Showing papers in "Journal of The Korean Mathematical Society in 1998"

Assouad dimension: antifractal metrization, porous sets, and homogeneous measures

Abstract: We prove that a non-empty separable metrizable space X admits a totally bounded metric for which the metric dimension of X in Assouad's sense equals the topological dimension of X, which leads to a characterization for the latter. We also give a characterization based on this Assouad dimension for the demension (embedding dimension) of a compact set in a Euclidean space. We discuss Assouad dimension and these results in connection with porous sets and measures with the doubling property. The elementary properties of Assouad dimension are proved in an appendix.

A new look at the fundamental theorem of asset pricing

Abstract: In this paper we consider a security market whose asset price process is a vector semimartingale. The market is said to be fair if there exists an equivalent martingale measure for the price process, deflated by a numeraire asset. It is shown that the fairness of a market is invariant under the change of numeraire. As a consequence, we show that the characterization of the fairness of a market is reduced to the case where the deflated price process is bounded. In the latter case a theorem of Kreps (1981) has already solved the problem. By using a theorem of Delbaen and Schachermayer (1994) we obtain an intrinsic characterization of the fairness of a market, which is more intuitive than Kreps' theorem. It is shown that the arbitrage pricing of replicatable contingent claims is independent of the choice of numeraire and equivalent martingale measure. A sufficient condition for the fairness of a market, modeled by an Ito process, is given.

A unified fixed point theory of multimaps on topological vector spaces

Abstract: We give general fixed point theorems for compact multimaps in the "better" admissible class defined on admissible convex subsets (in the sense of Klee) of a topological vector space not necessarily locally convex. Those theorems are used to obtain results for -condensing maps. Our new theorems subsume more than seventy known or possible particular forms, and generalize them in terms of the involving spaces and the multimaps as well. Further topics closely related to our new theorems are discussed and some related problems are given in the last section.n.

Retrial queues with a finite number of sources

Abstract: In the theory of retrial queues it is usually assumed that the flow of primary customers is Poisson. This means that the number of independent sources, or potential customers, is infinite and each of them generates primary arrivals very seldom. We consider now retrial queueing systems with a homogeneous population, that is, we assume that a finite number K of identical sources generates the so called quasi-random input. We present a survey of the main results and mathematical tools for finite source retrial queues, concentrating on M/G/1//K and M/M/c//K systems with repeated attempts.

Domination in digraphs

Abstract: We establish bounds for the domination number of a digraph in terms of the minimum indegree and the order, and then we find a sharp upper bound for the domination number of a weak digraph with minimum indegree one. We also determine the domination number of a random digraph.

On existence of solutions of degenerate wave equations with nonlinear damping terms

Abstract: In this paper, we consider the existence and asymptotic behavior of solutions of the following problem: -(t, x) - (∥∇u(t, x)∥(equation omitted) ＋ ∥∇v(t, x) (equation omitted) u(t, x)＋│ (t, x)│sup p-1/ (t, x) = │u(t, x) u(t, x), x, t[0, T], (t, x) - (∥∇uu(t, x) (equation omitted) ＋ ∥∇v(t, x) (equation omitted)sup / v(t, x)＋ │ (t, x)│sup p-1/ (t, x) = u(t, x) u(t, x), x, t[0, T], u(0, x) = (x), (0, x) = (x), x, u(0, x) = (x), (0, x) = (x), x, u│∂=v│∂=0 T > 0, q > 1, p 1, > 0, R, 1 and is the Laplacian in .X> N/.

The knot $5_2$ and cyclically presented groups

Abstract: The cyclically presented groups which arise as fundamental groups of cyclic branched coverings of the knot are studied. The fundamental polyhedra for these groups are described. Moreover the cyclic covering manifolds are obtained in terms of Dehn surgery and as two-fold branched coverings of the 3-sphere.

Invariants of one-dimensional diffusion processes and applications

Abstract: One-dimensional diffusion processes are characterized by Feller's data of canonical scales and speed measures and, if we apply the theory of spectral functions of strings developed by M. G. Krein, Feller's data are determined by paris of spectral characteristic functions so that theses pairs may be considered as invariants of diffusions under the homeomorphic change of state spaces. We show by examples how these invariants are useful in the study of one-dimensional diffusion processes.

