• Korean Journal of Mathematics
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• 제29권3호
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• pp.603-612
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• 2021

We generalize 3-manifolds supporting non-positively curved metric to construct manifolds which have the following properties : (1) They are not locally CAT(0). (2) Their fundamental groups are residually finite. (3) They have subgroup separability for some abelian subgroups.

• 대한수학회논문집
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• 제25권1호
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• pp.83-96
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• 2010

Let ${\mathbb{H}}^{2n+1}$ be the (2n+1)-dimensional Heisenberg group equipped with a left-invariant metric. In this paper we study the Gaussian curvatures of the geodesic spheres and the volumes of geodesic balls in ${\mathbb{H}}^{2n+1}$.

• 대한수학회논문집
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• 제9권2호
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• pp.415-418
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• 1994

Let G be a compact Lie group and let $S^1$ denote the unit circle in $R^2$ with the standard metric. Since every smooth compact Lie group action on $S^1$ is smoothly equivalent to a linear action (cf. [3J TH 2.0), we may think of $S^1$ with a smooth G-action as S(V) the unit circle of a real 2-dimensional orthogonal G-module V.(omitted)

• 대한수학회지
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• 제56권1호
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• pp.53-65
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• 2019

Recently, Chung and Lee [2] introduced the notion of topological stability for a finitely generated group action, and proved a group action version of the Walters's stability theorem. In this paper, we introduce the concepts of continuous shadowing and continuous inverse shadowing of a finitely generated group action on a compact metric space X with respect to various classes of admissible pseudo orbits and study the relationships between topological stability and continuous shadowing and continuous inverse shadowing property of group actions. Moreover, we introduce the notion of structural stability for a finitely generated group action, and we prove that an expansive action on a compact manifold is structurally stable if and only if it is continuous inverse shadowing.

• 대한수학회지
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• 제33권3호
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• pp.625-639
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• 1996

A convex $RP^n$-structure on a smooth anifold M is a representation of M as a quotient of a convex domain $\Omega \subset RP^n$ by a discrete group $\Gamma$ of collineations of $RP^n$ acting properly on $\Omega$. When M is a closed surface of genus g > 1, then the equivalence classes of such structures form a moduli space $B(M)$ homeomorphic to an open cell of dimension 16(g-1) (Goldman [2]). This cell contains the Teichmuller space $T(M)$ of M and it is of interest to know what of the rich geometric structure extends to $B(M)$. In [3], a symplectic structure on $B(M)$ is defined, which extends the symplectic structure on $T(M)$ defined by the Weil-Petersson Kahler form.

• 대한수학회지
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• 제43권3호
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• pp.507-528
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• 2006

In this paper we show that the Koecher's Jordan automorphic generators of one variable on an irreducible symmetric cone are enough to determine the elements of scalar multiple of the Jordan identity on the attached simple Euclidean Jordan algebra. Its various geometric, Jordan and Lie theoretic interpretations associated to the Cartan-Hadamard metric and Cartan decomposition of the linear automorphisms group of a symmetric cone are given with validity on infinite-dimensional spin factors

• Nonlinear Functional Analysis and Applications
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• 제26권2호
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• pp.273-288
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• 2021

We proposed to give some new 𝜓-coupled fixed point theorems using simulation function coupled with other control functions in a complete partially ordered metric space which includes many related results. Further we prove the existence of solution of a fractional integral equation by using this fixed point theorem and explain it with the help of an example.

• 대한수학회보
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• 제60권6호
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• pp.1607-1620
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• 2023

In this paper, we mainly study the problem of the existence of homogeneous geodesics in sub-Finsler manifolds. Firstly, we obtain a characterization of a homogeneous curve to be a geodesic. Then we show that every compact connected homogeneous sub-Finsler manifold and Carnot group admits at least one homogeneous geodesic through each point. Finally, we study a special class of ℓ^p-type bi-invariant metrics on compact semi-simple Lie groups. We show that every homogeneous curve in such a metric space is a geodesic. Moreover, we prove that the Alexandrov curvature of the metric space is neither non-positive nor non-negative.

• Nutritional Sciences
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• 제2권2호
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• pp.93-101
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• 1999

The aim of this study was to investigate influence of body build on body composition, energy metabolic state and insulin concentration of blood. 29 male athletes and 36 male non-athletic students were recruited for the study. Anthropometry including chest depth and breadth, fat mass, fat fee mass, tricep skinfold thickness were measured. fasting glucose, lactate, triglyceride, fee fatty acid, and insulin concentration in serum were measured . Body build was assessed using metric index, which calculated by regression equations of Mohr and Greil. The athletic and non-athletic students were allocated to 3 body build, that is leptomorph, mesomorph, and pyknomorph. Resting metabolic rate was calculated. Respiratory quotient was determined through ratio of measured VO$_2$, and V$CO_2$. Most non-athletes have a leptomorphic body build, in contrast to athletes mesomorphic type. The body build type influenced body composition differently between non-athletic group and athletic group. Weight, body mass index, body fat mass and fat mass proportion (%), and fat-free mass increased from leptomorph to pyknormorph in non-athletic group. Pyknormorphic athletes have a significant higher body mass index, fat mass, fat free mass than other body build type. Serum glucose, triglyceride, lactate, insulin showed significant differences only in non-athletic group between leptomorph and mesomorph. RMR increased significantly from leptomorph to mesomorph in non-athletes. There was no significant difference of RQ among 3 body build types in both athletes and non-athletes. This study gives a coherent data on body build and body composition for athletes and non-athletes students. The influence of body builds on energy metabolic status of serum was different between athletes and non-athletes.

• 대한수학회보
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• 제42권4호
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• pp.757-776
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• 2005

In this paper we establish the stability of a Jensen type functional equation, namely f(xy) - f($xy^{-1}$) = 2f(y), on some classes of groups. We prove that any group A can be embedded into some group G such that the Jensen type functional equation is stable on G. We also prove that the Jensen type functional equation is stable on any metabelian group, GL(n, $\mathbb{C}$), SL(n, $\mathbb{C}$), and T(n, $\mathbb{C}$).