• 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.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.715-729
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• 2017

In this paper, we investigate the existence and multiplicity of solutions for systems driven by two non-local integrodifferential operators with homogeneous Dirichlet boundary conditions. The main tools are the Saddle point theorem, Ekeland's variational principle and the Mountain pass theorem.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.171-181
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• 1999

We investigate multiplicity of solutions for a nonlinear perturbation of a parabolic operator under Dirichlet boundary condition, in a bounded domain.

• Korean Journal of Crystallography
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• v.7 no.1
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• pp.88-93
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• 1996

The multiplicity factor, which is defined as the number of different planes in a form having identical interplanar spacing and identical intensity, is tabulated here for the 21 noncentrosymmetric point groups on the basis of their symmetries.

• East Asian mathematical journal
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• v.40 no.1
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• pp.85-94
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• 2024

In this paper we study the existence and multiplicity of positive solutions for p-Laplacian problems with a singular weight. Proofs mainly make use of Global Continuation Theorem and Fixed Point Index argument.

• 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.

• Proceedings of the Korean Information Science Society Conference
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• 1998.10a
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• pp.633-635
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• 1998

Farmer 모델에서 지원하는 다중성(multiplicity)은 하나의 개체를 구성하기 위하여 동일한 형태의 구성요소가 여러 번 발생하는 경우에 이의 대표적인 요소만을 표시하는 추상화 개념으로서 Farmer 모델에서만 지원하는 독특한 추상화 개념이다. 다중성 추상화 개념에서 정의된 대표개체는 자신의 인스턴스들을 가질 수 있다. 이들 인스턴스들은 IM-컴포넌트 타입 개체 노드 및 OM-컴포넌트 타입 개체 노드이며 다중성 인스턴스 링크를 이용하여 대표개체와 연결된다. 본 논문에서는 다중성 추상화 개념과 다중성 인스턴스 링크의 정의 및 예를 제시하며 실제 Farmer 모델링 알고리즘내에서 다중성 인스턴스 링크의 개념을 다중성 매핑 알고리즘을 통하여 구체화시켰다.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1311-1326
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• 2012

We are concerned with the multiplicity of semiclassical solutions of the following Schr$\ddot{o}$dinger system involving critical nonlinearity and magnetic fields $$\{-({\varepsilon}{\nabla}+iA(x))^2u+V(x)u=H_u(u,v)+K(x)|u|^{2*-2}u,\;x{\in}\mathbb{R}^N,\\-({\varepsilon}{\nabla}+iB(x))^2v+V(x)v=H_v(u,v)+K(x)|v|^{2*-2}v,\;x{\in}\mathbb{R}^N,$$ where $2^*=2N/(N-2)$ is the Sobolev critical exponent and $i$ is the imaginary unit. Under proper conditions, we prove the existence and multiplicity of the nontrivial solutions to the perturbed system.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.495-503
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• 2007

Symmetric interpolating refinable function vectors with compact support are of interest in several applications such as signal processing, image processing and computer graphics. It is known in [13] that orthogonal interpolating refinable function vectors can not be symmetric for multiplicity r = 2 and dilation d = 2. In this paper, we shall investigate symmetric interpolating refinable function vectors with compact support for multiplicity r = 2 and dilation d = 2 by omitting orthogonality. To illustrate our theorems and results in this paper, we shall also present some examples of symmetric interpolating refinable function vectors with compact support and high order of sum rules.