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

Foreword

The Editorial Office of Series III — 2024-09-03

No abstract

Influence of gravity and mechanical strip load on micropolar thermoelastic medium in the context of multi-temperatures theory

E.M. Abd-Elaziz — 2024-09-03

A new model of multi-temperatures for a generalized micropolar thermoelastic medium has been established in this paper. A medium is affected by a gravitational field and two types of mechanical strip load (continuous load and impact load). The technique called Laplace Fourier transform has been utilized to obtain the analytical expressions of variables under deliberation. The numerical and graphical illustration of the results has been carried out to indicate the differences among one temperature model, the classical dual-temperature model, and the hyperbolic dual-temperature model upon the Lord and Shulman theory. Also, in the case of Coupled Theory (CT) and Lord and Shulman's theory (L-S), we discussed the effect of the gravitational field and mechanical strip load. The most significant points are highlighted. The current investigation has led us to deduce some particular cases of special interest. When it comes to heat conduction’s new general model then this study will be extremely beneficial in developing a better understanding of the ingrained features.

A survey on perturbation invariance of quaternionic exponentially dichotomous operators

R.P. Agarwal — 2024-09-03

In this review paper, we present some basic notions and properties of quaternionic exponentially dichotomous operators. Some perturbation results of quaternionic exponentially dichotomous operators are illustrated which will help to consider the exponential dichotomous solutions to quaternionic evolution equations through semigroup theory.

Asymptotic partition of energies for a Cosserat thermoelastic medium

H. Altenbach — 2024-09-03

The main aim of this study is to obtain a partition of the asymptotic type of energy of a solution for the mixed problem considered in the context of the Cosserat thermoelastic media. The concept of asymptotic equipartition is a notion, frequently used, for differential equations theory. In a simple formulation, this concept is formulated as follows: potential and kinetic energy, for a classical solution with finite energy, tend to become asymptotically equal on average, when time tends to infinity.

Parametrized trigonometric derived Lp degree of approximation by various smooth integral operators

George A. Anastassiou — 2024-09-03

In this work we continue with the study of smooth Gauss-Weierstrass, Poisson-Cauchy, and trigonometric singular integral operators that started in [Anastassiou, G.A., Intelligent Mathematics: Computational Analysis, Springer, Heidelberg, New York, Chapter 12, 2011], see there chapters 10-14. This time the foundation of our research is a trigonometric Taylor’s formula. We prove the parametrized univariate Lp convergence of our operators to the unit operator with rates via Jackson-type parametrized inequalities involving the first Lp modulus of continuity. Of interest here is a residual appearing term. Note that our operators are not in general positive.

Exact solitary wave solutions of time fractional nonlinear evolution models: a hybrid analytic approach

M.M. Bhatti — 2024-09-03

In this article, we propose efficient techniques for solving fractional differential equations such as KdV-Burgers, Kadomtsev-Petviashvili, Zakharov- Kuznetsov with less computational efforts and high accuracy for both numerical and analytical purposes. The general exp_a-function method is employed to reckon with new exact solitary wave solutions of time-fractional nonlinear evolution equations (NLEEs) stemming from mathematical physics. Fractional complex transformation in conjunction with a modified Riemann-Liouville operator is used to tackle the fractional sense of the accompanying problems. A comparison between the existing conventional exp-function method and the improved exp-function method shows that the proposed recipe is more productive in terms of obtaining analytical solutions. The graphical depictions of extracted information show a strong relationship between fractional-order outcomes with those of classical ones.

Spatial behaviour in type III thermoelasticity with two porous structures

Adina Chirila — 2024-09-03

This article is about the spatial behaviour in one-dimensional type III thermoelasticity with two voids structures, with porous dissipation in one of the voids components. After deriving a preliminary integral identity of the Lagrange-Brun type, we prove the main results with the help of a timeweighted function.

