• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1329-1352
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• 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
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• v.10 no.2
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• pp.103-116
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• 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
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• v.56 no.5
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• pp.481-484
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.779-789
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• 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.

• The Journal of Society for e-Business Studies
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• v.17 no.4
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• pp.209-219
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• 2012

Objects such as products, product reviews, and user profiles are important in e-commerce domain. Vector is one of the most widely used object representation scheme. Information of e-commerce objects may be modeled by vectors in which the featured values are assigned to various dimensions. E-commerce objects are in general quantitatively large while some are similar or even same in reality. It Plays, therefore, an important role to measure the similarity between objects. In this paper, we survey the state-of-the -art vector similarity measures. Similarity measures are analyzed to feature the algebraic characteristics and relationship of those, and upon which we classify the related measures accordingly. We then present such features that standard vector similarity measures should convey.

• The Korean Journal of Applied Statistics
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• v.28 no.5
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• pp.871-883
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• 2015

Vector autoregressive (VAR) models in high dimension suffer from noisy estimates, unstable predictions and hard interpretation. Consequently, the sparse vector autoregressive (sVAR) model, which forces many small coefficients in VAR to exactly zero, has been suggested and proven effective for the modeling of high dimensional time series data. This paper studies coupling measures to select non-zero coefficients in sVAR. The basic idea based on the simulation study reveals that removing the effect of other variables greatly improves the performance of coupling measures. sVAR model coefficients are asymmetric; therefore, asymmetric coupling measures such as Granger causality improve computational costs. We propose two asymmetric coupling measures, filtered-cross-correlation and filtered-Granger-causality, based on the filtered residuals series. Our proposed coupling measures are proven adequate for heavy-tailed and high order sVAR models in the simulation study.

• East Asian mathematical journal
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• v.24 no.2
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• pp.201-212
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• 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
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• v.8 no.2
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• pp.6-17
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1579-1586
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• 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
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• v.3 no.1
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• pp.33-46
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• 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.