• Journal of the Korean Mathematical Society
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• v.38 no.4
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• pp.853-881
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• 2001

Multiplicity for doubly-periodic solutions and Dirichlet-Periodic solutions are treated.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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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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• v.38 no.1
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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.

• International Journal of Human Ecology
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• v.15 no.2
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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.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.489-496
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• 2010

In this paper we consider the Dirichlet problem for an fourth order elliptic equation on a open set in $R^N$. By using variational methods we obtain the multiplicity of nontrivial weak solutions for the fourth order elliptic equation.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.37-50
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• 2014

Using variational methods, we prove some results on the nonexistence and multiplicity of weak solutions for a class of semilinear elliptic systems of two equations involving Grushin type operators with sign-changing nonlinearities. We also shows that the similar results can be obtained for systems of m equations, where m is arbitrary.

• Journal of Pathology and Translational Medicine
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• v.52 no.6
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• pp.396-403
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• 2018

Background: In the current American Joint Committee on Cancer staging system of breast cancer, only tumor size determines T-category regardless of whether the tumor is single or multiple. This study evaluated if tumor multiplicity has prognostic value and can be used to subclassify breast cancer. Methods: We included 5,758 patients with invasive breast cancer who underwent surgery at Samsung Medical Center, Seoul, Korea, from 1995 to 2012. Results: Patients were divided into two groups according to multiplicity (single, n=4,744; multiple, n=1,014). Statistically significant differences in lymph node involvement and lymphatic invasion were found between the two groups (p<.001). Patients with multiple masses tended to have luminal A molecular subtype (p<.001). On Kaplan-Meier survival analysis, patients with multiple masses had significantly poorer disease-free survival (DFS) (p=.016). The prognostic significance of multiplicity was seen in patients with anatomic staging group I and prognostic staging group IA (p=.019 and p=.032, respectively). When targeting patients with T1-2 N0 M0, hormone receptor-positive, and human epidermal growth factor receptor 2 (HER2)-negative cancer, Kaplan-Meier survival analysis also revealed significantly reduced DFS with multiple cancer (p=.031). The multivariate analysis indicated that multiplicity was independently correlated with worse DFS (hazard ratio, 1.23; 95% confidence interval, 1.03 to 1.47; p=.025). The results of this study indicate that tumor multiplicity is frequently found in luminal A subtype, is associated with frequent lymph node metastasis, and is correlated with worse DFS. Conclusions: Tumor multiplicity has prognostic value and could be used to subclassify invasive breast cancer at early stages. Adjuvant chemotherapy would be necessary for multiple masses of T1-2 N0 M0, hormone-receptor-positive, and HER2-negative cancer.

• Nuclear Engineering and Technology
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• v.52 no.5
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• pp.1036-1042
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• 2020

Fast-Neutron Multiplicity Counter based on Liquid Scintillator Detector can directly measure the fast neutron multiplicity emitted by UO₂ rod. HPGe gamma spectrometer; which has superior energy resolution; is routinely used for the gamma energy spectrum measurement. Combing Fast-Neutron Multiplicity Counter and HPGe γ-spectrometer, the n/γ joint measurement system is developed. The fast neutron multiplicity and gamma energy spectrum of UO₂ rod assemblies under different conditions are measured by the n/γ joint measurement system. The induced fission rate and the ²³⁵U abundance, thereby the ²³⁵U mass; can be obtained for UO₂ rod assemblies. The ²³⁵U mass deviation of the measured value from the reference value is less than 5%. The results show that the n/γ joint measurement system is effective and applicable in the measurement of the ²³⁵U mass in samples.