Abstract: In this paper developed and realized absolutely new
algorithm for solving three-dimensional Poisson equation. This
equation used in research of turbulent mixing, computational fluid
dynamics, atmospheric front, and ocean flows and so on. Moreover in
the view of rising productivity of difficult calculation there was
applied the most up-to-date and the most effective parallel
programming technology - MPI in combination with OpenMP
direction, that allows to realize problems with very large data
content. Resulted products can be used in solving of important
applications and fundamental problems in mathematics and physics.
Abstract: In this paper a new concept of partial complement of a graph G is introduced and using the same a new graph parameter, called completion number of a graph G, denoted by c(G) is defined. Some basic properties of graph parameter, completion number, are studied and upperbounds for completion number of classes of graphs are obtained , the paper includes the characterization also.
Abstract: By means of the idea of three-wave method, we obtain some analytic solutions for high nonlinear form of Benjamin-Bona- Mahony-Burgers (shortly BBMB) equations in its bilinear form.
Abstract: Covering-based rough sets is an extension of rough
sets and it is based on a covering instead of a partition of the
universe. Therefore it is more powerful in describing some practical
problems than rough sets. However, by extending the rough sets,
covering-based rough sets can increase the roughness of each model
in recognizing objects. How to obtain better approximations from
the models of a covering-based rough sets is an important issue.
In this paper, two concepts, determinate elements and indeterminate
elements in a universe, are proposed and given precise definitions
respectively. This research makes a reasonable refinement of the
covering-element from a new viewpoint. And the refinement may
generate better approximations of covering-based rough sets models.
To prove the theory above, it is applied to eight major coveringbased
rough sets models which are adapted from other literature.
The result is, in all these models, the lower approximation increases
effectively. Correspondingly, in all models, the upper approximation
decreases with exceptions of two models in some special situations.
Therefore, the roughness of recognizing objects is reduced. This
research provides a new approach to the study and application of
covering-based rough sets.
Abstract: Leptospirosis occurs worldwide (except the
poles of the earth), urban and rural areas, developed and
developing countries, especially in Thailand. It can be
transmitted to the human by rats through direct and indirect
ways. Human can be infected by either touching the infected rats
or contacting with water, soil containing urine from the infected
rats through skin, eyes and nose. The data of the people who
are infected with this disease indicates that most of the
patients are adults. The transmission of this disease is studied
through mathematical model. The population is separated into human
and rat. The human is divided into two classes, namely juvenile
and adult. The model equation is constructed for each class. The
standard dynamical modeling method is then used for
analyzing the behaviours of solutions. In addition, the
conditions of the parameters for the disease free and endemic
states are obtained. Numerical solutions are shown to support the
theoretical predictions. The results of this study guide the way to
decrease the disease outbreak.
Abstract: Ranked set sampling (RSS) was first suggested to increase the efficiency of the population mean. It has been shown that this method is highly beneficial to the estimation based on simple random sampling (SRS). There has been considerable development and many modifications were done on this method. When a concomitant variable is available, ratio estimation based on ranked set sampling was proposed. This ratio estimator is more efficient than that based on SRS. In this paper some ratio type estimators of the population mean based on RSS are suggested. These estimators are found to be more efficient than the estimators of similar form using simple random sample.
Abstract: In this paper, penalized power-divergence test statistics have been defined and their exact size properties to test a nested sequence of log-linear models have been compared with ordinary power-divergence test statistics for various penalization, λ and main effect values. Since the ordinary and penalized power-divergence test statistics have the same asymptotic distribution, comparisons have been only made for small and moderate samples. Three-way contingency tables distributed according to a multinomial distribution have been considered. Simulation results reveal that penalized power-divergence test statistics perform much better than their ordinary counterparts.
Abstract: In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated.With the help of computer algebra system MATHEMATICA, the first 10 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 10 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems. At last, we give an system which could bifurcate 10 limit circles.
Abstract: This paper presents a procedure for estimating VAR
using Sequential Discounting VAR (SDVAR) algorithm for online
model learning to detect fraudulent acts using the telecommunications
call detailed records (CDR). The volatility of the VAR is observed
allowing for non-linearity, outliers and change points based on the
works of [1]. This paper extends their procedure from univariate
to multivariate time series. A simulation and a case study for
detecting telecommunications fraud using CDR illustrate the use of
the algorithm in the bivariate setting.
