Abstract: The incidences of dengue hemorrhagic disease (DHF)
over the long term exhibit a seasonal behavior. It has been
hypothesized that these behaviors are due to the seasonal climate
changes which in turn induce a seasonal variation in the incubation
period of the virus while it is developing the mosquito. The standard
dynamic analysis is applied for analysis the Susceptible-Exposed-
Infectious-Recovered (SEIR) model which includes an annual
variation in the length of the extrinsic incubation period (EIP). The
presence of both asymptomatic and symptomatic infections is
allowed in the present model. We found that dynamic behavior of the
endemic state changes as the influence of the seasonal variation of
the EIP becomes stronger. As the influence is further increased, the
trajectory exhibits sustained oscillations when it leaves the chaotic
region.
Abstract: In this paper we study the transformation of Euler equations 1 , u u u Pf t (ρ ∂) + ⋅∇ = − ∇ + ∂ G G G G ∇⋅ = u 0, G where (ux, t) G G is the velocity of a fluid, P(x, t) G is the pressure of a fluid andρ (x, t) G is density. First of all, we rewrite the Euler equations in terms of new unknown functions. Then, we introduce new independent variables and transform it to a new curvilinear coordinate system. We obtain the Euler equations in the new dependent and independent variables. The governing equations into two subsystems, one is hyperbolic and another is elliptic.
Abstract: Covering approximation spaces is a class of important
generalization of approximation spaces. For a subset X of a covering
approximation space (U, C), is X definable or rough? The
answer of this question is uncertain, which depends on covering
approximation operators endowed on (U, C). Note that there are many
various covering approximation operators, which can be endowed
on covering approximation spaces. This paper investigates covering
approximation spaces endowed ten covering approximation operators
respectively, and establishes some relations among definable subsets,
inner definable subsets and outer definable subsets in covering approximation
spaces, which deepens some results on definable subsets
in approximation spaces.
Abstract: Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.
Abstract: In this paper, a direct method based on variable step
size Block Backward Differentiation Formula which is referred as
BBDF2 for solving second order Ordinary Differential Equations
(ODEs) is developed. The advantages of the BBDF2 method over the
corresponding sequential variable step variable order Backward
Differentiation Formula (BDFVS) when used to solve the same
problem as a first order system are pointed out. Numerical results are
given to validate the method.
Abstract: We demonstrate a way to count the number of Young
tableau u of shape λ = (k, k,L, k) with | λ |= lk by expanding
Schur function. This result gives an answer to the question that was put
out by Jenny Buontempo and Brian Hopkins.
Abstract: Swarm principles are increasingly being used to design controllers for the coordination of multi-robot systems or, in general, multi-agent systems. This paper proposes a two-dimensional Lagrangian swarm model that enables the planar agents, modeled as point masses, to swarm whilst effectively avoiding each other and obstacles in the environment. A novel method, based on an extended Lyapunov approach, is used to construct the model. Importantly, the Lyapunov method ensures a form of practical stability that guarantees an emergent behavior, namely, a cohesive and wellspaced swarm with a constant arrangement of individuals about the swarm centroid. Computer simulations illustrate this basic feature of collective behavior. As an application, we show how multiple planar mobile unicycle-like robots swarm to eventually form patterns in which their velocities and orientations stabilize.
Abstract: In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi, Gaussian quadratures for approximate of fuzzy integrals, Applied Mathematics and Computation 170 (2005) 874-885]. The obtained results are illustrated by solving some numerical examples.
Abstract: Since the pioneering work of Zadeh, fuzzy set theory has been applied to a myriad of areas. Song and Chissom introduced the concept of fuzzy time series and applied some methods to the enrollments of the University of Alabama. In recent years, a number of techniques have been proposed for forecasting based on fuzzy set theory methods. These methods have either used enrollment numbers or differences of enrollments as the universe of discourse. We propose using the year to year percentage change as the universe of discourse. In this communication, the approach of Jilani, Burney, and Ardil is modified by using the year to year percentage change as the universe of discourse. We use enrollment figures for the University of Alabama to illustrate our proposed method. The proposed method results in better forecasting accuracy than existing models.
Abstract: A multi-agent system is developed here to predict
monthly details of the upcoming peak of the 24th solar magnetic
cycle. While studies typically predict the timing and magnitude of
cycle peaks using annual data, this one utilizes the unsmoothed
monthly sunspot number instead. Monthly numbers display more
pronounced fluctuations during periods of strong solar magnetic
activity than the annual sunspot numbers. Because strong magnetic
activities may cause significant economic damages, predicting
monthly variations should provide different and perhaps helpful
information for decision-making purposes. The multi-agent system
developed here operates in two stages. In the first, it produces twelve
predictions of the monthly numbers. In the second, it uses those
predictions to deliver a final forecast. Acting as expert agents, genetic
programming and neural networks produce the twelve fits and
forecasts as well as the final forecast. According to the results
obtained, the next peak is predicted to be 156 and is expected to
occur in October 2011- with an average of 136 for that year.
Abstract: Based on the classical algorithm LSQR for solving (unconstrained) LS problem, an iterative method is proposed for the least-squares like-minimum-norm symmetric solution of AXB+CYD=E. As the application of this algorithm, an iterative method for the least-squares like-minimum-norm biymmetric solution of AXB=E is also obtained. Numerical results are reported that show the efficiency of the proposed methods.
