有限维希尔伯特空间q广义相干态振幅平方压缩

构造了有限维希尔伯特空间q变形非简谐振子广义相干态,研究了它的振幅平方压缩效应,结果表明,该量子态存在振幅平方压缩效应,并且给出了压缩条件与参数s,r,q之间的关系。     

Kac-系统与Morita等价

本文讨论与Hilbert C~*-模相关的Kac-系统在C~*-代数上的作用的性质,给出了两个Morita等价的C~*-代数(在Kac-系统的作用下得到的C~*-代数的余交叉积是Morita等价的)。从而,Baaj和Skandalis等人的结论是本文定理的特殊情况。     

Introduction to Hardy Spaces

Basic material from the theory of Hardy spaces is presented. The principle of positive energy representations is used as motivation to introduce these spaces.     

可补Hilbert C*-模及其有界模映射

给出了可补Hilbert C^*-模一系列等价刻画，获得了一类有界模映射的分解定理。     

Ultrametric spaces and related Hilbert spaces

We present simple proofs of the possibility of embedding ultrametric spaces in Hilbert spaces. The main part of the paper deals with ultrametric spaces that we call totally infinite spaces. Related Hilbert spaces, automorphisms of totally infinite spaces, and the corresponding linear operators are considered. Transplated fromMatematicheskie Zametki, Vol. 62, No. 2, pp. 223–237, August, 1997. Translated by V. E. Nazaikinskii     

Hilbert algebras as implicative partial semilattices

The infimum of elements a and b of a Hilbert algebra are said to be the compatible meet of a and b, if the elements a and b are compatible in a certain strict sense. The subject of the paper will be Hilbert algebras equipped with the compatible meet operation, which normally is partial. A partial lower semilattice is shown to be a reduct of such an expanded Hilbert algebra i ?both algebras have the same ?lters.An expanded Hilbert algebra is actually an implicative partial semilattice (i.e., a relative subalgebra of an implicative semilattice),and conversely.The implication in an implicative partial semilattice is characterised in terms of ?lters of the underlying partial semilattice.     

Constant Q-curvature metrics in arbitrary dimension

Working in a given conformal class, we prove existence of constant Q-curvature metrics on compact manifolds of arbitrary dimension under generic assumptions. The problem is equivalent to solving a nth-order non-linear elliptic differential (or integral) equation with variational structure, where n is the dimension of the manifold. Since the corresponding Euler functional is in general unbounded from above and below, we use critical point theory, jointly with a compactness result for the above equation.     

Determination of the optimal initial function and the parameters for nonlinear time-delay systems

This paper deals with dynamic systems described by nonlinear differential-difference equations of retarded type. The problem considered is to determine the initial function and certain system parameters which minimize a given cost functional. A computational method is presented and some convergence results are given. Numerical examples of linear and nonlinear systems are also included.     

A minimum average risk approach to shrinkage estimators of the normal mean

For the problem of estimating the normal mean based on a random sample X ₁,...,X _n when a prior value ₀ is available, a class of shrinkage estimators % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaubeaeqaje% aWbaGaamOBaaWcbeqdbaGafqiVd0MbaKaaaaGccaqGGaGaaiikaiaa% dUgacaGGPaGaeyypa0Jaam4AaiaacIcadaqfqaqabKqaahaacaqGUb% aaleqaneaacaqGubaaaOGaaiykaiaabccadaqfqaqabKqaahaacaWG% UbaaleqaneaaceqGybGbaebaaaGccaqGGaGaey4kaSIaaeiiaiaacI% cacaaIXaGaaeiiaiabgkHiTiaabccacaWGRbGaaiikamaavababeqc% baCaaiaab6gaaSqab0qaaiaabsfaaaGccaGGPaGaaiykamaavababe% qcbaCaaiaad6gaaSqab0qaaiabeY7aTbaaaaa!5615!\[\mathop {\hat \mu }\nolimits_n {\rm{ }}(k) = k(\mathop {\rm{T}}\nolimits_{\rm{n}} ){\rm{ }}\mathop {{\rm{\bar X}}}\nolimits_n {\rm{ }} + {\rm{ }}(1{\rm{ }} - {\rm{ }}k(\mathop {\rm{T}}\nolimits_{\rm{n}} ))\mathop \mu \nolimits_n \] is considered, where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaubeaeqaje% aWbaGaamOBaaWcbeqcdawaaiaadsfaaaGccaqGGaGaaeypaiaabcca% caWGUbWaaWbaaSqabeaacaaIXaGaai4laiaaikdaaaGccaGGOaWaa0% aaaeaacaWGybaaamaaBaaajeaWbaGaamOBaaWcbeaakiaabccacqGH% sislcaqGGaWaaubeaeqajeaWbaGaaGimaaWcbeqdbaGaaeiVdaaaki% aacMcacaqGGaGaae4laiabeccaGiabeo8aZbaa!4C33!\[\mathop T\nolimits_n {\rm{ = }}n^{1/2} (\overline X _n {\rm{ }} - {\rm{ }}\mathop {\rm{\mu }}\nolimits_0 ){\rm{ /}} \sigma \] and k is a weight function. For certain choices of k, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaubeaeqaje% aWbaGaamOBaaWcbeqdbaGafqiVd0MbaKaaaaGccaqGGaGaaiikaiaa% dUgacaGGPaaaaa!3CEE!\[\mathop {\hat \mu }\nolimits_n {\rm{ }}(k)\] coincides with previously studied preliminary test and shrinkage estimators. We consider choosing k from a natural non-parametric family of weight functions so as to minimize average risk relative to a specified prior p. We study how, by varying p, the MSE efficiency (relative to \-X) properties of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaubeaeqaje% aWbaGaamOBaaWcbeqdbaGafqiVd0MbaKaaaaGccaqGGaGaaiikaiaa% dUgacaGGPaaaaa!3CEE!\[\mathop {\hat \mu }\nolimits_n {\rm{ }}(k)\] can be controlled. In the process, a certain robustness property of the usual family of posterior mean estimators, corresponding to the conjugate normal priors, is observed.     

Hereditary optimal control problems: Numerical method based upon a padé approximation

In this paper, we consider a particular approximation scheme which can be used to solve hereditary optimal control problems. These problems are characterized by variables with a time-delayed argumentx(t – ). In our approximation scheme, we first replace the variable with an augmented statey(t) x(t - ). The two-sided Laplace transform ofy(t) is a product of the Laplace transform ofx(t) and an exponential factor. This factor is approximated by a first-order Padé approximation, and a differential relation fory(t) can be found. The transformed problem, without any time-delayed argument, can then be solved using a gradient algorithm in the usual way. Four problems are solved to illustrate the validity and usefulness of this technique.This research was supported in part by the National Aeronautics and Space Administration under NASA Grant NCC-2-106.