Advances in Mathematics: Scientific Journal

Journal Information
ISSN / EISSN : 1857-8365 / 1857-8438
Published by: Union of Researchers of Macedonia (10.37418)
Total articles ≅ 1,425
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A. Guemmaz, E.A. Djeffal, B. Bounibane
Advances in Mathematics: Scientific Journal, Volume 11, pp 453-471; https://doi.org/10.37418/amsj.11.5.3

Abstract:
In this paper, we consider primal-dual Interior Point Method $(IPMs)$ for semidefinite optimization problem $(SDO)$ problems, based on a new kernel function with a logarithmic barrier term, which play an important role for generating a new design of primaldual (IPM) algorithms. New search directions and proximity functions are proposed, based on this kernel function.We proved that our algorithm has $\mathbf{O}\left( qsn^{\frac{sq+1}{2sq}}\log \left( \frac{n}{\epsilon }\right) \right) $ iteration bound for large-update methods and $\mathbf{O}\left(q^{2}s^{2}\sqrt{n}\log \left( \frac{n}{\epsilon }\right) \right) $ iteration bound for small-update methods. Finally, for its numerical tests, some strategies are used and indicate that the algorithm is efficient.
H. Nacera, M. Tawfiq Fawzi, O. Hakim
Advances in Mathematics: Scientific Journal, Volume 11, pp 433-451; https://doi.org/10.37418/amsj.11.5.2

Abstract:
In this paper, we will try to adjust the behavior of the US Federal Funds interest rate to a model of autoregressive Levy-stable. We will conduct a series of tests after which it will offer the best model for this data series distributed in time, in this case, a linear model type AR (1) stationary whose distribution i.i.d. innovations would be a stable Lévy law and proceed thereafter to the estimation of nine parameters for this model.
D. Nagarajan, A. Rameshkumar
Advances in Mathematics: Scientific Journal, Volume 11, pp 415-432; https://doi.org/10.37418/amsj.11.5.1

Abstract:
In this article, the companion matrix of the cyclotomic and inverse cyclotomic polynomial is found. To determine the flat, gap, jump of the $\Phi_{n}(x)$ and $\Psi_{n}(x)$ for the binary, ternary, quaternary, quinary cyclotomic polynomial. To find some properties of the cyclotomic and inverse cyclotomic polynomial.
T.R.H. Andrianantenainarinoro, R.A. Randrianomenjanahary, T.J. Rabeherimanana
Advances in Mathematics: Scientific Journal, Volume 11, pp 383-413; https://doi.org/10.37418/amsj.11.4.7

Abstract:
Andrianantenainarinoro\cite{maReference101} remarked that the price amplitudes of financial models may not correspond to the reality and we propose here a model in continuous time Fractionally Integrated WASC Stochastic Volatility Jump. To do this, we introduce a fractal index in the WASC Stochastic Volatility Jump model and we have two others characteristics: amplitude adjustment and memory of process. We present also several theories in stochastic calculus, algebraic, differential geometry, numerical method and estimating method which can use to financial such us: sense of a fractional integral, relationship between trace and determinant operator, Euler's approximation for an unresolved differential equation and convergence speed.
Zineb Arab
Advances in Mathematics: Scientific Journal, Volume 11, pp 369-382; https://doi.org/10.37418/amsj.11.4.6

Abstract:
This work is devoted to deal with a stochastic space-time fractional integro-differential equation in the Hilbert space $ L^{2}(0,1) $, by studing its spatial approximation. Precisely, we use the spectral Galerkin method to prove that the spatial approximation converges strongly (i.e. in the space $ L^{p}(\Omega, L^{2}(0,1)) $), by imposing only a regularity condition on the initial value.
D. Halidini, E. Xhafaj, R. Kosova, A. Reka, B. Boci, D. Guxholli, N. Gjikaj
Advances in Mathematics: Scientific Journal, Volume 11, pp 353-367; https://doi.org/10.37418/amsj.11.4.5

