• Journal of the Korean Chemical Society
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• v.14 no.1
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• pp.119-122
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• 1970

In those six kinds of diamine salt crystal of which their structures had already been determined up to date, commonly one molecule of diamine and two molecules of acid were combined; although the crystal of benzidine perchlorate, only one molecule each of benzidine and perchloric acid were combined. At the case of benzidine perchlorate, one molecule acts as the role of two molecules by coincidence of the center of symmetry point of both the lattice and molecule, and perchlorate ion is locating symmetrically between two -$NH_2$ groups of different benzidine molecule, therefore benzidine and acid could be combined together with 1:1 by mole ratio. When forming the salt with diamine and acid, the combining mole ratio would be determined in accordance with the relationship between the symmetry element that presented by the space group and the symmetry element of diamine salt melecule.

• The Pure and Applied Mathematics
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• v.11 no.2
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• pp.167-173
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• 2004

Given vectors x and y in a separable Hilbert space $\cal H$, an interpolating operator is a bounded operator A such that Ax = y. In this article, we investigate Hilbert-Schmidt interpolation problems for vectors in a tridiagonal algebra. We show the following: Let $\cal L$ be a subspace lattice acting on a separable complex Hilbert space $\cal H$ and let x = ($x_{i}$) and y = ($y_{i}$) be vectors in $\cal H$. Then the following are equivalent; (1) There exists a Hilbert-Schmidt operator A = ($a_{ij}$ in Alg$\cal L$ such that Ax = y. (2) There is a bounded sequence {$a_n$ in C such that ${\sum^{\infty}}_{n=1}\mid\alpha_n\mid^2 < \infty$ and $y_1 = \alpha_1x_1 + \alpha_2x_2$ ... $y_{2k} =\alpha_{4k-1}x_{2k}$ $y_{2k=1} = \alpha_{4kx2k} + \alpha_{4k+1}x_{2k+1} + \alpha_{4k+1}x_{2k+2}$ for K $\epsilon$ N.

• The Pure and Applied Mathematics
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• v.15 no.4
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• pp.401-406
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• 2008

Given operators X and Y acting on a separable complex Hilbert space H, an interpolating operator is a bounded operator A such that AX=Y. In this article, we investigate Hilbert-Schmidt interpolation problems for operators in a tridiagonal algebra and we get the following: Let ${\pounds}$ be a subspace lattice acting on a separable complex Hilbert space H and let X=$(x_{ij})$ and Y=$(y_{ij})$ be operators acting on H. Then the following are equivalent: (1) There exists a Hilbert-Schmidt operator $A=(a_{ij})$ in Alg${\pounds}$ such that AX=Y. (2) There is a bounded sequence $\{{\alpha}_n\}$ in $\mathbb{C}$ such that ${\sum}_{n=1}^{\infty}|{\alpha}_n|^2<{\infty}$ and $$y1_i={\alpha}_1x_{1i}+{\alpha}_2x_{2i}$$ $$y2k_i={\alpha}_{4k-1}x_2k_i$$ $$y{2k+1}_i={\alpha}_{4k}x_{2k}_i+{\alpha}_{4k+1}x_{2k+1}_i+{\alpha}_{4k+2}x_{2k+2}_i\;for\;all\;i,\;k\;\mathbb{N}$$.

• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.187-196
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• 2023

This study is about spin half add operations in 𝓑₂ and 𝓑₃. The burden of technological structures has increased due to the increase in the use of today's technological applications or the processes in the digital systems used. This has increased the importance of fast transactions and storage areas. For this, less transactions, more gain and storage space are foreseen. We have handle tit (triple digit) system instead of bit (binary digit). 729 is reached in 3⁶ in 𝓑₃ while 256 is reached with 2⁸ in 𝓑₂. The volume and number of transactions are shortened in 𝓑₃. The limited storage space at the maximum level is storaged. The logic connectors and the complement of an element in 𝓑₂ and the course of the connectors and the complements of the elements in 𝓑₃ are examined. "Carry" calculations in calculating addition and "borrow" in calculating difference are given in 𝓑₃. The logic structure 𝓑₂ is seen to embedded in the logic structure 𝓑₃. This situation enriches the logic structure. Some theorems and lemmas and properties in logic structure 𝓑₂ are extended to logic structure 𝓑₃.

• Proceedings of the Korea Contents Association Conference
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• 2007.11a
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• pp.209-211
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• 2007

The computational time of Stocahstic Diagonalization (SD) calculation for 2-dimensional interacting fermion systems is reduced by using several methods including symmetry operations. First, each lattice is subdivided into spin-up and spin-down lattices separately, thus allowing a bi-partite lattice. A valid basis state is then obtained from stacking up an up-spin configuration on top of a down-spin configuration. As a consequence, the memory space to be used in saving the trial basis state reduces significantly. Secondly, the matrix elements of a Hamiltonianin are reconrded in a look-up table when making basis state set. Thus the repeated calculation of the matrix elements of the Hamiltonian are avoided during SD process. Thirdly, by applying symmetry operations to the basis state set the original basis state is transformed to a new basis state whose elements are the eigenvectors of the symmetry operations. The ground state wavefunction is constructed from the elements of symmetric - bonding state - basis state set. As a result, the total number of basis states involved in SD calculation is reduced upto 50 percentage by using symmetry operations.

