이차원 선형 탄성방정식을 소개하고 약한 형식 타원성을 보여준다(P-1)순응 유한요소를 사용할 때 나타나는 잠김현상을 설명하고 그 해결책으로서 비순응 유한요소법과 penalty 항을 가진 혼합문제, 일계 최소자승법 등을 소개한다.

Wurful gave a characterization of those rings R which satisfy that for every ring extension $R{\subset}S$. Ho $m_{R}$(S, -) preserves injective envelopes. In this note, we consider an analogous problem concerning injective covers.

In this paper we introduce the notion of quotient in-cline and obtain the structure of incline algebra. Moreover, we also introduce the notion of prime and maximal ideal in incline, and study some relations between them in incline algebra.

Let η be the complex upper half plane, let h($\tau$) be a cusp form, and let $\tau$ be an imaginary quadratic in η. If h($\tau$)$\in$$\Omega$( $g_{2}$($\tau$)$^{m}$ $g_{3}$ ($\tau$)$^{ι}$with $\Omega$the field of algebraic numbers and m. l positive integers, then we show that h($\tau$) is integral over the ring Q[h/$\tau$/n/)…h($\tau$+n-1/n)] (No Abstract.see full/text)

Using p-adic class number formula, we derive a congru-ence relation for class numbers of the simplest cubic fields which can be considered as a cubic analogue of Ankeny-Artin-Chowlas theo-rem, Furthermore, we give an elementary proof for an upper bound for the class numbers of the simplest cubic fields.

Rassias obtained the Hyers-Ulam stability of the gen-eral Euler-Lagrange functional equation. In this paper we general-ized this stability in the spirit of Hyers, Ulam, Rassias and Gavruta.

Let { $A_{>o}$ t= exp(M log t)} $_{t}$ be a dilation group where M is a real n$\times$n matrix whose eigenvalues has strictly positive real part, and let $\rho$be an $A_{t}$ -homogeneous distance function defined on ( $R^{n}$ ). Suppose that K is a function defined on ( $R^{n}$ ) such that /K(x)/$\leq$ (No Abstract.see full/text) for a decreasing function defined on (t) on R+ satisfying where wo(x)=│log│log (x)ll. For f$\in$ $L_{1}$ ( $R^{n}$ ), define f(x)=sup t>0 Kt*f(x)=t-v K(Al/tx) and v is the trace of M. Then we show that \ulcorner is a bounded operator of $L_{-{1}( $R^{n}$ ) into $L^1$,$\infty$( $R^{n}$).

In this paper, we first introduce the modified Yeh-Wiener integral and then consider the modified conditional Yeh-Wiener integral. Here we use the space of continuous functions on a different region which was discussed before. We also evaluate some modified conditional Yeh-Wiener integral with examples using the simple formula for the modified conditional Yeh-Wiener integral.

An n-dimensional ME-manifold ME $X_{n}$ is a general-ized Riemannian manifold connected by the ME-connection which is both Einstein and of the form (2.13). The purpose of this paper is to study the properties of the ME-curvature tensors, the con-tracted ME-curvature tensors and the field equations in ME $X_{n}$)n)

We shall find the condition for a Finsler space with a special ($\alpha$.$\beta$)-metric L($\alpha$.$\beta$) satisfying L$^2$ =2$\alpha$$\beta$ to be a Douglas space. The special Randers change of the above Finsler metric by $\beta$ is also studied.

The aim of this paper is to derive the analytical so-lution of the queue: H$_{r}$/M/c/k/N for machine interference with balking and reneging, and FIFO (first in, first out) service disci-pline.e.

We consider a nonsmooth multiobjective opimization problem(PE) involving locally Lipschitz functions and define gen-eralized invexity for locally Lipschitz functions. Using Fritz John type optimality conditions, we establish Fritz John type sufficient optimality theorems for (PE) under generalized invexity.

Doubly stochastic matrices are n$\times$n nonnegative ma-trices whose row and column sums are all 1. Convex polytope $\Omega$$_{n}$ of doubly stochastic matrices and more generally (R,S), so called transportation polytopes, are important since they form the domains for the transportation problems. A theorem by Birkhoff classifies the extremal matrices of , $\Omega$$_{n}$ and extremal matrices of transporta-tion polytopes (R,S) were all classified combinatorially. In this article, we consider signed version of $\Omega$$_{n}$ and (R.S), obtain signed Birkhoff theorem; we define a new class of convex polytopes (R,S), calculate their dimensions, and classify their extremal matrices, Moreover, we suggest an algorithm to express a matrix in (R,S) as a convex combination of txtremal matrices. We also give an example that a polytope of signed matrices is used as a domain for a decision problem. In this context of finite reflection(Coxeter) group theory, our generalization may also be considered as a generalization from type $A_{*}$ n/ to type B$_{n}$ D$_{n}$. n/.

We computed zero mean Gaussian of average error bounds pf Simpsons quadrature with convariances in [2]. In this paper, we compute zero mean Gaussian of average error bounds between Simpsons quadrature and composite Simpsons quadra-ture on four consecutive subintervals. The reason why we compute these on subintervals is because these results enable us to compute a posteriori error bounds on the whole interval in the later paper.