• Korean Journal of Acupuncture
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• 제22권1호
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• pp.67-74
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• 2005

Objectives : This study was carried to identify the component of the Pericardium Meridian Muscle in human. Methods : The regional muscle group was divided into outer, middle, and inner layer. The inner part of body surface were opened widely to demonstrate muscles, nerve, blood vessels and to expose the inner structure of the Pericardium Meridian Muscle in the order of layers. Results We obtained the results as follows; He Perfcardium Meridian Muscle composed of the muscles, nerves and blood vessels. In human anatomy, it is present the difference between terms (that is, nerves or blood vessels which control the muscle of the Pericardium Meridian Muscle and those which pass near by the Pericardium Meridian Muscle). The inner composition of the Pericardium Meridian Muscle in human is as follows ; 1) Muscle P-1 : pectoralis major and minor muscles, intercostalis muscle(m.) P-2 : space between biceps brachialis m. heads. P-3 : tendon of biceps brachialis and brachialis m. P-4 : space between flexor carpi radialis m. and palmaris longus m. tendon(tend.), flexor digitorum superficialis m., flexor digitorum profundus m. P-5 : space between flexor carpi radialis m. tend. and palmaris longus m. tend., flexor digitorum superficialis m., flexor digitorum profundus m. tend. P-6 : space between flexor carpi radialis m. tend. and palmaris longus m. tend., flexor digitorum profundus m. tend., pronator quadratus m. H-7 : palmar carpal ligament, flexor retinaculum, radiad of flexor digitorum superficialis m. tend., ulnad of flexor pollicis longus tend. radiad of flexor digitorum profundus m. tend. H-8 : palmar carpal ligament, space between flexor digitorum superficialis m. tends., adductor follicis n., palmar interosseous m. H-9 : radiad of extensor tend. insertion. 2) Blood vessel P-1 : lateral cutaneous branch of 4th. intercostal artery, pectoral br. of Ihoracoacrornial art., 4th. intercostal artery(art) P-3 : intermediate basilic vein(v.), brachial art. P4 : intermediate antebrachial v., anterior interosseous art. P-5 : intermediate antebrarhial v., anterior interosseous art. P-6 : intermediate antebrachial v., anterior interosseous art. P-7 : intermediate antebrachial v., palmar carpal br. of radial art., anterior interosseous art. P-8 : superficial palmar arterial arch, palmar metacarpal art. P-9 : dorsal br. of palmar digital art. 3) Nerve P-1 : lateral cutaneous branch of 4th. intercostal nerve, medial pectoral nerve, 4th. intercostal nerve(n.) P-2 : lateral antebrachial cutaneous n. P-3 : medial antebrachial cutaneous n., median n. musrulocutaneous n. P-4 : medial antebrachial cutaneous n., anterior interosseous n. median n. P-5 : median n., anterior interosseous n. P-6 : median n., anterior interosseous n. P-7 : palmar br. of median n., median n., anterior interosseous n. P-8 : palmar br. of median n., palmar digital br. of median n., br. of median n., deep br. of ulnar n. P-9 : dorsal br. of palmar digital branch of median n. Conclusions : This study shows some differences from already established study on meridian Muscle.

• 대한수학회지
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• 제55권2호
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• pp.373-390
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• 2018

In this paper we study the small-data scattering of the d dimensional fractional $Schr{\ddot{o}}dinger$ equations with d = 2, 3, $L{\acute{e}}vy$ index 1 < ${\alpha}$ < 2 and Hartree type nonlinearity $F(u)={\mu}({\mid}x{\mid}^{-{\gamma}}{\ast}{\mid}u{\mid}^2)u$ with max(${\alpha}$, ${\frac{2d}{2d-1}}$) < ${\gamma}{\leq}2$, ${\gamma}$ < d. This equation is scaling-critical in ${\dot{H}}^{s_c}$, $s_c={\frac{{\gamma}-{\alpha}}{2}}$. We show that the solution scatters in $H^{s,1}$ for any s > $s_c$, where $H^{s,1}$ is a space of Sobolev type taking in angular regularity with norm defined by ${\parallel}{\varphi}{\parallel}_{H^{s,1}}={\parallel}{\varphi}{\parallel}_{H^s}+{\parallel}{\nabla}_{{\mathbb{S}}{\varphi}}{\parallel}_{H^s}$. For this purpose we use the recently developed Strichartz estimate which is $L^2$-averaged on the unit sphere ${\mathbb{S}}^{d-1}$ and utilize $U^p-V^p$ space argument.

• 대한수학회지
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• 제43권2호
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• pp.399-411
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• 2006

Let L be a subspace lattice on a Hilbert space H and X and Y be operators acting on a Hilbert space H. Let P be the projection onto $\frac\;{R(X)}$, where RX is the range of X. If PE = EP for each $E\;\in\;L$, then there exists an operator A in AlgL such that AX = Y if and only if $$sup\{{\parallel}E^{\bot}Yf{\parallel}/{\parallel}E^{\bot}Xf{\parallel}\;:\;f{\in}H,\; E{\in}L}=K\;<\;\infty$$ Moreover, if the necessary condition holds, then we may choose an operator A such that AX = Y and ${\parallel}A{\parallel} = K.$ Let x and y be vectors in H and let $P_x$ be the projection onto the singlely generated space by x. If $P_xE = EP_x$ for each $E\inL$, then the assertion that there exists an operator A in AlgL such that Ax = y is equivalent to the condition $$K_0\;:\;=\;sup\{{\parallel}E^{\bot}y{\parallel}/{\parallel}E^{\bot}x\;:\;E{\in}L}=<\;\infty$$ Moreover, we may choose an operator A such that ${\parallel}A{\parallel} = K_0$ whose norm is $K_0$ under this case.