On selfsimilar and semi-selfsimilar processes with independent increments

Abstract: After the review of known results on the connections between selfsimilar processes with independent increments (processes of class L) and selfdecomposable distributions and between semi-selfsimilar processes with independent increments and semi-selfdecomposable distributions, dichotomy of those processes into transient and recurrent is discussed. Due to the lack of stationarity of the increments, transience and recurrence are not expressed by finiteness and infiniteness of mean sojourn times on bound sets. Comparison in transience-recurrence of the Levy process and the process of class L associated with a common distribution of class L is made.

The arithmetic of carlitz polynomials

Abstract: Some interesting properties of Carlitz cyclotomic polynomials analogous to those of classical cyclotomic polynomials are given.

Semialgebraic G CW complex structure of semialgebraic G spaces

Abstract: Let G be a compact Lie group and M a semialgebraic G space in some orthogonal representation space of G. We prove that if G is finite then M has an equivariant semialgebraic triangulation. Moreover this triangulation is unique. When G is not finite we show that M has a semialgebraic G CW complex structure, and this structure is unique. As a consequence compact semialgebraic G space has an equivariant simple homotopy type.

Multivariate distributions with selfdecomposable projections

Abstract: A random vector X on with the following properties is constructed: the distribution of X is infinitely divisible and not selfdecomposable, but every linear transformation of X to a lower-dimensional space has a selfdecomposable distribution.

RADIAL SYMMETRY OF POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS IN $R^n$

Abstract: Symmetry properties of positive solutions for semilinear elliptic problems in n are considered. We give a symmetry result for the problem in the feneral case, and then derive various results for certain classes of demilinear elliptic equations. We employ the moving plane method based on the maximum principle on unbounded domains to obtain the result on symmetry.

WEIGHTED BLOCH SPACES IN $C^n$

Abstract: In this paper, weighted Bloch spaces $B_q (q > 0)$ are considered on the open unit ball in $C^n$. These spaces extend the notion of Bloch spaces to wider classes of holomorphic functions. It is proved that the functions in a weighted Bloch space admit certain integral representation. This representation formula is then used to determine the degree of growth of the functions in the space $B_q$. It is also proved that weighted Bloch space is a Banach space for each weight q > 0, and the little Bloch space $B_q,0$ associated with $B_q$ is a separable subspace of $B_q$ which is the closure of the polynomials for each $q \geq 1$.

Forced oscillations of solutions of impulsive nonlinear parabolic differential-difference equations

Abstract: Sufficient conditions for forced oscillations of the solutions of impulsive nonlinear parabolic differential-difference equations are obtained.

The g-sequence of a map and its exactness

Abstract: In this paper, we extend the G-sequence of a CW-pair to the G-sequence of a map and show the existence of a map with nonexact G-sequence. We also give an example of a finite CW-pair with nontrivial -homology in high order.

Homology of the triple loop space of the exceptional lie group F 4

Abstract: We study the homology of the triple loop space of the exceptional Lie group F4 by exploiting the spectral sequences and the homology operations

SELECTION THEOREMS WITH n-CONNECTDENESS

Abstract: We give a generalization of the selection theorem of Ben-El-Mechaiekh and Oudadess to complete LD-metric spaces with the aid of the notion of n-connectedness. Our new selection theorem is used to obtain new results of fixed points and coincidence points for compact lower semicontinuous set-valued maps with closed values consisting of D-sets in a complete LD-metric space.

Genus distributions for bouquets of dipoles

Abstract: We compute genus distributions for bouquets of dipoles by using the method concerning the cycle structure of permutations in the symmetric group. From this, we can deduce that every bouquet of dipoles is upper embeddable. We find a foumula for computing the embedding polynomials for bouquets of dipoles.

Two-link approximation schemes for linear loss networks without controls

Abstract: This paper is concerned with the performance evaluation of loss networks. We shall review the Erlang Fixed Point (EFP) method for estimating the blocking probabilities, which is based on an assumption that links are blocked independently. For networks with linear structure, the behaviour of adjacent links can be highly correlated. We shall give particular attention to recently-developed fixed-point methods which specifically account for the dependencies between neighbouring links. For the network considered here, namely a ring network with two types of traffic, these methods produce relative errors typically of that found using the basic EFP approximation.

A sharp bound for Ito processes

Abstract: Let X and Y be Ito processes with dX = dB ＋ ds and dY = (equation omitted)dB ＋ ξds. Burkholder obtained a sharp bound on the distribution of the maximal function of Y under the assumption that │Y││X│,│ζ│││, │ξ│││ and that X is a nonnegative local submartingale. In this paper we consider a wider class of Ito processes, replace the assumption │ξ│││ by a more general one │ξ│ ││ , where a 0 is a constant, and get a weak-type inequality between X and the maximal function of Y. This inequality, being sharp for all a 0, extends the work by Burkholder.der.urkholder.der.

