University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
03
2
2016
06
01
The analysis of a disease-free equilibrium of Hepatitis B model
1
11
EN
Reza
Akbari
Department of Mathematical Sciences, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.
r9reza@yahoo.com
Ali
Vahidian Kamyad
Department of Mathematics Sciences, University of Ferdowsi, Mashhad, Iran.
avkamyad@yahoo.com
Ali akbar
Heydari
Research Center for Infection Control and Hand Hygiene, Mashhad University Of Medical Sciences, Mashhad, Iran.
heydariaa@mums.ac.ir
Aghileh
Heydari
Department of Mathematical Sciences, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.
a_heidari@pnu.ac.ir
In this paper we study the dynamics of Hepatitis B virus (HBV) infection under administration of a vaccine and treatment, where the disease is transmitted directly from the parents to the offspring and also through contact with infective individuals. Stability of the disease-free steady state is investigated. The basic reproductive rate, $R_0$, is derived. The results show that the dynamics of the model is completely determined by the basic reproductive number $R_0$. If $R_0<1$, the disease-free equilibrium is globally stable and the disease always dies out and if $R_0>1$, the disease-free equilibrium is unstable and the disease is uniformly persistent.
Hepatitis B virus (HBV),Basic reproduction number ($R_0$),Compound matrices,Disease-Free equilibrium state,Global stability
https://scma.maragheh.ac.ir/article_19749.html
https://scma.maragheh.ac.ir/article_19749_d6277da45d18a2b9e2617791b8dbcc92.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
03
2
2016
06
01
Growth analysis of entire functions of two complex variables
13
24
EN
Sanjib
Kumar Datta
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.
sanjib_kr_datta@yahoo.co.in
Tanmay
Biswas
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.
tanmaybiswas_math@rediffmail.com
In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.
Entire functions,Generalized relative order,Generalized relative lower order,Two complex variables,Composition,growth
https://scma.maragheh.ac.ir/article_19750.html
https://scma.maragheh.ac.ir/article_19750_9a173f57343ef9c61aa8f0ee7cdf9b6d.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
03
2
2016
06
01
Menger probabilistic normed space is a category topological vector space
25
32
EN
Ildar
Sadeqi
Department of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.
esadeqi@sut.ac.ir
Farnaz
Yaqub Azari
University of Payame noor, Tabriz, Iran.
fyaqubazari@gmail.com
In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces in probabilistic normed spaces.
Category of probabilistic normed space,Category of topological vector space,Fuzzy continuous operator
https://scma.maragheh.ac.ir/article_19784.html
https://scma.maragheh.ac.ir/article_19784_ea968e7794474539e5edcca66c4af05b.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
03
2
2016
06
01
On certain fractional calculus operators involving generalized Mittag-Leffler function
33
45
EN
Dinesh
Kumar
0000-0001-5415-1777
Department of Mathematics \& Statistics, Jai Narain Vyas University, Jodhpur - 342005, India.
dinesh_dino03@yahoo.com
The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators are the generalization of the Saigo fractional calculus operators. The established results provide extensions of the results given by Gupta and Parihar [3], Saxena and Saigo [30], Samko et al. [26]. On account of the general nature of the generalized Mittag-Leffler function and generalized Wright function, a number of known results can be easily found as special cases of our main results.
Marichev-Saigo-Maeda fractional calculus operators,Generalized Mittag-Leffler function,Generalized Wright hypergeometric function
https://scma.maragheh.ac.ir/article_19751.html
https://scma.maragheh.ac.ir/article_19751_f8cba31ae3575443d6bc568443f37036.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
03
2
2016
06
01
Multistep collocation method for nonlinear delay integral equations
47
65
EN
Parviz
Darania
Department of Mathematics, Faculty of Science, Urmia University, P.O.Box 5756151818, Urmia-Iran.
p.darania@urmia.ac.ir
The main purpose of this paper is to study the numerical solution of nonlinear Volterra integral equations with constant delays, based on the multistep collocation method. These methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. Also, we analyze the convergence of the multistep collocation method when used to approximate smooth solutions of delay integral equations. Finally, numerical results are given showing a marked improvement in comparison with exact solution.
Delay integral equations,Collocation method,Multistep collocation method,Convergence
https://scma.maragheh.ac.ir/article_19832.html
https://scma.maragheh.ac.ir/article_19832_4aa04e21bad2368df51e6e1a4c4fdbda.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
03
2
2016
06
01
On the topological centers of module actions
67
74
EN
Kazem
Haghnejad Azar
0000-0002-2591-3362
Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.
haghnejad@uma.ac.ir
In this paper, we study the Arens regularity properties of module actions. We investigate some properties of topological centers of module actions ${Z}^ell_{B^{**}}(A^{**})$ and ${Z}^ell_{A^{**}}(B^{**})$ with some conclusions in group algebras.
Arens regularity,Topological centers,Module actions
https://scma.maragheh.ac.ir/article_19748.html
https://scma.maragheh.ac.ir/article_19748_3fb8c456b2e4d1f04f48b4146fde0d2d.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
03
2
2016
06
01
Inverse Sturm-Liouville problems with a Spectral Parameter in the Boundary and transmission conditions
75
89
EN
Mohammad
Shahriari
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
shahriari@maragheh.ac.ir
In this manuscript, we study the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. By defining a new Hilbert space and using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at some interior point and parts of two sets of eigenvalues.
Inverse Sturm-Liouville problem,Jump conditions,Non self-adjoint operator,Parameter dependent condition
https://scma.maragheh.ac.ir/article_17973.html
https://scma.maragheh.ac.ir/article_17973_6df44ee2ee8037955d17cb29c9f1d581.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
03
2
2016
06
01
On multiplicative (strong) linear preservers of majorizations
91
106
EN
Mohammad Ali
Hadian Nadoshan
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.
ma.hadiann@gmail.com
Ali
Armandnejad
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.
armandnejad@vru.ac.ir
In this paper, we study some kinds of majorizations on $textbf{M}_{n}$ and their linear or strong linear preservers. Also, we find the structure of linear or strong linear preservers which are multiplicative, i.e. linear or strong linear preservers like $Phi $ with the property $Phi (AB)=Phi (A)Phi (B)$ for every $A,Bin textbf{M}_{n}$.
Doubly stochastic matrix,Linear preserver,Multiplicative map
https://scma.maragheh.ac.ir/article_18507.html
https://scma.maragheh.ac.ir/article_18507_6efe0e20f27345279deaf253dedbf98a.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
03
2
2016
06
01
On $n$-derivations
107
115
EN
Mohammad Hossein
Sattari
Department of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53751-71379, Tabriz, Iran.
sattari@azaruniv.ac.ir
In this article, the notion of $n-$derivation is introduced for all integers $ngeq 2$. Although all derivations are $n-$derivations, in general these notions are not equivalent. Some properties of ordinary derivations are investigated for $n-$derivations. Also, we show that under certain mild condition $n-$derivations are derivations.
$n$-derivation,$n$-homomorphism,Banach algebra
https://scma.maragheh.ac.ir/article_19780.html
https://scma.maragheh.ac.ir/article_19780_83b63b675701b909f6b32e3f6bb7c3aa.pdf