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Vol.13 No.2

Mondal Taras Kumar ; Samanta S.K. pp.71-94
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Abstract

In this paper we study lattice valued fuzzy gradation of openness so that fuzzy gradation of openness [13] could be obtained as a particular case. Some of its properties are studied. We also give definitions of lattice valued graded fuzzy filters, graded, fuzzy grills, graded fuzzy preproximities and proximities.

Sen M.K. ; Maity S.K. pp.95-111
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Abstract

In [6], we have recently proved that an additive inverse semiring S is a Clifford semifield if and only if S is a subdirect product of a field and a distributive lattice. In this paper, we study the matrix semiring over a Clifford semifield.

Cho Yong-Uk ; Chelvam T.Tamizh ; Meenakumari N. pp.113-120
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Abstract

In this paper, we introduce the concept of P(r,m) <TEX>$\Gamma$</TEX>-near-ring and obtain some characterization of P(r,m) <TEX>$\Gamma$</TEX>-near-rings through regularity conditions.

Belbas S.A. ; Park Jong-Seo pp.121-136
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Abstract

We formulate and analyze a hybrid system model that involves Volterra integral operators with multiple integrals and two types of impulsive terms. We give a constructive proof, via an iteration method, of existence and uniqueness of solutions.

Lin C.S. pp.137-149
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Abstract

We introduce the notion of the generalized covariance and variance for bounded linear operators on Hilbert space, and prove that the generalized covariance-variance inequality holds. It turns out that the inequality is a useful formula in tile study of inequality involving linear operators in Hilbert spaces.

Song Tai-Sung pp.151-155
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Abstract

Let <TEX>$\gamma$</TEX> be a <TEX>$C_2$</TEX> curve in the open unit disk <TEX>$\mathbb{D}</TEX>. Flinn and Osgood proved that <TEX>$K_{\mathbb{D}}(z,\gamma){\geq}1$</TEX> for all <TEX>$z{\in}{\gamma}$</TEX> if and only if the curve <TEX>${\Large f}o{\gamma}$</TEX> is convex for every convex conformal mapping <TEX>$\Large f$</TEX> of <TEX>$\mathbb{D}</TEX>, where <TEX>$K_{\mathbb{D}}(z,\;\gamma)$</TEX> denotes the hyperbolic curvature of <TEX>$\gamma$</TEX> at the point z. In this paper we establish a generalization of the Flinn-Osgood characterization for a curve with the hyperbolic curvature at least 1.

Chelvam Thirugnanam Tamizh ; Cho Yong-Uk pp.157-165
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Abstract

The notion of regularity in near-ring was generalized by the concept of b-regular and some characterizations of the same was obtained through the substructures viz bi-ideals in near-rings. In this paper, we generalize further and introduce tile notion of weakly b-regular near-rings and obtain a characterization of tile same.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics