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991.
Arie Leizarowitz 《Set-Valued Analysis》2002,10(2-3):185-207
The order reduction method for singularly perturbed optimal control systems consists of employing the system obtained while setting the small parameter to be zero. In many situations the differential-algebraic system thus obtained indeed provides an appropriate approximation to the singularly perturbed problem with a small parameter. In this paper we establish that if relaxed controls are allowed then the answer to the question whether or not this method is valid depends essentially on one simple parameter: the dimension of the fast variable, denoted n. More specifically, if n=1 then the order reduction method is indeed applicable, while if n>1 then the set of singularly perturbed optimal control systems for which it is not applicable is dense (in the L
norm). 相似文献
992.
Yixun Shi 《Numerical Linear Algebra with Applications》2002,9(3):195-203
This paper studies the possibility of combining interior point strategy with a steepest descent method when solving convex programming problems, in such a way that the convergence property of the interior point method remains valid but many iterations do not request the solution of a system of equations. Motivated by this general idea, we propose a hybrid algorithm which combines a primal–dual potential reduction algorithm with the use of the steepest descent direction of the potential function. The complexity of the potential reduction algorithm remains valid but the overall computational cost can be reduced. Our numerical experiments are also reported. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
993.
Tadeusz Iwaniec 《Transactions of the American Mathematical Society》2002,354(5):1961-1995
This paper has arisen from an effort to provide a comprehensive and unifying development of the -theory of quasiconformal mappings in . The governing equations for these mappings form nonlinear differential systems of the first order, analogous in many respects to the Cauchy-Riemann equations in the complex plane. This approach demands that one must work out certain variational integrals involving the Jacobian determinant. Guided by such integrals, we introduce two nonlinear differential operators, denoted by and , which act on weakly differentiable deformations of a domain .
Solutions to the so-called Cauchy-Riemann equations and are simply conformal deformations preserving and reversing orientation, respectively. These operators, though genuinely nonlinear, possess the important feature of being rank-one convex. Among the many desirable properties, we give the fundamental -estimate
In quest of the best constant , we are faced with fascinating problems regarding quasiconvexity of some related variational functionals. Applications to quasiconformal mappings are indicated.
994.
Athanassios G. Kartsatos Igor V. Skrypnik 《Transactions of the American Mathematical Society》2002,354(4):1601-1630
The purpose of this paper is to demonstrate that it is possible to define and compute the index of an isolated critical point for densely defined operators of type acting from a real, reflexive and separable Banach space into This index is defined via a degree theory for such operators which has been recently developed by the authors. The calculation of the index is achieved by the introduction of a special linearization of the nonlinear operator at the critical point. This linearization is a new tool even for continuous everywhere defined operators which are not necessarily Fréchet differentiable. Various cases of operators are considered: unbounded nonlinear operators with unbounded linearization, bounded nonlinear operators with bounded linearization, and operators in Hilbert spaces. Examples and counterexamples are given in 2,$"> illustrating the main results. The associated bifurcation problem for a pair of operators is also considered. The main results of the paper are substantial extensions and improvements of the classical results of Leray and Schauder (for continuous operators of Leray-Schauder type) as well as the results of Skrypnik (for bounded demicontinuous mappings of type Applications to nonlinear Dirichlet problems have appeared elsewhere.
995.
We considered the factors due to which the dependences between the uranium–oxygen distances R
0 and the frequencies of valence vibrations as for complex compounds of uranyl are described by two independent expressions generally represented by equations of the type R
0 = a + bas
–2/3 (b > 0) with the coefficients a and b differing in the regions R
0 < 0.178 nm and R
0 > 0.178 nm. It is shown that the reason is that there is a mutual effect of the ligands in the uranyl complex responsible for different partial contributions of the uranium orbitals and of the atoms of the first coordination sphere to the chemical bonding. 相似文献
996.
We propose a simple scheme to generate two-mode entangled coherent state in two separated cavities and realize the entanglement
reciprocation between the superconducting charge qubits and continuous-variable system. By measuring the state of charge qubits,
we find that the entanglement of two charge qubits, which are initially prepared in the maximally entangled state, can be
transferred to the two-cavity field, and at this time the two-cavity field is in the entangled coherent state. We also find
that the entanglement can be retrieved back to the two charge qubits after measuring the state of the two-cavity field.
相似文献
997.
The structure preserving rank reduction problem arises in many important applications. The singular value decomposition (SVD), while giving the closest low rank approximation to a given matrix in matrix L
2 norm and Frobenius norm, may not be appropriate for these applications since it does not preserve the given structure. We present a new method for structure preserving low rank approximation of a matrix, which is based on Structured Total Least Norm (STLN). The STLN is an efficient method for obtaining an approximate solution to an overdetermined linear system AX B, preserving the given linear structure in the perturbation [E F] such that (A + E)X = B + F. The approximate solution can be obtained to minimize the perturbation [E F] in the L
p norm, where p = 1, 2, or . An algorithm is described for Hankel structure preserving low rank approximation using STLN with L
p norm. Computational results are presented, which show performances of the STLN based method for L
1 and L
2 norms for reduced rank approximation for Hankel matrices. 相似文献
998.
S. V. Astashkin 《Mathematical Notes》1999,65(4):407-417
In this paper it is proved that from any uniformly bounded orthonormal system {f
n}
n=1
∞
of random variables defined on the probability space (Ω, ε, P), one can extract a subsystem {fni}
i
Emphasis>=1/∞
majorized in distribution by the Rademacher system on [0, 1]. This means that {
}, whereC>0 is independent of m∈N, ai∈N (i=1,…,m) andz>0.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 483–495, April, 1999. 相似文献
999.
Henrik Bresinsky Lê Tuâ n Hoa 《Proceedings of the American Mathematical Society》1999,127(5):1257-1263
The main result of the paper confirms, for generic coordinates, a conjecture which states that . Here is a homogeneous polynomial ideal in and and are the reduction numbers.
1000.
M. Keil T. Kolling K. Bergmann W. Meyer 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》1999,7(1):55-64
The process of dissociative attachment (DA) of low-energy electrons ) to vibrationally excited sodium dimer molecules is studied with high electron energy resolution () in a supersonic molecular beam. A novel photoelectron source, based on two-step photoionization of the sodium atoms in the
beam, may deliver a current of up to 1 nA and has been used with a current of typically 0.2 nA in this experiment. The energy
dependence of the rate of sodium anion formation is determined by ion detection based on a time-of-flight analysis. The molecules
are selectively excited to levels using the technique of coherent population transfer by delayed pulses (STIRAP). The comparison of the experimental data with
recent resonance model calculations based on improved potential curves reveals generally good agreement for levels v
”>12. For some distinct differences between theoretical and experimental results persist.
Received: 21 November 1998 / Received in final form: 7 April 1999 相似文献