]>
2020
20
4
91
Stability of a general discrete-time HIV dynamics model with three categories of infected CD4\(^{+}\) T-cells and multiple time delays
Stability of a general discrete-time HIV dynamics model with three categories of infected CD4\(^{+}\) T-cells and multiple time delays
en
en
In this paper, we construct delayed HIV dynamics models with impairment of
B-cell functions. Two forms of the incidence rate have been considered,
bilinear and general. Three types of infected cells and five-time delays
have been incorporated into the models. The well-posedness of the models is
justified. The models admit two equilibria which are determined by the basic
reproduction number \(R_{0}\). The global stability of each equilibrium is
proven by utilizing the Lyapunov function and LaSalle's invariance principle.
The theoretical results are illustrated by numerical simulations.
264
282
A. M.
Elaiw
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
a_m_elaiw@yahoo.com
M. A.
Alshaikh
Department of Mathematics, Faculty of Science
Department of Mathematics, Faculty of Science
King Abdulaziz University
Taif University
Saudi Arabia
Saudi Arabia
matukaalshaikh@gmail.com
HIV infection
latent reservoirs
time delay
global stability
Lyapunov function
discrete time model
Article.1.pdf
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A. M. Elaiw, M. A. Alshaikh, Stability analysis of a general discrete-time pathogen infection model with humoral immunity, J. Differ. Equ. Appl., 2019 (2019), 1-24
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A. M. Elaiw, M. A. Alshaikh, Stability of discrete-time HIV dynamics models with three categories of infected CD4$^{+}$ T-cells, Adv. Difference Equ., 2019 (2019), 1-24
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A. M. Elaiw, N. H. AlShamrani, Stability of a general delay-distributed virus dynamics model with multi-staged infected progression and immune response, Math. Methods Appl. Sci., 40 (2017), 699-719
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A. M. Elaiw, N. H. AlShamrani, Stability of an adaptive immunity pathogen dynamics model with latency and multiple delays, Math. Methods Appl. Sci., 36 (2018), 125-142
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A. M. Elaiw, E. K. Elnahary, A. A. Raezah, Effect of cellular reservoirs and delays on the global dynamics of HIV, Adv. Difference Equ., 2018 (2018), 1-36
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A. M. Elaiw, A. A. Raezah, S. A. Azoz, Stability of delayed HIV dynamics models with two latent reservoirs and immune impairment, Adv. Difference Equ., 2018 (2018), 1-25
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]
A finite-difference scheme for initial boundary value problem of the Gamma equation in the pricing of financial derivatives
A finite-difference scheme for initial boundary value problem of the Gamma equation in the pricing of financial derivatives
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en
In the article, we consider the initial boundary value problem for the Gamma equation, which can be derived by transforming the nonlinear Black-Scholes equation for option price into a quasilinear parabolic equation for the second derivative of the option price. We develop unconditionally monotone finite-difference schemes of second-order of local approximation on uniform grids for the initial boundary value problem for the Gamma equation. Two-side estimates of the solution of the scheme are established. By means of regularization principle, the previous results are generalized for construction of unconditionally monotone finite-difference scheme (the maximum principle is satisfied without constraints on relations between the coefficients and grid parameters) of the second-order of approximation on uniform grids for this equation. With the help of difference maximum principle, the two-side estimates for difference solution are obtained at the arbitrary non-sign-constant input data of the problem. A priori estimate in the maximum norm \(C\) is proved. It is interesting to note that the proven two-side estimates for difference solution are fully consistent with the differential problem, and the maximal and minimal values of the difference solution do not depend on the diffusion and convection coefficients. Computational experiments, confirming the theoretical conclusions, are given.
