Compactly Supported Tight Affine Frames with Integer Dilations and Maximum Vanishing Moments

When a cardinal B-spline of order greater than 1 is used as the scaling function to generate a multiresolution approximation of L ²=L ²(R) with dilation integer factor M2, the standard matrix extension approach for constructing compactly supported tight frames has the limitation that at least one of the tight frame generators does not annihilate any polynomial except the constant. The notion of vanishing moment recovery (VMR) was introduced in our earlier work (and independently by Daubechies et al.) for dilation M=2 to increase the order of vanishing moments. This present paper extends the tight frame results in the above mentioned papers from dilation M=2 to arbitrary integer M2 for any compactly supported M-dilation scaling functions. It is shown, in particular, that M compactly supported tight frame generators suffice, but not M–1 in general. A complete characterization of the M-dilation polynomial symbol is derived for the existence of M–1 such frame generators. Linear spline examples are given for M=3,4 to demonstrate our constructive approach.     

On type basic hypergeometric orthogonal polynomials

The five parameter family of Koornwinder's multivariable analogues of the Askey-Wilson polynomials is studied with four parameters generically complex. The Koornwinder polynomials form an orthogonal system with respect to an explicit (in general complex) measure. A partly discrete orthogonality measure is obtained by shifting the contour to the torus while picking up residues. A parameter domain is given for which the partly discrete orthogonality measure is positive. The orthogonality relations and norm evaluations for multivariable -Racah polynomials and multivariable big and little -Jacobi polynomials are proved by taking suitable limits in the orthogonality relations for the Koornwinder polynomials. In particular new proofs of several well-known -analogues of the Selberg integral are obtained.

     

Einstein and Brans–Dicke Frames in Multidimensional Cosmology

Inhomogeneous multidimensional cosmological models with a higher-dimensional space-time manifold _{0 i=1} ⁿ M_i (n 1) are in stigated under dimensional reduction to a D ₀-dimensional effective non-minimally coupled -model which generalizes the familiar Brans–Dicke model. The general form of the Einstein frame representation of multidimensional solutions known in the Brans–Dicke frame is given with respect to cosmic synchronous time. As an example, the transformation is demonstrated explicitly for the generalized Kasner solutions where it is shown that solutions in the Einstein frame show no inflation of the external space although they can undergo deflation after the cosmic synchronous time inversion.     

q-Analogue of the Watanabe Unitary Transform Associated to the q-Continuous Gegenbauer Polynomials

We associate a family of Hilbert spaces H _q ^2;(D) of analytic functions on the unit disk D=z :|z|<1 the q-continuous Gegenbauer polynomials C _n (x;q) on the interval]–1;1[ and give a q-analogue of the unitary integral transform that Watanabe constructed from the Hilbert space L ²(]–1;1[;(1–x ²)^– dx onto the weighted Hilbert space H ^2;(D).     

真空中不同极化电磁波在微波等离子体喷流中的衰减特性实验研究

在真空环境中，利用空间反射电磁波测量装置，开展微波等离子体喷流对垂直和水平极化电磁波衰减的实验研究，分析不同极化电磁波在等离子体中衰减的影响因素.实验结果表明：以氩气为工质，真空室中微波等离子体喷流对垂直和水平极化电磁波具有显著的吸收效应.发生器流量、功率以及实验真空度对垂直极化电磁波在等离子体中的衰减影响明显.真空度和发生器功率对水平极化电磁波没有显著影响. 关键词： 等离子体中的电磁波 等离子体基本性质 电磁波     

Purification of carbon nanotubes grown by thermal CVD

We show the results of a set of purifications on carbon nanotubes (CNT) by acid and basic treatments. CNTs were obtained by thermal decomposition of camphor at 850 °C in a CVD growth system, by means of a growth process catalyzed by iron clusters originating from the addition of ferrocene in the precursors mixture. The purification procedures involved HNO₃, H₂SO₄, HSO₃Cl and NaOH for different process temperatures.As-grown CNTs showed a consistent presence of metal catalyst (about 6 wt%), evidenced by TGA. The purification treatments led to a certain amount of opening of the CNT tips, with a consequent loss of metal catalyst encapsulated in tips. This is also confirmed by BET analysis, which showed an increase of the surface area density of CNT after the purification.FT-IR and XPS revealed the presence of carboxylic groups on the CNT surface chemically modified by the harsh environment of the purification process.Among the various treatments that have been tested, the 1:3 solution of nitric and sulphuric acid was the most effective in modifying the CNT surface and inducing the formation of functional groups.     

Asymptotics of the regression quantile basic solution under misspecification

We consider the asymptotic distribution of covariate values in the quantile regression basic solution under weak assumptions. A diagnostic procedure for assessing homogeneity of the conditional densities is also proposed. The research for this paper was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.     

Modified frames with block size 3

A modified (k, λ)‐frame of type g^u is a modified (k, λ)‐GDD whose blocks can be partitioned into holey parallel classes, each of which is with respect to some group. Modified frames can be used to construct some other resolvable designs such as resolvable group divisible designs and semiframes. In this article, we shall investigate the existence of modified frames with block size 3. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 351–363, 2008     

不需加人工变量的两阶段法

A method is provided to achieve an initial basic feasible solution of a linear programming in this paper. This method dose not need introducing any artificial variable, but needs only solving an auxiliary linear programming. Compared with the traditional two-phase method, it has advantages of saving the memories and reducing the computational efforts.     

以PBL法进行药学实验基本技能教学的探索与实践*

根据西部少数民族地区院校的客观条件和教学特点,提出用以问题为导向的教学法(PBL)进行药学基本技能实验教学。实践证明,实验组(PBL法)的实践基本技能操作水平和发现、分析并解决问题的能力均显著高于对照组(传统教学法)。该法对提高西部少数民族地区药学本科生的创新能力具有较大意义,对其他地区药学本科生创新能力的培养也有一定的借鉴作用。