<abstract>
<title style='display:none'>Abstract</title>
In this paper, we establish a fixed point theorem for generalized contraction mappings in <italic>b</italic>-metric spaces endowed with a digraph. As an application of this result, we obtain fixed points of cyclical mappings in the setting of <italic>b</italic>-metric spaces. Our results extend and generalize several existing results in the literature.
</abstract>

Fixed Point Results for Generalized Contraction Mappings and Cyclical Mappings in <italic>b</italic>-Metric Spaces Endowed with a Digraph

<abstract>
<title style='display:none'>Abstract</title>
Some inequalities of Hermite-Hadamard type for <italic>GG-</italic>convex functions defined on positive intervals are given. Applications for special means are also provided.
</abstract>

Inequalities of Hermite-Hadamard Type for <italic>GG</italic>-Convex Functions

<abstract><title style='display:none'>Abstract</title> In recent years significant work has been done to use Neural Networks in game AI, and harness the advantages of such a technique. This paper would like to show that it is possible using neuroevolution to evolve a neural network topology optimized for a given task and avoiding over or under complexification by human hands. In order to illustrate this we implement two agents capable of playing simple zero sum perfect information games with the help of the genetic algorithm Neuroevolution of augmenting topologies. To illustrate this optimization we load the resulting topologies onto an Android OS game app. </abstract>

Neuro-evolution in Zero-Sum Perfect Information Games on the Android OS

<abstract><title style='display:none'>Abstract</title> Let G = (V,E) be a simple connected molecular graph. In such a simple molecular graph, vertices represent atoms and edges represent chemical bonds, we denoted the sets of vertices and edges by V = V (G) and E = E(G), respectively. If d(u, ν) be the notation of distance between vertices u, ν ∈ V and is defined as the length of a shortest path connecting them. Then, Eccentricity connectivity polynomial of a molecular graph G is defined as ECP(G, x) = ∑ν∈V dG(ν)xecc(ν), where ecc(ν) is defined as the length of a maximal path connecting to another vertex of v. dG(ν) (or simply dv) is degree of a vertex ν ∈ V (G), and is defined as the number of adjacent vertices with v. In this paper, we focus on the structure of molecular graph circumcoronene series of benzenoid Hk (k ≥ 2) and counting the eccentricity connectivity polynomial ECP(Hk) and eccentricity connectivity index ξ(Hk), by new method (called Ring-cut Method). </abstract>

Computing Eccentricity Connectivity Polynomial of Circumcoronene Series of Benzenoid Hk by Ring-Cut Method

<abstract><title style='display:none'>Abstract</title> In this paper, we prove some sharp maximal function estimates for the commutators related to certain generalized fractional integral operator with general kernel and the BMO and Lipschitz functions. As an application, we obtain the boundedness of the commutators on Lebesgue, Morrey and Triebel-Lizorkin spaces. The operator includes fractional Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.</abstract>

Sharp Maximal Function Estimates and Boundedness for Commutator Related to Generalized Fractional Integral Operator

<abstract>
<title style='display:none'>Abstract</title>
The Riemann-Roch theorem is of utmost importance and a vital tool to the fields of complex analysis and algebraic geometry, specifically in the algebraic geometric theory of compact Riemann surfaces. It tells us how many linearly independent meromorphic functions there are having certain restrictions on their poles. The aim of this paper is to give two proofs of this important theorem and explore some of its numerous consequences. As an application, we compute the genus of some interesting algebraic curves or Riemann surfaces.
</abstract>

Riemann-Roch theorem and Kodaira-Serre duality

<abstract>
<title style='display:none'>Abstract</title>
In this paper, we propose an approximation technique to compute multiple integrals of a non-negative real continuous function over a hyper-rectangle Ω of ℝ<italic>n</italic>. The main idea is to use a reducing transformation procedure obtained by using α-dense curves. First, the region Ω<italic>f</italic> whose measure represents the value of the integral, is densified by a specific curve <italic>ℓ</italic>α(<italic>t</italic>) of finite length. Therefore, the multiple integral can be approached by a simple integral corresponding to <italic>ℓ</italic>α (<italic>t</italic>). Some numerical examples are given.
</abstract>

Efficient α-Dense Curve Strategies for Multiple Integrals over Hyper-rectangle Regions

<abstract>
<title style='display:none'>Abstract</title>
In this paper, we present a novel class of Copson-type inequalities involving the right-sided <italic>k</italic>-Hadamard fractional integral operator with all parameters of integrability <italic>p</italic> ≠ 0 and obtain some classical special cases of Copson inequalities. The main results will be proved by employing the Hölder inequality and the Fubini theorem.
</abstract>

Copson-type Inequalities via the <italic>k</italic>-Hadamard Operator

<abstract>
<title style='display:none'>Abstract</title>
We identify pointed vortex loops in the plane with low dimensional nonlinear flags decorated with volume forms. We show how submanifolds of such decorated nonlinear flags can be identified with coadjoint orbits of the area pre- serving diffeomorphism group and relate them to coadjoint orbits of pointed vortex loops. The subgroup of the dihedral group preserving the vorticity data plays a role in the description of these coadjoint orbits.
</abstract>

