Symmetry Groups and Exact Solutions of New （4＋1）-Dimensional Fokas Equation

In this paper, we investigate symmetries of the new （4＋1）-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symmetries. And then we transform the Fokas equation into a potential system and gain the potential symmetries of Fokas equation. Finally, we use the obtained point symmetries wave solutions and other solutions of the Fokas equation. and some constructive methods to get some doubly periodic In particular, some solitary wave solutions are also given.     

A Curtin–Hammett pentamethylene chain symmetrization process in the Bergman cyclization of an 11‐membered ring enediyne

Pentamethylene chain conformational effects for the Bergman cyclization of the 11‐membered ring enediyne, (3Z)‐3‐cycloundecene‐1,5‐diyne, 2, are examined theoretically with unrestricted Becke, three‐parameter, Lee–Yang–Parr/6‐31 G(d,p) calculations. A C₁ symmetric enediyne conformation was found to be the global minimum, where its nonsymmetric pentamethylene chain prevented π‐orbital alignment of the acetylene groups for C–C σ bond product formation. The Bergman cyclization of 2 was found to be conformationally dependent. In a Curtin–Hammett type process, the C₁ symmetric 2 inverts to one of the C_S or C₂ symmetric conformers required for the Bergman cyclization, which produced a C_S or C₂ symmetric 1,4‐diradical intermediate. The activation energy for the cyclization is slightly higher to reach the C₂ symmetry diradical compared with the C_S symmetry diradical. Copyright © 2012 John Wiley & Sons, Ltd.     

一种新的基于缺陷的软件测试描述语言-DBSTDL

在软件测试领域,缺乏统一的测试描述语言(TDL)已成为提高测试效率和复用程度的瓶颈。区别以设备、信号等为核心的传统测试语言,设计的测试描述语言(DBSTDL)面向软件缺陷,围绕软件缺陷与被测软件信息双重主线,设计了6类词, 3大类100多条基本语句, 3组句群, 2种主要的语言组合方式。应用DBSTDL语言实现了软件典型缺陷与测试样例库,验证了利用DBSTDL语言建库的思想。     

Time-like proton form factor measurement with P(-)ANDA

The electromagnetic probe is an excellent tool to investigate the structure of the nucleon. The nearly 4π detector PANDA, will allow to make a precise determination of the electromagnetic form factors of the proton in the time-like region with unprecedented precision. In the one-photon exchange approximation, the center of mass unpolarized differential cross section of the reaction pp → e~+e~- is a linear combination of the squared moduli of the electric G_E and magnetic G_M proton form factors. The precise measurement of the angular distribution over almost full angular range then directly gives these quantities. At present only two experiments have provided the ratio R = |G_E|/|G_M| but with large statistical uncertainties. It is shown that with strict PID cuts and a kinematic fit, the dominant background, (p)p→π~+π~-, can be supressed to much less than 1% of the signal, without affecting the extraction of the ratio R. PANDA will therefore offer a unique opportunity to measure the ratio with a precision ranging from <1% at low q~2 up to 30 % for q~2 =14 (GeV/c)~2.     

全变换半群Tn 与对称逆半群ISn 之间的同态

刻画了有限集合N上全变换半群T_n 与对称逆半群IS_n 之间的所有同态.     

Wronskian Form Solutions for a Variable Coefficient Kadomtsev–Petviashvili Equation

Starting from a simple transformation, and with the aid of symbolic computation, we establish the relation- ship between the solution of a generalized variable coefficient Kadomtsev-Petviashvili （vKP） equation and the solution of a system of linear partial differential equations. According to this relation, we obtain Wronskian form solutions of the vKP equation, and further present N-soliton-like solutions for some degenerated forms of the vKP equation. Moreover, we also discuss the influences of arbitrary constants on the soliton and N-soliton solutions of the KPII equation.     