On a Kuramoto-Velarde type equation

G.M. Coclite — 2024-09-03

Kuramoto-Velarde-type equations describe the evolution of the spinodal decomposition of phase-separating systems in an external field, or, the spatiotemporal evolution of the morphology of steps on crystal surfaces. Under appropriate assumptions on the initial data, on the time T, and on the coefficients of such equation, we prove the well-posedness of the classical solutions for the Cauchy problem, associated with this equation.

Analysis of a dynamic electro-viscoelastic contact problem

M.S. Ferhat — 2024-09-03

In this work, we analyze a mathematical problem for dynamic contact between two electro-viscoelastic bodies with adhesion, normal compliance, and damage. An inclusion of the parabolic type describes the evolution of damage. A first-order differential equation explains the development of the bonding field. We create a variational formulation for the model and demonstrate the existence and uniqueness of the weak solution. Parabolic inequalities, variational inequalities, and the Banach fixed point theorem form the foundation for the proof.

Permanent solutions for some MHD motions of generalized Burgers fluids through a porous medium in cylindrical domains

Constantin Fetecau — 2024-09-03

Some isothermal motions of the incompressible generalized Burgers fluids in cylindrical domains are investigated when the magnetic and porous effects are taken into consideration. Analytical expressions are established for the dimensionless steady-state velocity fields corresponding to motions between two infinite horizontal coaxial circular cylinders. The respective motions are generated by oscillatory or constant pressure gradients which act along the common axis of cylinders. Similar velocities for motions through an infinite circular cylinder are obtained as limiting cases of previous solutions. All results can be easily particularized to give similar solutions for the incompressible Burgers, Oldroyd-B, Maxwell, and Newtonian fluids. Finally, some numerical results are graphically represented and discussed. It was found that the fluid velocity diminishes with increasing values of the magnetic and porous parameters. It means the fluid moves slower in the presence of a magnetic field or porous medium.

Norm attaining multilinear forms on ℝn with the l1-norm

Sung Guen Kim — 2024-09-03

Let n,m ∈ ℕ with n,m ≥ 2. For given unit vectors x₁, ・・・ , x_n of a real Banach space E, we define NA(L(ⁿE))(x₁, ・・・ , x_n) = {T ∈ L(ⁿE) : |T(x₁, ・・・ , x_n)| = ∥T∥ = 1}, where L(ⁿE) denotes the Banach space of all continuous n-linear forms on E endowed with the norm ∥T∥ = sup_{∥xk∥=1,1≤k≤n} |T(x₁, . . . , x_n)|. In this paper, we present a characterization of the elements in the set NA(L(^mℓⁿ₁ ))(W₁, ・・・ ,W_m) for any given unit vectors W₁, . . . ,W_m ∈ ℓⁿ₁ , where ℓⁿ₁ = ℝⁿ with the ℓ_1-norm. This result generalizes the results from [7], and two particular cases for it are presented in full detail: the case n = 2, m = 2, and the case n = 3, m = 2.

Matrix representation of (d, k) - Fibonacci polynomials

B. Kuloglu — 2024-09-03

In this study, we define the (d, k)− Fibonacci polynomial and examine its properties. We give the generating function, characteristic equation, and matrix representation of this polynomial. Then we get the infinite sum for the (d, k)− Fibonacci polynomials. We give the relationship between (d, k)− Fibonacci polynomial and d− Fibonacci polynomial. Also, with the help of (d, k)− Fibonacci polynomial matrix representation and the Riordan matrix, the factorization of the Pascal matrix in two different ways is given. In addition, we define the infinite (d, k)− Fibonacci polynomial matrix and give their inverses. The Riordan arrays linked here help us understand patterns of number concepts and prove many theorems, as well as help us make an intuitive connection for solving combinatorial problems. Among our main goals is to combine Riordan arrays with the Fibonacci number sequence, which is the most important of the number sequences, and to expand this study to the k-Fibonacci number sequence, which is the general form of Fibonacci number sequences. Based on the information given above, Riordan array and Pascal matrices, which have an important place in matrix theory and combinatorics studies also derived an encoding of Pascal’s triangle in matrix form, were discussed in this study and a very different generalization of the Fibonacci number sequence was studied.

