Editorial

<abstract xmlns="http://www.w3.org/1999/xhtml">

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 xmlns="http://www.w3.org/1999/xhtml">

The aim of this paper is to study a frictional contact problem between an elastic body and a foundation. We focus on the optimal control of the model which consists of acting with a control on a portion of the boundary of the body and leading the stress tensor as close as possible to a given target. We state an optimal control problem for which we establish an existence theorem of the solution. We then introduce a sequence of regularized problems depending on a positive parameter <italic>α</italic> and we study the convergence of the sequence of the solutions when the parameter <italic>α</italic> tends to zero. Finally, an optimality condition is established for this problem.
</abstract>

Optimal control of a contact problem with slip dependent friction

<abstract xmlns="http://www.w3.org/1999/xhtml">

Let 𝒜 <italic>p </italic>be the class of functions <italic>f</italic> of the form <disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_awutm-2022-0004_eq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>z</mi></mrow><mi>p</mi></msup><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>p</mi><mo>+</mo><mn>1</mn></mrow></msub><msup><mrow><mi>z</mi></mrow><mrow><mi>p</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>p</mi><mo>+</mo><mn>2</mn></mrow></msub><msup><mrow><mi>z</mi></mrow><mrow><mi>p</mi><mo>+</mo><mn>2</mn></mrow></msup><mo>+</mo><mo>⋯</mo></mrow></math>
<tex-math>f\left( z \right) = {z^p} + {a_{p + 1}}{z^{p + 1}} + {a_{p + 2}}{z^{p + 2}} + \cdots</tex-math>
</alternatives>
</disp-formula> that are analytic in the open unit disk 𝕌. For <italic>f</italic> ∈ 𝒜 <italic>p</italic>, new integral and differential operator <italic>nf</italic> is considered. The object of the present paper is to discuss some interesting properties of <italic>nf</italic> and to consider some examples for our results.
</abstract>

Department of Mathematics and Computer Science, Faculty of Science and Letters

Department of Mathematics, Faculty of Science

Honorary Professor of “1 Decembrie 1918” University of Alba Iulia

Generalizations of Libera integral operator for analytic functions

<abstract xmlns="http://www.w3.org/1999/xhtml">

The aim of this paper is to give sufficient conditions for Ψ − conditional exponential 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 Exponential Asymptotic Stability of a Nonlinear Lyapunov Matrix Differential Equation with Integral Term as Right Side

<abstract xmlns="http://www.w3.org/1999/xhtml">

The object of the present article is to study the notion of <italic>η</italic>-Einstein-like LP-Sasakian manifolds admitting <italic>η</italic>-Ricci soliton. Furthermore, we study the <italic>η</italic>-Ricci soliton on LP-Sasakian manifolds when the potential vector field <italic>V</italic> is point-wise collinear.
</abstract>

<italic>η</italic>-Ricci soliton on <italic>η</italic>-Einstein-like LP-Sasakian manifolds

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this article, we study THA-surfaces in the Galilean space 𝔾3, which has finite type immersion.
</abstract>

