• The Pure and Applied Mathematics
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• v.12 no.2 s.28
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• pp.133-142
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• 2005

Generalizing the Cauchy-Rassias inequality in [Th. M. Rassias: On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300.] we consider a stability problem of quadratic functional equation in the spaces of generalized functions such as the Schwartz tempered distributions and Sato hyperfunctions.

• Journal of the Korean Statistical Society
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• v.28 no.3
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• pp.359-370
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• 1999

We considered a change-point hazard rate model generalizing constant hazard rate model. This type of model is very popular in the sense that the Weibull and exponential distributions formulating survival time data are the special cases of it. Maximum likelihood estimation and the asymptotic properties such as the consistency and its limiting distribution of the change-point estimator were discussed. A parametric bootstrap method for finding confidence intervals of the unknown change-point was also suggested and the proposed method is explained through a practical example.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.587-597
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• 2017

In this paper we define the (p, q)-analogue of Bernoulli numbers and polynomials by generalizing the Bernoulli numbers and polynomials, Carlitz's type q-Bernoulli numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with (p, q)-analogue of Bernoulli numbers and polynomials. Finally, we investigate the zeros of the (p, q)-analogue of Bernoulli polynomials by using computer.

• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.1-14
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• 1994

In the recent several years the theory of impulsive differential equations has made a rapid progress (see [1] and [2] and the references there). The questions of stability and periodicity of the solutions of these equations have been elaborated in sufficient details while their asymptotic behaviour has been little studied. In the present paper the asymptotic behaviour of the solutions of linear impulsive differential equations is investigated, generalizing the results of J. W. Macki and J.S. Muldowney, 1970 [3], related to ordinary differential equations without impulses.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.357-370
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• 2015

In this paper, we introduce the concept of (m, n)-ideals in a non-associative ordered structure, which is called an ordered Abel-Grassmann's groupoid, by generalizing the concept of (m, n)-ideals in an ordered semigroup [14]. We also study the (m, n)-regular class of an ordered AG-groupoid in terms of (m, n)-ideals.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.175-186
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• 1995

The concept of a fuzzy set, which was introduced in [9], provides a natural framework for generalizing many of the concepts of general topology to what might be called fuzzy topological spaces. The idea of fuzzy topological spaces was introduced by Chang [2]. The idea is more or less a generalization of oridinary topological spaces.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.575-591
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• 2018

Anosov families were introduced by A. Fisher and P. Arnoux motivated by generalizing the notion of Anosov diffeomorphism defined on a compact Riemannian manifold. Roughly, an Anosov family is a two-sided sequence of diffeomorphisms (or non-stationary dynamical system) with similar behavior to an Anosov diffeomorphisms. We show that the set consisting of Anosov families is an open subset of the set consisting of two-sided sequences of diffeomorphisms, which is equipped with the strong topology (or Whitney topology).

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.1033-1048
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• 2020

We synthesize the recent work done on conditionally defined Lucas and Fibonacci numbers, tying together various definitions and results generalizing the linear recurrence relation. Allowing for any initial conditions, we determine the generating function and a Binet-like formula for the general sequence, in both the positive and negative directions, as well as relations among various sequence pairs. We also determine conditions for periodicity of these sequences and graph some recurrent figures in Python.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1095-1110
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• 2017

The t-wise intersection is a useful property of a linear code due to its many applications. Recently, the second author determined the t-wise intersection of a relative two-weight code. By using this result and generalizing the finite projective geometry method, we will present the t-wise intersection of a relative three-weight code and its applications in this paper.

• Communications for Statistical Applications and Methods
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• v.6 no.2
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• pp.645-658
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• 1999

One of the most popular graphical techniques for goodness of fit problems is the quantile-quantile plot(Q-Q plot) Easton and McCulloch(1990) suggested a way of generalizing Q-Q plots to multivariate cases bases on finding a matching between the points of the data set whose shape is being examined and a reference sample. in this paper we investigated the asymptotic behavior of the generalized Q-Q plot for bivariate cases. As a result we concluded that the standard univariate Q-Q plot and the generalized Q-Q plot have the same limit if two variables are independent.