关于Parseval框架小波的刻画

In this paper,we characterize all generalized low pass filters and MRA Parseval frame wavelets in L 2 （R n ） with matrix dilations of the form （Df）（x） =√ 2f（Ax）,where A is an arbitrary expanding n × n matrix with integer coefficients,such that ｜det A｜ = 2.We study the pseudo-scaling functions,generalized low pass filters and MRA Parseval frame wavelets and give some important characterizations about them.Furthermore,we give a characterization of the semiorthogonal MRA Parseval frame wavelets and provide several examples to verify our results.     

用于抛物柱面空间功率合成天线的功分喇叭阵列

 提出了一种用于偏馈抛物柱面反射天线的功分喇叭。由于改善了口面上的电磁分布,该功分喇叭可以让馈源阵列的栅瓣电平抑制到－28 dB。用FEKO进行仿真发现,与传统用角锥喇叭阵列作为馈源的抛物柱面反射天线相比,使用功分喇叭直线阵列可以使空间功率合成天线的效率从68%提高到80%,同时天线的增益也能增加0.7 dB。     

Suppression of probe background signals via B(1) field inhomogeneity

A new approach combining a long pulse with the DEPTH sequence (Cory and Ritchey, Journal of Magnetic Resonance, 1988) greatly improves the efficiency for suppressing probe background signals arising from spinning modules. By applying a long initial excitation pulse in the DEPTH sequence, instead of a π/2 pulse, the inhomogeneous B(1) fields outside the coil can dephase the background coherence in the nutation frame. The initial long pulse and the following two consecutive EXORCYCLE π pulses function complementarily and prove most effective in removing background signals from both strong and weak B? fields. Experimentally, the length of the long pulse can be optimized around odd multiples of the π/2 pulse, depending on the individual probe design, to preserve signals inside the coil while minimizing those from probe hardware. This method extends the applicability of the DEPTH sequence to probes with small differences in B? field strength between the inside and outside of the coil, and can readily combine with well-developed double resonance experiments for quantitative measurement. In general, spin systems with weak internal interactions are required to attain efficient and uniform excitation for powder samples, and the principles to determine the applicability are discussed qualitatively in terms of the relative strength of spin interactions, r.f. power and spinning rate.     

Continuous symmetry reduction and return maps for high-dimensional flows

We present two continuous symmetry reduction methods for reducing high-dimensional dissipative flows to local return maps. In the Hilbert polynomial basis approach, the equivariant dynamics is rewritten in terms of invariant coordinates. In the method of moving frames (or method of slices) the state space is sliced locally in such a way that each group orbit of symmetry-equivalent points is represented by a single point. In either approach, numerical computations can be performed in the original state space representation, and the solutions are then projected onto the symmetry-reduced state space. The two methods are illustrated by reduction of the complex Lorenz system, a five-dimensional dissipative flow with rotational symmetry. While the Hilbert polynomial basis approach appears unfeasible for high-dimensional flows, symmetry reduction by the method of moving frames offers hope.     

Light-like noncommutativity,light-front quantization and new light on UV/IR mixing

We revisit the problem of quantizing field theories on noncommutative Moyal space–time with light-like   noncommutativity. To tackle the issues arising from noncommuting and hence nonlocal time, we argue that for this case light-front quantization procedure should be employed. In this appropriate quantization scheme we perform the non-planar loop analysis for the light-like noncommutative field theories. One of the important and peculiar features of light-front quantization is that the UV cutoff of the light-cone Hamiltonian manifests itself as an IR cutoff for the light-cone momentum, p⁺$p^{+}$. Due to this feature, the naive results of covariant quantization for the light-like case allude to the absence of the UV/IR mixing in the light-front quantization. However, by a careful analysis of non-planar loop integrals we show that this is not the case and the UV/IR mixing persists. In addition, we argue in favour of the perturbative unitarity of light-like noncommutative field theories in the light-front quantization scheme.     

THE MAIN INVARIANTS OF A COMPLEX FINSLER SPACE

In this paper we extend the results obtained in [3], where are investigated the general settings of the two-dimensional complex Finsler manifolds, with respect to a local complex Berwald frame. The geometry of such manifolds is controlled by three real invariants which live on T ′M : two horizontal curvature invariants K and W and one vertical curvature invariant I. By means of these invariants are defined both the horizontal and the vertical holomorphic sectional curvatures. The complex Landsberg and Berwald spaces are of particular interest. Complex Berwald spaces coincide with K¨ahler spaces, in the two-dimensional case. We establish the necessary and sufficient condition under which K is a constant and we obtain a characterization for the K¨ahler purely Hermitian spaces by the fact K = W = constant and I = 0. For the class of complex Berwald spaces we have K = W = 0.Finally, a classification of two-dimensional complex Finsler spaces for which the horizontal curvature satisfies a special property is obtained.     

Shrinking and boundedly complete Schauder frames in Fréchet spaces

We study Schauder frames in Fréchet spaces and their duals, as well as perturbation results. We define shrinking and boundedly complete Schauder frames on a locally convex space, study the duality of these two concepts and their relation with the reflexivity of the space. We characterize when an unconditional Schauder frame is shrinking or boundedly complete in terms of properties of the space. Several examples of concrete Schauder frames in function spaces are also presented.     

关于“一致有界的一族无穷小的积是无穷小”定理

针对微积分教材关于"无穷小的积是否是无穷小"的命题的模糊叙述,证明"一致有界的一族无穷小的积仍是无穷小".     

从几何的角度看微分中值定理

从平面几何中曲线之间的相切关系不依赖于坐标轴的选取这一基本事实去看数学分析中Rolle中值定理、Lagrange中值定理以及Cauchy中值定理.