad (J. Fixed Point Theory Appl. 17 (2015) 693-702) for Matkowski contractions employing a locally T-transitive binary relation. Our results improve and enrich several fixed point theorems of the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a perturbed first order non-convex sweeping process for a class of subsmooth moving sets depending on the time and the state. In the first result we study the existence of solution and the compactness of the attainable set, the perturbation considered here is an upper semi-continuous set-valued mapping with nonempty closed convex values unnecessarily bounded. In the second result, we prove the existence of solution for the autonomous problem under assumptions that do not require the convexity of the values of the perturbation and that weaken the assumption on the upper semi-continuity. Then, we deduce a solution of the time optimality problem and we describe the attainable set. [ABSTRACT FROM AUTHOR]

In this paper, we consider the higher-order multi-point fractional boundary value problem. We establish the criteria for the existence of at least one and three positive solutions for higher order nonlinear m-point fractional boundary value problem by using the Krasnosel'skii fixed point theorem and the Legget-Williams fixed point theorem, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the geometric properties of cosymplectic manifold. We give some classifications for a cosymplectic manifold endowed with some special vector fields, such as contact, concircular, recurrent, torse-forming and some characterizations for such a manifold admitting a Ricci soliton given as to be Einstein, η-Einstein, almost quasi-Einstein and nearly quasi-Einstein. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Diophantine equation Ln±Lm = kx² with k ∈ {1,2} and we find all solutions of this equation in nonnegative integers n,m, and x when n ≡ m(mod2). With the help of these solutions, we solve the equation Ln -Lm = 2a. In order to solve the last equation, we also use lower bounds for linear forms in logarithms and a version of the Baker-Davenport reduction method in diophantine approximation. [ABSTRACT FROM AUTHOR]

In this paper, we suggest some new and efficient iterative methods for solving nonlinear equations f (x) = 0. These methods are free from derivatives having high order of convergence. We also give some examples to illustrate the efficiency of these methods. Finally, numerical tests confirm the theoretical results and allow us to compare these variants with the classical Steffensen's method. These new methods can be considered as alternative of existing derivative-free methods. [ABSTRACT FROM AUTHOR]