• Water for future
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• v.8 no.2
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• pp.56-60
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• 1975

Traditional descriptions of water movement in soils and of calculations of infiltration rates neglect the air movement and its compressibility. The movement of two fluids in the bounded layered porous medium is treated analytically and computer simulations are conducted for given boundary conditions and initial saturation profiles. The movement of a given saturation across the interface between the different soil layers is theoretically developed by considering the conservation of mass. It is shown that the existence of the interface affects the infiltration rate when the average total velocity is greater than zero. The transition from one layer to another layer cause a change in the capillary drive and consequently influences the infiltration rate.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.153-161
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• 2016

It is shown that the algebra $\mathfrak{H}^{\infty}$ of bounded Dirichlet series is not a coherent ring, and has infinite Bass stable rank. As corollaries of the latter result, it is derived that $\mathfrak{H}^{\infty}$ has infinite topological stable rank and infinite Krull dimension.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.465-472
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• 2010

In this paper, we investigate the extent of the set on which the modulus of a meromorphic function is lower bounded by a term related to some Nevanlinna Theory functionals. A. I. Shcherba estimate the size of the set on which the modulus of an entire function is lower bounded by 1. Our theorem in this paper shows that the same result holds in the case that the lower bound is replaced by$lT(r,f)$, $0{\leq}l$ < 1, which improves Shcherba's result. We also give a similar estimation for meromorphic functions.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1003-1013
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• 1996

The existence of a bounded generalized solution on the real line for a nonlinear functional evolution problem of the type $$ (FDE) x'(t) + A(t,x_t)x(t) \ni 0, t \in R $$ in a general Banach spaces is considered. It is shown that (FDE) has a bounded generalized solution on the whole real line with well-known Crandall and Pazy's result and recent results of the functional differential equations involving the operator A(t).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.35-45
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• 2001

In this paper we point out an Ostrowski type inequality for the Riemann-Stieltjes integral ${\int}_a^b$ f (t) du (t), where f is of p-H-$H{\ddot{o}}lder$ type on [a,b], and u is of bounded variation on [a,b]. Applications for the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also given.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.829-836
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• 2005

In this note, we introduce a new proof of the unique-ness and existence of a negatively bounded solution for a parabolic partial differential equation. The uniqueness in particular implies the finiteness of the Fourier spanning dimension of the global attractor and the existence allows a construction of an inertial manifold.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.389-399
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• 2002

We prove that the results of Chang, Park and Cho in ［1］ concerning the iterative approximation of asymptotically pseudocontractive maps with bounded ranges can be extended to a certain class of asymptotically pseudocontractive maps whose ranges need not be bounded.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.999-1018
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• 1998

In this paper, we prove stability theorems for the operator-valued Feynman integral of certain functionals involving some Borel measures on (0, t) as a bounded linear operator from L$_1$(R) to $C_{0}$(R).

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.521-540
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• 2004

In this paper, we give a sharp estimate on the cardinality of the set generating the convex hull containing the image of harmonic maps with polynomial growth rate on a certain class of manifolds into a Cartan-Hadamard manifold with sectional curvature bounded by two negative constants. We also describe the asymptotic behavior of harmonic maps on a complete Riemannian manifold into a regular ball in terms of massive subsets, in the case when the space of bounded harmonic functions on the manifold is finite dimensional.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.215-223
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• 2007

We in this note introduce the concept of NCI rings which is a generalization of NI rings. We study the basic structure of NCI rings, concentrating rings of bounded index of nilpotency and von Neumann regular rings. We also construct suitable examples to the situations raised naturally in the process.