• East Asian mathematical journal
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• v.29 no.2
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• pp.241-254
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• 2013

In this paper, we investigate the contents of Rule of Excess and Deficit in the second volume of San Hak Jeong Ui (Arithmetic Definition) compiled by Nam Byong Kil and corrcted by Lee Sang Hyok in the Choson Dynasty period.(Emperor Ko Jong, 1867).

• East Asian mathematical journal
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• v.29 no.3
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• pp.327-335
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• 2013

In this paper we consider the quadratic matrix equation which can be defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown complex matrix, and A, B and C are $n{\times}n$ given matrices with complex elements. We first introduce a couple of condition numbers of the equation Q(X) and present normwise condition numbers. Finally, we compare the results and some numerical experiments are given.

• East Asian mathematical journal
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• v.29 no.3
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• pp.269-278
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• 2013

A fuzzy set A defined on a probability space (${\Omega}$, $\mathfrak{F}$, P) is called a fuzzy event. Zadeh defines the probability of the fuzzy event A using the probability P. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. We calculate the normal fuzzy probability for generalized trapezoidal fuzzy sets and give some examples.

• East Asian mathematical journal
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• v.29 no.3
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• pp.293-302
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• 2013

We research properties of ternary numbers and hyperholomorphic functions with values in $\mathbb{C}$(2). We represent reduced quaternion numbers and obtain some propertries in dual reduced quaternion systems in view of Clifford analysis. Moreover, we obtain Cauchy theorems with respect to dual reduced quaternions.

• East Asian mathematical journal
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• v.34 no.3
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• pp.265-285
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• 2018

The main purpose of this paper, by using the resolvent operator technique associated with randomly (A, ${\eta}$, m)-accretive operator is to establish an existence and convergence theorem for a class of system of random nonlinear equations with fuzzy mappings in Banach spaces. Our works are improvements and generalizations of the corresponding well-known results.

• East Asian mathematical journal
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• v.33 no.1
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• pp.37-44
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• 2017

We will prove size estimates of the Bergman kernel for the generalized Fock space ${\mathcal{F}}^2_{\varphi}$, where ${\varphi}$ belongs to the class $\mathcal{W} $. The main tool for the proof is to use the estimate on the canonical solution to the ${\bar{\partial}}$-equation. We use Delin's weighted $L^2$-estimate ([3], [6]) for it.

• East Asian mathematical journal
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• v.19 no.2
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• pp.241-249
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• 2003

In [11] the feeble continuity is introduced and then the weak and strong forms of feeble(or, equivalently $\alpha$-continuity) continuity are studied. In this note, we introduce a type of function called a slightly $\alpha$-continuous function and study several properties of it

• East Asian mathematical journal
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• v.19 no.2
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• pp.305-316
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• 2003

In the present paper, we are to find the conditions that a cubic Finsler space is a Berwald space and a two-dimensional cubic Finsler space is a Landsberg space. It is shown that if a two-dimensional cubic Finsler space is a Landsberg space, then it is a Berwald space.

• East Asian mathematical journal
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• v.14 no.1
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• pp.21-26
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• 1998

The Fulgede-Putnam theorem asserts as if A and Bare normal operators and X is an operator such that AX=XB, then A*X=XB*. In this paper, we show that if A is k-quasihyponormal and B* is invertible k-quasihyponormal such that AX=XB for a Hilbert-Schmidt operator X, then A*X=XB*.

• East Asian mathematical journal
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• v.26 no.3
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• pp.389-395
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• 2010

In this paper, a class of g-demi-pseudomonotone mappings is introduced and the solvability of a class of generalized vector F-complementarity problems with the mappings in Banach spaces is considered.