A remark on Andrews-Askey integral

In this paper, we use the Andrews-Askey integral and the q-Chu-Vandermonde formula to derive a more general integral formula. Applications of the new integral formula are also given, which include to derive the q-Pfaff-Saalschütz formula and the terminating Sears's View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X07013297-si1.gif"> transformation formula.     

The H2+ molecular ion: Low-lying states

Matching for a wavefunction the WKB expansion at large distances and Taylor expansion at small distances leads to a compact, few-parametric uniform approximation found in Turbiner and Olivares-Pilon (2011). The ten low-lying eigenstates of H₂⁺ of the quantum numbers (n,m,Λ,±)$(n,m,\Lambda ,\pm )$  with n=m=0$n=m=0$ at Λ=0,1,2$\Lambda =0,1,2$, with n=1$n=1$, m=0$m=0$ and n=0$n=0$, m=1$m=1$ at Λ=0$\Lambda =0$ of both parities are explored for all interproton distances R$R$. For all these states this approximation provides the relative accuracy ?10⁻⁵$?10^{-5}$ (not less than 5 s.d.) locally, for any real coordinate x$x$ in eigenfunctions, when for total energy E(R)$E\left(R\right)$ it gives 10-11 s.d. for R∈[0,50]$R\in [0,50]$  a.u. Corrections to the approximation are evaluated in the specially-designed, convergent perturbation theory. Separation constants are found with not less than 8 s.d. The oscillator strength for the electric dipole transitions E1$E1$ is calculated with not less than 6 s.d. A dramatic dip in the E1$E1$ oscillator strength f_{1sσg−3pσu}$f_{1s{\sigma }_g-3p{\sigma }_u}$ at R∼R_eq$R\sim R_{eq}$ is observed. The magnetic dipole and electric quadrupole transitions are calculated for the first time with not less than 6 s.d. in oscillator strength. For two lowest states (0,0,0,±)$(0,0,0,\pm )$ (or, equivalently, 1sσ_g$1s{\sigma }_g$ and 2pσ_u$2p{\sigma }_u$ states) the potential curves are checked and confirmed in the Lagrange mesh method within 12 s.d. Based on them the Energy Gap between 1sσ_g$1s{\sigma }_g$ and 2pσ_u$2p{\sigma }_u$ potential curves is approximated with modified Pade Re^−R[Pade(8/7)](R)$R{e}^{-R}\left[Pade(8/7)\right]\left(R\right)$ with not less than 4-5 figures at R∈[0,40]$R\in [0,40]$ a.u. Sum of potential curves E_1sσg+E_2pσu$E_{1s{\sigma }_g}+E_{2p{\sigma }_u}$ is approximated by Pade 1/R[Pade(5/8)](R)$1/R\left[Pade(5/8)\right]\left(R\right)$ in R∈[0,40]$R\in [0,40]$ a.u. with not less than 3-4 figures.     

Synthesis of lariat organochalcogenoethers based on azacalix[3]arenes for the potentiometric detection of [UO2] ions

The syntheses of organochalcogen-supported azacalix[3]arenes are described in a one-pot manner in satisfactory yields. A remarkably selective potentiometric response was accomplished for uranyl ions over a variety of other metal ions, including alkali (Na⁺, K⁺), alkaline-earth (Mg²⁺, Ca²⁺, Ba²⁺), transition and heavy metal ions (Co²⁺, Ni²⁺, Cu²⁺, Ag⁺, Fe³⁺, Zn²⁺, Cd²⁺ and Pb²⁺) using an ion-selective electrode based on compound 3 incorporated into a polymeric (PVC) membrane.     

Projective functors for algebraic groups

We investigate the regular subquotient category introduced by Soergel in [W. Soergel, On the relation between intersection cohomology and representation theory in positive characteristic, J. Pure Appl. Algebra 152 (1–3) (2000) 311–335]. A detailed study of projective functors enables one to relate those categories for semi-simple algebraic group G and its subgroup schemata G_rT. As an application we derive some information about the characters of tilting modules for G.     

The global Cauchy problem for the NLS and NLKG with small rough data

By using the unit-cube decomposition to the frequency spaces, we study the Cauchy problem for the nonlinear Schrödinger equation and the nonlinear Klein-Gordon equation. Some global well posedness results are obtained for the small Cauchy data in some modulation spaces View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022039606003524-si1.gif">.     

Elliptic enumeration of nonintersecting lattice paths

We enumerate lattice paths in the planar integer lattice consisting of positively directed unit vertical and horizontal steps with respect to a specific elliptic weight function. The elliptic generating function of paths from a given starting point to a given end point evaluates to an elliptic generalization of the binomial coefficient. Convolution gives an identity equivalent to Frenkel and Turaev's View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0097316506001178-si1.gif"> summation. This appears to be the first combinatorial proof of the latter, and at the same time of some important degenerate cases including Jackson's View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0097316506001178-si2.gif"> and Dougall's View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0097316506001178-si3.gif"> summation. By considering nonintersecting lattice paths we are led to a multivariate extension of the View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0097316506001178-si4.gif"> summation which turns out to be a special case of an identity originally conjectured by Warnaar, later proved by Rosengren. We conclude with discussing some future perspectives.     

基于JNDD模型面向虚拟视绘制的快速深度图编码

为降低深度数据的编码复杂度并保证重建虚拟视点的质量,提出了一种基于JNDD模型面向虚拟视点绘制的快速深度图编码算法,引入最小可觉深度差模型,将深度图划分为对绘制失真敏感的竖直边缘区域与失真难以被人眼察觉的平坦区域,并相应地为编码过程中的宏块模式选择设计了两种搜索策略。实验结果表明,与JM编码方案相比,本文所提出的方法在保证虚拟视质量与编码码率基本不变的前提下,显著降低了编码复杂度,有助于在三维视频系统中提高深度编码模块的编码速度。     

SAW技术实现宽带扩频信号解扩解调的研究

采用EDA软件System View对直扩系统基带和中频段进行了仿真，实际信号的波形与仿真结果吻合。通过采用255位声表面波匹配滤波器实现了10Mbps的宽带直扩信号的实时解扩，延迟时间为25ps、相对带宽大于30％、插损小于50dB的SAW固定延迟线实现了中频相关峰延迟差分解调与解码。时钟抖动小于5ns。