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Vol.8 No.1

Tripathi, Mukut-Mani pp.1-8
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Abstract

Semi-invariant submanifolds of Lorentzian almost paracontact mani-folds are studied. Integrability of certain distributions on the submanifold are in vestigated. It has been proved that a LP-Sasakian manifold does not admit a proper semi-invariant submanifold.

Rhee, Hyang-Joo pp.9-14
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Abstract

In some problems of abstract approximation theory the approximating set depends on some parameter p. In this paper, we make a set M(f) depends on the element f, <TEX>$\phi$</TEX> and then best approximations are sought from a subset M(f) of M.

Kim, Kwon-Wook pp.15-23
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Abstract

This paper gives the sufficient conditions for the existence of positive solution of a quasilinear elliptic with homogeneous Dirichlet boundary conditon.

Kim, Si-Ju ; Park, Yong-Kil pp.25-32
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Abstract

Let A be a nonnegative matrix of size <TEX>$n \times n$</TEX>. A is said to be nearly convertible if A(i│j) is convertible for all integers i, j<TEX>$\in$</TEX>{1,2,…, n} where A(i│j) denote the submatrix obtained from A by deleting the i-th row and the j-th col-umn. We investigate some properties of nearly convertible matrices and existence of (maximal)nearly convertible matrices of size n is proved for any integers <TEX>$n(\geq 3)$</TEX>.

Jin, Dae-Ho pp.33-46
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Abstract

The purpose of this paper is to study totally umbilical coisotropic sub-manifold(M. g, SM) of a semi-Riemannian manifold(M,g)

Kwean, Hyuk-Jin pp.47-51
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Abstract

We establish the global existence of nonnegative solutions to some reaction-diffusion equation for exponential nonlinearity for small initial data.

Yoon, Ju-Han pp.53-59
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Abstract

In this paper, we define the <TEX>$H_1$</TEX>-Stieltjes representable, nearly <TEX>$H_1$</TEX>-Stieltjes represnetable for vector-valued function, which is the generalization of Bochner representable and than study some properties of these operators.

Yang, Ki-Yeol pp.61-69
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Abstract

The purpose of this paper is to introduce the Nielsen root number for the complement N(f:X-A,c) which shares such properties with the Nielsen root number N(f;c) as lower bound and homotopy invariance.

Kim, Bong-Jin pp.71-78
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Abstract

In 1984, Johnson[A bounded convergence theorem for the Feynman in-tegral, J, Math. Phys, 25(1984), 1323-1326] proved a bounded convergence theorem for hte Feynman integral. This is the first stability theorem of the Feynman integral as an <TEX>$L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$</TEX> theory. Johnson and Lapidus [Generalized Dyson series, generalized Feynman digrams, the Feynman integral and Feynmans operational calculus. Mem, Amer, Math, Soc. 62(1986), no 351] studied stability theorems for the Feynman integral as an <TEX>$L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$</TEX> theory for the functional with arbitrary Borel measure. These papers treat functionals which involve only a single integral. In this paper, we obtain the stability theorems for the Feynman integral as an <TEX>$L(L_1 (\mathbb{R}^N), L_{\infty}(\mathbb{R}^{N}))$</TEX>theory for the functionals which involve double integral with some Borel measures.

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