On M-projective curvature tensor of Lorentzian β-Kenmotsu manifold

A.K. Mishra — 2024-09-03

In this paper, we explore the characteristics of Lorentzian β - Kenmotsu manifolds admitting M - projective curvature tensor. We demonstrate that M - projectively flat and irrotational M - projective curvature tensor of Lorentzian β - Kenmotsu manifolds are locally isometric to hyperbolic space Hⁿ(c), where c = −β². Further, we deal with the M - projectively flat Lorentzian β - Kenmotsu manifold that satisfies the condition R(X, Y )・S = 0. The Lorentzian β - Kenmostu manifold with conservative M - projective curvature tensor is the subject of our next analysis. Finally, we obtain certain geometrical facts if the Lorentzian β - Kenmotsu manifold satisfies the relation M(X, Y )・R = 0.

On the convergence of the Newton-Raphson method and some of its generalizations

Adriana Mitre — 2024-09-03

The article aims to improve the solving algorithms and methods of increasing the speed of convergence of the solution of nonlinear algebraic systems or even ill-conditioned, as well as some generalizations of the proposed method, in the sense of broadening the conditions of its application. These algebraic systems come, for example, from discretization with the method of finite elements of some boundary value problems that also contain nondifferentiable terms given by some boundary conditions and which are smoothed using the regularization methods. To solve these algebraic systems, an incremental-iterative algorithm is chosen, which involved a great computational effort, but proved to be useful. These proposed algorithms can simulate the evolution in time of some processes, such as quasistatic or dynamic cases, and the article proves that the use of the Newton- Raphson method and generalizations lead to an increase in the speed of convergence with a decrease in the calculation effort and to broadening the conditions of applicability.

Sharp bounds of logarithmic coefficients for a class of univalent functions

M. Obradovic — 2024-09-03

Let U(α, λ), 0 < α < 1, 0 < λ < 1, be the class of functions f(z) = z + a₂z² + a₃z³ + ・・・ satisfying |(z/f(z))^1+α f ′(z) − 1|< λ in the unit disc D. For f ∈ U(α, λ) we give sharp bounds of its initial logarithmic coefficients γ₁, γ₂, γ₃.

A simplified teaching approach to the classical laminate theory of layered composite materials

Andreas Ochsner — 2024-09-03

The classical laminate theory is a common engineering approach to investigate the mechanical response of layered composite materials. This two-dimensional approach and the underlying continuum mechanical modeling might be very challenging for some students, particularly at universities of applied sciences. Thus, a reduced approach, the so-called simplified classical laminate theory, has been developed. The idea is to use solely isotropic one-dimensional elements, i.e., a superposition of bar and beam elements, to introduce the major calculation steps of the classical laminate theory. Understanding this simplified theory is much easier and the final step is to highlight the differences when moving to the general two-dimensional case.

On Marx-Strohacker type results for multivalent functions and their nth root

Dorina Raducanu — 2024-09-03

Two Marx-Strohhacker type results for multivalent functions and their nth root are given. Both results provide a lower bound over the unit disk of ℜ ⁿ√f(z)/z^p for functions that are p-valent starlike of a given order and uniformly p-valent starlike of a given order, respectively. Connections with previous results are indicated.

Regularity of the solutions to quasi-linear parabolic systems with the singular coefficients

Mykola Ivanovich Yaremenko — 2024-09-03

This article establishes the regularity properties of solutions to the parabolic quasilinear parabolic systems in the divergent form

∂/∂_t⃗u, −d/dx_i⃗ai (x, t, ⃗u, ∇⃗u) +⃗b (x, t, ⃗u, ∇⃗u) = 0,

under rather general conditions on its coefficients. To prove solvability, we apply the Leray-Schauder theory and method of apriori estimations.