Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science

Foreword

The Editorial Office of Series III — 2023-12-18

No abstract

Paltanea’s operators: old and new results

U. Abel — 2023-12-18

This note concerns the study of an approximation linear positive process introduced by R. Paltanea in 2008. Considering the impact of this class of operators that depends on two parameters, in a distinct section we present a brief radiograph of the main properties highlighted over time in various papers. Our contribution materializes in the definition and study of the approximation properties of the King variant of these operators.

Bernstein polynomials and dual functionals

A.-M. Acu — 2023-12-18

The divided differences of Bernstein polynomials were investigated by Alexandru Lupas in 1995. We extend the results of that investigation. Moreover, we establish new relations between them and the theory of dual functionals.

(p,q)-Post-Widder operators of semi exponential type

G. Agrawal — 2023-12-18

We deal here with the (p, q)-variant of the Post-Widder operators of semiexponential type. By using the basic properties of post-quantum properties, we calculate the moments of these operators and obtain some direct findings for such (p, q)-semi-exponential Post-Widder operators.

q-Deformed and λ-parametrized A-generalized logistic function based Banach space valued ordinary and fractional neural network approximation

George A. Anastassiou — 2023-12-18

Here we research the univariate quantitative approximation, ordinary and fractional, of Banach space valued continuous functions on a compact interval or all the real line by quasi-interpolation Banach space valued neural network operators. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged function or its Banach space valued high order derivative of fractional derivatives. Our operators are defined by using a density function generated by a q-deformed and λ-parametrized A-generalized logistic function, which is a sigmoid function. The approximations are pointwise and of the uniform norm. The related Banach space valued feed-forward neural networks are with one hidden layer.

Numerical approximations and asymptotic limits of some nonlinear problems

A. Ben Mabrouk — 2023-12-18

In the present work, a numerical approach is dedicated to the approximation to the solutions of a time-independent nonlinear Schr¨odinger equation in a mixed case provided with numerical tests on the asymptotic limits of the solution according to some parameters. A finite difference discretization with calibrations is applied leading to a quasi-linear algebraic system. where the its solvability is investigated as well as its stability and convergence via Von Neumann method. Some numerical experiments are developed to validate the result, and to test the effect of some parameters on the asymptotic limit of the problem.

On a Hilfer type fractional integro-differential inclusion

Aurelian Cernea — 2023-12-18

A boundary value problem associated to a Hilfer generalized proportional fractional integro-differential inclusion is studied. The existence of solutions is established in the case when the set-valued map has nonconvex values.

Plane strain of isotropic micropolar bodies with pores

Iana M. Fudulu — 2023-12-18

The aim of this work is defined by the study of the plane deformation for micropolar isotropic materials in equilibrium theory, where, in addition to displacement and absolute temperature, the particles of the mentioned materials have pores and microrotations.The determined solution to the field equations helps us to study the effect of heat sources and pores on the deformation of the body, which deformation is studied later.

Semi-discrete Voronovskaya-type theorem for positive linear operators based on Hermite interpolation with two double knots

Sorin G. Gal — 2023-12-18

Since the classical asymptotic theorems of Voronovskaya-type for positive and linear operators are in fact based on the Taylor’s formula which is a very particular case of Lagrange-Hermite interpolation formula, in the recent paper Gal [3], I have obtained semi-discrete quantitative Voronovskaya-type theorems based on other Lagrange-Hermite interpolation formulas. These include Lagrange interpolation on two and three simple knots and Hermite interpolation on two knots, one simple and the other one double. In the present paper we obtain a semi-discrete quantitative Voronovskaya-type theorems based on Hermite interpolation on two double knots.

A weak solution to a Kirchhoff type problem with discontinuous nonlinearities

A. Kassidi — 2023-12-18

This paper is devoted to the study of a class of Kirchhoff-type problems with discontinuous nonlinearities with Neumann boundary data. Here, by employing the topological degree methods for the abstract Hammerstein equation, we establish the existence of at least one solution.

On geometrically convex functions with some applications

N. Minculete — 2023-12-18

This paper aims to present several new properties of geometrically convex functions similar to some those known properties for convex functions. Finally, we show some improvements of Young’s inequality.

Logarithmic coefficients for a class of analytic functions defined by subordination

A. Nistor-Șerban — 2023-12-18

In this paper we consider a class of functions Mα(φ) defined by subordination, consisting of functions f ∈ A satisfying the condition (1 −α) zf′(z)/ f(z) + α (1 + zf′′(z)/ f′(z) )≺ φ(z), z ∈ U. In the study of univalent functions, estimates on the Taylor coefficients are usually given. Another significant problem deals with the estimates of logarithmic coefficients. For the class S of univalent functions no sharp bounds for the modulus of the individual logarithmic coefficients are known if n ≥ 3. For different subclasses of S the results are not better and in most cases only th e first three initial coefficients of log f(z)/z are considered. For the class Mα(φ) we obtain upper bounds for the logarithmic coefficients γ_n, n ∈ {1, 2, 3} and also for Γ_n, n ∈ {1, 2, 3}, the logarithmic coefficients of the inverse of Mα(φ). Connections with previous known results are pointed out.

On the iterates of uni-and multidimensional operators

Radu Precup — 2023-12-18

The problem of the convergence of the iterates of operators or of a sequence of operators is discussed in a general framework related to the fixed point theory, but with a permanent look towards the theory of linear approximation operators. The results are obtained for operators not necessarily linear. Some examples including the class of approximation operators defined by H. Brass are given.

On a third-order modulus of smoothness

Maria Talpau Dumitru — 2023-12-18

In this paper we define a new third-order modulus of smoothness and we prove the conservation by Stancu operators of the Lipschitz classes defined with this modulus.

