rss_2.0Sciendo RSS Feed for Annals of West University of Timisoara - Mathematics and Computer Sciencehttps://sciendo.com/journal/AWUTMhttps://www.sciendo.comhttps://sciendo-parsed.s3.eu-central-1.amazonaws.com/6470cfba71e4585e08aa61a8/cover-image.jpghttps://sciendo.com/journal/AWUTM140216https://sciendo.com/article/10.2478/awutm-2024-0010<abstract><title style='display:none'>Abstract</title> <p>Some work has been done in the study of non-geodesic III-harmonic curves in some model spaces. In this paper, we study III-harmonic curves in <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_awutm-2024-0010_eq_002.png"/> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mtext>SL</mml:mtext></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:mi>ℝ</mml:mi></mml:mrow><mml:mo stretchy="true">˜</mml:mo></mml:mover></mml:mrow></mml:math> <tex-math>\widetilde {{\rm{S}}{{\rm{L}}_2}\mathbb{R}}</tex-math> </alternatives> </inline-formula> space. We give necessary and su cient conditions for helices to be III-harmonic. Also, we characterize III-harmonic curves in terms of their curvature and torsion.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2024-00102024-12-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2024-0009<abstract> <title style='display:none'>Abstract</title> <p>The aim of this paper is to develop, via the least squares variational method, the Lagrange-Hamilton geometries (in the sense of nonlinear connections, d-torsions and Lagrangian Yang-Mills electromagnetic-like energy) produced by Pikovsky-Rabinovich dynamical system from cryptography. From a geometrical point of view, the Jacobi stability of the Pikovsky-Rabinovich system is discussed.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2024-00092024-11-21T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2024-0008<abstract> <title style='display:none'>Abstract</title> <p>Over the last decade, we have witnessed the emergence of numerous online social media platforms and a growing research interest in understanding their underlying structures and mechanisms. This paper investigates the formation and evolution of the EcoNation social media platform, which is designed to foster collaboration for environmental sustainability.</p> <p>The network structure of EcoNation is introduced and analyzed using a comprehensive dataset covering the platform’s initial years of development. This analysis is conducted using the social network analysis toolbox, which enables the exploration of various aspects of user interactions, connectivity, and engagement patterns. By delving into the data, the aim is to uncover the dynamics that drive the growth and development of EcoNation’s network.</p> <p>The dataset includes information on user registrations, actions performed, validations, and connections formed over time. By examining this data, key trends and behaviors that have shaped the platform’s evolution can be identified. To facilitate further research and enable other scholars to build on this paper’s findings, the exported data was made publicly available.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2024-00082024-09-20T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2024-0007<abstract> <title style='display:none'>Abstract</title> <p>The Penguin Search Optimization (PeSOA) is an optimization method based on collaborative hunting strategy of penguins. In this work, a solving linear equation systems method based on PeSOA is proposed. A dual population for PeSOA part was also tested. Experimental results obtained with our proposed method compared with those obtained with classical math methods, showed positive perspectives regarding possible extensions of the proposed method for systems of equations of larger dimensions. Conclusions as well as future research directions are also included.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2024-00072024-09-07T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2024-0006<abstract> <title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2024-00062024-07-05T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2024-0005<abstract> <title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2024-00052024-06-11T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2024-0004<abstract> <title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2024-00042024-06-07T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2024-0003<abstract> <title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2024-00032024-03-02T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2024-0002<abstract> <title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2024-00022024-03-02T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2024-0001<abstract> <title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2024-00012024-02-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2023-0012<abstract> <title style='display:none'>Abstract</title> <p>Along this paper, we study an evolution inclusion governed by the so-called sweeping process. The right side of the inclusion contains a set-valued perturbation, supposed to be the external forces exercised on the system. We prove existence and relaxation results under weak assumptions on the perturbation by taking a truncated Lipschitz condition. These perturbations have non-convex and unbounded values without any compactness condition; we just assume a linear growth assumption on the element of minimal norm. The approach is based on the construction of approximate solutions. The relaxation is obtained by proving the density of the solution set of the original problem in a closure of the solution set of the relaxed one.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00122023-12-01T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2023-0011<abstract> <title style='display:none'>Abstract</title> <p>This paper deals with the existence and uniqueness of common fixed points in metric and dislocated metric spaces. In addition, an application and some illustrative examples are given in order to justify the validity and credibility of our results, also, their superiority over some similar theorems existing in unique common fixed points theory’s domain.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00112023-09-21T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2023-0010<abstract> <title style='display:none'>Abstract</title> <p>The paper studies a Cournot game involving <italic>n</italic> private firms, where the firms’ interactions are analyzed in a discrete-time setting with time delay. The past production levels of other private firms have an impact on the production levels of each private firm. We performed a local stability analysis on the nonlinear system associated with the model and found that it has only one equilibrium point, which is asymptotically stable if and only if some conditions involving the number of firms, the degree of product di erentiation and the time delay are fulfilled. In addition, numerical examples are presented in this paper, which illustrate the theoretical results obtained.