Exact solution of a coagulation equation with a product kernel in the multicomponent case

In this paper, we obtain the general solution for the continuous Smoluchowski equation in the multicomponent case with a product kernel as a series expansion. The solution of the problem involves the Laplace transform in several dimensions. We obtain a nonlinear partial differential equation (PDE) of the advective kind generalizing the one previously given by other authors for the mono-component case.As in its relative mono-component case, gelation is produced at some point, the conditions for its occurrence being the same as those for the mono-component case, though substituting a sum of derivatives by a derivative in the Laplace transform field. We demonstrate that for a multicomponent particle size distribution (PSD) of multiplicative form, it is sufficient for one of the marginal PSDs to generate instantaneous gelation for the occurrence of instantaneous gelation in the multicomponent PSD.The general solution is applied to several specific cases, a discrete case that recovers a previously known solution, and another two continuous cases which can be used to check numerical methods designed to directly solve the Smoluchowski equation in more general cases.We have compared the solutions for the multicomponent PSD for constant, additive and product kernels and we conjecture about the relation existing between the functional forms for the solutions both in the mono-component and the multicomponent case.Finally, we have analysed the shape of the solutions for multicomponent PSD for constant, additive and product kernels for very small masses of components, obtaining a qualitatively different behaviour for the product kernel. This has effects in the mixing state of the sol phase as time passes.     

Research of the planar optical fiber Bragg grating hydrophone probe

This paper presents the planar Fiber Bragg Grating （FBG） hydrophone probe sensing principle, and theoretically and experimentally researches the probe structure sensitivity, the receiving sensitivity frequency response characteristic and the acceleration response property. Planar sheet is made of stainless steel, its thickness is 0.15 mm, its diameter is 15mm, and the length of hollow circular shell is 20 mm. For this size of the structure, the probe structure sensitivity is up to 23 fm/Pa, which is about 7300 times of the value of the bare fiber. The resonance frequency is 6.5 kHz, and the amplitude-frequency curve of the receiving sensitivity response is relatively flat within the frequency range of 100 Hz to 5.5 kHz. The output yielded by one unit acceleration （1m/s2） is equivalent to （2.52 to 3.26 Pa） acoustic pressure acting output. This probe structure is easy to form FBG hydrophone array by multiplexing technique. The research shows that this planar structure not only can form FBG hydrophone probe, but also can constitute optical FBG laser hydrophone probe. The structure can realize different bandwidth, different range acoustic pressure measurement by adjusting the geometrical size of the sheet.     

On the spurious eigenvalues for a concentric sphere in BIEM

In this paper, the null-field integral equation method is employed to study the occurring mechanism of spurious eigenvalues for a concentric sphere. By expanding the fundamental solution into degenerate kernels and expressing the boundary density in terms of spherical harmonics, all boundary integrals can be analytically determined. It is noted that our null-field integral formulation can locate the collocation point on the real boundary thanks to the degenerate kernel. In addition, the spurious eigenvalues are parasitized in the formulations while true eigensolutions are dependent on the boundary condition such as the Dirichlet or Neumann problem. By using the updating term and updating document of singular value decomposition (SVD) technique, true and spurious eigenvalues can be extracted out, respectively. Besides, true and spurious boundary eigenvectors are obtained in the right and left unitary vectors in the SVD structure of the influence matrices. This finding agrees with that of 2D cases.     

Kernel polynomial representation for imaginary-time Green's functions in continuous-time quantum Monte Carlo impurity solver

Inspired by the recently proposed Legendre orthogonal polynomial representation for imaginary-time Green s functions G(τ),we develop an alternate and superior representation for G(τ) and implement it in the hybridization expansion continuous-time quantum Monte Carlo impurity solver.This representation is based on the kernel polynomial method,which introduces some integral kernel functions to filter the numerical fluctuations caused by the explicit truncations of polynomial expansion series and can improve the computational precision significantly.As an illustration of the new representation,we re-examine the imaginary-time Green's functions of the single-band Hubbard model in the framework of dynamical mean-field theory.The calculated results suggest that with carefully chosen integral kernel functions,whether the system is metallic or insulating,the Gibbs oscillations found in the previous Legendre orthogonal polynomial representation have been vastly suppressed and remarkable corrections to the measured Green's functions have been obtained.