• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.133-135
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• 1995

In this note, we will investigate the radial symmetry of some kind of solutions of nonlinear ellipitic equations $$ \Delta U = f(U) $$ $$ (1.1) U = 0 in B $$ $$ U \in C^2 (\bar{B}) on \partial B$$ Here f is $C^1$ and B denotes a n-dimensional unit ball in $R^n$.

• Korean Journal of Crystallography
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• v.12 no.3
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• pp.150-156
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• 2001

Nea-inositol is triclinic P???, with a =4.799(1), b=6.520(1), c=6.505(1) Å, α=70.61(1), β=69.41(1), γ=73.66(1)°, Z=1, molecular symmetry ???. Scyllo-inositol, from A, is monoclinic, P2₂/c, with a=5.089(1), c=11.948(2)Å, β=116.98(2)°, Z=2, molecular symmetry ???. Form B is triclinic, P???, with a=6.725(1), b=6.797(1), c=8.635(2)° Å, α=95.45(2), β=99.49(2), γ=99.19(2)°, Z=2, molecular symmetry ???. This crystal structure is pseudo-monoclinic, having two centrosymmetrical molecules with the almost identical conformation and orientation in the crystal lattice. The molecules have the expected chair conformations with puckering parameters of Q=0.609(2)Å for n대, 0.581(2)Å for Scyllo-A, and 0.566(2) Å for Scyllo-B. The bond lengths and angles are normal, C-C, 1.505 to 1.531 8A, C-O, 1.415 to 1.440 Å, C-C-C, 108.2 to 112.9°. The molecules are linked by systems of finite and infinite chains of hydrogen bonds.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.289-303
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• 2004

The non-rigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field of chemistry. Smeyers in a series of papers applied this notion to determine the character table of restricted NRG of some molecules. In this work, a simple method is described, by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of NH3 groups attached to a rigid framework. We study the full non-rigid group (f-NRG) of tetraammineplatinum(II) with two separate symmetry groups C2v and C4v. We prove that they are groups of order 216 and 5184 with 27 and 45 conjugacy classes, respectively. Also, we will compute the character tables of these groups.

• Bulletin of the Korean Chemical Society
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• v.31 no.11
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• pp.3385-3390
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• 2010

$Li^+$ ion complex of azacrown ether with restricted motion of freedom and pseudo-bilateral symmetry was studied by infrared spectroscopy, which has shown simplified and broadened vibrational features. The C=O and N-H stretching bands, in particular, shows anomalous broadening nearly ${\sim}50\;cm^{-1}$. The density functional calculation at the level of BP86/6-31+$G^{**}$ shows that $Li^+$ ion is trapped and rather free to move around inside the cavity, as much as about $0.70\;{\AA}$. Through the relocation of $Li^+$ ion inside the cavity, the conformational changes would occur rapidly in its symmetry $C_1\;{\rightleftarrows}\;C_2\;{\rightleftarrows}\;C_1$$. The potential barrier was obtained to be merely ~2.2 kJ/mol for $C_1\;{\rightarrow}\;C_2$. During this conformational alteration, the amide backbone twists concurrently its dihedral angle side to side about up to ${\pm}3$ degree. Selected vibrational modes were interpreted in terms of the force constant variations of local symmetry coordinates between conformations in the framework of $C_1\;{\rightleftarrows}\;C_2\;{\rightleftarrows}\;C_1$.

• Progress in Superconductivity
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• v.2 no.2
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• pp.65-70
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• 2001

$Pb/Bi_2Sr_2CaCu_2O_{8+\delta}$-single-crystal junctions with the tunneling direction along the c axis of the crystal were fabricated to obtain an s-wave-superconductor/d-wave-superconductor Josephson junctions. The tunneling R (T) curves and current-voltage characteristics show distinct features which can be explained only under the assumption that the order parameter of high-$T_c/Bi_2Sr_2CaCu_2O_{8+{\delta}}$ superconductors has a pure d-wave symmetry, which is in contrast to the case of $YBa_2Cu_3O_{7+{\delta$}}$erconductors where a minor s-wave component is also present..

