Journal of Advances in Applied Mathematics

7

Authors: Yu Wang, Yong Yu

The aim of this paper is to study two particular GV-semigroups whose full subsemigroups form 0-semidistributive lattices. The structure of GV-inverse semigroups whose full subsemigroup lattices are 0-semidistributive is first characterized. Moreover, much more explicit structural description is obtained for orthodox GV-semigroups by establishing an inverse semigroup congruence.

10

Authors: Ruiying Wang, Shouqiang Du, Zhimin Liu

In this paper, we consider the Newton type methods for solving the nonsmooth equations with finitely many maximum functions. A new ∂∗-differential is used in the given Newton-type methods. The Newton-type methods also include a new parameterized combination. The superlinear convergence of the given methods is presented. Finally, the numerical experiments highlight the efficiency of the given methods.

11

Authors: Amine Bernoussi, Abdelilah Kaddar, Said Asserda

In this paper, we investigate the global asymptotic stability of the possible equilibria for an SIRI epidemic model with a distributed latent period and a general incidence function. By using the method of Lyapunov functions and the LaSalle invariance principle, we show that the global asymptotic stability is completely determined by the basic reproduction number R0. The originality of this work is to have a basic reproduction number R0 which depends on the distribution of the latent period. Finally, we use a nonstandard discretization method of Mickens to illustrate numerically our theoretical results.

19

Authors: Bhuvaneswari Sambandham, Aghalaya S Vatsala

Generalized monotone method together with coupled lower and upper solutions yield monotone sequences which converge uniformly and monotonically to coupled minimal and maximal solutions of the nonlinear problem under consideration. In this work, we have developed generalized monotone method for sequential Caputo fractional boundary value problem with mixed boundary conditions which are in terms of Caputo fractional derivative. For that purpose, we have obtained a representation form for the corresponding linear Caputo sequential boundary value problem in terms of the Green’s function. In addition, we have obtained a linear comparison result for the linear sequential differential inequalities with linear mixed boundary conditions. The comparison result is useful in proving the monotonicity of the iterates as well as the uniqueness of the solution of the nonlinear sequential boundary value problem. Our method yields the integer results as a special case. Some numerical examples for the linear sequential Caputo fractional boundary value problems have also been presented.

8

Authors: Sanaa ElFadily, Abdelilah Kaddar, Khalid Najib

In this paper, we propose a model of mutual interactions between the economically active population and the economic growth. Our principal goal is to introduce a delayed equation of the active population evolution. The time delay, resulting from the recruitment processes, is incorporated in the effective labor demand. The dynamics are studied in terms of local stability and of the description of the Hopf bifurcation, is proven to exist as the delay (taken as a parameter of bifurcation) cross some critical value. Some numerical simulations are given to illustrate our theoretical results. Additionally we conclude with some remarks.

10

Authors: Lin-Chang Shen, Yue-Ying Yang, Wei-Mao Qian

In this paper, we give the explicit formulas for Neuman means of the second kind NGQ(a, b) and NQG(a, b), and find the best possible parameters αi, βi ∈ (0, 1)(i = 1, 2, 3, · · · , 6) such that the double inequalities α1Q(a, b) + (1 − α1)G(a, b) < NQG(a, b) < β1Q(a, b) + (1 − β1)G(a, b), α2 G(a, b) + 1 − α2 Q(a, b) < 1 NQG(a, b) < β2 G(a, b) + 1 − β2 Q(a, b) , α3Q(a, b) + (1 − α3)G(a, b) < NGQ(a, b) < β3Q(a, b) + (1 − β3)G(a, b), α4 G(a, b) + 1 − α4 Q(a, b) < 1 NGQ(a, b) < β4 G(a, b) + 1 − β4 Q(a, b) , α5Q(a, b) + (1 − α5)V (a, b) < NQG(a, b) < β5Q(a, b) + (1 − β5)V (a, b), α6Q(a, b) + (1 − α6)U(a, b) < NGQ(a, b) < β6Q(a, b) + (1 − β6)U(a, b), holds for all a, b > 0 with a 6= b, where G(a, b) and Q(a, b) are the classical geometric and quadratic means, V (a, b), U(a, b), NQG(a, b) and NGQ(a, b) are Yang and Neuman mean of the second kind.

