Study on rectangular ultrasonic radiator of flexural resonant vibration in high modes

Based on the theory of coupling vibration and flexural vibration of thin rod of rectangular cross section, the fiexural vibration of rectangular thin plate was studied. The frequency equation was derived under the condition of freeboundaries. The normal modes and the relation between the normal modes and the resonant frequency were obtained. Experiments showed that the calculated resonant frequencies agree well with the measured results, and the rectangular thin plate in flexural vibration has abundant resonant frequencies. The radiator of flexural vibration used in ultrasonic cleaning and other techniques has the advantages of large acoustic radiating area, uniform acoustic field and easy adjustment of resonant frequencies, proving that it is a promising ultrasonic source.     

矩阵的多行拟相合分类及其应用

本文把方阵的拟相合概念推广为长方阵的多行拟相合概念，并对最简情形即Ｍ２，４（Ｆｐ）给出分类结果．此概念之一应用出现在有限环的同构分类之中．     

Loss in a rectangular optical waveguide induced by the crossover of a second waveguide

We calculate the loss induced in a single-mode rectangular optical waveguide by the presence of a second waveguide, perpendicular to the first, which crosses over the first waveguide at a variable distance d. Our calculation is applied to the analysis of several doped silica waveguides of practical importance for optical circuit design.     

The chemical etching of fission fragment tracks in natural fluorite

An experimental study of the mechanism for chemical etching of fission fragment tracks in the natural mineral fluorite is described. A systematic search showed that a 3:1 mixture by volume of sulphuric to hydrochloric acids was a most appropriate etchant. Experiments directed at determining the etching efficiency as a function of solvent temperature are also discussed. The preferential track etch ratioVt/Vg, the track length and the track density all depend upon the time and temperature of annealing.

It is variations of the fission track density in fluorite, with etching time and annealing temperature, which make possible an overall geophysical interpretation of annealing data for the mineral in terms of the paleoisotherm of its intrinsic fission track clock.

An interactive image analysis system INTIMAN, assembled for the swift and automatic readout of fission fragment track measurements, in both crystalline and non-crystalline materials, is described. Normal procedures for measuring and analyzing tracks are outlined.     

On the number of hypercubic bipartitions of an integer

For n≤2^k$n\le 2^k$ we study the maximum number of edges of an induced subgraph on n$n$ vertices of the k$k$-dimensional hypercube _Qk$Q_k$. In the process we revisit a well-known divide-and-conquer maximin recurrence f(n)=max(min(_n1,_n2)+f(_n1)+f(_n2))$f\left(n\right)=max(min(n_1,n_2)+f\left(n_1\right)+f\left(n_2\right))$ where the maximum is taken over all proper bipartitions n=_n1+_n2$n=n_1+n_2$. We first use known results to present a characterization of those bipartitions n=_n1+_n2$n=n_1+n_2$ that yield the maximum f(n)=min(_n1,_n2)+f(_n1)+f(_n2)$f\left(n\right)=min(n_1,n_2)+f\left(n_1\right)+f\left(n_2\right)$. Then we use this characterization to present the main result of this article, namely, for a given n∈N$n\in \mathbb{N}$, the determination of the number h(n)$h\left(n\right)$ of these bipartitions that yield the said maximum f(n)$f\left(n\right)$. We present recursive formulae for h(n)$h\left(n\right)$, a generating function h(x)$h\left(x\right)$, and an explicit formula for h(n)$h\left(n\right)$ in terms of a special representation of n$n$.     

Singular values of a real rectangular tensor

Real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we systematically study properties of singular values of a real rectangular tensor, and give an algorithm to find the largest singular value of a nonnegative rectangular tensor. Numerical results show that the algorithm is efficient.     

Interpolatory Hermite splines on rectangular domains

Based on Bittner and Urban’s construction of interpolatory multiwavelets [Kai Bittner, Karsten Urban, On interpolatory divergence-free wavelets, Math. Comput. 76 (258) (2007) 903-929], we use the truncation method to obtain interpolatory multiwavelets on rectangular domains in this paper. In addition, the characterization for the corresponding functional spaces is given.     

TM模场入射到金属光栅的表面增强喇曼散射计算分析

以纳米量级金属履带矩形光栅为模型,研究了表面增强喇曼散射的特性.针对TM模的入射光,采用严格的耦合波原理对金属表面的衍射场进行了分析,并用数值计算方法讨论了光栅深度、光栅占空比等参量对金属表面增强的影响以及增强因子随光栅深度的变化关系.结果显示：当入射光波长为700 nm、入射角度为10°、光栅周期p=600 nm、 光栅深度d=37.5 nm、占空比为1/3时,获得最大增强,增强因子G达104倍.     

Singular value inclusion sets for rectangular tensors

Two singular value inclusion sets for rectangular tensors are given. These sets provide two upper bounds and lower bounds for the largest singular value of nonnegative rectangular tensors, which can be taken as a parameter of an algorithm presented by Zhou et al. (Linear Algebra Appl. 2013; 438: 959–968) such that the sequences produced by this algorithm converge rapidly to the largest singular value of an irreducible nonnegative rectangular tensor.     

Two-dimensional Hermite-Gaussian solitons in strongly nonlocal nonlinear medium with rectangular boundaries

An analytical solution of self-similar waves, Hermite-Gaussian solitons, emerging in a strongly nonlocal thermal nonlinear medium with the rectangular boundaries was found. The theoretical analysis and numerical simulation showed that the Hermite-Gaussian solitons are elliptic and form a rectangular matrix cluster. Moreover, the symmetries of the soliton and matrix cluster depend not only on the boundary conditions, but also on the symmetry and power of the input beam as well as the propagation distance. The particular interest lies in that the intensities of the solitons in the edges of the rectangular cluster are bigger than those on the center, the most intense solitons occurring at four angles.