• Proceedings of the KIEE Conference
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• 2000.07e
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• pp.35-39
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• 2000

$ZnIn_2S_4$ and $ZnGaInS_4:Er^{3+}$ single crystals crystallized in the rhombohedral (hexagonal) space group $C_{3v}^5(R3m)$, with lattice constants $a=3.852{\AA},\;c=37.215{\AA}$ for $ZnIn_2S_4$, and $a=3.823{\AA}$, and $c=35.975{\AA}$ for $ZnIn_2S_4:Er^{3+}$. The optical absorption measured near the fundamental band edge showed that the optical energy band structure of there compounds had a direct and indirect band gap, the direct and indirect energy gaps are found to be 2.778 and 2.682 eV for $ZnIn_2S_4$, and 2.725 and 2.651eV for $ZnIn_2S_4:Er^{3+}$ at 293 K. The photoluminescence spectra of $ZnIn_2S_4:Er^{3+}$ measured in the wavelength ranges of $500nm{\sim}900nm$ at 10 K. Eight sharp emission peaks due to $Er^{3+}$ ion are observed in the regions of $549.5{\sim}550.0nm,\;661.3{\sim}676.5nm$, and $811.1{\sim}834.1nm$, and $1528.2{\sim}1556.0nm$ in $CdGaInS_4:Er^{3+}$ single crystal. These PL peaks were attributed to the radiative transitions between the split electron energy levels of the $Er^{3+}$ ions occupied at $C_{2v}$, symmetry of the $ZnIn_2S_4$ single crystals host lattice.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.7
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• pp.765-773
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• 2016

The vehicle interior noise caused by exterior fluid flow field is one of critical issues for product developers in a design stage. Especially, turbulence and vortex flow around A-pillar and side mirror affect vehicle interior noise through a side window. The reliable numerical prediction of the noise in a vehicle cabin due to exterior flow requires distinguishing between the aerodynamic (incompressible) and the acoustic (compressible) surface pressures as well as accurate computation of surface pressure due to this flow, since the transmission characteristics of incompressible and compressible pressure waves are quite different from each other. In this paper, effective signal processing technique is proposed to separate them. First, the exterior flow field is computed by applying computational aeroacoustics techniques based on the Lattice Boltzmann method. Then, the wavenumber-frequency analysis is performed for the time-space pressure signals in order to characterize pressure fluctuations on the surface of a vehicle side window. The wavenumber-frequency diagrams of the power spectral density shows clearly two distinct regions corresponding to the hydrodynamic and the acoustic components of the surface pressure fluctuations. Lastly, decomposition of surface pressure fluctuation into incompressible and compressible ones is successfully accomplished by taking the inverse Fourier transform on the wavenumber-frequency diagrams.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.63-69
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• 2002

Given vectors x and y in a Hilbert space, an intepolating operator is a bounded operator T such that Tx=y. an interpolating operator for n vectors satisfies the equation Tx$_{i}$=y, for i=1, 2,…, n. In this article, we obtained the fellowing : Let x = (x$_{i}$) and y = (y$_{i}$) be two vectors in H such that x$_{i}$$\neq$0 for all i = 1, 2,…. Then the following statements are equivalent. (1) There exists an operator A in AlgＬ such that Ax = y, A is a trace-class operator and every E in Ｌ reduces A. (2) (equation omitted).mitted).

• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.137-144
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• 1998

A common geoboard puzzel serves as the point of departure for an investigation that lends itself to whole-group discussion with a class of prospective secondary school teachers. Students are provided with opportunities to devise and carry out problem-solving strategies (called 'heuristics' by Polya); exploit inerrelationships among geometry, arithmetic and algebra; formulate generalizations and conjectures; plan and execute an computational project; construct mathematical arguments to establish theorems; and find counter-examples to dispose of a false conjecture. In recent tears, Eugene F. Krause wrote two papers having the same title except for the numeral In that papers he arrives at an theorem about the sizes of squares with lattice point vertices in the coordinate plane, In this paper we follow a different path genearlization to coordinate 3-space

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1549-1552
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• 1997

In this paper, a optimal algorithm that can produce the FOV is proposed in terms of using the Kohonen's Self-Organizing Map(KSOM). A FOV, that stands for "Field Of View", means maximum area where a camera could be wholly seen and influences the total time of inspection of vision system. Therefore, we draw algorithm with a KSOM which aims to map an input space of N-dimensions into a one-or two-dimensional lattice of output layer neurons in order to optimize the number and location of FOV, instead of former sequentila method. Then, we show demonstratin through computer simulation using the real PCB data. PCB data.