• Structural Engineering and Mechanics
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• v.42 no.4
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• pp.449-469
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• 2012

For generally damped linear systems with repeated eigenvalues and defective eigenvectors, this study provides a decomposition method based on residue matrix, which is suitable for engineering applications. Based on this method, a hybrid approach is presented, incorporating the merits of the modal superposition method and the residue matrix decomposition method, which does not need to consider the defective characteristics of the eigenvectors corresponding to repeated eigenvalues. The method derived in this study has clear physical concepts and is easily to be understood and mastered by engineering designers. Furthermore, this study analyzes the applicability of step-by-step methods, including the Newmark beta and Runge-Kutta methods for dynamic response calculation of defective systems. Finally, the implementation procedure of the proposed hybrid approach is illustrated by analyzing numerical examples, and the correctness and the effectiveness of the formula are judged by comparing the results obtained from the different methods.

• Bulletin of the Korean Chemical Society
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• v.13 no.3
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• pp.334-336
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• 1992

Through two different techniques TGA and DSC the thermal decomposition processes of salicyaldehyde G-P complexes having the general formula: $$[MCl_2(L)_2]^{2+}$2Cl^-$; where L = salicyaldehyde carbohydrazone pyridinum cation, and M= Fe(III), Co(II), Cu(II) and Zn(II), have been studied. From the obtained thermogravimetric curves the following parameters n, $E_{\alpha}$, A, ${\Delta}S^{\neq}$, ${\Delta}H^{\neq}$ and ${\Delta}G^{\neq}$ were evaluated. The effect of the nature of the metal ions present in the complexes studied upon the calculated thermodynamic parameters was reported. A suitable mechanism for the thermal decomposition process was suggested.

• Korean Journal of Materials Research
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• v.11 no.11
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• pp.953-959
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• 2001

Homogeneous spherical W-Co salt powders were made by spray drying of aqueous solution of ammonium $metatungstate(NH_4)_6(H_2W_{12}O_{40}){\cdot}4H_2O,\; AMT)$ and cobalt nitrate $hexahydrate(Co(NO_3)_2{\cdot}6H_2O)$. The thermal decomposition process of spray dried W-Co salt powders was studied by TG, XRD, SEM, TEM and FT-IR. Spray dried W-Co salt powders were calcined for 1 hour in the temperature from$ 350^{\circ}C$ to $800^{\circ}C$ in atmosphere of air. At the temperatures over $600^{\circ}C$, spherical $CoWO_4/WO_3$ composite oxide powders were obtained. The primary particle size of W/Co composite oxide powders increased with increasing thermal decomposition temperature due to the particle growth. The observed crystallite size by TEM was in the range of 60nm and that of $CoWO_4$ calculated by Scherrer's formula at $800^{\circ}C$ was smaller than 55nm. The crystallite site was identified by XRD and TEM.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.309-320
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• 1999

Models of single-server queues with vacations have been widely used to study the performance of many computer communi-cation and production systems. In this paper we analyze an M/G/1 queue with generalized vacations and exhaustive service. This sys-tem has been shown to possess a stochastic decomposition property. That is the customer waiting time in this system is distributed as the sum of the waiting time in a regular M/G/1 queue with no va-cations and the additional delay due to vacations. Herein a general formula for the additional delay is derived for a wide class of vacation policies. The formula is also extended to cases with multiple types of vacations. Using these new formulas existing results for certain vacation models are easily re-derived and unified.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.191-207
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• 2000

Let R be a ommutative ring with unity and F a finite free R-module. For a nonnegative integer r, there exists a natural filtration of$S_r(S_2F)$ such that its associated graded module is isomorphic to $\Sigma_{{\lambda}{\epsilon}{\tau}_r}\;L_{\lambda}F$, where ${\Gamma}_{\gamma}$ set of partitions such that $$\mid${\lambda}$\mid$-2r,{{\widetilde}{\lambda}}-{{\widetilde}{\lambda}}_1},...,{{\widetilde}{\lambda}}_k},\;each\;{{\widetilde}{\lambda}}_t}$,is even. We call such filtrations plethysm formulas. We extend the above plethysm formula to the version of chain complexes. By plethysm formula we mean the composition of universally free functors. $Let{\emptyset}:G->F$ be a morphism of finite free R-modules. We construct the natural decomposition of $S_{r}(S_2{\emptyset})$,up to filtrations, whose associated graded complex is isomorphic to ${\Sigma}_{{\lambda}{\varepsilon}{\tau}}_r}\;L_{\lambda}{\emptyset}$.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.48
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• pp.153-164
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• 1998