12

Authors: Marta Demma, Peyman Salimi, Pasquale Vetro

We establish partial coupled fixed point and coupled fixed point results for mixed monotone mappings satisfying a generalized contractive condition in ordered partial metric spaces and ordered metric spaces. Our results generalize some interesting coupled fixed point theorems obtained in [T. G. Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications”, Nonlinear Anal., vol. 65, pp. 1379–1393, 2006].

4

Authors: Zhengyuan Wei, Yunfeng Luo, Juan Li, Xiaoyang Zheng

We present some elementary proof methods for Wallis product formula by the use of integration equation, Wallis sine formula and gamma function.

7

Authors: Mauricio Tejo, Sebastian Niklitschek-Soto

Search patterns in species can give us relevant information about abundance/lack of its food availability. This survey reviews three marked patterns: the Brownian motion, the Lévy flight and an intermediary displacement. After defining the corresponding mathematical models and some of its properties, we consider a general Euler scheme in which these kind of processes can be simulated. Finally, we discuss some possible implications and future researches.

9

Authors: M. Tarık Atay, Musa Basbük, Aytekin Eryılmaz

In this paper, we investigated a numeric integration based on Magnus series expansion namely Magnus Series Expansion Method (NMG) for nonlinear Human T-Cell Lymphotropic Virus I (HTLV-I) infection of CD4+ T-cells model. Fourth order Magnus series expansion method (NMG4) and explicit Runge-Kutta (RK45) are used to obtain numerical solutions of HTLV-I infection of CD4+ T-cells model. The results obtained by NMG4 and RK45 are compared.

6

Authors: Hariwan Z. Ibrahim

The main purpose of the present paper is to introduce a new class of functions called almost β-γ-continuous functions which is contained in the class of almost β-continuous functions and contains the class of β-γ-continuous functions.

12

Authors: Mohammed Ibrahim Shaik, Suneetha Karna

The article is focused on the effects of Soret and chemical reaction on MHD free convection flow through a vertical porous surface in the presence of heat source, viscous dissipation and radiation. The dimensionless governing equations for this investigation are solved analytically using perturbation technique. Numerical evaluation of the numerical results is performed and the results for velocity, temperature and concentration profiles within the boundary layer are discussed and shown graphically. Also skin-friction coefficient due to velocity, Nusselt number coefficient due to temperature and Sherwood number coefficient due to concentration fields are evaluated.

15

Authors: Xiaoyang Zheng, Zhengyuan Wei, Jiangping He

This paper presents a new numerical approach, i.e., discontinuous Legendre wavelet Galerkin (DLWG) technique, to solve the Lane-Emden equations. This scheme incorporates Legendre wavelet into discontinuous Galerkin (DG) method, thus it has the advantages of both wavelet Galerkin (WG) method and DG technique. Specifically, the variational formulation of the equation and numerical fluxes are first derived and clearly calculated, then the Lane-Emden equations are converted into solutions to systems of equations. It is pointed that the proposed approach needs less storage space and execution time than the other methods because of the use of discontinuous elements producing lower dimensional, block-diagonal and sparse mass matrices. Furthermore, numerical experiments demonstrate the efficiency and applicability of this technique.

17

Authors: Blake James Huebner, Rhonda C Magel

Drugs within three categories used in hip replacement surgery are compared based on their association with total hospital costs and length of stay. The drugs are also compared based on their associations with proportions of early readmissions. Multiple regression, logistic regression, chisquare tests, and multiple comparison techniques are used. The combination of warfarin and enoxaparin is associated with the highest cost and length of stay of the anticoagulants studied. There is no clear regional anesthesia drug used associated with the highest hospital cost and longest length of stay. Tranexamic acid is found to be associated with a smaller proportion of blood transfusions, a shorter length of stay, with no significant difference in cost found and no significant difference found in the proportion of early readmissions.