Abstract: A kind of singularly perturbed boundary value problems is under consideration. In order to obtain its approximation, simple upwind difference discretization is applied. We use a moving mesh iterative algorithm based on equi-distributing of the arc-length function of the current computed piecewise linear solution. First, a maximum norm a posteriori error estimate on an arbitrary mesh is derived using a different method from the one carried out by Chen [Advances in Computational Mathematics, 24(1-4) (2006), 197-212.]. Then, basing on the properties of discrete Green-s function and the presented posteriori error estimate, we theoretically prove that the discrete solutions computed by the algorithm are first-order uniformly convergent with respect to the perturbation parameter ε.
Abstract: We present a discussion of three adaptive filtering
algorithms well known for their one-step termination property, in
terms of their relationship with the minimal residual method. These
algorithms are the normalized least mean square (NLMS), Affine
Projection algorithm (APA) and the recursive least squares algorithm
(RLS). The NLMS is shown to be a result of the orthogonality
condition imposed on the instantaneous approximation of the Wiener
equation, while APA and RLS algorithm result from orthogonality
condition in multi-dimensional minimal residual formulation. Further
analysis of the minimal residual formulation for the RLS leads to
a triangular system which also possesses the one-step termination
property (in exact arithmetic)
Abstract: In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given.
Abstract: Let G be a graph of order n. The second stage adjacency matrix of G is the symmetric n × n matrix for which the ijth entry is 1 if the vertices vi and vj are of distance two; otherwise 0. The sum of the absolute values of this second stage adjacency matrix is called the second stage energy of G. In this paper we investigate a few properties and determine some upper bounds for the largest eigenvalue.
Abstract: This paper study the behavior of the solution at the crack edges for an elliptical crack with developing cusps, Ω in the plane elasticity subjected to shear loading. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over Ω and it is then transformed into a similar equation over a circular region, D, using conformal mapping. An appropriate collocation points are chosen on the region D to reduce the hypersingular integral equation into a system of linear equations with (2N+1)(N+1) unknown coefficients, which will later be used in the determination of shear stress intensity factors and maximum shear stress intensity. Numerical solution for the considered problem are compared with the existing asymptotic solution, and displayed graphically. Our results give a very good agreement to the existing asymptotic solutions.
Abstract: Let the vertices of a graph such that every two
adjacent vertices have different color is a very common problem in
the graph theory. This is known as proper coloring of graphs. The
possible number of different proper colorings on a graph with a given
number of colors can be represented by a function called the
chromatic polynomial. Two graphs G and H are said to be
chromatically equivalent, if they share the same chromatic
polynomial. A Graph G is chromatically unique, if G is isomorphic to
H for any graph H such that G is chromatically equivalent to H. The
study of chromatically equivalent and chromatically unique problems
is called chromaticity. This paper shows that a wheel W12 is
chromatically unique.
Abstract: In this paper, a self starting two step continuous block
hybrid formulae (CBHF) with four Off-step points is developed using
collocation and interpolation procedures. The CBHF is then used to
produce multiple numerical integrators which are of uniform order
and are assembled into a single block matrix equation. These
equations are simultaneously applied to provide the approximate
solution for the stiff ordinary differential equations. The order of
accuracy and stability of the block method is discussed and its
accuracy is established numerically.
Abstract: To increase precision and reliability of automatic control systems, we have to take into account of random factors affecting the control system. Thus, operational matrix technique is used for statistical analysis of first order plus time delay system with uniform random parameter. Examples with deterministic and stochastic disturbance are considered to demonstrate the validity of the method. Comparison with Monte Carlo method is made to show the computational effectiveness of the method.
Abstract: The notion of intuitionistic fuzzy sets was introduced
by Atanassov as a generalization of the notion of fuzzy sets. Y.B. Jun
and S.Z. Song introduced the notion of intuitionistic fuzzy points.
In this paper we find some relations between the intuitionistic fuzzy
ideals of a semigroup S and the set of all intuitionistic fuzzy points
of S.
Abstract: This work concerns the evolution and the maintenance
of an ontological resource in relation with the evolution of the corpus
of texts from which it had been built.
The knowledge forming a text corpus, especially in dynamic domains,
is in continuous evolution. When a change in the corpus occurs, the
domain ontology must evolve accordingly. Most methods manage
ontology evolution independently from the corpus from which it is
built; in addition, they treat evolution just as a process of knowledge
addition, not considering other knowledge changes. We propose a
methodology for managing an evolving ontology from a text corpus
that evolves over time, while preserving the consistency and the
persistence of this ontology.
Our methodology is based on the changes made on the corpus to
reflect the evolution of the considered domain - augmented surgery
in our case. In this context, the results of text mining techniques,
as well as the ARCHONTE method slightly modified, are used to
support the evolution process.
Abstract: The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.