283
291
Le Minh
Hieu
University of Economics
The University of Danang
Vietnam
hieulm@due.edu.vn
Truong Thi Hieu
Hanh
University of Economics
The University of Danang
Vietnam
hanhtth@due.edu.vn
Dang Ngoc Hoang
Thanh
Department of Information Systems, School of Business Information Technology
University of Economics Ho Chi Minh city
Vietnam
hoangthanh@ueh.edu.vn
Gamma equation
maximum principle
two-side estimates
monotone finite-difference scheme
quasi-linear parabolic equation
scientific computing
Article.2.pdf
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]
Analytical properties of extended Hermite-Bernoulli polynomials
Analytical properties of extended Hermite-Bernoulli polynomials
en
en
This article aims to present a new family of extended Hermite-Bernoulli polynomials by making use of the Mittag-Leffler function. We also derive some analytical properties of our proposed extended Hermite-Bernoulli polynomials systematically. Furthermore, some concluding remarks of our present investigation are also pointed out in the last section.
292
301
Nabiullah
Khan
Department of Applied Mathematics
Aligarh Muslim University
India
nukhanmath@gmail.com
Naeem
Ahmad
Department of Mathematics, College of Science
Jouf University
Saudi Arabia
naataullah@ju.edu.sa
Mohd
Ghayasuddin
Department of Mathematics
Integral University Campus
India
ghayas.maths@gmail.com
Hermite polynomials
Bernoulli polynomials
Hermite-Bernoulli polynomials
Mittag-Leffler function
Article.3.pdf
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]
Rough Pythagorean fuzzy ideals in ternary semigroups
Rough Pythagorean fuzzy ideals in ternary semigroups
en
en
A ternary semigroup is a nonempty set equipped with an associative ternary operation. A Pythagorean fuzzy set is one of the generalizations of the fuzzy set. The aim of this paper is to study rough Pythagorean fuzzy ideals in ternary semigroups. This idea is extended to the lower and upper approximations of Pythagorean fuzzy ideals.
302
312
Ronnason
Chinram
Algebra and Applications Research Unit, Department of Mathematics and Statistics, Faculty of Science
Centre of Excellence in Mathematics
Prince of Songkla University
CHE
Thailand
Thailand
ronnason.c@psu.ac.th
Thammarat
Panityakul
Centre of Excellence in Mathematics
CHE
Thailand
Fuzzy sets
Pythagorean fuzzy sets
rough sets
ternary semigroups
Article.4.pdf
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M. A. Ansari, N. Yaqoob, $T$-rough ideals in ternary semigroups, Int. J. Pure Appl. Math., 86 (2013), 411-424
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R. Chinram, Rough prime ideals and rough fuzzy prime ideals in gamma-semigroups, Commun. Korean Math. Soc., 24 (2009), 341-351
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H. Garg, A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making, Int. J. Intell. Syst., 31 (2016), 886-920
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H. Garg, Generalized Pythagorean fuzzy geometric interactive aggregation operators using Einstein operations and their application to decision making, J. Exper. Theor. Artif. Intell., 30 (2018), 763-794
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A. Hussain, T. Mahmood, M. I. Ali, Rough Pythagorean fuzzy ideals in semigroups, Comput. Appl. Math., 38 (2019), 1-15
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A. Iampan, Some properties of ideal extensions in ternary semigroups, Iran. J. Math. Sci. Inform., 8 (2013), 67-74
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Exponential B-spline collocation method for solving the generalized Newell-Whitehead-Segel equation
Exponential B-spline collocation method for solving the generalized Newell-Whitehead-Segel equation
en
en
In this work, we present a collocation method based on exponential basis spline functions for solving generalized Newell-Whitehead-Segel equation. The time derivative is discretized by finite difference scheme and the exponential basis spline functions are employed to interpolate spatial derivatives. The convergence and stability of the proposed algorithm are established. Numerical results demonstrate the accuracy of the proposed method.
