临近空间高超声速气动布局研究

临近空间飞行器存在多种不同的布局形式,而针对不同气动布局概念之间的系统研究则相对缺乏．采用数值模拟方法,对临近空间飞行器三类典型气动布局概念--扁平升力体、翼身融合体和翼身组合体开展系统的计算与分析,通过对比不同布局的升阻特性、静稳定特性、舵效特性等,获得不同布局概念气动性能优劣的初步评估．结果表明：扁平升力体的升力和阻力比较大,升阻比最低,容积率则最大,侧向稳定性最好;翼身组合体的升力和阻力比较小,升阻比最高,容积率比较低,侧向静稳定性较差;翼身融合体布局的特性介于翼身组合体和扁平升力体布局之间．     

Explicit polynomial preserving trace liftings on a triangle

We give an explicit formula for a right inverse of the trace operator from the Sobolev space H¹(T) on a triangle T to the trace space H^1/2(?T) on the boundary. The lifting preserves polynomials in the sense that if the boundary data are piecewise polynomial of degree N, then the lifting is a polynomial of total degree at most N and the lifting is shown to be uniformly stable independently of the polynomial order. Moreover, the same operator is shown to provide a uniformly stable lifting from L₂(?T) to H^1/2(T). Finally, the lifting is used to construct a uniformly bounded right inverse for the normal trace operator from the space H (div; T) to H^–1/2(?T) which also preserves polynomials. Applications to the analysis of high order numerical methods for partial differential equations are indicated (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Theta lifting of holomorphic discrete series: The case of

Let be a reductive dual pair in the stable range. We investigate theta lifts to of unitary characters and holomorphic discrete series representations of , in relation to the geometry of nilpotent orbits. We give explicit formulas for their -type decompositions. In particular, for the theta lifts of unitary characters, or holomorphic discrete series with a scalar extreme -type, we show that the structure of the resulting representations of is almost identical to the -module structure of the regular function rings on the closure of the associated nilpotent -orbits in , where is a Cartan decomposition. As a consequence, their associated cycles are multiplicity free.

     

Hilbert modules over a class of semicrossed products

Given the disk algebra and an automorphism , there is associated a non-self-adjoint operator algebra called the semicrossed product of with . Buske and Peters showed that there is a one-to-one correspondence between the contractive Hilbert modules over and pairs of contractions and on satisfying . In this paper, we show that the orthogonally projective and Shilov Hilbert modules over correspond to pairs of isometries on satisfying . The problem of commutant lifting for is left open, but some related results are presented.     

Dendrites and light mappings

It is shown that a metric continuum is a dendrite if and only if for every compact space (continuum) and for every light confluent mapping such that there is a copy of in for which the restriction is a homeomorphism. As a corollary it follows that only dendrites have the lifting property with respect to light confluent mappings. Other classes of mappings are also discussed. This is a continuation of a previous study by the authors (2000), where open mappings were considered.

     

适合于图像压缩的7/5小波基的构造

通过利用提升算法和检验双正交小波稳定性的充分必要条件Cohen-Daubechies准则,构造了一个适合于图像压缩的7/5双正交小波基.为了便于小波变换的硬件实现,选取四个提升系数中的三个为二进制分数,而另一提升因子为1/10的倍数.本文中所构造的7/5小波基虽然在压缩性能上低于CDF9/7小波,但由于提升系数为二进制分数和1/10的倍数,所以该小波基的小波变换更易于采用硬件来实现,并且其小波变换速度比CDF9/7小波要快.实验的结果表明该小波的压缩性能优于Daubechies5/3小波,同时与[6]所构造的两组7/5小波基相比较,该小波变换不仅能方便于硬件的实现,而且其压缩性能优于或相当于[6]中的两组7/5小波基.     

A unifying Radon-Nikodym theorem for vector measures

It is a known fact that certain derivation bases from martingales with a directed index set. On the other hand it is also true that the strong convergence of certain abstract martingales is a consequence of the Radon-Nikodym theory for vector measures (cf. Uhl, J. J., Jr., Trans. Amer. Math. Soc.145 1969, 271–285). Many other connections and applications of the latter theory with multidimensional problems in stochastic processes and representation theory are known (cf. Dinculeanu, N., Studia Math.25 1965, 181–205; Dinculeanu, N., and Foias, C., Canad. J. Math.13 1961, 529–556; Rao, M. M., Ann. Mat. pura et applicata76 1967, 107–132; Rybakov, V. I., Izv. Vys?. U?ebn. Zaved. Matematika19 1968, 92–101; Rybakov, V. I., Dokl. Akad. Nauk SSSR180 1968, 620–623). Starting from various vantage points, many authors have proposed several hypotheses for establishing abstract Radon-Nikodym theorems. In view of the great interest and importance of this problem in the areas mentioned above, it is natural to obtain a unifying result with a general enough hypothesis to deduce the various forms of the Radon-Nikodym theorem for vector measures. This should illuminate the Radon-Nikodym theory for vector measures and stimulate further work in abstract martingale problems. In this paper the first problem is attacked, leaving the martingale part and other applications for another study.The main result (Theorem 7 of Section 2) provides the desired unification and from if the Dunford-Pettis theorem, the Phillips theorem and several others are obtained. As martingale-type arguments are constantly present, a careful reader may note the easy translation of the hypothesis to the martingale convergence problem but we treat only the Radon-Nikodym problem using the language of measure theory and linear analysis.     

Multifilters with and without Prefilters

To explore the full approximation order and thus compression power of a multifilter, it is usually necessary to incorporate prefilters. Using matrix factorization techniques, we describe an explicit construction of such prefilters. Although in the case of approximation order 1 these prefilters are simply bi-infinite block diagonal matrices, they can become very intricate as soon as one aims for higher approximation order. For this reason, we introduce a particular class of multifilters which we call full rank multifilters. These filters have a peculiar structure which allows us to obtain approximation order without the use of prefilters. The construction of such filters via the lifting scheme is pointed out and examples of the performance of these filters for image compression are given.     

An algebraic construction of k-balanced multiwavelets via the lifting scheme

Multiwavelets have been revealed to be a successful generalization within the context of wavelet theory. Recently Lebrun and Vetterli have introduced the concept of “balanced” multiwavelets, which present properties that are usually absent in the case of classical multiwavelets and do not need the prefiltering step. In this work we present an algebraic construction of biorthogonal multiwavelets by means of the well-known “lifting scheme”. The flexibility of this tool allows us to exploit the degrees of freedom left after satisfying the perfect reconstruction condition in order to obtain finite k-balanced multifilters with custom-designed properties which give rise to new balanced multiwavelet bases. All the problems we deal with are stated in the framework of banded block recursive matrices, since simplified algebraic conditions can be derived from this recursive approach. This revised version was published online in June 2006 with corrections to the Cover Date.