• Journal of the Korea Computer Industry Society
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• v.2 no.10
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• pp.1261-1268
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• 2001

Despite of various useful features, functional languages do not provide an efficient way of representing states. To improve expressiveness of functional language, it is required a method representing explicit state without violating of functional semantic properties. In this paper, imperative functional language, $\lambda$st-calculus is designed to represent states without compromising the properties of pure functional languages. And we construct an algorithm to reduce proposed imperative functional language. $\lambda$st-calculus model which is an extension of the $\lambda$-calculus model with explicit state constructor without violating their semantic properties. it improves expressiveness of syntax through a concept of state composition and simplified reduction rules.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.31-36
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• 2003

Using a short time expansion of the fundamental solution of heat equation by analysis of Wiener functional with the help of Malliavin calculus, we obtain the asymptotic expansion of the mean distance of Brownian motion on Riemannian manifolds.

• Bulletin of the Korean Mathematical Society
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• v.8 no.1
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• pp.9-15
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• 1971

The purpose of this note is to use primitive recursive functions and predicates similar to those presented by Davis [2] to show the well-known result first proved by Godel in [3] that the well-formed formulas of a pure functional calculus form a recursive set. The technique shown in this paper immediately suggests a unique approach to Theorem proving using a computer.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.193-207
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• 2004

In this expository article we survey some recent developments on the construction of a holomorphic functional calculus for an infinite number of elements in a commutative unital Banach algebra.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.191-198
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• 2012

Minimal surfaces with given boundaries are the solutions of Plateau's problem. In studying the calculus of variations for the minimal surfaces, the functional ${\varepsilon}$, corresponding to the energy of surfaces, is introduced in [Ki09]. In this paper we derive a formula for the second derivative of ${\varepsilon}$, which is necessary for further theories of the calculus of variations.

• The Transactions of the Korea Information Processing Society
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• v.3 no.3
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• pp.478-492
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• 1996

For parallel implementations of functional programs without concurrent primitives, the λ-calculus encodings have been introduced. A functional program may be trans for med into a process network using process calculiby the λ-calculus encoding and there sult of a program can be obtained by a deal of communication actions in it's process network. But the λ-calculus encodings cause too many communication actions even in constant expressions. This paper shows the encoding for a combinator program without concurrency primitives which can combine the graph reduction and the process-net reduction using computable processes,'chores'. A 'chore' may have graph reduction functions for primitive operations of constants for which local graph reduction may be possible, and be encoded from a 'G-reducible' subexpression which is obtained by an annotation and trans for mati-on for a combinator program, assuring that it does not include any combinator application. Also, we show that a process network with chores raises less commu-nication actions than one without chores.

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.3
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• pp.141-149
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• 2008

Most functional programming languages allows programmers to write ambiguous rules, under the strategy that pattern-matching will be performed in a direction of 'from top to bottom' way. While providing programmers with convenience and intuitive understanding of defining default rules, such ambiguous rules may make the semantics of functional languages unclear. More specifically, it may fail to apply the equational reasoning, one of most significant advantage of functional programming, and may cause to obscure finding a formal way of translating functional languages into the ${\lambda}$-calculus; as a result, we only get an ad hoc translation. In this paper, we associate with separability of term rewriting systems, holding purely-declarative property, pattern-matching semantics of lazy functional languages. Separability can serve a formalism for translating lazy functional languages into the ${\lambda}$-calculus.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.211-227
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• 2008

As a mathematical model proposed to understand the behaviors of interacting species, cross-diffusion systems with functional responses of prey-predator type are considered. In order to obtain $W^{1_2}$-estimates of the solutions, we make use of several forms of calculus inequalities and embedding theorems. We consider the quasilinear parabolic systems with the cross-diffusion terms, and without the self-diffusion terms because of the simplicity of computations. As the main result we derive the uniform $W^{1_2}$-bound of the solutions and obtain the global existence in time.

• Communications of the Korean Mathematical Society
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• v.4 no.2
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• pp.297-302
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• 1989

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.71-81
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• 2021

The main object of this present paper is to study some majorization problems for certain classes of analytic functions defined by means of q-calculus operator associated with exponential function.