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Vol.13 No.4
Abstract
Category Fuz of fuzzy sets has a similar function to the topos Set. But Category Fuz forms a weak topos. We show that supports split weakly(SSW) and with some properties, implicity axiom of choice(IAC) holds in weak topos Fuz. So weak axiom of choice(WAC) holds in weak topos Fuz. Also we show that weak extensionality principle for arrow holds in weak topos Fuz.
Abstract
In 1994, Lavoie et al. have obtained twenty tree interesting results closely related to the classical Dixon's theorem on the sum of a <TEX>$_3F_2$</TEX> by making a systematic use of some known relations among contiguous functions. We aim at showing that these results can be derived by using the same technique developed by Bailey with the help of Gauss's summation theorem and generalized Kummer's theorem obtained by Lavoie et al..
Abstract
A local convergence analysis of Newton's method for perturbed generalized equations is provided in a Banach space setting. Using center Lipschitzian conditions which are actually needed instead of Lipschitzian hypotheses on the <TEX>$Fr\'{e}chet$</TEX>-derivative of the operator involved and more precise estimates under less computational cost we provide a finer convergence analysis of Newton's method than before [5]-[7].
Abstract
Recently <TEX>$L_{\delta}$</TEX>-groups were introduced in the study of geometric group theory. Three levels of <TEX>$L_{\delta}$</TEX>-groups are difined and discussed. It is shown that each of these levels of <TEX>$L_{\delta}$</TEX>-groups is closed under taking a direct product.
Abstract
Many partial differential equations defined on a rectangular domain can be solved numerically by using a domain decomposition method. The most commonly used decompositions are the domain being decomposed in stripwise and rectangular way. Theories for non-overlapping domain decomposition(in which two adjacent subdomains share an interface) were often focused on the stripwise decomposition and claimed that extensions could be made to the rectangular decomposition without further discussions. In this paper we focus on the comparisons of the two ways of decompositions. We consider the unconditionally stable scheme, the MIP algorithm, for solving parabolic partial differential equations. The SOR iterative method is used in the MIP algorithm. Even though the theories are the same but the performances are different. We found out that the stripwise decomposition has better performance.
Abstract
We Investigate the relation between the multi-variable bi-additive functional equation f(x+y+z,u+v+w)=f(x,u)+f(x,v)+f(x,w)+f(y,u)+f(y,v)+f(y,w)+f(z,u)+f(z,v)+f(z,w) and the multi-variable quadratic functional equation g(x+y+z)+g(x-y+z)+g(x+y-z)+g(-x+y+z)=4g(x)+4g(y)+4g(z). Furthermore, we find out the general solution of the above two functional equations.
Abstract
M. <TEX>$Bre\v{s}ar$</TEX> and J. Vukman obtained some results concerning orthogonal derivations in semiprime rings which are related to the result that is well-known to a theorem of Posner for the product of two derivations in prime rings. In this paper, we present orthogonal generalized derivations in semiprime near-rings.
Abstract
In this paper we establish some new identities involving Stirling numbers of both kinds. These identities are obtained via Riodan arrays with a variable x. Some well-known identities are obtained as special cases of the new identities for the specific number x.