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Bulletin of the Korean Mathematical Society
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The Korean Mathematical Society
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Volume 28, Issue 2 - Aug 1991
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APPROXIMATE CONTROLLABILITY AND CONTROLLABILITY FOR DELAY VOLTERRA SYSTEM
Kwun, Young-Chel ; Park, Jong-Yeoul ; Ryu, Jong-Won ;
Bulletin of the Korean Mathematical Society, volume 28, issue 2, 1991, Pages 131~145
The purpose of this paper is to prove the approximate controllability results, which were shown in  for the abstract semilinear control system, here, for the delay volterra system in the case of trajectories.
CONDITIONAL GENERALIZED WIENER MEASURES
Kang, Soon-Ja ;
Bulletin of the Korean Mathematical Society, volume 28, issue 2, 1991, Pages 147~161
In this paper we define the conditional generalized Wiener measure and then express the conditional generalized Wiener integral over this new measure. In particular we consider a conditional expectation of functionals of the generalized Brownian paths under the condition that the paths pass through the given points .xi.
, .., .xi.
at times t
, .., t
REMARKS ON SOME VARIATIONAL INEQUALITIES
Park, Sehie ;
Bulletin of the Korean Mathematical Society, volume 28, issue 2, 1991, Pages 163~174
This is a continuation of the author's previous work . In this paper, we consider mainly variational inequalities for single-valued functions. We first obtain a generalization of the variational type inequality of Juberg and Karamardian  and apply it to obtain strengthened versions of the Hartman-Stampacchia inequality and the Brouwer fixed point theorem. Next, we obtain fairly general versions of Browder's variational inequality  and its subsequent generalizations due to Brezis et al , Takahashk , Shih and Tan , Simons , and others. Finally, in this paper, we obtain a variational inequality for non-real locally convex t.v.s. which generalizes a result of Shih and Tan .
THE WEAK F-REGULARITY OF COHEN-MACAULAY LOCAL RINGS
Cho, Y.H. ; Moon, M.I. ;
Bulletin of the Korean Mathematical Society, volume 28, issue 2, 1991, Pages 175~180
In ,  and , Hochster and Huneke introduced the notions of the tight closure of an ideal and of the weak F-regularity of a ring. This notion enabled us to give new proofs of many results in commutative algebra. A regular ring is known to be F-regular, and a Gorenstein local ring is proved to be F-regular provided that one ideal generated by a system of parameters (briefly s.o.p.) is tightly closed. In fact, a Gorenstein local ring is weakly F-regular if and only if there exists a system of parameters ideal which is tightly closed . But we do not know whether this fact is true or not if a ring is not Gorenstein, in particular, a ring is a Cohen Macaulay (briefly C-M) local ring. In this paper, we will prove this in the case of an 1-dimensional C-M local ring. For this, we study the F-rationality and the normality of the ring. And we will also prove that a C-M local ring is to be Gorenstein under some additional condition about the tight closure.
SOME PROPERTIES OF HYPOELLIPTIC PSEUDODIFFERENTIAL OPERATORS
Jang, Lee-Chae ;
Bulletin of the Korean Mathematical Society, volume 28, issue 2, 1991, Pages 181~184
ALMOST INVERTIBILITY MODULO CLOSED IDEALS
Kim, Yong-Tae ; Lee, Woo-Young ; Lee, Hae-Jin ;
Bulletin of the Korean Mathematical Society, volume 28, issue 2, 1991, Pages 185~190
The concept of "almost invertibility modulo closed ideals" in L(X, Y) was introduced, implicitly, by Robin Harte [1, Theorem 3.9.5]. The aims of this note are to make the formal definition of "almost left and right invertible modulo closed ideals" operators and show that they form open sets.they form open sets.
