• 대한수학회논문집
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• 제34권3호
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• pp.729-741
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• 2019

In this paper we give a full characterization of prime submodules of a finitely generated projective module M over a commutative ring R with identity. Also we study the existence of primary decomposition of a submodule of a finitely generated projective module and characterize the minimal primary decomposition of this submodule. Finally, we characterize the radical of an arbitrary submodule of a finitely generated projective module M and study submodules of M which satisfy the radical formula.

• 대한수학회보
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• 제55권4호
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• pp.1221-1230
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• 2018

We derive a sharp decomposition formula for the state polytope of the Hilbert point and the Hilbert-Mumford index of reducible varieties by using the decomposition of characters and basic convex geometry. This proof captures the essence of the decomposition of the state polytopes in general, and considerably simplifies an earlier proof by the authors which uses a careful analysis of initial ideals of reducible varieties.

• 자원ㆍ환경경제연구
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• 제9권5호
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• pp.811-827
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• 2000

Since improved thermal efficiency reduces capacity requirements and energy costs, electricity producers often treat thermal efficiency as a measure of management or economic performance. The conventional measure of the thermal efficiency of a fossil-fuel generation system is the ratio of total electricity generation to the simple sum of energy inputs. As a refined approach, we present a novel thermal efficiency measure using the concept of the Divisia index number. Application of this approach to the Korean power sector shows improvement of thermal efficiency of 1.1% per year during 1970-1998. This is higher than the 0.9% improvement per year given by the conventional method. The difference is attributable to the effect of fuel substitution. In the Divisia decomposition context, we also show the limitations of the popular $T{\ddot{o}}rnqvist$ index formula and the superiority of the Sato-Vartia formula.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.81-96
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• 2004

The level-m scaled circulant factor matrix over the complex number field is introduced. Its diagonalization and spectral decomposition and representation are discussed. An explicit formula for the entries of the inverse of a level-m scaled circulant factor matrix is presented. Finally, an algorithm for finding the inverse of such matrices over the quaternion division algebra is given.

• Journal of Pharmaceutical Investigation
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• 제11권3호
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• pp.21-26
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• 1981

The rate of decomposition of calcium thioglycollate in aqueous solution was shown to increase with increasing temperature and with diluting concentration of calcium thioglycollate. The effect of additive on oxidation rate of calcium thioglycollate was studied to prepare the more stable depilatory formula using additives, such as thiourea, mannitol, sodium thiocyanide, nicotinamide, triethanolamine and ethylenediamine. In all cases, the rate of oxidation was reduced when the additive was present in the solution, among them triethanolamine and ethylenediamine inhibited the decomposition rate remarkably. It is assumed that the decomposition reaction in aqueous solution is pseudo-first order reaction.

• 충청수학회지
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• 제37권1호
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• pp.1-17
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• 2024

The boundary conditions $\tilde{P}_0$ and $\tilde{P}_1$ were introduced in [5] by using the Hodge decomposition on the de Rham complex. In [6] the Atiyah-Bott-Lefschetz type fixed point formulas were proved on a compact Riemannian manifold with boundary for some special type of smooth functions by using these two boundary conditions. In this paper we slightly extend the result of [6] and give two examples showing these fixed point theorems.

• 한국세라믹학회지
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• 제21권1호
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• pp.67-73
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• 1984

A stable intercalation complex was formed by adsorption of alcanol (ROH, R; $C_{10}H_2$, $C_{12}H_{25}$, $C_{14}H_{29}$) on the surfaces of Yongil bentonite in which the interlayer cation had been exchanged by n-decylammonium ion $(C_{10}H_{21}NH_3^+)$ The layer charge density calculated from the increaments of basal spacings was 0.34 per unit chemical formula. Thermochemical properties of synthesized $C_{10}H_{21}NH_3^+$ montmorillonite were studied by means of DSC, TGA, DTG, Thermal analysis showed two steps of desoption behavior of $C_{10}H_{21}NH_3^+$ ion namely nonyl $(CH_3(CH_2)_8$ decomposition reaction of 40$0^{\circ}C$ and methyleneammonium decomposition reaction of 78$0^{\circ}C$ The activation energy of nonyl decomposition reaction of $C_{10}H_{21}NH_3^+$ -montmorillonite respectively.

• Journal of Advanced Marine Engineering and Technology
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• 제28권2호
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• pp.200-209
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• 2004

The fuzzy control based on $\alpha$-level fuzzy set decomposition. It is known to produce quick response and calculating time of fuzzy inference. This paper derived the embodiment computational algorithm for defuzzification by min-max fuzzy inference and the center of gravity method based on $\alpha$-level fuzzy set decomposition. It is easy to realize the fuzzy controller hardware. based on the calculation formula. In addition. this study proposed a circuit that generates PWM actual signals ranging from fuzzy inference to defuzzification. The fuzzy controller was implemented with mixed analog-digital logic circuit using the computational fuzzy inference algorithm by min-min-max and defuzzification by the center of gravity method. This study confirmed that the fuzzy controller worked satisfactorily when it was applied to the position control of a dc servo system.

• 대한수학회지
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• 제52권4호
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• pp.853-868
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• 2015

Let G be a complex semisimple simply connected linear algebraic group. The main result of this note is to give several equivalent criteria for the untwistedness of the twisted cubes introduced by Grossberg and Karshon. In certain cases arising from representation theory, Grossberg and Karshon obtained a Demazure-type character formula for irreducible G-representations as a sum over lattice points (counted with sign according to a density function) of these twisted cubes. A twisted cube is untwisted when it is a "true" (i.e., closed, convex) polytope; in this case, Grossberg and Karshon's character formula becomes a purely positive formula with no multiplicities, i.e., each lattice point appears precisely once in the formula, with coefficient +1. One of our equivalent conditions for untwistedness is that a certain divisor on the special fiber of a toric degeneration of a Bott-Samelson variety, as constructed by Pasquier, is basepoint-free. We also show that the strict positivity of some of the defining constants for the twisted cube, together with convexity (of its support), is enough to guarantee untwistedness. Finally, in the special case when the twisted cube arises from the representation-theoretic data of $\lambda$ an integral weight and $\underline{w}$ a choice of word decomposition of a Weyl group element, we give two simple necessary conditions for untwistedness which is stated in terms of $\lambda$ and $\underline{w}$.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.471-479
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• 2008

Let $R\;{\in}\;C^{m{\times}m}$ and $S\;{\in}\;C^{n{\times}n}$ be nontrivial unitary involutions, i.e., $R^*\;=\;R\;=\;R^{-1}\;{\neq}\;I_m$ and $S^*\;=\;S\;=\;S^{-1}\;{\neq}\;I_m$. We say that $G\;{\in}\;C^{m{\times}n}$ is a generalized reflexive matrix if RGS = G. The set of all m ${\times}$ n generalized reflexive matrices is denoted by $GRC^{m{\times}n}$. In this paper, an efficient method for the least squares solution $X\;{\in}\;GRC^{m{\times}n}$ of the matrix equation AXB = D with arbitrary coefficient matrices $A\;{\in}\;C^{p{\times}m}$, $B\;{\in}\;C^{n{\times}q}$and the right-hand side $D\;{\in}\;C^{p{\times}q}$ is developed based on the canonical correlation decomposition(CCD) and, an explicit formula for the general solution is presented.