Decorated Nonlinear Flags, Pointed Vortex Loops and the Dihedral Group

<abstract>
<title style='display:none'>Abstract</title>
The aim of this paper is to give sufficient conditions for Ψ − conditional asymptotic stability of the Ψ − bounded solutions of a nonlinear Lyapunov matrix differential equation with integral term as right side.
</abstract>

On the Ψ − Conditional Asymptotic Stability of a Nonlinear Lyapunov Matrix Differential Equation with Integral Term as Right Side

<abstract>
<title style='display:none'>Abstract</title>
This paper discusses the global convergence of successive approximations methods for solving integro-differential equation via resolvent operators in Banach spaces. We prove a theorem on the global convergence of successive approximations to the unique solution of the problems. An example is given to show the application of our result.
</abstract>

Existence and Successive Approximations of Mild Solution for Integro-differential Equations in Banach Spaces

<abstract>
<title style='display:none'>Abstract</title>
The assembly of billions of short sequencing reads into a contiguous genome is a daunting task. The foundation knowledge of current DNA assembly models is concentrated among a select group, where the solution to the genome assembly challenge lies in proper ordering the genomic data. This contribution’s objective is to provide an overview of the original graph models used in DNA sequencing by hybridization. With the updated analytical approach based on the bidirectional bipartite graph class, the theoretical basic structure of the DNA assembly model has been described in new perspective by incorporating few short hypothetical DNA sequences. On the Galaxy platform, by using Spades assembler and Velvet assembler, the comparative outcomes of an experiment are presented, and we also identify their working schemes. Here, the working principle of de Bruijn graph has been discussed in broader point of view.
</abstract>

A Study of Computational Genome Assembly by Graph Theory

<abstract><title style='display:none'>Abstract</title> In this paper, generalized Hirota Satsuma coupled KdV system is solved with tanh method and q-Homotopy analysis method. New fractional derivative definition called “conformable fractional derivative” used in the solution procedure. Tanh method with conformable derivative firstly introduced in the literature. By the graphics of analytical and approximate solutions, it is shown that, both methods provide an effective and powerful mathematical tool for solving nonlinear PDEs containing conformable fractional derivative. </abstract>

On the New Solutions of the Conformable Time Fractional Generalized Hirota-Satsuma Coupled KdV System

<abstract><title style='display:none'>Abstract</title> Fuzzy ordered linear spaces, Riesz spaces, fuzzy Archimedean spaces and σ-complete fuzzy Riesz spaces were defined and studied in several works. Following the efforts along this line, we define fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections and establish their fundamental properties. </abstract>

Fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections

<abstract><title style='display:none'>Abstract</title>In this paper, the existence of positive solutions for a nonlinear fourth-order two-point boundary value problem with integral condition is investigated. By using Krasnoselskii’s fixed point theorem on cones, sufficient conditions for the existence of at least one positive solutions are obtained.</abstract>

Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), Department of Mathematics, University of Oran 1 Ahmed Benbella, 31000 Oran,

Department of Physics, University of Sciences and Technology of Oran-MB, El Mnaouar, BP 1505, 31000 Oran, Algeria; Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), Department of Mathematics, University of Oran 1 Ahmed Benbella, 31000 Oran,

Positive Solutions of a Nonlinear Fourth-order Integral Boundary Value Problem

<abstract><title style='display:none'>Abstract</title> In this paper we consider the following problems: (1) Which weakly Picard operators satisfy a retraction- displacement condition? (2) For which weakly Picard operators the fixed point problem is well posed? (3) Which weakly Picard operators have Ostrowski property? Some applications and open problems are also presented. </abstract>

Relevant Classes of Weakly Picard Operators

<abstract><title style='display:none'>Abstract</title> In this paper we shall introduce two equivalent techniques in order to evaluate reliability analysis of electrical aircrafts systems (EAS): (i) graph theory technique, and (ii) simplifying diffeomorphism technique. Geometric modeling of reliability models is based on algebraic hypersurfaces, whose intrinsic properties are able to select those models which are relevant for applications. The basic idea is to cover the reliability hypersurfaces by exponentially decay curves. Most of the calculations made in this paper have used Maple and Matlab software. </abstract>

Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Babylon, Iraq

Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, RO-060042, Bucharest, Romania

Equivalent reliability polynomials modeling EAS and their geometries

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Annals of West University of Timisoara - Mathematics and Computer Science

The Journal of West University of Timisoara

 Annals of West University of Timisoara - Mathematics and Computer Science, first issued in 1963, publishes peer-reviewed original and quality papers in all branches of Mathematics and...

 Annals of West University of Timisoara - Mathematics and Computer Science, first issued in 1963, publishes peer-reviewed original and quality...

Annals of West University of Timisoara - Mathematics and Computer Science

The Journal of West University of Timisoara

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