• Journal of the Korean Chemical Society
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• v.26 no.5
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• pp.265-273
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• 1982

The effect of ${\pi}$ bonds on the calculated dipole moments for square planar and tetrahedral [M(II)$O_2S_2$]] type complexes has been investigated by two different approaches. One is the approximate molecular orbital method based on the assumption that the mixing coefficient CM of the valence basis sets for the central metal ion and the appropriate ligand orbitals is equal for all ${\sigma}$ and ${\pi}$ bonding molecular orbitals. The other is the more refined calculation based on the semiempirical LCAO-MO method. If ${\sigma}$ bonds only are assumed to be formed, the calculated dipole moments for square planar and tetrahedral complexes are lower than those of the experimental values. If the contribution of ${\pi}$ bonds to the calculated dipole moments are fully considered, the calculated dipole moments for both square planar and tetrahedral [M(II)$O_2S_2$]] type complexes are higher than the experimental values. However if ${\pi}$ bonds are assumed to be delocalzed, the calculated dipole moments for tetrahedral [M(II$O_2S_2$]] type complexes fall in the range of the experimental values, but those for square planar complexes deviate from the experimental values. These results suggest that [M(II)$O_2S_2$]] type complexes may have the tetrahedral structure in inert solvent solution. This structure is in agreement with the experimental one. The calculated dipole moments for tetrahedral [M(II)$O_2S_2$]] type complexes indicate that the contribution of ${\pi}$ bonds to the calculated dipole moments may not be neglected.

• Nuclear Engineering and Technology
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• v.52 no.3
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• pp.485-498
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• 2020

A diffusion synthetic acceleration (DSA) technique for the S_N transport equation discretized with the linear discontinuous expansion method with subcell balance (LDEM-SCB) on unstructured tetrahedral meshes is presented. The LDEM-SCB scheme solves the transport equation with the discrete ordinates method by using the subcell balances and linear discontinuous expansion of the flux. Discretized DSA equations are derived by consistently discretizing the continuous diffusion equation with the LDEM-SCB method, however, the discretized diffusion equations are not fully consistent with the discretized transport equations. In addition, a fine mesh rebalance (FMR) method is devised to accelerate the discretized diffusion equation coupled with the preconditioned conjugate gradient (CG) method. The DSA method is applied to various test problems to show its effectiveness in speeding up the iterative convergence of the transport equation. The results show that the DSA method gives small spectral radii for the tetrahedral meshes having various minimum aspect ratios even in highly scattering dominant mediums for the homogeneous test problems. The numerical tests for the homogeneous and heterogeneous problems show that DSA with FMR (with preconditioned CG) gives significantly higher speedups and robustness than the one with the Gauss-Seidel-like iteration.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.1-16
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• 2007

In order to generalize theory of series in Iksan(翼算), we introduce a concept of double sequence of partial sums and elementary double sequence of partial sums, which play a dominant role in the study of double sequences of partial sums. We introduce a concept of finitely generated double sequence of partial sums and find a necessary and sufficient condition for those double sequences. Finally we prove a multiplication theorem for tetrahedral numbers and for 4 dimensional tetrahedral numbers.

• Bulletin of the Korean Chemical Society
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• v.18 no.7
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• pp.743-749
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• 1997

Local structure refinement of the BaFe1-xSnxO3-y system (x=0.00-0.50) has been carried out with Fe K-edge x-ray absorpion spectroscopic studies. It is found out that the Fe ions are placed in two different symmetric sites such as tetrahedral and octahedral sites in the compounds by comparison with Fe K-edge x-ray absorption near edge structure (XANES) spectrum of the γ-Fe2O3 compound as a reference. Small absorption peaks of dipole-forbiden transitions appear at a pre-edge region of 7111 eV due to the existence of Fe ions in the tetrahedral and octahedral sites. The peak intensity decreases with the substitution amount of Sn ion. Three different absorption peaks of 1s→4p dipole-allowed transition appear on the energy region between 7123 and 7131 eV. The peaks correspond to 1s→4p main transition of Fe ions in tetrahedral and octahedral sites and 1s→4p transition followed by the shakedown process of ligand to metal charge transfer. The bond distances between Fe ions in the tetrahedral site and nearest neighboring oxygen atom (Fe-4O), and those in octahedral site (Fe-6O) are determined with the extended x-ray absorption fine structure (EXAFS) analysis. Two different interatomic distances increase with the substitution amount of Sn ion and also the bond lengths of Fe-4O are shorter than those of Fe-6O in all compounds.

