• 대한수학회논문집
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• 제32권3호
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• pp.653-659
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• 2017

Let $p{\geq}1$ be a real number. A tuple $T=(T_1,{\ldots},T_n)$ of commuting bounded linear operators on a Banach space X is called an ${\ell}^p$-spherical isometry if ${\sum_{i=1}^{n}}{\parallel}T_ix{\parallel}^p={\parallel}x{\parallel}^p$ for all $x{\in}X$. The tuple T is called a toral isometry if each Ti is an isometry. By a result of Ansari, Hedayatian, Khani-Robati and Moradi, for every $n{\geq}1$, there is a supercyclic ${\ell}^2$-spherical isometric n-tuple on ${\mathbb{C}}^n$ but there is no supercyclic ${\ell}^2$-spherical isometry on an infinite-dimensional Hilbert space. In this article, we investigate the supercyclicity of ${\ell}^p$-spherical isometries and toral isometries on Banach spaces. Also, we introduce the notion of semicommutative tuples and we show that the Banach spaces ${\ell}^p$ ($1{\leq}p$ < ${\infty}$) support supercyclic ${\ell}^p$-spherical isometric semi-commutative tuples. As a result, all separable infinite-dimensional complex Hilbert spaces support supercyclic spherical isometric semi-commutative tuples.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 1995년도 춘계공동학술대회논문집; 전남대학교; 28-29 Apr. 1995
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• pp.629-634
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• 1995

The purpose of this paper is to develop a method of Collision-Free Path Planning (CFPP) for an articulated robot. First, the configuration of the robot is formed by a set of robot joint angles derived fromm robot inverse kinematics. The joint space that is made of the joint angle set, forms a Configuration space (Cspace). Obstacles in the robot workcell are also transformed and mapped into the Cspace, which makes Cobstacles in the Cspace. (The Cobstacles represented in the Cspace is actually the configurations of the robot causing collision.) Secondly, a connected graph, a kind of roadmap, is constructed from the free configurations in the 3 dimensional Cspace, where the configurations are randomly sampled form the free Cspace. Thirdly, robot paths are optimally in order to minimize of the sum of joint angle movements. A path searching algorithm based on A is employed in determining the paths. Finally, the whole procedures for the CFPP method are illustrated with a 3 axis articulated robot. The main characteristics of the method are; 1) it deals with CFPP for an articulated robot in a 3-dimensional workcell, 2) it guarantees finding a collision free path, if such a path exists, 3) it provides distance optimization in terms of joint angle movements. The whole procedures are implemented by C on an IBM compatible 486 PC. GL (Graphic Library) on an IRIS CAD workstation is utilized to produce fine graphic outputs.

• 한국수학사학회지
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• 제28권2호
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• pp.103-115
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• 2015

Contemporary differential geometry owes much to the theory of connections on the bundles over manifolds. In this paper, following the work of Gauss on surfaces in 3 dimensional space and the work of Riemann on the curvature tensors on general n dimensional Riemannian manifolds, we will investigate how differential geometry had been developed from mid 19th century to early 20th century through lives and mathematical works of Christoffel, Ricci-Curbastro and Levi-Civita. Christoffel coined the Christoffel symbol and Ricci used the Christoffel symbol to define the notion of covariant derivative. Levi-Civita completed the theory of absolute differential calculus with Ricci and discovered geometric meaning of covariant derivative as parallel transport.

• 충청수학회지
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• 제21권4호
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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.

• 대한화학회지
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• 제16권1호
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• pp.18-24
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• 1972

Benzidine dihydrochloride crystallizes in the triclinic system. The space group is $P_1$. The unit cell dimensions are; a = 4.38${\pm}$0.01, b = 5.76${\pm}$0.01, c = 12.82${\pm}$0.02${\AA}$, $\alpha$ = 101.5${\pm}$0.2, $\beta$ = 99.5${\pm}$0.2, $\gamma$ = 99.5${\pm}$0.2$^{\circ}$; with one molecule per unit cell. The crystal structure has been solved by two dimensional Patterson and by trial and error methods, and refined by means of two dimensional differential synthesis. The bond distances are C-C(*) = 1.40${\pm}$0.02, C-C = 1.52${\pm}$0.02, C-N = 1.51${\pm}$0.03 and N-H${\cdot}{\cdot}{\cdot}$Cl = 3.21${\pm}$0.03${\AA}$. The structure consists of hydrogen bonded molecular layers, extending to the (100) plane, and the hydrogen bonding scheme is similar to that of p-phenylenediamine dihydrochloride. The adhesion between hydrogen bonded molecular layers is due to van der Waals forces.

