• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.315-326
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• 2005

In this paper, we define the weak dimension and the chain-weak dimension of an ordered set by using weak orders and chain-weak orders, respectively, as realizers. First, we prove that if P is not a weak order, then the weak dimension of P is the same as the dimension of P. Next, we determine the chain-weak dimension of the product of k-element chains. Finally, we prove some properties of chain-weak dimension which hold for dimension.

• Korean Journal of Mathematics
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• v.21 no.3
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• pp.351-363
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• 2013

We study the properties of weak extended order algebras having adjoint pairs (triples) or Galois pairs. In particular, we investigate the various laws on weak extended order algebras.

• Journal of the Korean Statistical Society
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• v.25 no.3
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• pp.313-336
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• 1996

In this paper we consider weak convergence of some rescaled transi-tion probabilities of a real-valued, k-th order (k $\geq$ 1) stationary Markov chain. Under the assumption that the joint distribution of K + 1 consecutive variables belongs to the domain of attraction of a multivariate extreme value distribution, the paper gives a sufficient condition for the weak convergence and characterizes the limiting distribution via the multivariate extreme value distribution.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.23-41
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• 2018

The main aim of this paper is to prove some results related to the growth rates of composite entire and meromorphic functions on the basis of their relative (p, q)-th order, relative (p, q)-th lower order, relative (p, q)-th type and relative (p, q)-th weak type where p and q are any two positive integers.

• The Pure and Applied Mathematics
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• v.26 no.1
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• pp.13-33
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• 2019

The main aim of this paper is to establish some comparative growth properties of composite entire functions on the basis of their relative (p, q)-th order, relative (p, q)-th lower order, relative (p, q)-th type, relative (p, q)-th weak type of entire function with respect to another entire function where p and q are any two positive integers.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.105-121
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• 2020

The principal objective of this paper is to introduce the ideas of relative 𝜑-type, relative 𝜑-weak type of entire functions of several complex variables and study some growth properties concerning them.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.745-764
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• 2016

The object of the present paper is to obtain new estimates about the (p, q)-th lower order and (p, q)-th weak type of entire functions under some interesting conditions.

• Honam Mathematical Journal
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• v.37 no.1
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• pp.65-97
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• 2015

Orders and types of entire functions have been actively investigated by many authors. In this paper, we aim at investigating some basic properties in connection with sum and product of relative type and relative weak type of entire functions.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.819-845
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• 2020

In this paper, we established sum and product theorems connected to (p, q)-𝜑 relative Gol'dberg type and (p, q)-𝜑 relative Gol'dberg weak type of entire functions of several complex variables with respect to another one under somewhat different conditions.

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.69-91
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• 2022

In the paper we establish some new results depending on the comparative growth properties of composite transcendental entire and meromorphic functions using relative (p, q, t)L-th order, relative (p, q, t)L-th type and relative (p, q, t)L-th weak type and that of Wronskian generated by one of the factors.