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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
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The Pure and Applied Mathematics
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Korea Society of Mathematical Education
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Volume & Issues
Volume 15, Issue 4 - Nov 2008
Volume 15, Issue 3 - Aug 2008
Volume 15, Issue 2 - May 2008
Volume 15, Issue 1 - Feb 2008
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ON A DISCUSSION OF NONLINEAR INTEGRAL EQUATION OF TYPE VOLTERRA-HAMMERSTEIN
El-Borai, M.M. ; Abdou, M.A. ; El-Kojok, M.M. ;
The Pure and Applied Mathematics, volume 15, issue 1, 2008, Pages 1~17
Here, we consider the existence and uniqueness solution of nonlinear integral equation of the second kind of type Volterra-Hammerstein. Also, the normality and continuity of the integral operator are discussed. A numerical method is used to obtain a system of nonlinear integral equations in position. The solution is obtained, and many applications in one, two and three dimensionals are considered.
NEW ALGORITHM FOR THE DETERMINATION OF AN UNKNOWN PARAMETER IN PARABOLIC EQUATIONS
Yue, Sufang ; Cui, Minggen ;
The Pure and Applied Mathematics, volume 15, issue 1, 2008, Pages 19~34
A new algorithm for the solution of an inverse problem of determining unknown source parameter in a parabolic equation in reproducing kernel space is considered. Numerical experiments are presented to demonstrate the accuracy and the efficiency of the proposed algorithm.
APPROXIMATING SOLUTIONS OF EQUATIONS BY COMBINING NEWTON-LIKE METHODS
Argyros, Ioannis K. ;
The Pure and Applied Mathematics, volume 15, issue 1, 2008, Pages 35~45
In cases sufficient conditions for the semilocal convergence of Newtonlike methods are violated, we start with a modified Newton-like method (whose weaker convergence conditions hold) until we stop at a certain finite step. Then using as a starting guess the point found above we show convergence of the Newtonlike method to a locally unique solution of a nonlinear operator equation in a Banach space setting. A numerical example is also provided.
CONCERNING THE RADII OF CONVERGENCE FOR A CERTAIN CLASS OF NEWTON-LIKE METHODS
Argyros, Ioannis K. ;
The Pure and Applied Mathematics, volume 15, issue 1, 2008, Pages 47~55
Local convergence results for three Newton-like methods in Banach space are provided. A comparison is given between the three convergence radii. Then we show that using the largest convergence radius we can pick an initial guess from with we start the corresponding iteration. It turns out that after a finite number of steps we can always use the iterate found as the starting guess for a faster method, since this iterate will be inside the convergence domain of the new method.
NUMERICAL RESULTS ON ALTERNATING DIRECTION SHOOTING METHOD FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
Kim, Do-Hyun ;
The Pure and Applied Mathematics, volume 15, issue 1, 2008, Pages 57~72
This paper is concerned with the numerical solutions to steady state nonlinear elliptical partial differential equations (PDE) of the form
, where D, E, F are functions of x, y, u,
, and G is a function of x and y. Dirichlet boundary conditions in a rectangular region are considered. We propose alternating direction shooting method for solving such nonlinear PDE. Numerical results show that the alternating direction shooting method performed better than the commonly used linearized iterative method.
INTUITIONISTIC FUZZY COMMUTATIVE IDEALS OF BCK-ALGEBRAS
Jun, Young-Bae ; Lee, Dong-Soo ; Park, Chul-Hwan ;
The Pure and Applied Mathematics, volume 15, issue 1, 2008, Pages 73~84
After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Aranassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to commutative ideals in BCK-algebras. The notion of an intuitionistic fuzzy commutative ideal of a BCK-algebra is introduced, and some related properties are investigated. Characterizations of an intuitionistic fuzzy commutative ideal are given. Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy commutative ideal are given. Using a collection of commutative ideals, intuitionistic fuzzy commutative ideals are established.
ON THE WEAK FORMS OF CHOICE IN TOPOI
Kim, Ig-Sung ;
The Pure and Applied Mathematics, volume 15, issue 1, 2008, Pages 85~92
In topoi, there are various forms of the axiom of choice such as (ES), (AC) and (WO). And also there are various weak forms of the axiom of choice such as (DES), (IAC) and (ASC). First we investigate the relation between (IAC) and (ASC), and then we study the relation between (AC) and (WO). We get equivalent forms of the axiom of choice in a well-pointed topos.
ON HEINZ-KATO-FURUTA INEQUALITY WITH BEST BOUNDS
Lin, C.S. ;
The Pure and Applied Mathematics, volume 15, issue 1, 2008, Pages 93~101
In this article we shall characterize the Heinz-Kato-Furuta inequality in several ways, and the best bound for sharpening of the inequality is obtained by the method in .