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00102023-09-21T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2023-0009<abstract> <title style='display:none'>Abstract</title> <p>In this article, our aim is to study analytic functions related with Salagean operator and associated with the right half of the lemniscate of Bernoulli. We find the estimates of the third Hankel determinant for new family of analytic functions. It is important to mention that our results generalize a number of existence results in the literature.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00092023-07-31T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2023-0008<abstract> <title style='display:none'>Abstract</title> <p>In this paper we consider three concepts of uniform dichotomy in mean for stochastic skew-evolution semiflows: uniform exponential dichotomy in mean, uniform polynomial dichotomy in mean and uniform <italic>h</italic>- dichotomy in mean. Some characterizations of these notions and connections between these concepts are given. The obtained results can be considered generalizations to the dichotomy case of the results from [29].</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00082023-07-31T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2023-0002<abstract> <title style='display:none'>Abstract</title> <p>In this review paper, we recall, in a unifying manner, our recent results concerning the Lie symmetries of nonlinear Fokker-Plank equations, associated to the (weighted) Tsallis and Kaniadakis entropies. The special values of the Tsallis parameters, highlighted by the classification of these symmetries, clearly indicate algebraic and geometric invariants which differentiate the Lie algebras involved. We compare these values with the ones previously obtained by several authors, and we try to establish connections between our theoretical families of entropies and specific entropies arising in several applications found in the literature.</p> <p>We focus on the discovered correlations, but we do not neglect dissimilarities, which might provide -in the future-deeper details for an improved extended panorama of the Tsallis entropies.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00022023-05-03T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2023-0001ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00012023-05-03T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2023-0003<abstract> <title style='display:none'>Abstract</title> <p>In this paper we prove among others that, if (<italic>A_j</italic>)_{<italic>j</italic>=1,...,<italic>m</italic>} are positive definite matrices of order <italic>n</italic> ≥ 2 and <italic>q_j</italic> ≥ 0, <italic>j</italic> = 1, ..., <italic>m</italic> with <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_awutm-2023-0003_eq_001.png"/><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="M1"><mml:mstyle displaystyle="true"><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:msubsup><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mstyle></mml:math><tex-math>$$\sum\nolimits_{j = 1}^m {{q_j} = 1} $$</tex-math></alternatives></inline-formula>, then <disp-formula id="j_awutm-2023-0003_eq_002"><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_awutm-2023-0003_eq_002.png"/><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block" id="M2"><mml:mtable columnalign="left"><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mn>0</mml:mn></mml:mtd><mml:mtd columnalign="left"><mml:mrow><mml:mo>≤</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>min</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>∈</mml:mo><mml:mo>{</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo>}</mml:mo></mml:mrow></mml:msub><mml:mrow><mml:mo>{</mml:mo> <mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow> <mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:mtd></mml:mtr><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mo>×</mml:mo></mml:mtd><mml:mtd columnalign="left"><mml:mrow><mml:mrow><mml:mo>[</mml:mo> <mml:mrow><mml:munderover><mml:mrow><mml:msup><mml:mo>∑</mml:mo><mml:mtext>​</mml:mtext></mml:msup></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:msub><mml:mi>q</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>[</mml:mo> <mml:mrow><mml:mi>det</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow> 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<mml:mrow><mml:mi>det</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:munderover><mml:mrow><mml:msup><mml:mo>∑</mml:mo><mml:mtext>​</mml:mtext></mml:msup></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:msub><mml:mi>q</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow> <mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mo>≤</mml:mo></mml:mtd><mml:mtd 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<mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow> <mml:mo>]</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math> <tex-math><?CDATA \begin{eqnarray}0 &#x0026; \le \frac{1}{1-{\min }_{i\in \{1,\ldots ,m\}}\{{q}_{i}\}}\\ \times &#x0026; [\underset{i=1}{\overset{m}{{\sum }^{\text{}}}}{q}_{i}(1-{q}_{i}){[\det ({A}_{i})]}^{-1}-{2}^{n+1}\mathop{{\sum }^{\text{}}}\limits_{1\le i\lt j\le m}{q}_{i}{q}_{j}{[\det ({A}_{i}+{A}_{j})]}^{-1}]\\ \le &#x0026; \underset{i=1}{\overset{m}{{\sum }^{\text{}}}}{q}_{i}{[\det ({A}_{i})]}^{-1}-{[\det (\underset{i=1}{\overset{m}{{\sum }^{\text{}}}}{q}_{i}{A}_{i})]}^{-1}\\ \le &#x0026; \frac{1}{{\min }_{i\in \{1,\ldots ,m\}}\{{q}_{i}\}}\\ \times &#x0026; [\underset{i=1}{\overset{m}{{\sum }^{\text{}}}}{q}_{i}(1-{q}_{i}){[\det ({A}_{i})]}^{-1}-{2}^{n+1}\mathop{{\sum }^{\text{}}}\limits_{1\le i\lt j\le m}{q}_{i}{q}_{j}{[\det ({A}_{i}+{A}_{j})]}^{-1}].\end{eqnarray}?></tex-math></alternatives></disp-formula></p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00032023-05-03T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2023-0004<abstract> <title style='display:none'>Abstract</title> <p>The aim of this paper is to study the existence of the unique mild solution for non-linear fractional integro-differential equations with state-dependent nonlocal condition. The result was obtained by using nonlinear alternative of Granas-Frigon for contraction in Fréchet spaces. To illustrate the result, an example is provided.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00042023-05-03T00:00:00.000+00:00https://sciendo.com/article/10.2478/awutm-2023-0005<abstract> <title style='display:none'>Abstract</title> <p>Here we examine the multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝ^{<italic>N</italic>} , <italic>N</italic> ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are derived by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by a hyperbolic tangent like sigmoid function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/awutm-2023-00052023-05-03T00:00:00.000+00:00en-us-1