Abstract: Although the usefulness of fuzzy databases has been
pointed out in several works, they are not fully developed in numerous
domains. A task that is mostly disregarded and which is the topic
of this paper is the determination of suitable inequalities for fuzzy
sets in fuzzy query languages. This paper examines which kinds
of fuzzy inequalities exist at all. Afterwards, different procedures
are presented that appear theoretically appropriate. By being applied
to various examples, their strengths and weaknesses are revealed.
Furthermore, an algorithm for an efficient computation of the selected
fuzzy inequality is shown.
Abstract: This paper deals with a periodic-review substitutable
inventory system for a finite and an infinite number of periods. Here
an upward substitution structure, a substitution of a more costly item
by a less costly one, is assumed, with two products. At the beginning
of each period, a stochastic demand comes for the first item only,
which is quality-wise better and hence costlier. Whenever an arriving
demand finds zero inventory of this product, a fraction of unsatisfied
customers goes for its substitutable second item. An optimal ordering
policy has been derived for each period. The results are illustrated
with numerical examples. A sensitivity analysis has been done to
examine how sensitive the optimal solution and the maximum profit
are to the values of the discount factor, when there is a large number
of periods.
Abstract: An optimal control problem for a mathematical model of efficiency of antiviral therapy in hepatitis B virus infections is considered. The aim of the study is to control the new viral production, block the new infection cells and maintain the number of uninfected cells in the given range. The optimal controls represent the efficiency of antiviral therapy in inhibiting viral production and preventing new infections. Defining the cost functional, the optimal control problem is converted into the constrained optimization problem and the first order optimality system is derived. For the numerical simulation, we propose the steepest descent algorithm based on the adjoint variable method. A computer program in MATLAB is developed for the numerical simulations.
Abstract: In the present paper, we investigate a differential subordination
involving multiplier transformation related to a sector in the
open unit disk E = {z : |z| < 1}. As special cases to our main
result, certain sufficient conditions for strongly starlike and strongly
convex functions are obtained.
Abstract: Meshing is the process of discretizing problem
domain into many sub domains before the numerical calculation can
be performed. One of the most popular meshes among many types of meshes is tetrahedral mesh, due to their flexibility to fit into almost
any domain shape. In both 2D and 3D domains, triangular and tetrahedral meshes can be generated by using Delaunay triangulation.
The quality of mesh is an important factor in performing any Computational Fluid Dynamics (CFD) simulations as the results is
highly affected by the mesh quality. Many efforts had been done in
order to improve the quality of the mesh. The paper describes a mesh
generation routine which has been developed capable of generating
high quality tetrahedral cells in arbitrary complex geometry. A few
test cases in CFD problems are used for testing the mesh generator.
The result of the mesh is compared with the one generated by a
commercial software. The results show that no sliver exists for the
meshes generated, and the overall quality is acceptable since the percentage of the bad tetrahedral is relatively small. The boundary
recovery was also successfully done where all the missing faces are
rebuilt.
Abstract: Assume that we have m identical graphs where the
graphs consists of paths with k vertices where k is a positive integer.
In this paper, we discuss certain labelling of the m graphs called
c-Erdösian for some positive integers c. We regard labellings of the
vertices of the graphs by positive integers, which induce the edge
labels for the paths as the sum of the two incident vertex labels.
They have the property that each vertex label and edge label appears
only once in the set of positive integers {c, . . . , c+6m- 1}. Here,
we show how to construct certain c-Erdösian of m paths with 2 and
3 vertices by using Skolem sequences.
Abstract: In the present study, a numerical analysis is carried
out to investigate unsteady MHD (magneto-hydrodynamic) flow and
heat transfer of a non-Newtonian second grade viscoelastic fluid
over an oscillatory stretching sheet. The flow is induced due to an
infinite elastic sheet which is stretched oscillatory (back and forth) in
its own plane. Effect of viscous dissipation and joule heating are
taken into account. The non-linear differential equations governing
the problem are transformed into system of non-dimensional
differential equations using similarity transformations. A newly
developed meshfree numerical technique Element free Galerkin
method (EFGM) is employed to solve the coupled non linear
differential equations. The results illustrating the effect of various
parameters like viscoelastic parameter, Hartman number, relative
frequency amplitude of the oscillatory sheet to the stretching rate and
Eckert number on velocity and temperature field are reported in
terms of graphs and tables. The present model finds its application in
polymer extrusion, drawing of plastic films and wires, glass, fiber
and paper production etc.
Abstract: We present a new quadrature rule based on the spline
interpolation along with the error analysis. Moreover, some error
estimates for the reminder when the integrand is either a Lipschitzian
function, a function of bounded variation or a function whose
derivative belongs to Lp are given. We also give some examples
to show that, practically, the spline rule is better than the trapezoidal
rule.
Abstract: Fuzzy sets theory affirmed that the linguistic value for
every contraries relation is complementary. It was stressed in the
intuitionistic fuzzy sets (IFS) that the conditions for contraries
relations, which are the fuzzy values, cannot be greater than one.
However, complementary in two contradict phenomena are not
always true. This paper proposes a new idea condition for conflicting
bifuzzy sets by relaxing the condition of intuitionistic fuzzy sets.
Here, we will critically forward examples using triangular fuzzy
number in formulating a new condition for conflicting bifuzzy sets
(CBFS). Evaluation of positive and negative in conflicting
phenomena were calculated concurrently by relaxing the condition in
IFS. The hypothetical illustration showed the applicability of the new
condition in CBFS for solving non-complement contraries
intuitionistic evaluation. This approach can be applied to any
decision making where conflicting is very much exist.