본 논문은 2-상태 시스템의 신뢰도 계산을 위하여 Heidtmann[3]이 제시한 가역 알고리즘을 부울 대수를 사용하여 경로집합으로부터 절단집합을 유도하거나, 역으로 절단집합으로부터 경로집합을 유도함으로서 효율성을 입증하였으며, 포함-불포함 공식(inclusion-exclusion formula)과 추축 분해법칙(pivotal decomposition rule)을 이용하여 직·병렬구조 및 복합구조의 신뢰도를 계산할 수 있는 알고리즘을 개발, 분석하였다.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.741-747
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• 2021

The Cayley-Bacharach theorem says that every cubic curve on an algebraically closed field that passes through a given 8 points must contain a fixed ninth point, counting multiplicities. Ren et al. introduced a concrete formula for the ninth point in terms of the 8 points [4]. We would like to consider a different approach to find the ninth point via the theory of truncated moment problems. Various connections between algebraic geometry and truncated moment problems have been discussed recently; thus, the main result of this note aims to observe an interplay between linear algebra, operator theory, and real algebraic geometry.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.191-200
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• 1995

Simple Lie albegras over algebraically closed field with characteristic p > 7 were classified by H. Strade and R. L. Wilson in 1991 [7]. All modular representations of simple Lie algebras, however, are not classified although some restricted modular representations have been done earlier by Curtis and Steinberg. In connection with this, we would like to decompose basic $sp_4$(F)-modules $sl_4$-(F) and $gl_4$(F) over nonzero characteristic by way of characteristic zero case.

• Wind and Structures
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• v.9 no.3
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• pp.231-243
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• 2006

An improvement to the spectral representation algorithm for the simulation of wind velocity fields on large scale structures is proposed in this paper. The method proposed by Deodatis (1996) serves as the basis of the improved algorithm. Firstly, an interpolation approximation is introduced to simplify the computation of the lower triangular matrix with the Cholesky decomposition of the cross-spectral density (CSD) matrix, since each element of the triangular matrix varies continuously with the wind spectra frequency. Fast Fourier Transform (FFT) technique is used to further enhance the efficiency of computation. Secondly, as an alternative spectral representation, the vectors of the triangular matrix in the Deodatis formula are replaced using an appropriate number of eigenvectors with the spectral decomposition of the CSD matrix. Lastly, a turbulent wind velocity field through a vertical plane on a long-span bridge (span-wise) is simulated to illustrate the proposed schemes. It is noted that the proposed schemes require less computer memory and are more efficiently simulated than that obtained using the existing traditional method. Furthermore, the reliability of the interpolation approximation in the simulation of wind velocity field is confirmed.

• Bulletin of the Korean Chemical Society
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• v.34 no.11
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• pp.3420-3424
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• 2013

The reaction of $LnCl_3{\cdot}7H_2O$ [Ln = La (1), Ce (2)] with salicylic acid (HL) and 1,10-phenanthroline (Phen) at $20^{\circ}C$ in $H_2O$/ethanol gave after work-up and recrystallization two novel lanthanide complexes with general formula $[Ln(Phen)_2(L)_3(HL)]{\cdot}H_2O$. Compounds 1 and 2 were characterized by IR and UV-Vis spectroscopy, TGA, CHN as well as by X-ray analysis. According to these results, compounds 1 and 2 are isostructural and contain $Ln^{3+}$ ions with coordination number nine. Complexes 1 and 2 consist of two Phen, one neutral HL and three L anions (two L anions act as monodentate ligands and the third one is chelating to $Ln^{3+}$). Thermal decomposition led to primary loss of the Phen molecules. Then HL molecules and finally L moieties left the material to give $Ln_2O_3$.