313
324
Imtiaz
Wasim
Department of Mathematics
University of Sargodha
Pakistan
Muhammad
Abbas
Department of Mathematics
University of Sargodha
Pakistan
muhammad.abbas@uos.edu.pk
Muhammad Kashif
Iqbal
Department of Mathematics
Government College University
Pakistan
Afzaal Mubashir
Hayat
Department of Mathematics
National College of Business Administration \(\&\) Economics
Pakistan
Non-linear generalized Newell-Whitehead-Segel equation
exponential B-spline collocation method
convergence
stability
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A. Aasaraai, Analytic solution for Newell--Whitehead--Segel equation by differential transform method, Middle-East J. Sci. Res., 10 (2011), 270-273
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]
On \(BF\)-semigroups and Fuzzy \(BF\)-semigroups
On \(BF\)-semigroups and Fuzzy \(BF\)-semigroups
en
en
We introduce and establish the notion of \(BF\)-semigroups. We construct quotient \(BF\)-semigroups via \(BF\)-ideals and we investigate homomorphisms of \(BF\)-semigroups and establish the isomorphism theorems for \(BF\)-semigroups. Moreover, we apply the concept of fuzzy sets to \(BF\)-semigroups.
325
333
Mae
Manahon
Mathematics Department
Negros Oriental State University
Philippines
maedmanahon513@gmail.com
Jenette
Bantug
Mathematics Department
Silliman University
Philippines
jenettesbantug@su.edu.ph
Joemar
Endam
Department of Mathematics
Negros Oriental State University
Philippines
joemar.endam@norsu.edu.ph
\(BF/BF_1/BF_2\)-semigroup
sub \(BF\)-semigroup
\(BF\)-ideal
quotient \(BF\)-semigroup
fuzzy sub \(BF\)-semigroup
Article.6.pdf
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Analytical technique for neutral delay differential equations with proportional and constant delays
Analytical technique for neutral delay differential equations with proportional and constant delays
en
en
Neutral delay differential equations (NDDEs) are a type of delay differential equations (DDEs) that arise in numerous areas of applied sciences and play a vital role in mathematical modelling of real-life phenomena. Some techniques have experienced difficulties in finding the approximate analytical solution which converges rapidly to the exact solution of these equations. In this paper, an analytical approach is proposed for solving linear and nonlinear NDDEs with proportional and constant delays based on the homotopy analysis method (HAM) and natural transform method where the nonlinear terms are simply calculated as a series of, He's polynomial. The proposed method produces solutions in the form of a rapidly convergent series which leads to the exact solution from only a few numbers of iterations. Some illustrative examples are solved, and the convergence analysis of the proposed techniques was also provided. The obtained results reveal that the approach is very effective and efficient in handling both linear and nonlinear NDDEs with proportional and constant delays and can also be used in various types of linear and nonlinear problems.
334
348
Normah
Maan
Department of Mathematical Sciences
Universiti Teknologi
Malaysia
normahmaan@utm.my
Aminu
Barde
Department of Mathematical Sciences
Department of Mathematical Sciences
Universiti Teknologi
Abubakar Tafawa Balewa University
Malaysia
Nigeria
Neutral delay differential equations
He's polynomial
natural transform method
homotopy analysis method
Article.7.pdf
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]
A space-efficient algorithm for computing the minimum cycle mean in a directed graph
A space-efficient algorithm for computing the minimum cycle mean in a directed graph
en
en
An algorithm is introduced for computing the minimum cycle mean
in a strongly connected directed graph with \(n\) vertices and \(m\) arcs
that requires \(O (n)\) working space.
This is a considerable improvement for sparse graphs
in comparison to the classical algorithms
that require \(O (n^2)\) working space.
The time complexity of the algorithm is still \(O (n m)\).
An implementation in C++ is made publicly available
at
http://www.pawelpilarczyk.com/cymealg.
349
355
Paweł
Pilarczyk
Gdańsk University of Technology
ul.
Poland
pawel.pilarczyk@pg.edu.pl
Directed graph
weighted graph
sparse graph
algorithm
minimum cycle mean
mean cycle weight
rigorous numerics
floating-point arithmetic
rounding
Article.8.pdf
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