• Korean Journal of Materials Research
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• v.16 no.6
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• pp.394-399
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• 2006

Ferroelectric $HoMnO_3$ thin films were deposited on the Si(100) substrate at $700^{\circ}C$ for 2 hrs by metalorganic chemical vapor deposition (MOCVD) and post-annealed at 850oC by rapid thermal process (RTP). Electrical properties and crystalline phases of $HoMnO_3$ thin films were investigated as a function of postannealing time. Single phase of hexagonal symmetry with c-axis preferred orientation was obtained from $HoMnO_3$ thin films post-annealed at $850^{\circ}C$ for 5 min, while the c-axis preferred orientation was decreased with the increase of post-annealing time, and the thin films post-annealed at $850^{\circ}C$ for 15 min showed the mixture phases of hexagonal and orthorhombic symmetry. P-E (Polarization-Electric field) hysteresis loop of ferroelectric $HoMnO_3$ thin films was observed only for the single phase of hexagonal symmetry, but that was not observed for the mixture phases of the hexagonal and orthorhombic symmetry, which was discussed with the bond valence of Mn ion of crystalline phase. Leakage current density was dependent on the microstructure of thin films as well as the change of valence of Mn ion.

• Bulletin of the Korean Chemical Society
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• v.30 no.2
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• pp.445-448
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• 2009

This study examined the effect of the uptake of one and two electrons on the atomic structure of three isomers of $C_{20}$ clusters, namely the ring, bowl (corannulene like), and cage (the smallest fullerene). Geometry optimizations were performed using the hybrid density functional (B3LYP) methods for neutral, singly and doubly charged $C_{20},\;{C_{20}}^-,and\;{C_{20}}^{2-}$. These results show that the symmetry of the lowest energies for ring and bowl isomers were not changed, whereas the increasing order of energy for the cage (the smallest fullerene) isomers was changed from $D_{2h}\;<\;C_{2h}\;{\leq}\;C_2\;of\;C_{20}\;through\;Ci\;<\;C_{2h}\;<\;C_2\;<\;D_{2h}\;of\;{C_{20}}^-\;to\;Ci\;<\;C_2\;<\;D_{2h}\;<\;C_{2h}\;of\;{C_{20}}^{2-}$. The reduced symmetry isomers of the cage have comparative energy and the ground state symmetry of the neutral and single and double charged $C_{20}$ decreased with increasing number of electrons taken up in the point of energetics. Interestingly, the difference in energy between the ground state and the next higher energy state of ${C_{20}}^{2-}$ was 3.5kcal/mol, which is the largest energy gap of the neutral, single anion and double anion of the cage isomers examined.

• 한국초전도학회:학술대회논문집
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• v.10
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• pp.99-102
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• 2000

We have studied the effects of d-wave symmetry on the critical current of YBa$_2$Cu$_3$O$_7$ step-edge Josephson junctions. The critical current along various misorientation angle was measured and analyzed with the concept of grain-boundary junctions with d-wave symmetry. Experimental results of c-oriented YBCO step-edge junctions with various in-plane misorientation angles were qualitatively in good agreement with the theory. The out-of-plane misorientation angle is usually formed between two grains with the c axes perpendicular to each other and is normally not controllable.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.115-122
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• 2004

We characterize the additive operators preserving rank-additivity on symmetry matrix spaces. Let $S_{n}(F)$ be the space of all $n\;\times\;n$ symmetry matrices over a field F with 2, $3\;\in\;F^{*}$, then T is an additive injective operator preserving rank-additivity on $S_{n}(F)$ if and only if there exists an invertible matrix $U\;\in\;M_n(F)$ and an injective field homomorphism $\phi$ of F to itself such that $T(X)\;=\;cUX{\phi}U^{T},\;\forallX\;=\;(x_{ij)\;\in\;S_n(F)$ where $c\;\in;F^{*},\;X^{\phi}\;=\;(\phi(x_{ij}))$. As applications, we determine the additive operators preserving minus-order on $S_{n}(F)$ over the field F.

• Korean Journal of Crystallography
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• v.7 no.2
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• pp.105-112
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• 1996

The structure of the tetra-tert-butyl-dipropionyloxy-dihydroxycalis[4]arene (C50H64O6) has been determined by X-ray diffraction methods. The crystal is monoclinic, space group C2/c, unit cell constant a=16.067(2), b=26.391(17), c=10.335(1)Å, β=94.26(1)°, Z=4, V=4370.2(29)Å3, Dc=1.16, Dm=1.2 gcm-3. The intensity data were collected on an Enraf-Nonius CAD-4 Diffractometer with a graphite monochromated Cu-Kα radiation (λ=1.5418Å). The structure was solved by direct methods and refined by least-squares methods. The final R value was 0.07 for 2354 observed reflections. The molecule has the 1, 3-alternate conformation with own two-fold symmetry axis, : two propionyloxy phenyl groups are up and the other two hydroxy phenyl groups are down.