• 분석과학
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• 제21권6호
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• pp.562-568
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• 2008

A novel two-dimensional cadmium(II)-nickel(II) bimetallic host clathrate, $[Cd{NH_2CH_2CH_2OH}_2Ni(CN)_4]{\cdot}3C_6H_5NH_2{\cdot}H_2O$, 1, has been synthesized and structurally characterized by X-ray single crystallographic method. The clathrate 1 crystallizes in the monoclinic system, space group $P2_1/c$ with a = 14.370(3), b = 7.728(1), c = 28.172(4) ${\AA}$, ${\beta}=97.58(1)^{\circ}$, V = 3101.1(9) ${\AA}^3$, Z = 4. The host framework of the clathrate 1 is built of the cyanide bridges between octahedral Cd(II) atom and square planar Ni(II) atom. The octahedral Cd atoms ligated by two 2-aminoethanol molecules and four cyanide ligands bridged with square planar Ni atoms. The Ni atoms bridges to four Cd atoms via cyanides is made up of puckered quadrangles of composition $\{CdNi(CN)_2\}_2$, all edges are shared. This cyanide bridges form an infinite two-dimensional host networks stacking along b axis. 2-Aminoethanol ligands bond to Cd atom through N atom as a monodentate ligand in the axial position and four cyanides take an equatorial plane with all in trans-configurations. The aniline guest molecules and water molecules are located in between the host layer sheets, respectively.

• 대한수학회논문집
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• 제27권3호
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• pp.565-570
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• 2012

In this note we investigate Weyl's theorem for *-paranormal operators on a separable infinite dimensional Hilbert space. We prove that if T is a *-paranormal operator satisfying Property $(E)-(T-{\lambda}I)H_T(\{{\lambda}\})$ is closed for each ${\lambda}{\in}{\mathbb{C}}$, where $H_T(\{{\lambda}\})$ is a local spectral subspace of T, then Weyl's theorem holds for T.

• 대한수학회논문집
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• 제17권2호
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• pp.279-293
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• 2002

In this paper, we prove that if every totally real bisectional curvature of an n($\geq$3)-dimensional complete Kahler submanifold of a complex projective space of constant holomorphic sectional curvature c is greater than (equation omitted) (3n$^2$+2n-2), then it is totally geodesic and compact.

• East Asian mathematical journal
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• 제33권5호
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• pp.571-585
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• 2017

Let M be a connected n-dimensional submanifold of a Euclidean space $E^{n+k}$ equipped with the induced metric and ${\Delta}$ its Laplacian. If the position vector x of M is decomposed as a sum of three vectors $x=x_1+x_2+x_0$ where two vectors $x_1$ and $x_2$ are non-constant eigen vectors of the Laplacian, i.e., ${\Delta}x_i={\lambda}_ix_i$, i = 1, 2 (${\lambda}_i{\in}R$) and $x_0$ is a constant vector, then, M is called a 2-type submanifold. In this paper we showed that a 2-type surface M in $E^3$ satisfies ${\langle}{\Delta}x,x-x_0{\rangle}=c$ for a constant c, where ${\langle},{\rangle}$ is the usual inner product in $E^3$, then M is an open part of a circular cylinder. Also we showed that if a quadric hypersurface M in a Euclidean space satisfies ${\langle}{\Delta}x,x{\rangle}=c$ for a constant c, then it is one of a minimal quadric hypersurface, a genaralized cone, a hypersphere, and a spherical cylinder.

• 한국결정학회지
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• 제8권2호
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• pp.144-148
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• 1997

단결정 X-ray 회절법을 이용하여 Bentazone, C10H12N2O3S의 결정 및 부자구조를 규명하였다. 공간군은 P21/c이며 a=9.7818(9)Å, b=9.6095(9)Å, c=13.5737(9)Å, β=97.269(1)', Z=4, V=1136.1(6) Å. 직접법으로 개략적인 분자모델을 설정하고, 1396(Fo2>4σFo2)개의 독립 회절반점에 완전행력 최소자승법으로 정밀화하여 최종신뢰도값, R=0.045인 최종적인 분자모형을 구하였다. 분자내의 Thiocarbazin ring과 Isopropyl작용기는 staggered conformation을 이루고 있으며, 수소결합에 의하여 결합된 분자들은 c-축 방향으로 교차 하면서 packing 되어 있다.