Considerations on efficient lexical analysis in the context of compiler design

A. Baicoianu — 2023-12-18

Each programming language needs a mechanism of translating source code into code understood by the computer, i.e., machine code or assembly. This is done by a compiler. A compiler is thus a fundamental tool for software development. Lexical analysis, as the first step of compilation, has an important role and should be performed in an optimal way. But not only compilers rely on lexical analysis. Its role lies nowadays also in pattern recognition or natural language processing. In this paper, we present some of the main aspects of lexical analysis and how to efficiently perform it. Our aim is to offer some guidelines in constructing a modern and efficient scanner (lexer), outlining the criteria, which should be considered, presenting some pitfalls, and comparing existent tools for compiler construction. The main contribution of the paper is to offer practical guidelines and recommendations, especially to graduate students and programmers, in constructing an efficient scanner (lexer), considering also the proper tools currently available.

Tetra geoemtric mean Runge-Kutta analysis of bioeconomic fisheries model

V. Chauhan — 2023-12-18

The optimal management and utilization of natural resources is eventually important, due to increase in the consumption of natural resources and in view of this, the main aim of fisheries is to maintain the marine organisms at levels that produces maximum sustainable yield (MSY). In this study, the one step numerical approximations schemes are developed to find the solution of such bioeconomic fisheries models whose analytical solution is not possible. In the proposed work, the explicit Runge-Kutta scheme based on fourth order tetra geometric mean is established and this method solve fishery management models of Schaefer and Gordon-Schaefer. The models analyze bioeconomic growth rate, carrying capacity, total and marginal costs and revenues. In solving, the models through proposed tetra geometric mean Runge-Kutta method, it is obtained that the method is easy to implement. The results obtained are much better as compared to other methods when compared in terms of errors and central processing unit (CPU) time.

Non-linear model of the macroeconomic system dynamics: multiplier-accelerator

O. Dorokhov — 2023-12-18

The article discusses one of the classic problems of macroeconomic dynamics, on which the neo-Keynesian theory of growth is based, so that the interaction between the multiplier and the accelerator. A new approach was proposed to develop a mathematical model of the dynamics of the mutual multiplier, which indicates the marginal propensity to save as a result of the GDP growth, and the accelerator, which reflects the growth of capital of the national income in the multiplier. The model is based on the hypothesis of non-linear dependence of the consumption on the amount of profit. This assumes that consumption growth is limited, i.e., a saturation effect occurs. In addition, the model took into account the delayed reaction of the accelerator to the influence of the multiplier. Under building the model, the considered processes were considered continuous in time. This made it possible to provide the mathematical model ”accelerator - multiplier” as a system of two differential equations of the first order. The application of the developed model to the analysis of the dynamic properties of the macroeconomic system makes it possible to evaluate the parameters at which the ”multiplier-accelerator” system enters a critical state. It has been proven that the conditions for the occurrence of self-oscillations depend on the critical value of the accelerator power. The presence of a two-fold limit cycle with corresponding ”soft” and ”hard” modes of birth (death) of the limit cycle was also founded. The applied usefulness of the model is that the choice of management decisions taking into account these results allow us preventing the occurrence of bifurcations and disasters in the process of evolution of the macroeconomic systems.

The power of SymPy for programming in geometry

Ernest Scheiber — 2023-12-18

For didactic purposes the capabilities of SymPy to solve synthetic geometrical problems are highlighted. There is exemplified the Apollonius problem: construct a circle tangent to other three circles. The problem is solved using inversion and some code is provided.

A comprehensive application architecture for unlocking the potential of student feedback

D. Simian — 2023-12-18

This article proposes a novel solution aimed at streamlining the student feedback, enabling them to assess various aspects and activities within their institution. Different from the classical solution of collecting students feedback using a set of questions grouped in one or many forms, we designed a solution capable to empower students of all age groups to enhance their higher education experiences by openly expressing opinions about their enrolled faculties, providing valuable guidance to prospective college students. Our proposal introduces a generic application architecture designed to integrate the presentation of the main opportunities and offers from many universities with the student reviews on all aspects of these universities. Thus, we avoid a number of factors that reduce the quantity and objectivity of student feedback. Important elements in our architecture refer to reviewing and rating system as well as the search system which facilitate the use of the existing evaluations on different aspects of an university. We devised a generic architecture for a client-server application, specifying a minimum set of required functionalities. For validation, we designed and implemented a client-server application based on the generic architecture we outlined. The application offers several key advantages, including robust information security measures, and diverse communication channels for authenticated users within the platform. The application’s architecture includes an encryption system based on multiple encryption techniques. Additionally, an algorithm for search optimization within the platform have been developed, further enhancing its utility.

Advances in CUDA for computational physics

Delia Spiridon — 2023-12-18

Advances in the graphics processing unit (GPU) development led to the opportunity for software developers to increase the execution speed for their programs by massive parallelization of the algorithms using GPU programming. NVIDIA company developed an arhitecture for parallel computing named Compute Unified Device Architecture (CUDA) which includes a set of CUDA instructions and the hardware for parallel computing. Computational Physics is an interdisciplinary field which is in continuous progress and which studies, develops and optimizes numerical algorithms and computational techniques for their application in solving various physics problems. Computational Physics has applicability in all sub-branches of physics and related fields such as: biophysics, astrophysics, plasma physics, biomechanics, fluid physics, etc. Moreover, with the evolution of technology in the last few decades, this relatively new field has helped to quickly obtain results in these fields, facilitating the connection between theoretical and experimental physics. In this paper, some of the latest researches and results obtained in computational physics by using GPU computing with CUDA architecture are reviewed.