THA-surfaces of finite type in the Galilean space 𝔾3

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper we show that, if that the function <italic>f</italic> : [0, ∞) → 𝔾 is operator monotone in [0, ∞) then there exist <italic>b</italic> ≥ 0 and a positive measure <italic>m</italic> on [0, ∞) such that <disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_awutm-2022-0008_eq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable columnalign="left"><mtr columnalign="left"><mtd columnalign="left"><mrow><mrow><mo>[</mo> <mrow><mi>f</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow><mo>-</mo><mi>f</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mrow> <mo>]</mo></mrow><mrow><mo>(</mo><mrow><mi>B</mi><mo>-</mo><mi>A</mi></mrow><mo>)</mo></mrow><mo>=</mo></mrow></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mrow><mo>=</mo><mi>b</mi><msup><mrow><mrow><mrow><mo>(</mo><mrow><mi>B</mi><mo>-</mo><mi>A</mi></mrow><mo>)</mo></mrow></mrow></mrow><mn>2</mn></msup><mo>+</mo><mrow><msubsup><mo>∫</mo><mn>0</mn><mo>∞</mo></msubsup><mrow><msup><mrow><mi>s</mi></mrow><mn>2</mn></msup><mrow><mo>[</mo> <mrow><mrow><msubsup><mo>∫</mo><mn>0</mn><mn>1</mn></msubsup><mrow><msup><mrow><mrow><mrow><mo>[</mo> <mrow><msup><mrow><mrow><mrow><mo>(</mo><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>-</mo><mi>t</mi></mrow><mo>)</mo></mrow><mi>A</mi><mo>+</mo><mi>t</mi><mi>B</mi><mo>+</mo><mi>s</mi></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mrow><mi>B</mi><mo>-</mo><mi>A</mi></mrow><mo>)</mo></mrow></mrow> <mo>]</mo></mrow></mrow></mrow><mn>2</mn></msup><mi>d</mi><mi>t</mi></mrow></mrow></mrow> <mo>]</mo></mrow><mi>d</mi><mi>m</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></mrow></mrow></mrow></mtd></mtr></mtable></mrow></math>
<tex-math>\matrix{ {\left[ {f\left( B \right) - f\left( A \right)} \right]\left( {B - A} \right) = } \hfill \cr { = b{{\left( {B - A} \right)}^2} + \int_0^\infty {{s^2}\left[ {\int_0^1 {{{\left[ {{{\left( {\left( {1 - t} \right)A + tB + s} \right)}^{ - 1}}\left( {B - A} \right)} \right]}^2}dt} } \right]dm\left( s \right)} } \hfill \cr }</tex-math>
</alternatives>
</disp-formula> for all <italic>A, B</italic> > 0. Some necessary and sufficient conditions for the operators <italic>A, B</italic> > 0 such that the inequality <disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_awutm-2022-0008_eq_002.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>f</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow><mi>B</mi><mo>+</mo><mi>f</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mi>A</mi><mo>≥</mo><mi>f</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mi>B</mi><mo>+</mo><mi>f</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow><mi>A</mi></mrow></math>
<tex-math>f\left( B \right)B + f\left( A \right)A \ge f\left( A \right)B + f\left( B \right)A</tex-math>
</alternatives>
</disp-formula>
holds for any operator monotone function <italic>f</italic> on [0, ∞) are also given.
</abstract>

Some inequalities for operator monotone functions

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we are concerned with a class of nonlinear fractional differential equation with delays. By means of the contraction mapping principle, we prove the existence of a unique solution and investigate the continuous dependence of the solution upon the initial data and two types of Ulam stability: Ulam-Hyers and Ulam-Hyers-Rassias ones. Then, we give an example to illustrate the main results.
</abstract>

Existence and stability for a semilinear fractional differential equation with two delays

<abstract xmlns="http://www.w3.org/1999/xhtml">

We consider the development of the direct method for the numerical solution of second order differential equations and corresponding initial value problems. Our technique based on the method of finite difference approximations. We obtain a quadratic order accurate an explicit method using the set of initial conditions in a natural way and approximations for the approximate numerical solution after the discretization of the continuous problem under appropriate conditions. We discuss the development of the method and the periodic property of the solution of the problem. In the numerical experiment, we consider both linear and nonlinear model problems to test the efficiency and accuracy of the method. The tabulated numerical results in computational experiments approve the quadratic order accuracy and efficiency of the method.
</abstract>

An explicit second order uniformly convergent difference algorithm for an initial value problem associated to second order differential equations

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Annals of West University of Timisoara - Mathematics and Computer Science

 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 Computer Science. The works devoted to interdisciplinary topics and relevant applications are also considered. The journal publishes research papers, expository papers and also short notes. Generally, the survey papers are only invited articles. The papers must be new, correct and of interest relative to the recent advances in the fields of Mathematics and Computer Science. Proposals for special issues are welcome and should be sent to the Editor-in-Chief. From volume 2023 Annals of West University of Timisoara - Mathematics and Computer Science publishes in a continuous model.     Why subscribe and read   It publishes original papers in all areas of Mathematics and Computer Science   Why submit    Fast and constructive peer-review   It publishes research papers, surveys and book reviews in any topic belonging to Mathematics or Computer Science      Rejection Rate    30%      Archiving   Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.   Plagiarism Policy   The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. Target Group    - researchers in all branches of mathematics and computer science 