Abstract:
The development of the online technologies has impacted the higher education to improve true knowledge. This paper aims to evaluate the eight constructs of the Unified Theory of Acceptance and Use of Technology 2 (UTAUT2) Performance Expectancy, Effort Expectancy, Social Influence, Facilitating Conditions, Hedonic Motivation, Habit, Behavioral Intention, and the last Use Behavior, based on the use of an online learning application such as Google Classroom. The main reason that is chosen this application is that it's free and students can easily access it. The proposed method to classify the eight constructs of the UTAUT2 model from the most important to the last important is Fuzzy Z-AHP with triangular fuzzy numbers (TFN). This method achieves effective results based on Z- numbers and also on their reliability. The data were collected through a survey of 210 samples from students of the University of Durres during the pandemic Covid-19 The findings suggested that the most important construct was Social Influence (SI) and the last important was Facilitating Conditions (FC). This results help the higher education policies to be oriented better regarding the online learning.
S. Esen Almali, D. Kayabasi
Advances in Mathematics: Scientific Journal, Volume 11, pp 335-352; https://doi.org/10.37418/amsj.11.4.4

Abstract:
In this paper, a general form of the family of Urysohn-type nonlinear integral operators with kernel $K_{\lambda }\left( x,t,g\right) $ is discussed and theorems about the point convergence of this family at ${p}$--Lebesgue points of a function in $L_{p}$ are given. Here, $\lambda$ is the accumulation point and is a positive parameter that changes in the real numbers. Kernel function $K_{\lambda }\left( x,t,g\left( t\right) \right)$ is an entire analytic function with respect to its third variable.
M. Boudersa, M. Dilmi, H. Benseridi
Advances in Mathematics: Scientific Journal, Volume 11, pp 301-319; https://doi.org/10.37418/amsj.11.4.2

Abstract:
In this paper, we consider the asymptotic analysis for the elasticity problem with a dissipative and source terms in a three dimensional thin domain $\Omega ^{\varepsilon }$. Firstly, we obtain the variational formulation of the problem. Then we establish some estimates independent of the parameter $\varepsilon$. Finally, we give a specific Reynolds equation associated and prove the uniqueness of the limit problem.
M.S. Ponmudi, A. Ramesh Kumar
Advances in Mathematics: Scientific Journal, Volume 11, pp 321-334; https://doi.org/10.37418/amsj.11.4.3

Abstract:
An $n\times n$ matrix is called a $Q_{N^{1}_{0}}$ matrix if for every $k=\lbrace 1,2,3,\ldots ,n \rbrace $ the sum of all $ k \times k $ principal minors is non-positive. A digraph $D$ is said to have $Q_{N^{1}_{0}}$-completion if every partial $Q_{N^{1}_{0}}$-matrix specifying $D$ can be completed to a $Q_{N^{1}_{0}}$-matrix. In this paper $Q_{N^{1}_{0}}$-matrix completion problem is considered. It is shown that partial non-positive $Q_{N^{1}_{0}}$ -matrices representing all digraphs of order $5$ with $q = 0$ to $7$ have $Q_{N^{1}_{0}}$ completion.
Advances in Mathematics: Scientific Journal, Volume 11, pp 275-299; https://doi.org/10.37418/amsj.11.4.1

Abstract:
In most previous works dealing with the modelling and numerical simulation of salinity gradient solar ponds, the heat diffusion is 1D or 2D, the diffusion of salt is very slow and that there are small convection movements, which obviously supposes that the wind speed is negligible. The studies are often limited to sodium chloride-based ponds where only relatively clear water is considered. The present work comes to fulfil the lack of 3D thermal behaviour prediction where, in one hand, we simulated solar ponds by a mixture of three different techniques, which are stable and well adapted to this type of problem using the method of finite differences in conjunction with the schemes of ADI-Gunn, Adams-Bashford and Schneider and al, which finds its first application in this type of problems. On the other hand, in order to validate our numerical results, we conducted an experiment on three identical parallelepiped ponds with {2.3040}$\,\text{m}^2$ of area and {1.200}$\,\text{m}$ depth; each one containing the same fungicide salt namely \ce{KH2PO4}, that has never been used before.
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