Space-like surfaces with 1-type generalized gauss map

Abstract: Chen and Piccinni (7) have classified all compact sur­ faces in a Euclidean space R2+p with I-type generalized Gauss map. Being motivated by this result, the purpose of this paper is to consider the Lorentz version of the classification theorem and to obtain a complete classification of space-like surfaces in indefinite Euclidean space R~+P with I-type generalized Gauss map.

Fixed point theorems on generalized convex spaces

Abstract: We obtain new fixed point theorems on maps defined on "locally G-convex" subsets of a generalized convex spaces. Our first theorem is a Schauder-Tychonoff type generalization of the Brouwer fixed point theorem for a G-convex space, and the second main result is a fixed point theorem for the Kakutani maps. Our results extend many known generalizations of the Brouwer theorem, and are based on the Knaster-Kuratowski-Mazurkiewicz theorem. From these results, we deduce new results on collectively fixed points, intersection theorems for sets with convex sections and quasi-equilibrium theorems.

White noise approach to fluctuations

Abstract: We are interested in random phenomena that will vary as time goes by, being interfered with by fluctuation These phenomena are often expressed as functionals of white noise We therefore discuss the analysis of those functionals, where the white noise is understood as a system of idealized elementary random variables The system is, in many cases, taken to be the innovation of the given random phenomena The use of the innovation provides a powerful tool to investigate stochastic processes and random fields in line with white noise analysis

The riemann problem for a system of conservation laws of mixed type (i)

Abstract: We prove the existence of solutions of the Reimann problem for a system of conservation laws of mixed type using the method of vanishing viscosity term.

Generalized white noise functionals on classical wiener space

Abstract: In this note we reformulate the white noise calculus on the classical Wiener space (C', C). It is shown that most of the examples and operators can be redefined on C without difficulties except the Hida derivative. To overcome the difficulty, we find that it is sufficient to replace C by L[0,1] and reformulate the white noise on the modified abstract Wiener space (C', L[0, 1]). The generalized white noise functionals are then defined and studied through their linear functional forms. For applications, we reprove the Ito formula and give the existence theorem of one-side stochastic integrals with anticipating integrands.

ON THE MODULAR FUNCTION $j_4$ OF LEVEL 4

Abstract: Since the modular curves X(N) = (N)\(equation omitted)＊ (N =1,2,3) have genus 0, we have field isomorphisms K(X(l))(equation omitted)C(J), K(X(2))(equation omitted)(λ) and K(X(3))(equation omitted)( ) where J, λ are the classical modular functions of level 1 and 2, and can be represented as the quotient of reduced Eisenstein series. When N = 4, we see from the genus formula that the curve X(4) is of genus 0 too. Thus the field K(X(4)) is a rational function field over C. We find such a field generator (z) = x(z)/y(z) (x(z) = ((equation omitted)), y(z) = ((equation omitted)) Jacobi theta functions). We also investigate the structures of the spaces ((4)), ((4)), M(equation omitted)((equation omitted)(4)) and S(equation omitted)((equation omitted)(4)) in terms of x(z) and y(z). As its application, we apply the above results to quadratic forms.rms.

A collision avoidance control problem for moving objects and a robot arm

Abstract: We propose the new controls constructed via the second or direct method of Liapunov to solve the collision avoidance control problems for moving objects and a robot arm in the plane. We also explicate the controlling effect by the simulations.

THE ${M_1},{M_/2}/G/l/K$ RETRIAL QUEUEING SYSTEMS WITH PRIORITY

Abstract: We consider an M, M/G/1/ K retrial queueing system with a finite priority queue for type I calls and infinite retrial group for type II calls where blocked type I calls may join the retrial group. These models, for example, can be applied to cellular mobile communication system where handoff calls have higher priority than originating calls. In this paper we apply the supplementary variable method where supplementary variable is the elapsed service time of the call in service. We find the joint generating function of the numbers of calls in the priority queue and the retrial group in closed form and give some performance measures of the system.

Optimal gevrey exponents for some degenerate elliptic operators

Abstract: We shall show first general Metivier operators -hypoellipticity in the vicinity of the origin (0,0), where (＞1), and finally the optimality of these exponents {, d} will be shown.