• 대한수학회논문집
• /
• 제35권4호
• /
• pp.1329-1352
• /
• 2020

In this paper we consider a class of nonlinear evolution equations on infinite dimensional Banach spaces driven by vector measures. We prove existence and uniqueness of solutions and continuous dependence of solutions on the control measures. Using these results we prove existence of optimal controls for Bolza problems. Based on this result we present necessary conditions of optimality.

• Korean Journal of Mathematics
• /
• 제10권2호
• /
• pp.103-116
• /
• 2002

We characterize operators between Banach spaces sending compact sets into sets that lie in the range of a vector measure. Further, we describe operators between Banach spaces taking compact sets into sets that lie in the range of a vector measure of bounded variation.

• Journal of Preventive Medicine and Public Health
• /
• 제56권5호
• /
• pp.481-484
• /
• 2023

Epidemiological models, also known as host-agent-vector-environment models, are utilized in public health to gain insights into disease occurrence and to formulate intervention strategies. In this paper, we propose an epidemiological model that incorporates both conventional measures and tobacco endgame policies. Our model suggests that conventional measures focus on relationships among agent-vector-host-environment components, whereas endgame policies inherently aim to change or eliminate those components at a fundamental level. We also found that the vector (tobacco industry) and environment (physical and social surroundings) components were insufficiently researched or controlled by both conventional measures and tobacco endgame policies. The use of an epidemiological model for tobacco control and the tobacco endgame is recommended to identify areas that require greater effort and to develop effective intervention measures.

• 대한수학회보
• /
• 제48권4호
• /
• pp.779-789
• /
• 2011

In this paper we study the Banach space $L^1$(G) of real valued measurable functions which are integrable with respect to a vector measure G in the sense of D. R. Lewis. First, we investigate conditions for a scalarly integrable function f which guarantee $f{\in}L^1$(G). Next, we give a sufficient condition for a sequence to converge in $L^1$(G). Moreover, for two vector measures F and G with values in the same Banach space, when F can be written as the integral of a function $f{\in}L^1$(G), we show that certain properties of G are inherited to F; for instance, relative compactness or convexity of the range of vector measure. Finally, we give some examples of $L^1$(G) related to the approximation property.

• 한국전자거래학회지
• /
• 제17권4호
• /
• pp.209-219
• /
• 2012

전자 상거래 시스템 환경에서 상품, 상품평, 사용자 특성 등은 주요한 정보 객체이다. 벡터는 객체의 표현기법으로 널리 사용되고 있다. 전자 상거래 데이터 객체들은 벡터로서 모델되어 각 특질에 해당하는 차원의 숫자 값으로 표현될 수 있다. 전자 상거래의 특성상 이러한 객체들은 방대한 분량이 되고 있고, 이중 여러 객체들은 실제로 같거나 유사한 객체일 수 있다. 따라서 객체간 유사도 측정은 전자상거래 시스템에서 중요한 역할을 한다. 본 논문에서는 벡터 객체에서 사용되는 대표적인 유사도 측정 함수들을 고찰한다. 유사 함수들은 각각의 대수적 특성을 가지고 있고 서로 연결된 특성을 보인다. 이러한 특성을 분석하고 또한 유사 함수들을 분류해 본다. 이러한 과정은 표준 벡터 유사도 함수가 가져야 할 대수적 특성을 제시해준다.

• 응용통계연구
• /
• 제28권5호
• /
• pp.871-883
• /
• 2015

벡터자기회귀모형은 다차원의 시계열 자료간의 선형종속 관계를 연구하는데 효율적인 모형이다. 하지만 차원이 높아질 경우 추정해야할 모수가 급격히 증가하여 추정이 불안정해지고 예측력의 저하 및 해석의 어려움을 동반하는 문제를 가지고 있다. 이를 보완하기 위해서 많은 계수를 0으로 두는 희박벡터자기회귀모형이 제안되었고 고차원 시계열 분석에서 유용함이 밝혀졌다. 이 논문에서는 희박벡터자기회귀모형 추정에 있어서 어떠한 계수를 0으로 두어야 하는지를 판단해주는 한 쌍의 변수에 대한 상관 정도를 추정해주는 커플링 측도를 제안한다. 먼저 이 논문에서는 부분 스펙트럼 일관성에 기반을 둔 커플링 측도를 사용한 변수 선택의 경우 다른 변수의 효과를 제거한 잔차에 기반을 두었기에 좋은 효율성을 보임을 밝힌다. 하지만 부분 스펙트럼 일관성의 경우 벡터자기회귀모형 계수의 비대칭성을 고려하지 못한다는 단점이 있어 이를 보완하고자 필터링을 통해 다른 변수의 효과를 제거한 잔차에 기반을 둔 동시에 비대칭성을 가지는 커플링 측도들, 필터링된 잔차를 이용한 교차 상관성과 그래인저 인과관계를 제안한다. 모의실험을 통해 우리가 제안한 방법론들이 두터운 꼬리를 가지거나 높은 차수의 희박벡터자기회귀모형의 경우에도 매우 정확하게 0이 아닌 변수를 선택함을 보인다.

• East Asian mathematical journal
• /
• 제24권2호
• /
• pp.201-212
• /
• 2008

We characterize operators between Banach spaces sending unconditionally weakly p-summable sequences into sequences that lie in the range of a vector measure of bounded variation. Further, we describe operators between Banach spaces taking unconditionally weakly p-summable sequences into sequences that lie in the range of a vector measure.

• Journal of Information Science Theory and Practice
• /
• 제8권2호
• /
• pp.6-17
• /
• 2020

Word similarity is often measured to enhance system performance in the information retrieval field and other related areas. This paper reports on an experimental comparison of values for word similarity measures that were computed based on 50 intentionally selected words from a Reuters corpus. There were three targets, including (1) co-occurrence-based similarity measures (for which a co-occurrence frequency is counted as the number of documents or sentences), (2) context-based distributional similarity measures obtained from a latent Dirichlet allocation (LDA), nonnegative matrix factorization (NMF), and Word2Vec algorithm, and (3) similarity measures computed from the tf-idf weights of each word according to a vector space model (VSM). Here, a Pearson correlation coefficient for a pair of VSM-based similarity measures and co-occurrence-based similarity measures according to the number of documents was highest. Group-average agglomerative hierarchical clustering was also applied to similarity matrices computed by individual measures. An evaluation of the cluster sets according to an answer set revealed that VSM- and LDA-based similarity measures performed best.

• 대한수학회보
• /
• 제52권5호
• /
• pp.1579-1586
• /
• 2015

In this paper we investigate the barrellednes of some spaces of X-valued measures, X being a barrelled normed space, and provide examples of non barrelled spaces of bounded linear operators from a Banach space X into a barrelled normed space Y, equipped with the uniform convergence topology.

• Journal of the Korean Data and Information Science Society
• /
• 제3권1호
• /
• pp.33-46
• /
• 1992

The set of eigenvectors of the second moment matrix and the mean vector are the measures of orientation for a distribution supported on the unit sphere. Bootstrap confidence cone for the eigenvector is constructed and the consistency of this method is discussed. The performance of our bootstrap cone for the eigenvector is compared with that of the asymptotic confidence cones for two measures under the parametric assumptions for the underlying distributions and that of the bootstrap cone for the mean vector by Monte Carlo simulation.