• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.801-813
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• 2019

In this paper, using the Baire category theorem we investigate the Hyers-Ulam stability problem of pexiderized Jensen functional equation $$2f(\frac{x+y}{2})-g(x)-h(y)=0$$ and pexiderized Jensen type functional equations $$f(x+y)+g(x-y)-2h(x)=0,\\f(x+y)-g(x-y)-2h(y)=0$$ on a set of Lebesgue measure zero. As a consequence, we obtain asymptotic behaviors of the functional equations.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.697-711
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• 2017

Let X, Y be real normed vector spaces. We exhibit all the solutions $f:X{\rightarrow}Y$ of the functional equation f(rx + sy) + rsf(x - y) = rf(x) + sf(y) for all $x,y{\in}X$, where r, s are nonzero real numbers satisfying r + s = 1. In particular, if Y is a Banach space, we investigate the Hyers-Ulam stability problem of the equation. We also investigate the Hyers-Ulam stability problem on a restricted domain of the following form ${\Omega}{\cap}\{(x,y){\in}X^2:{\parallel}x{\parallel}+{\parallel}y{\parallel}{\geq}d\}$, where ${\Omega}$ is a rotation of $H{\times}H{\subset}X^2$ and $H^c$ is of the first category. As a consequence, we obtain a measure zero Hyers-Ulam stability of the above equation when $f:\mathbb{R}{\rightarrow}Y$.

• Language and Information
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• v.14 no.2
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• pp.71-84
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• 2010

The aim of this paper is to propose that a category P is encapsulated within a functional layer above the lexical layer, just like vP containing a lexical VP. As is well known, the category P has long been in the obscure domain of syntactic studies: Marantz (2001) and den Dikken (2003), for example, argue that P is a lexical category, but Emonds (1985), Grimshaw (1991), and Baker (2003), maintain that the category P is functional and is a closed category without its own intrinsic meaning. On the other hand, Zwart (2005) argues that it does have some meaning. Following the works of Svenonius (2003, 2006, 2007), and the spirit of Rizzi's (1997) split CP hypothesis, we elaborate and develop Svenonius' idea of split-pP analysis with detailed schematic representations of the novel examples in English, Korean, and Chinese in this paper. Unlike Svenonius, however, this paper incorporates KP into pP-Shell, which is a substantial simplification. Furthermore, Chinese Localizers that have long been considered as Postpositions are now under the category of Prepositions. This proposal renders an X-bar theoretic consistency over the categorical status of Chinese phrasal structures. In short, the present analysis accounts for inconsistency found in English complex preposition phrase (Quirk, et al, 1972, 1985), Chinese circumposition phrase (Ernst 1988, Liu, 2002) and Korean postposition phrase in a unified and consistent manner. Furthermore, by proposing a finer-grained phrasal architecture for the category P, the controversial status of the category subsides within this analysis.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.437-445
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• 2008

We show the existence of at least four nontrivial critical points of the $C^{1,1}$ functional f on the Hilbert space $H=X_0{\oplus}X_1{\oplus}X_2{\oplus}X_3{\oplus}X_4$, $X_i$, i = 0, 1, 2, 3 are finite dimensional, with f(0) = 0 when two sublevel subsets, torus with three holes and sphere, of f link, the functional f satisfies sup-inf variatinal linking inequality on the linking subspaces, the functional f satisfies $(P.S.)_c$ condition, and $f{\mid}_{X_0{\oplus}X_4}$ has no critical point with level c. We use the deformation lemma, the relative category theory and the critical point theory for the proof of main result.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.311-319
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• 2009

Let H be a Hilbert space which is the direct sum of five closed subspaces $X_0,\;X_1,\;X_2,\;X_3$ and $X_4$ with $X_1,\;X_2,\;X_3$ of finite dimension. Let J be a $C^{1,1}$ functional defined on H with J(0) = 0. We show the existence of at least four nontrivial critical points when the sublevels of J (the torus with three holes and sphere) link and the functional J satisfies sup-inf variational inequality on the linking subspaces, and the functional J satisfies $(P.S.)^*_c$ condition and $f|X_0{\otimes}X_4$ has no critical point with level c. For the proof of main theorem we use the nonsmooth version of the classical deformation lemma and the limit relative category theory.

• The Journal of Korean Physical Therapy
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• v.27 no.5
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• pp.320-324
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• 2015

Purpose: The purpose of this study was to provide methods for assessment of functional balance through study of correlation with the weight bearing ratio, functional balance, and functional gait on patients with stroke. Methods: Thirty-nine patients with stroke participated in this study. The timed up and go test was used to measure balance and the functional ambulation category test to measure functional gait. Weight bearing was measured in the quiet standing posture and weight bearing in the quiet standing posture immediately after performing the standing-task. Results: Both timed up and go test and functional ambulation category test showed significant correlation with balance in the quiet standing posture immediately after performing the standing task. Conclusion: Measurement of balance in the quiet standing posture immediately after performing the standing-task was considered a meaningful scale for measurement of both balance function and gait function of patients with stroke.

• Research in Community and Public Health Nursing
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• v.21 no.4
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• pp.386-397
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• 2010

Purpose: The purpose of this study was to compare functional status and the level of health care needs in elderly Koreans in health care institutions. Methods: Data were collected from 2,521 elderly patients admitted in 50 health care institutions (hospitals, oriental hospitals, geriatric hospitals, and health care facilities) selected through proportional stratified sampling in 2008. We used a long-term care (LTC) assessment tool developed by the government, which consists of 52 items with 5 subscales. Results: Statistically significant differences were detected in functional status and the level of health care needs among the subjects in different health care institutions. Of the sample population in geriatric hospitals, 48.9% were eligible for LTC Category 1, 20.9% for Category 2, and 17.2% for Category 3, and 13.1% of the subjects were not eligible for any of the categories. Of the sample population in health care facilities, 29.9% were eligible for LTC Category 1, 20.5% for Category 2, and 21.8% for Category 3, and 27.0% of the subjects were not eligible for any of the categories. Conclusion: The findings of this study indicate the necessity of the development of an evaluation system that helps determine whether a subject is eligible for LTC.

• Journal of Microbiology and Biotechnology
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• v.16 no.5
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• pp.748-756
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• 2006

We propose a genome-scale clustering approach to identify whole genome relationships using the functional groups given by the Kyoto Encyclopedia of Genes and Genomes Orthology (KO) database. The metabolic capabilities of each organism were defined by the number of genes in each functional category. The archaeal, bacterial, and eukaryotic genomes were compared by simultaneously applying a two-step clustering method, comprised of a self-organizing tree algorithm followed by unsupervised hierarchical clustering. The clustering results were consistent with various phenotypic characteristics of the organisms analyzed and, additionally, showed a different aspect of the relationship between genomes that have previously been established through rRNA-based comparisons. The proposed approach to collect and cluster the metabolic functional capabilities of organisms should make it a useful tool in predicting relationships among organisms.

• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.311-324
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• 2006

The Support Vector Machine(SVM) is very functional and efficient classification method to any other classification analysis method. However, its optimal extension to more than two classes is not obvious. In this paper several multi-category SVM methods are introduced and compared using simulation and real data sets. Also comparison with traditional multi-category classification and SVM based methods is performed.

• Annual Conference on Human and Language Technology
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• 1990.11a
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• pp.164-171
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• 1990

A commutative productive category is proposed to the current CCG for the syntactic analysis of free word order languages like Korean. The introduction of this sort of category is quite natural for categorial lexicon and functional operations. We present the theorical basis of productive category and examine the linguistic availability through typical syntactic structures of Korean.