椭圆方程双侧障碍问题解的局部有界性

研究非齐次椭圆方程divA(x,u,■u)=f(x)的双侧障碍问题,获得了解的局部有界性结果,这可以认为是经典结果的推广.     

C imaging by double resonance scalar-coupling editing

The two-dimensional FT Imaging of ¹³C-glucose obtained with twin spin-echo double resonance sequence is presented. The images have been obtained by a doubly tuned surface coil on samples containing water and ¹³C-enriched glucose in water. It is shown, both theoretically and experimentally, that the whole editing capability of the twin spin-echo double resonance imaging sequence is also preserved in the presence of the radiofrequency field inhomogeneity produced by the surface coil. As in an efficient selective irradiation method, the enhancement in the signal-to-noise ratio with respect to the direct ¹³C detection, depends on the number of protons J-coupled to ¹³C.     

M2B7-(M=Mg,Zn)团簇的双重芳香性促进Mg-Mg和Zn-Zn单键的形成

本文使用密度泛函理论设计了两个无需配体的具有Mg-Mg和Zn-Zn单键的团簇Mg₂B₇^-和Zn₂B₇^-. 这两种团簇的全局能量最低构型均以M₂²⁺(B₇^3-)的形式存在,其中M-M单键处于准平面六边形形状的B₇部分的上方. 化学键分析证实了这些团簇中Mg-Mg和Zn-Zn单键的存在,这些单键是在异常稳定的B₇^3-的驱动下生成的. 该B₇^3-部分同时具有σ和π双重芳香性. 计算得到Mg₂B₇^-和Zn₂B₇^-的垂直跃迁能分别为2.79 eV和2.94 eV.     

On a double degenerate fourth-order parabolic equation

The existence of solutions to a fourth-order p-Laplacian equation with boundary degeneracy is studied. For the purpose of solving the corresponding non-degenerate (with respect to the coefficient of fourth-order term) regularized problem, a fourth-order semi-discrete elliptic problem with homogeneous boundary conditions is established and its existence and uniqueness are obtained by the functional minimization method. It follows that the approximate solutions of the non-degenerate parabolic problem are constructed and the corresponding existence and uniqueness are discovered by a limit procedure from the energy estimation method and a compactness argument. Finally, the existence and regularity of solutions for the problem with boundary degeneracy is obtained by using a regularization parameter vanishing limit.     

Comparison Theorems for Four Dimensional Regular Matrices

A four dimensional summability matrix is stronger than convergence in the Pringsheim sense if it sums a divergent double sequence. Presented in this paper are sufficient conditions on a four dimensional matrix transformation which ensure that the summability matrix is stronger than convergence in the Pringsheim sense. Also other sufficient conditions will be presented to ensure the failure of inclusion between two summability matrices.AMS Subject Classification (2000): Primary 40B05.     

Double-Wronskian solitons and rogue waves for the inhomogeneous nonlinear Schrödinger equation in an inhomogeneous plasma

Plasmas are the main constituent of the Universe and the cause of a vast variety of astrophysical, space and terrestrial phenomena. The inhomogeneous nonlinear Schrödinger equation is hereby investigated, which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping. By virtue of the double Wronskian identities, the equation is proved to possess the double-Wronskian soliton solutions. Analytic one- and two-soliton solutions are discussed. Amplitude and velocity of the soliton are related to the damping coefficient. Asymptotic analysis is applied for us to investigate the interaction between the two solitons. Overtaking interaction, head-on interaction and bound state of the two solitons are given. From the non-zero potential Lax pair, the first- and second-order rogue-wave solutions are constructed via a generalized Darboux transformation, and influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave is discussed.     

Real double flag varieties for the symplectic group

In this paper we study a key example of a Hermitian symmetric space and a natural associated double flag variety, namely for the real symplectic group G and the symmetric subgroup L, the Levi part of the Siegel parabolic $P_S$. We give a detailed treatment of the case of the maximal parabolic subgroups Q of L corresponding to Grassmannians and the product variety of $G/P_S$ and $L/Q$; in particular we classify the L-orbits here, and find natural explicit integral transforms between degenerate principal series of L and G.     

Image encryption using exclusive-OR with DNA complementary rules and double random phase encoding

We propose an optical image encryption scheme based on the Deoxyribonucleic Acid (DNA) theory and the double random phase encoding (DRPE) technique. The piecewise linear chaotic map (PWLCM) is used to generate key images and random phase masks, and to determine DNA encoding rules. In order to achieve ultra-fast DNA encryption, we propose using an optical exclusive-OR (XOR) gate to achieve XOR operation in DNA encryption. Different plaintexts use different initial values of PWLCM, which are generated by Message Digest Algorithm 5 (MD5). The plaintext is encrypted by two rounds of DNA and then by DRPE to form a ciphertext. Numerical simulation and the analysis of attacks on encrypted image are implemented to demonstrate the security and validity of the proposed approach.