• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.331-340
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• 1998

We define the spherical non-commutative torus $L_{\omega}$/ as the crossed product obtained by an iteration of l crossed products by actions of, the first action on C( $S^{2n＋l}$). Assume the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus $A_{p}$ with a matrix algebra $M_{m}$ ( ) (m > 1). We prove that $L_{\omega}$/ $M_{p}$ (C) is not isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{mp}$ (C), and that the tensor product of $L_{\omega}$/ with a UHF-algebra $M_{p{\infty}}$ of type $p^{\infty}$ is isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{m}$ (C) $M_{p{\infty}}$ if and only if the set of prime factors of m is a subset of the set of prime factors of p. Furthermore, it is shown that the tensor product of $L_{\omega}$/, with the C＊-algebra K(H) of compact operators on a separable Hilbert space H is not isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{m}$ (C) K(H) if Prim( $L_{\omega}$/) is homeomorphic to $L^{k}$ (n)$\times$ $T^{l'}$ for k and l' non-negative integers (k > 1), where $L^{k}$ (n) is the lens space.$T^{l'}$ for k and l' non-negative integers (k > 1), where $L^{k}$ (n) is the lens space.e.

• Journal of Korean Neurosurgical Society
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• v.61 no.1
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• pp.66-74
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• 2018

Objective : The aim of this study was to identify the susceptibility genes responsible for lumbar spondylosis (LS) in Korean patients. Methods : Data from 1427 subjects were made available for radiographic grading and genome wide association studies (GWAS) analysis. Lateral lumbar spine radiographs were obtained and the various degrees of degenerative change were semi-quantitatively scored. A pilot GWAS was performed using the AffymetrixGenome-Wide Human single-nucleotide polymorphisms (SNPs), 500K array. A total of 352228 SNPs were analyzed and the association between the SNPs and case-control status was analyzed by stepwise logistic regression analyses. Results : The top 100 SNPs with a cutoff p-value of less than $3.7{\times}10^{-4}$ were selected for joint space narrowing, while a cutoff p-value of $6.0{\times}10^{-4}$ was applied to osteophytes and the Kellgren-Lawrence (K-L) osteoarthritis grade. The SNPs with the strongest effect on disc space narrowing, osteophytes, and K-L grade were serine incorporator 1 (rs155467, odds ratio [OR]=17.58, $p=1.6{\times}10^{-4}$), stromal interaction molecule 2 (STIM1, rs210781, OR=5.53, $p=5{\times}10^{-4}$), and transient receptor potential cation channel, subfamily C (rs11224760, OR=3.99, $p=4.8{\times}10^{-4}$), respectively. Leucine-rich repeat-containing G protein-coupled receptor 4 was significantly associated with both disc space narrowing and osteophytes (rs1979400, OR=2.01, $p=1.1{\times}10^{-4}$ for disc space narrowing, OR=1.79, $p=3{\times}10^{-4}$ for osteophytes), while zinc finger and BTB domain containing 7C was significantly and negatively associated with both osteophytes and a K-L grade >2 (rs12457004,OR=0.25, $p=5.8{\times}10^{-4}$ and OR=0.27, $p=5.3{\times}10^{-4}$, respectively). Conclusion : We identified SNPs that potentially contribute to the pathogenesis of LS. This is the first report of a GWAS in an Asian population.

• Journal of Preventive Medicine and Public Health
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• v.54 no.3
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• pp.208-217
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• 2021

Objectives: In spite of the importance of green space for reducing obesity-related problems, there has been little exploration of whether access to green space (e.g., parks and recreational facilities) influences the obesity rate of adults in the United States. The purpose of the study was to investigate the relationships among accessibility of green space, obesity rates, and socioeconomic and demographic variables among adults living in the State of Indiana, United States. Methods: We conducted a secondary data analysis to investigate the relationships among accessibility to green space, obesity rates, and socio-demographic variables with employing Geographic Information System in order to measure the accessibility of green space. Results: This study found that accessibility of green space served as a strong predictor of reduced obesity rates among adults (β=-2.478; p<0.10). In addition, adults with higher education levels, as well as better access to green space, were found to have even lower obesity rates (β=-0.188; p<0.05). Other control variables such as unemployment rates, food security, and physical inactivity are additional factors that influence obesity rates among adults. Conclusions: Accessibility of green space may play an important role in facilitating physical activity participation and reducing obesity rates.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.975-1002
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• 2005

On the setting of the upper half-space H of the Eu­clidean n-space, we show the boundedness of weighted Bergman projection for 1 < p < $\infty$ and nonorthogonal projections for 1 $\leq$ p < $\infty$ . Using these results, we show that Bergman norm is equiva­ lent to the normal derivative norms on weighted harmonic Bergman spaces. Finally, we find the dual of b$\_{$^{1}$.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.449-457
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• 2003

On the setting of the upper half-space of the Euclidean space $R^{n}$, we show that to each weighted harmonic Bergman function $u\;\epsilon\;b^p_{\alpha}$, there corresponds a unique conjugate system ($upsilon$_1,…, $upsilon_{n-1}$) of u satisfying $upsilon_j{\epsilon}\;b^p_{\alpha}$ with an appropriate norm bound.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.327-332
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• 2002

In this paper we prove that if M is a J-invariant sub-manifold of codimension 2 in a complex projective space $P_{n+1}(C)$, and the second fundamental tensor is cyclic-parallel or M has harmonic curvature, then M is locally complex quadric Q$_n$(C) or P$_n$(C).

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.299-309
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• 2010

The Weyl group of a compact connected Lie group is a reflection group. If such Lie groups are locally isomorphic, the representations of the Weyl groups are rationally equivalent. They need not however be equivalent as integral representations. Turning to the invariant theory, the rational cohomology of a classifying space is a ring of invariants, which is a polynomial ring. In the modular case, we will ask if rings of invariants are polynomial algebras, and if each of them can be realized as the mod p cohomology of a space, particularly for dihedral groups.

• East Asian mathematical journal
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• v.21 no.1
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• pp.41-48
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• 2005

In this paper we first introduce a space of homogeneous type X, and then consider a kind of generalized upper half-space $X{\times}(0,\;\infty)$. We are mainly considered with inequalities for the $L^p$ norms of area functions associated with approach regions in $X{\times}(0,\;\infty)$.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.68-72
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• 1986

Upper bounds of the perturbed Co-semigroups of the infinite dimensional systems are investigated by using the algebraic Riccati equation(ARE). In the case that the solution P of the ARE is strictly positive, the perturbed semigroups are uniformly bounded. A sufficient condition for the solution P to be strictly positive is provided. The uniform boundedness plays an important role in extending approximately weak stability to weak stability on th whole space. Exponential Stability of the perturbed semigroups is studied by using the Young's inequlity. Some further discussions on the uniform boundedness of the perturbed semigroups are given.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.519-529
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• 2002

In this paper. We Study (n + 1)-dimensional Contact CR-submanifolds of (n - 1) contact CR-dimension immersed in a Sasakian space form M$\^$2m+1/(c) (2m=n+p, p>0), and especially determine such submanifolds under additional condition concerning with shape operator.