• 제어로봇시스템학회:학술대회논문집
• /
• 1994.10a
• /
• pp.747-752
• /
• 1994

Ussing's flux ratio theorem (1978) reflects a reciprocal relationship behavior between the unidirectional fluxes in asymmetric steady diffusion-convection in a membrane slab. This surprising result has led to many subsequent studies in a wide range of applications, in particular involving linear models of time dependent problems in biology and physiology. Ussing's theorem and its extensions are inherently linear in character. It is of considerable interest to ask to what extent these results apply, if at all, in situations involving, for example, nonlinear reaction. A physiologically interesting situation has been considered by Weisiger et at. (1989, 1991, 1992) and by McNabb et al. (1990, 1991) who studied the role of albumin in the transport of ligands across aqueous diffusion barriers in a liver membrane slab. The results are that there exist reciprocal relationships between unidirectional fluxes in the steady state, although albumin is chemically interacting in a nonlinear way of the diffusion processes. However, the results do not hold in general at early times. Since this type of study first started, it has been speculated about when and how the Ussing's flux ratio theorem fails in a general diffusion-convection-reaction system. In this paper we discuss the validity of Ussing-type theorems in time-dependent situations, and consider the limiting time behavior of a general nonlinear diffusion system with interaction.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.33-41
• /
• 2002

In this paper we study the properties of positive-normal operators and show that Wey1's theorem holds for some totally positive-normal operators.

• Journal for History of Mathematics
• /
• v.25 no.3
• /
• pp.15-27
• /
• 2012

This paper aims to examine Alan Turing's life at the centenary of his birth and to discuss a philosophical implication of his work by concentrating on halting theorem particularly. Turing negatively solved Hilbert's decision problem by proving impossibility of solving halting problem. In this paper I claim that the impossibility implies limits of reason, and accordingly that the marginality in cognition and/or in action should be recognized.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.303-315
• /
• 2001

In this paper, we investigate the topology of complex Finsler manifolds. For a complex Finsler manifold (M, F), we introduce a certain condition on the Finsler metric F on M. This is a generalization of Kahler condition for the Hermitian metric. Under this condition, we can produce a Kahler metric on M. This enables us to use the usual techniques in the Kahler and Riemannian geometry. We show that if the holomorphic sectional curvature of $ M is\geqC^2>0\; for\; some\; c>o,\; then\; diam(M)\leq\frac{\pi}{c}$ and hence M is compact. This is a generalization of the Bonnet\`s theorem in the Riemannian geometry.

• Communications of the Korean Mathematical Society
• /
• v.27 no.1
• /
• pp.77-95
• /
• 2012

For a bounded linear operator T we prove the following assertions: (a) If T is algebraically (p, k)-quasihyponormal, then T is a-isoloid, polaroid, reguloid and a-polaroid. (b) If $T^*$ is algebraically (p, k)-quasihyponormal, then a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$, where $Hol({\sigma}(T))$ is the space of all functions that analytic in an open neighborhoods of ${\sigma}(T)$ of T. (c) If $T^*$ is algebraically (p, k)-quasihyponormal, then generalized a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$. (d) If T is a (p, k)-quasihyponormal operator, then the spectral mapping theorem holds for semi-B-essential approximate point spectrum $\sigma_{SBF_+^-}(T)$, and for left Drazin spectrum ${\sigma}_{lD}(T)$ for every $f{\in}Hol({\sigma}T))$.

• East Asian mathematical journal
• /
• v.17 no.2
• /
• pp.233-237
• /
• 2001

The authors aim at presenting summation formulas of Appell's function $F_1$: $$F_1(a;b,b';1+a+b-b'+i;1,-1)\;(i=0,\;{\pm}1,\;{\pm}2,\;{\pm}3,\;{\pm}4,\;{\pm}5)$$, which, for i=0, yields a known result due to Srivastava.

• Journal of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.1087-1103
• /
• 2009

Given a system of s independent 1-forms on a smooth manifold M of dimension m, we study the existence of integral manifolds by means of various generalized versions of the Frobenius theorem. In particular, we present necessary and sufficient conditions for there to exist s'-parameter (s' < s) family of integral manifolds of dimension p := m-s, and a necessary and sufficient condition for there to exist integral manifolds of dimension p', p' $\leq$ p. We also present examples and applications to complex analysis in several variables.

• Bulletin of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.421-436
• /
• 1997

In this paper we first give a simple proof of the analytic characterization theorems of the operator symbols by using the characterization theorem for white noise functionals. We next give a criterion for the convergence of operators on white noise functionals in terms of their symbols and then use this result to give a proof for the Fock expansion theorem of operators on white noise functionals.

• Honam Mathematical Journal
• /
• v.34 no.3
• /
• pp.439-449
• /
• 2012

In a recent paper, M. Balaj [B] established an alternative principle. The principle was applied to a matching theorem of Ky Fan type, an analytic alternative, a minimax inequality, and existence of solutions of a vector equilibrium theorem. Based on the first author's fixed point theorems, in the present paper, we obtain generalizations of the main result of Balaj [B] and their applications.

• Journal of the Korean Statistical Society
• /
• v.23 no.2
• /
• pp.504-512
• /
• 1994

A simple proof for the random central limit theorem is given for a family of stationary linear lattice processes, which belogn to a class of 2 dimensional random fields, applying the Beveridge and Nelson decomposition in time series context. The result is an extension of Fakhre-Zakeri and Fershidi (1993) dealing with the linear process in time series to the case of the linear lattice process with 2 dimensional indices.