A Bilinear Control Problem Solved by the Fractional Step Scheme

We consider a control problem for which the cost functional consists of locally Lipschitz functions and is governed by a bilinear multivalued differential equation. We study this problem using the fractional step scheme. Two particular examples are solved using the proposed method.     

Minimal Terminal ℚ-Factorial Models of Drinfeld Coarse Moduli Schemes

In this article we formally prove that the coarse moduli scheme M^r(1) of rational Drinfeld modules of rank r is an affine -factorial equivariant compactification of M^r(1) and we prove the uniqueness of such a compactification. Finally, the coarse moduli surface M³(1) is described in detail.     

A Note on Thin P-Polynomial and Dual-Thin Q-Polynomial Symmetric Association Schemes

Let Y denote a d-class symmetric association scheme, with d 3. We show the following: If Y admits a P-polynomial structure with intersection numbers p _ij ^h and Y is 1-thin with respect to at least one vertex, then p _ll ^l =0 p _li ⁱ =0 1 i - 1. If Y admits a Q-polynomial structure with Krein parameters q _ij ^h , and Y is dual 1-thin with respect to at least one vertex, then q _ll ^l = 0 q _li ⁱ = 01 i d-1.     

Hydration scheme of the purine and pyrimidine bases and base-pairs of the nucleic acids

The hydration scheme of the bases of the nucleic acids, leading to a representation of their first hydration shell, was computed using the overlap multipole procedure. The shell involves five, four, four and three bound water molecules in G, A, C and T respectively. The formation of the base pairs displaces one water molecule in the A-T pair and four water molecules in the G-C pair from the hydration shell. The hydration produces a destabilization of the pairing energy in comparison to the binding in vacuo, greater for the G-C pair than for the A-T pair. There remains nevertheless an appreciable residual affinity for inter-base hydrogen bonding in water.     

An efficient data compression method for the Davidson subspace diagonalization scheme

Summary A flexible and efficient compression scheme for the expansion and product vectors Hamiltonian matrix times expansion vectors is presented within the Davidson diagonalization method. Our approach is based on an error analysis of the energy in terms of the aforementioned vectors and on a compression scheme for representing floating point numbers with a variable length mantissa. For a selection of typical quantum chemical test cases total saving factors of up to ten are reported. The method is expected to work especially well for extended multi-reference CI and full CI cases. As a general outcome of our analysis we obtain limits of possible sizes of a CI expansion within the Davidson procedure in relation to the energy and the desired accuracy of the energy assuming the usual IEEE floating point standard.     

A compound adaptive approach to degenerate nonlinear quenching problems

Quenching phenomena play important roles in both steady and unsteady combustion processes. This article studies a compound finite difference method for solving a nonlinear degenerate combustion model problem. The approach combines procedures of semidiscretization, adaptive ODE solver, and highly stable rational approximation for handling the spatial degeneracy and quenching singularity involved. A second‐order adaptive scheme is constructed, which provides monotone convergence of the numerical solution and direct computations of critical quenching values. It has a simple, yet accurate and reliable, structure and is easy to use. We further demonstrate advantages of the scheme by comparing it to existing algorithms. Numerical examples are presented to further strengthen our results. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 29–47, 1999     

Numerical solution of the optimal boundary control of transverse vibrations of a beam

Boundary control is an effective means for suppressing excessive structural vibrations. By introducing a quadratic index of performance in terms of displacement and velocity, as well as the control force, and an adjoint problem, it is possible to determine the optimal control. This optimal control is expressed in terms of the adjoint variable by utilizing a maximum principle. With the optimal control applied, the determination of the corresponding displacement and velocity is reduced to solving a set of partial differential equations involving the state variable, as well as the adjoint variable, subject to boundary, initial, and terminal conditions. The set of equations may not be separable and analytical solutions may only be found in special cases. Furthermore, the computational effort to determine an analytic solution may also be excessive. Herein a numerical algorithm is presented, which easily solves the optimal boundary control problem in the space‐time domain. An example of a continuous system is analyzed. This is the case of the vibrating cantilever beam. Using a finite element recurrence scheme, numerical solutions are obtained, which compare the behavior of the controlled and uncontrolled systems. Also, the analytic solution to the problem is compared with the results obtained using the numerical scheme presented. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 558–568, 1999     

New Colored Visual Secret Sharing Schemes

Visual secretsharing (VSS) schemes are used to protect the visual secret bysending n transparencies to different participantsso that k-1 or fewer of them have no informationabout the original image, but the image can be seen by stackingk or more transparencies. However, the revealedsecret image of a conventional VSS scheme is just black and white.The colored k out of n VSS scheme sharinga colored image is first introduced by Verheul and Van Tilborg[1]. In this paper, a new construction for the colored VSS schemeis proposed. This scheme can be easily implemented on basis ofa black & white VSS scheme and get much better block lengththan the Verheul-Van Tilborg scheme.     

双曲型守恒律方程组的Godunov格式中离散激波的渐近稳定性

１引言我们研究求解守恒律初值问题的Ｇｏｄｕｎｏｖ格式,其中ｆ：ＲＮ→ＲＮ,并且方程（１）是严格双曲型的．我们还假定　的特征值（）,…,Ｎ（）均为非零,并且每一个特征在Ｌａｘ意义下或者是真正非线性的,或者是线性退化的．利用Ｍａｊｄａ和Ｒａｌｓｔｏｎ的一个结果［６］,我们将证明离散行波激波的存在性,然后证明激波的渐近稳定性,也即,如果初值是激波的一个小的摄动,则当ｔ→由Ｇｏｄｕｎｏｖ格式得到的解趋于一个平移了的行波激波．在［１０］中我们证明了对于Ｌａｘ－Ｆｒｉｅｄｒｉｃｈｓ格式的渐近稳定性,所用的加…     

Nonisothermal two‐ and three‐dimensional flow simulations of inelastic and viscoelastic fluids by a finite‐volume method

This paper applies the finite‐volume method to computations of steady flows of viscous and viscoelastic incompressible fluids in complex two and three‐dimensional geometries. The materials adopted in the study obey different constitutive laws: Newtonian, purely viscous Carreau–Yasuda as also Upper‐Convected Maxwell and Phan‐Thien/Tanner differential models, with a Williams–Landel–Ferry (WLF) equation for temperature dependence. Specific analyses are made depending on the rheological model. A staggered grid is used for discretizing the equations and unknowns. Stockage possibilities allow us to solve problems involving a great number of degrees of freedom, up to 1 500 000 unknowns with a desk computer. In relation to the fluid properties, our numerical simulations provide flow characteristics for various 2D and 3D configurations and demonstrate the possibilities of the code to solve problems involving complex nonlinear constitutive equations with thermal effects. Copyright © 2009 John Wiley & Sons, Ltd.