FUZZY P-LIMIT SPACES
Min, Kyung-Chan ;
Bulletin of the Korean Mathematical Society, volume 28, issue 2, 1991, Pages 191~199
The notion of convergence in a fuzzy topological space was intorduced in various aspects as a local theory of fuzzy topologies [2,9,10,11,12,15,19,20]. In  a notion of fuzzy limitierung on a set is defined in terms of prefilters convergent to a fuzzy point and allows natural function structure in it. In this paper using fuzzy x-filters we introduce a notion of convergence to a point in a set, called a fuzzy p-limitierung, generalizing that of fuzzy neighborhood system introduced by Warren , which characterizes fuzzy topology. The notion of fuzzy p-limitierung enables us to form a convenient class containing all fuzzy topological spaces and all limit spaces. In section 4 we show that in fuzzy topology there is no natural function space structure. We show that fuzzy p-limit spaces form a quasitopos and give explicitly natural function space structure in it, providing an exponential law C(X*Y,Z)=C(X,C(Y,Z)). Form a categorical point of view the category FpLim of fuzzy p-limit spaces and fuzzy continuous maps is shown to be a quasitopos (=topological universe) containing the category FTop of fuzzy topological spaces as a bireflective subcategory and the category Lim of limit spaces as a bicoreflective subcategory. Throughout this paper, we use Lowen's notion of fuzzy topology. For categorical background we refer to [4, 6]
SOME REMARK ON GENERALIZATION OF DELIGNE ESTIMATE
Koo, Ja-Kyung ;
Bulletin of the Korean Mathematical Society, volume 28, issue 2, 1991, Pages 201~205
A STUDY ON NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS
Yu, Dong-Won ;
Bulletin of the Korean Mathematical Society, volume 28, issue 2, 1991, Pages 207~217
In this paper, we consider an exponentially dominant order .alpha. of a problem, and the matrix A is replaced by this number .alpha. in the above function. In Section 1, the Runge-Kutta method and the multistep methods generalized by this function. when the exponentially dominat order is positive, its numerical solutions can be accurately computed by these generalized methods. In Section 2, A- and B-stability of the generalized Runge-Kutta methods are tested. finally, in Section 3, a concept of AB-stability is introduced. And we study some sufficient conditions under which the generalized runge-kutta methods are AB-stable
ON A QUESTION OF KIM CONCERNING CERTAIN GROUP PRESENTATIONS
Thomas, Richard M. ;
Bulletin of the Korean Mathematical Society, volume 28, issue 2, 1991, Pages 219~224
A GENERALIZATION OF DIFFERENTIAL FORMS AND ITS APPLICATION
Shikata, Yoshihiro ; Hong, Suk-Ho ;
Bulletin of the Korean Mathematical Society, volume 28, issue 2, 1991, Pages 225~229
Our final purpose may be to introduce generalized differential forms on the space Map(S, M) of mappings from a manifold S into a manifold M and discuss the differential geometry of the space Map(S, M) from the point of the generalized forms. Here we take a subspace X of the space Map(S,M) and we introduce the generalized differential forms on X, taking the dual to the chain space with the flat norm. This method of construction allows us to discuss a sufficient condition for a subspace Y of X to admit the generalized differential forms and the natural integration as the dual operation.
ON THE TRANSVERSAL CONFORMAL CURVATURE TENSOR ON HERMITIAN FOLIATIONS
Pak, Hong-Kyung ;
Bulletin of the Korean Mathematical Society, volume 28, issue 2, 1991, Pages 231~241
Recently, many mathematicians([NT], [Ka], [TV], [CW], etc.) studied foliated structures on a smooth manifold with the viewpoint of transversal differential geometry. In this paper, we shall discuss certain hermitian foliations F on a riemannian manifold with a bundle-like metric, that is, their transversal bundles to F have hermitian structures.
DUAL ALGORITHM FOR
ISOTONIC OPTIMIZATION WITH WEIGHTS ON A PARTIALLY ORDERED SET
Chung, Seiyoung ;
Bulletin of the Korean Mathematical Society, volume 28, issue 2, 1991, Pages 243~254
For a given function f.mem.F and a set of functions J.subeq.F, the problem of isotonic optimization is to determine an element in the set nearest to f in some sense. Specifically, let X be a partially ordered finite set with a partial order << and, let F"=F(X) be the linear space of all bounded real valued functions on X. A function g.mem.F is said to be an isotonic function if g(x).leq.g(y) whenever x,y.mem.X and x << y.<< y.