• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.731-749
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• 2005

In this paper, we study the two dimensional g-Navier­Stokes equations on some unbounded domain ${\Omega}\;{\subset}\;R^2$. We prove the existence of the global attractor for the two dimensional g-Navier­Stokes equations under suitable conditions. Also, we estimate the dimension of the global attractor. For this purpose, we exploit the concept of asymptotic compactness used by Rosa for the usual Navier-Stokes equations.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.105-110
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• 2010

In this paper, we introduce the concept of $\beta$-preconvex sets on preconvexity spaces. We study some properties for $\beta$-preconvex sets by using the co-convexity hull and the convexity hull. Also we introduce and study the concepts of ${\beta}c$-convex function and $\beta^*c$-convex function.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1625-1647
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• 2014

By making use of the familiar concept of neighborhoods of analytic functions, we prove several inclusion relationships associated with the (n, ${\delta}$)-neighborhoods of certain subclasses of p-valent analytic functions of complex order with missing coefficients, which are introduced here by means of the Saitoh operator. Special cases of some of the results obtained here are shown to yield known results.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.359-367
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• 2007

We consider the intuitionistic fuzzification of the concept of several ${\Gamma}$-ideals in a ${\Gamma}$-semigroup S, and investigate some properties of such ${\Gamma}$-ideals.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.177-191
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• 2017

In this note we consider the right unit-duo ring property on the powers of elements, and introduce the concept of weakly right unit-duo ring. We investigate first the properties of weakly right unit-duo rings which are useful to the study of related studies. We observe next various kinds of relations and examples of weakly right unit-duo rings which do roles in ring theory.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.707-723
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• 1996

We first define the concept of the generalized analytic Fourier-Feynman transforms of a class of functionals on function space induced by a generalized Brownian motion process and study of functionals which plays on important role in physical problem of the form $ F(x) = {\int^{T}_{0} f(t, x(t))dt} $ where f is a complex-valued function on $[0, T] \times R$. We next show that the generalized analytic Fourier-Feynman transform of the convolution product is a product of generalized analytic Fourier-Feynman transform of functionals on functin space.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.61-76
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• 2001

In this paper we define the concept of a conditional Fourier-Feynman transform and a conditional convolution product and obtain several interesting relationships between them. In particular we show that the conditional transform of the conditional convolution product is the product of conditional transforms, and that the conditional convolution product of conditional transforms is the conditional transform of the product of the functionals.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.535-541
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• 2002

In this paper, we introduce the concept of lower semi-continuous from above functions and show that many well-known results, such as Ekland's and Caristi's theorems, remain also true under lower semi-continuous from above functions.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.595-600
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• 1996

We give a characterization of a deductive system. We introduce the concept of maximal deductive systems and show that every bounded Hilbert algebra with at least two elements contains at least one maximal deductive system. Moreover, we introduce the notion of radical and semisimple in a Hilbert algebra and prove that if H is a bounded Hilbert algebra in which every element is an involution, then H is semisimple.