• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제2권1호
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• pp.1-14
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• 1998

Multiplicity results of doubly-periodic solution for semilinear heat equations having coercive nonlinearity are discussed. Our proofs rely on Mawhin's continuation theorem.

• 대한수학회보
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• 제60권2호
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• pp.515-528
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• 2023

In this paper, we formulate the set of all saturated numerical semigroups with prime multiplicity. We characterize the catenary degrees of elements of the semigroups we obtained which are important invariants in factorization theory. We also give the proper characterizations of the semigroups under consideration.

• Journal of the Korean Data and Information Science Society
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• 제10권1호
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• pp.79-89
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• 1999

중복수가 있는 조사는 추출단위 (병원, 가구)가 단순임의추출 또는 층화임의추출을 통해 추출되고 추출단위들이 여러 조사단위 (환자, 사람)들과 서로 연결되어 있는 경우를 말한다. 연결형태에 따른 조사단위의 집합을 network라 정의하면 network는 하나 이상의 추출단위와 연결될 것이고 하나의 추출단위는 하나이상의 network와 연결이 될 것이다. 본 논문에서는 두 개 이상의 변수가 연결되는 중복수가 있는 다변량 층화임의추출의 경우에 배분문제를 연구하였다.

• 대한수학회지
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• 제37권5호
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• pp.737-737
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• 2000

• International Journal of Human Ecology
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• 제15권2호
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• pp.81-92
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• 2014

This paper explores factors associated with multiple concurrent care and education arrangements in early childhood in South Korea. It draws on a subsample from the Korean Longitudinal Survey of Women and Families. Results show that about one-fifth of the families utilized multiple arrangements for their first preschool child. The primary non-parental option in multiplicity was nurseries or kindergartens. Home care and education options such as home study materials were found to be most prevalent secondary non-parental option, followed by services at private institution as well as relative care. Children's age, care cost, non-parental care time and time constraints were found to be positively related to the incidence of multiplicity for the first preschool child while family income and cost constraints were negatively associated. As a secondary option in the multiplicity, services at private institutions increased with children's age, care cost and when the grandparents live far from the parents' house. Home care and education utilization was found more among mothers with low degree of time constraints. Utilization of relative support decreased with the children's age and meant lower care cost and increased with mother's employment, fathers' education, family income, cost constraints and when grandparents live nearby. This paper, based on the associated factors, suggests how issues of children enrichment and constraints might be related to the multiplicity.

• 대한수학회지
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• 제31권4호
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• pp.619-628
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• 1994

The multiplicity theory initiated by C. Chevalley was the one with respect to ideals generated by a system of parameters of a local ring containing a field [3] and [4]. Samuel generalized the definition to primary ideals belonging the maximal ideal of a local ring which contains a field by a device which used the Hilbert characteristic function [9]. Furthermore Samuel defined multiplicity also in local rings which contain no field [10].

• 대한수학회지
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• 제55권3호
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• pp.605-622
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• 2018

The original mixed multiplicity theory considered the class of mixed multiplicities concerning the terms of highest total degree in the Hilbert polynomial. This paper defines a broader class of mixed multiplicities that concern the maximal terms in this polynomial, and gives many results, which are not only general but also more natural than many results in the original mixed multiplicity theory.

• 대한수학회지
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• 제56권5호
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• pp.1309-1331
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• 2019

We study the homogeneous Dirichlet boundary value problem of generalized Laplacian systems with a singular weight which may not be in $L^1$. Using the well-known fixed point theorem on cones, we obtain the multiplicity results of positive solutions under two different asymptotic behaviors of the nonlinearities at 0 and ${\infty}$. Furthermore, a global result of positive solutions for one special case with respect to a parameter is also obtained.

• East Asian mathematical journal
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• 제38권1호
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• pp.13-20
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• 2022

We establish multiplicity results for positive solutions to the Schrödinger-type singular positone problem: -∆u + V (x)u = λf(u) in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in ℝ^N, N > 2, λ is a positive parameter, V ∈ L^∞(Ω) and f : [0, ∞) → (0, ∞) is a continuous function. In particular, when f is sublinear at infinity we discuss the existence of at least three positive solutions for a certain range of λ. The proofs are mainly based on the sub- and supersolution method.

• 충청수학회지
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• 제19권4호
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• pp.393-402
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• 2006

We investigate relations between multiplicity of solutions and source terms in a elliptic equation. We have a concerne with a sharp result for multiplicity of a nonlinear Laplacian differential equation.