Advances in Mathematics: Scientific Journal

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ISSN / EISSN : 1857-8365 / 1857-8438
Published by: Union of Researchers of Macedonia (10.37418)
Total articles ≅ 1,367
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N. Memic, A. Pecenkovic
Advances in Mathematics: Scientific Journal, Volume 10, pp 3327-3336; https://doi.org/10.37418/amsj.10.10.4

Abstract:
This work gives the form of derivation introduced in \cite{K} in the context of dyadic field. We discuss the relation of this derivative to Fourier transform as well as its appropriate anti derivative.
Ibrahima Toure
Advances in Mathematics: Scientific Journal, Volume 10, pp 3307-3325; https://doi.org/10.37418/amsj.10.10.3

Abstract:
Let $N$ be a connected and simply connected nilpotent Lie group, $K$ be a compact subgroup of $Aut(N)$, the group of automorphisms of $N$ and $\delta$ be a class of unitary irreducible representations of $K$. The triple $(N,K,\delta)$ is a commutative triple if the convolution algebra $\mathfrak{U}_{\delta}^{1}(N)$ of $\delta$-radial integrable functions is commutative. In this paper, we obtain first a parametrization of $\delta$ spherical functions by means of the unitary dual $\widehat{N}$ and then an inversion formula for the spherical transform of $F\in \mathfrak{U}_{\delta}^{1}(N)$.
K.A. George, M. Sumathi
Advances in Mathematics: Scientific Journal, Volume 10, pp 3297-3306; https://doi.org/10.37418/amsj.10.10.2

Abstract:
The initial level of mortality and the rate at which mortality rises with age are generally expressed in terms of the Gompertz force of mortality (hazard function). In their paper, James W. Vaupel and others define the Gompertz force of mortality as the rate at which mortality rises with age and the modal age at death. In this paper we estimate the Gompertz force of mortality and prove uniqueness theorem.
S. Rechdaoui, A. Taakili
Advances in Mathematics: Scientific Journal, Volume 10, pp 3283-3296; https://doi.org/10.37418/amsj.10.10.1

Abstract:
This work deals with the numerical solution of a control problem governed by the Timoshenko beam equations with locally distributed feedback. We apply a fourth-order Compact Finite Difference (CFD) approximation for the discretizing spatial derivatives and a Forward second order method for the resulting linear system of ordinary differential equations. Using the energy method, we derive energy relation for the continuous model, and design numerical scheme that preserve a discrete analogue of the energy relation. Numerical results show that the CFD approximation of fourth order give an efficient method for solving the Timoshenko beam equations.
H. Umair, H. Zainuddin, K.T. Chan, Sh.K. Said Husein
Advances in Mathematics: Scientific Journal, Volume 10, pp 3241-3251; https://doi.org/10.37418/amsj.10.9.13

Abstract:
Geometric Quantum Mechanics is a formulation that demonstrates how quantum theory may be casted in the language of Hamiltonian phase-space dynamics. In this framework, the states are referring to points in complex projective Hilbert space, the observables are real valued functions on the space and the Hamiltonian flow is defined by Schr{\"o}dinger equation. Recently, the effort to cast uncertainty principle in terms of geometrical language appeared to become the subject of intense study in geometric quantum mechanics. One has shown that the stronger version of uncertainty relation i.e. the Robertson-Schr{\"o}dinger uncertainty relation can be expressed in terms of the symplectic form and Riemannian metric. In this paper, we investigate the dynamical behavior of the uncertainty relation for spin $\frac{1}{2}$ system based on this formulation. We show that the Robertson-Schr{\"o}dinger uncertainty principle is not invariant under Hamiltonian flow. This is due to the fact that during evolution process, unlike symplectic area, the Riemannian metric is not invariant under the flow.
M.E.H. Hafidzuddin, R. Nazar, N.M. Arifin, I. Pop
Advances in Mathematics: Scientific Journal, Volume 10, pp 3273-3282; https://doi.org/10.37418/amsj.10.9.16

Abstract:
The problem of steady laminar three-dimensional stagnation-point flow on a permeable stretching/shrinking sheet with second order slip flow model is studied numerically. Similarity transformation has been used to reduce the governing system of nonlinear partial differential equations into the system of ordinary (similarity) differential equations. The transformed equations are then solved numerically using the \texttt{bvp4c} function in MATLAB. Multiple solutions are found for a certain range of the governing parameters. The effects of the governing parameters on the skin friction coefficients and the velocity profiles are presented and discussed. It is found that the second order slip flow model is necessary to predict the flow characteristics accurately.
H. Umair, H. Zainuddin, K.T. Chan, Sh.K. Said Husein
Advances in Mathematics: Scientific Journal, Volume 10, pp 3253-3262; https://doi.org/10.37418/amsj.10.9.14

Abstract:
Geometric Quantum Mechanics is a version of quantum theory that has been formulated in terms of Hamiltonian phase-space dynamics. The states in this framework belong to points in complex projective Hilbert space, the observables are real valued functions on the space, and the Hamiltonian flow is described by the Schr{\"o}dinger equation. Besides, one has demonstrated that the stronger version of the uncertainty relation, namely the Robertson-Schr{\"o}dinger uncertainty relation, may be stated using symplectic form and Riemannian metric. In this research, the generalized Robertson-Schr{\"o}dinger uncertainty principle for spin $\frac{1}{2}$ system has been constructed by considering the operators corresponding to arbitrary direction.
M.E.H. Hafidzuddin, R. Nazar, N.M. Arifin, I. Pop
Advances in Mathematics: Scientific Journal, Volume 10, pp 3263-3272; https://doi.org/10.37418/amsj.10.9.15

Abstract:
An analysis is carried out to theoretically investigate the unsteady three dimensional stagnation-point of a viscous flow over a permeable stretching/shrinking sheet. A similarity transformation is used to reduce the governing system of nonlinear partial differential equations to a set of nonlinear ordinary (similarity) differential equations, which are then solved numerically using the \texttt{bvp4c} function in MATLAB. Results show that multiple solutions exist for a certain range of unsteadiness and stretching/shrinking parameters. The effects of the governing parameters on the skin friction coefficients and the velocity profiles are presented and discussed.
F. Shujat, A.Z. Ansari, K. Kumar
Advances in Mathematics: Scientific Journal, Volume 10, pp 3233-3240; https://doi.org/10.37418/amsj.10.9.12

Abstract:
In the present note, we discuss the notion of symmetric bi-semiderivations on rings and prove some commutativity results for commuting bi-semiderivations. Moreover, we obtain the characterization of symmetric bi-semiderivation on prime ring.
Kwara Nantomah
Advances in Mathematics: Scientific Journal, Volume 10, pp 3227-3231; https://doi.org/10.37418/amsj.10.9.11

Abstract:
In this paper, we prove that for $s\in(0,\infty)$, the harmonic mean of $E_k(s)$ and $E_k(1/s)$ is always less than or equal to $\Gamma(1-k,1)$. Where $E_k(s)$ is the generalized exponential integral function, $\Gamma(u,s)$ is the upper incomplete gamma function and $k\in \mathbb{N}$.
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