• 대한수학회논문집
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• 제2권1호
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• pp.47-52
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• 1987

• 대한수학회논문집
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• 제11권2호
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• pp.349-357
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• 1996

Using a special property of Bloch functions with Hardmard gaps and using the geometric properties of the self maps of the unit disc, we give a way of constructing explicit examples of Bloch functions f whose derivative is in $H^p$ (0 < p < 1) but $f \notin BMOA$.

• 대한수학회보
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• 제57권1호
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• pp.207-218
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• 2020

Some modular representations of reflection groups related to Weyl groups are considered. The rational cohomology of the classifying space of a compact connected Lie group G with a maximal torus T is expressed as the ring of invariants, H*(BG; ℚ) ≅ H*(BT; ℚ)^W(G), which is a polynomial ring. If such Lie groups are locally isomorphic, the rational representations of their Weyl groups are equivalent. However, the integral representations need not be equivalent. Under the mod p reductions, we consider the structure of the rings, particularly for the Weyl group of symplectic groups Sp(n) and for the alternating groups A_n as the subgroup of W(SU(n)). We will ask if such rings of invariants are polynomial rings, and if each of them can be realized as the mod p cohomology of a space. For n = 3, 4, the rings under a conjugate of W(Sp(n)) are shown to be polynomial, and for n = 6, 8, they are non-polynomial. The structures of H*(BT^n-1; 𝔽_p)^A_n will be also discussed for n = 3, 4.

• 충청수학회지
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• 제4권1호
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• pp.103-113
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• 1991

Some properties of a path space and the fundamental group ${\sigma}(X,x_0,G)$ of a topological transformation group (X, G, ${\pi}$) are described. It is shown that ${\sigma}(X,x_0,H)$ is a normal subgroup of ${\sigma}(X,x_0,G)$ if H is a normal subgroup of G ; Let (X, G, ${\pi}$) be a transformation group with the open action property. If every identification map $p:{\Sigma}(X,x,G)\;{\longrightarrow}\;{\sigma}(X,x,G)$ is open for each $x{\in}X$, then ${\lambda}$ induces a homeomorphism between the fundamental groups ${\sigma}(X,x_0,G)$ and ${\sigma}(X,y_0,G)$ where ${\lambda}$ is a path from $x_0$ to $y_0$ in X ; The space ${\sigma}(X,x_0,G)$ is an H-space if the identification map $p:{\Sigma}(X,x_0,G)\;{\longrightarrow}\;{\sigma}(X,x_0,G)$ is open in a topological transformation group (X, G, ${\pi}$).

• 호남수학학술지
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• 제24권1호
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• pp.9-23
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• 2002

For a closed densely defined linear operator T on a Hilbert space H, let ${\prod}$ denote the function which corresponds to T, the orthogonal projection from $H{\oplus}H$ onto the graph of T. We extend some ordinary norm ineqralites comparing ${\parallel}{\Pi}(A)-{\Pi}(B){\parallel}$ and ${\parallel}A-B{\parallel}$ to the Schatten p-norm where A and B are bounded operators on H.

• 대한수학회논문집
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• 제9권4호
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• pp.905-915
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• 1994

Let $M_g$ be the moduli space of isomorphism classes of genus g smooth curves. It is a quasi-projective variety of dimension 3g - 3, when $g > 2$. It is known that a complete subvariety of $M_g$ has dimension $< g-1 [D]$. In general it is not known whether this bound is rigid. For example, it is not known whether $M_4$ has a complete surface in it. But one knows that there is a complete curve through any given finite points [H]. Recently, an explicit example of a complete curve in moduli space is given in [G-H]. In [G-H] they constructed a complete curve of $M_3$ as an intersection of five hypersurfaces of the Satake compactification of $M_3$. One way to get a complete curve of $M_3$ is to find a complete one dimensional family $p : X \to B$ of plane quartics which gives a nontrivial morphism from the base space B to the moduli space $M_3$. This is because every non-hyperelliptic smooth curve of genus three can be realized as a nonsingular plane quartic and vice versa. This paper has come out from the effort to find such a complete family of plane quartics. Since nonsingular quartics form an affine space some fibers of p must be singular ones. In this paper, due to the semistable reduction theorem [M], we search singular plane quartics which can occur as singular fibers of the family above. We first list all distinct plane quartics in terms of singularities.

• 대한수학회보
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• 제58권3호
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• pp.745-765
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• 2021

Let Ω be a proper open subset of ℝⁿ and p(·) : Ω → (0, ∞) be a variable exponent function satisfying the globally log-Hölder continuous condition. In this article, the author introduces the "geometrical" variable Hardy spaces H^p(·)_r (Ω) and H^p(·)_z (Ω) on Ω, and then obtains the grand maximal function characterizations of H^p(·)_r (Ω) and H^p(·)_z (Ω) when Ω is a strongly Lipschitz domain of ℝⁿ. Moreover, the author further introduces the "geometrical" variable local Hardy spaces h^p(·)_r (Ω), and then establishes the atomic characterization of h^p(·)_r (Ω) when Ω is a bounded Lipschitz domain of ℝⁿ.