• 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 the Institute of Electronics Engineers of Korea SP
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• v.44 no.4 s.316
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• pp.70-77
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• 2007

Two kinds of QMF(Quadrature Mirror Filter) pairs are used in JPEG2000 standard, which don't have QMF distortions. However, the QMF pairs have the main disadvantages such that there are gentle roll-off rate, ripples in the passband and unequal band decomposition. In this paper, Maxflat(maximally flat) QMF pairs with a half-band gain are proposed for overcoming these problems. Maxflat QMF pairs are realized due to generalized closed-form formulas, and the filters have maximally flat response in the passband/stopband as well as sharp roll-off rate in the transition band. Comparing proposed filters and JPEG2000's filters in frequency domain, it is found that proposed filters have better performance JPEG2000's filters. Moreover, Maxflat QMF pairs show stopband-attenuation exceeding 200 dB almost everywhere.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.2
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• pp.95-109
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• 1993

In this study, the optimal configuration of arch structure has been tested by a decomposition technique. The object of this study is to provide the method of optimizing the shapes of both two hinged and fixed arches. The problem of optimal configuration of arch structures includes the interaction formulas, the working stress, and the buckling stress constraints on the assumption that arch ribs can be approximated by a finite number of straight members. On the first level, buckling loads are calculated from the relation of the stiffness matrix and the geometric stiffness matrix by using Rayleigh-Ritz method, and the number of the structural analyses can be decreased by approximating member forces through sensitivity analysis using the design space approach. The objective function is formulated as the total weight of the structures, and the constraints are derived by including the working stress, the buckling stress, and the side limit. On the second level, the nodal point coordinates of the arch structures are used as design variables and the objective function has been taken as the weight function. By treating the nodal point coordinates as design variable, the problem of optimization can be reduced to unconstrained optimal design problem which is easy to solve. Numerical comparisons with results which are obtained from numerical tests for several arch structures with various shapes and constraints show that convergence rate is very fast regardless of constraint types and configuration of arch structures. And the optimal configuration or the arch structures obtained in this study is almost the identical one from other results. The total weight could be decreased by 17.7%-91.7% when an optimal configuration is accomplished.