• Journal of Microbiology and Biotechnology
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• v.15 no.3
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• pp.587-594
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• 2005

The contribution of electrostriction of water molecules to the stabilization of the negatively charged tetrahedral transition state of a lipase-catalyzed reaction was examined by means of kinetic studies involving high-pressure and solvent dielectric constant. A good correlation was observed between the increased catalytic efficiency of lipase and the decreased solvent dielectric constant. When the dielectric constant of solvents was lowered by 5.00 units, the losses of activation energy and free energy of activation were 7.92 kJ/mol and 11.24 kJ/mol, respectively. The activation volume for $k_{cat}$ decreased significantly as the dielectric constant of solvent decreased, indicating that the degree of electrostriction of water molecules around the charged tetrahedral transition state has been enhanced. These observations demonstrate that the increase in the catalytic efficiency of the lipase reaction with decreasing dielectric constant resulted from the stabilization of electrostatic energy for the formation of an oxyanion hole, and that this stabilization was caused by the increase of electrostricted water around the charged tetrahedral transition state. Therefore, we conclude that the control of solvent dielectric constant can stabilize the tetrahedral transition state, thus lowering the activation energy.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.3 no.6
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• pp.667-681
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• 2009

We describe a method to decompose a cube with trilinear interpolation into a collection of tetrahedra with linear interpolation, where the isosurface topology is preserved for all isovalues during decomposition. Visualization algorithms that require input scalar data to be defined on a tetrahedral grid can utilize our method to process 3D rectilinear data with topological correctness. As one of many possible examples, we apply the decomposition method to topologically accurate tetrahedral mesh extraction of an interval volume from trilinear volumetric imaging data. The topological correctness of the resulting mesh can be critical for accurate simulation and visualization.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.10
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• pp.1517-1525
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• 2004

Shell finite elements are widely used for the analysis of thin section objects such as sheet metal parts, automobile bodies and et al. due to their computational efficiency. Since many of input data for finite element analysis are given as solid models or triangulated surface models, one should extract midsurface information from these input data initially and then construct shell meshes on the extracted midsurfaces. In this paper, a method of generating shell elements on midsurfaces directly from input models has been proposed, in which midsurface generating process can be omitted. In order to construct shell meshes, the input models should be triangulated on surfaces first, and then tetrahedral elements are generated by using an advancing front method, and finally mid shell surfaces are obtained from tetrahedral meshes. Some examples are given to demonstrate the efficiency of the proposed method.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.389-394
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• 1997

Consider a tetrhedron is composed of six dihedral angles .phi.(i=1,2..., 6), and a vertex of a tetrahedron is also three dihedral angles. It will assume that a vertex A, for an example, is composed of there angles definded such as .alpha..betha. and .gamma. !. then there is a corresponding angle can be given as .phi1.,.phi2.,.phi3.. Here, in order to differentiate between a conventional triangle and dihedral angle, if a dihedral angle degined in this paper is symbolized as .phi..LAMBDA.,the value of cos.theta.of .phi./sab a/, in a trigonometric function rule,can be defined to tecos.phi..LAMBD/sab A/., and it is defined as a tetradedral cosine .phi. or simply called a tecos.phi.. Moreover, in a simillar method, the dihedral angle of tetrahedron .phi..LAMBDA. is given as : value of sin .theta. can defind a tetra-sin.phi..LAMBDA., and value of tan .theta. of .phi..LAMBDA. is a tetra-tan .phi..LAMBDA. By induction it can derive that a tetrahedral geometry on the basis of suggesting a geometric tetrahedron

• Journal of Mechanical Science and Technology
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• v.16 no.2
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• pp.211-218
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• 2002

This paper proposes an unstructured tetrahedral meshing algorithm for CAD models in the IGES format. The work presented is based on the advancing front method, which was proposed by the third author. Originally, the advancing front method uses three basic operators, namely, trimming, wedging, and digging. In this research, in addition to the basic operators, three new operators splitting, local finishing, and octahedral-are added to stabilize the meshing process. In addition, improved check processes are applied to obtain better-shaped elements. The algorithm is demonstrated and evaluated by four examples.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.1605-1608
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• 2003

A unstructured tetrahedral mesh generation algorithm has been presented. To make better meshes in interior region using an advancing front technique, a connecting operator has been developed in addition to the existing operators. Before applying digging operators that generate new nodes inside of a meshing region, a connecting operator is employed that uses existing nodes which satisfy certain conditions for producing well-conditioned elements if possible. By introducing this new operator, tetrahedral meshing process becomes more robust and produces better quality of meshes.