高阶色散效应常系数Ginzburg-Landau方程自相似脉冲演化的解析分析

采用自相似分析方法,基于常系数高阶色散的Ginzburg-Landau方程,通过分离变量法得出了高阶色散效应自相似脉冲演化的解析解,给出了自相似脉冲的振幅、相位、啁啾以及脉冲宽度的一般表达式.研究表明,在增益光纤的二阶正常色散区域,同时考虑高阶色散和增益色散双重效应影响下演化的自相似孤子脉冲仍然保持线性啁啾;振幅解析解的三阶色散效应显著.这与数值计算的结果非常一致. 关键词： 三阶色散 Ginzburg-Landau方程 自相似脉冲 二阶正常色散     

A family of quantum projective spaces and related -hypergeometric orthogonal polynomials

A one-parameter family of two-sided coideals in is defined and the corresponding algebras of infinitesimally right invariant functions on the quantum unitary group are studied. The Plancherel decomposition of these algebras with respect to the natural transitive -action is shown to be the same as in the case of a complex projective space. By computing the radial part of a suitable Casimir operator, we identify the zonal spherical functions (i.e. infinitesimally bi-invariant matrix coefficients of finite-dimensional irreducible representations) as Askey-Wilson polynomials containing two continuous and one discrete parameter. In certain limit cases, the zonal spherical functions are expressed as big and little -Jacobi polynomials depending on one discrete parameter.

     

A joint TDOA and FDOA estimation algorithm based on second-order cone programming

ABSTRACT

Considering the low estimation accuracy of the traditional interpolation method, this paper, on the basis of second-order cone programming (SOCP), proposes a novel joint time difference of arrival (TDOA) and frequency difference of arrival (FDOA) estimation interpolation method, which can attain the sub-sample precision. The proposed method uses several discrete samples produced by cross ambiguity function (CAF) to structure the convex optimization models with regard to the interpolation surface. Then, the SOCP is utilized to obtain the interpolation surface which matches the discrete surface of CAF well. Finally, the method achieves the precision superior to the traditional TDOA and FDOA estimation directly through the search for the maximum of the continuous approximate surface. This method decreases the computational load without loss of precision and can efficiently reduce the limitation of finite sampling interval and sampling time in estimation precision. Numerical simulations show that the method in this paper is efficient and outperforms existing interpolation algorithms about estimation precision.     

Convergence of the Augmented Lagrangian Method for Nonlinear Optimization Problems over Second-Order Cones

The paper analyzes the rate of local convergence of the augmented Lagrangian method for nonlinear second-order cone optimization problems. Under the constraint nondegeneracy condition and the strong second order sufficient condition, we demonstrate that the sequence of iterate points generated by the augmented Lagrangian method locally converges to a local minimizer at a linear rate, whose ratio constant is proportional to 1/τ with penalty parameter τ not less than a threshold . Importantly and interestingly enough, the analysis does not require the strict complementarity condition. Supported by the National Natural Science Foundation of China under Project 10771026 and by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.     

Heat capacity of superfine oxides of iron under applied magnetic fields

Heat capacity is one of the most characteristic and important properties when the peculiarities of magnetic nanosystems are studied. In these systems the magnetic ordering becomes obvious due to the thermal effects such as heat capacity anomalies. It was considered earlier that heat capacity change under magnetic fields applied is slight and it cannot be taken into account in thermodynamic calculations. However the experimental heat capacity data for ferrofluids under magnetic fields applied show that field and temperature heat capacity dependences have a complicated behavior and in magnetic fields an essential heat capacity change takes place. On the other hand in the literature the contradictory data about heat capacity of nanoparticles appear. According to some papers nanoparticles heat capacity can exceed heat capacity of a bulk material a few times.     

Rotation-Inversion Isomerization of Tertiary Carbamates: Potential Energy Surface Analysis of Multi-Paths Isomerization Using Boltzmann Statistics

Potential energy surface (PES) analyses at the SMD[MP2/6–311++G(d,p)] level and higher-level energies up to MP4(fc,SDTQ) are reported for the fluorinated tertiary carbamate N-ethyl-N-(2,2,2-trifluoroethyl) methyl carbamate ( VII ) and its parent system N,N-dimethyl methyl carbamate ( VI ). Emphasis is placed on the analysis of the rotational barrier about the CN carbamate bond and its interplay with the hybridization of the N-lone pair (NLP). All rotational transition state (TS) structures were found by computation of 1D relaxed rotational profiles but only 2D PES scans revealed the rotation-inversion paths in a compelling fashion. We found four unique chiral minima of VII , one pair each of E- and Z-rotamers, and we determined the eight unique rotational TS structures associated with every possible E/Z-isomerization path. It is a significant finding that all TS structures feature N-pyramidalization whereas the minima essentially contain sp²-hybridized nitrogen. We will show that the TS stabilities are affected by the synergetic interplay between NLP/CO₂ repulsion minimization, NLP→σ^*(CO) negative hyperconjugation, and two modes of intramolecular through-space electrostatic stabilization. We demonstrate how Boltzmann statistics must be applied to determine the predicted experimental rotational barrier based on the energetics of all eight rotamerization pathways. The computed barrier for VII is in complete agreement with the experimentally measured barrier of the very similar fluorinated carbamate N-Boc-N-(2,2,2-trifluoroethyl)-4-aminobutan-1-ol II . NMR properties of VII were calculated with a variety of density functional/basis set combinations and Boltzmann averaging over the E- and Z-rotamers at our best theoretical level results in good agreement with experimental chemical shifts δ(¹³C) and J(¹³C,¹⁹F) coupling constants of II (within 6 %).     

Burgers方程的一类自相似解

利用李群理论中的伸缩变换群,将二阶非线性偏微分方程-Burgers方程化为一类Riccati方程和三类二阶非线性常微分方程,从而Riccati方程和这三类二阶非线性常微分方程给出了Burgers方程的自相似解的表现形式.     

On the asymptotics of the number of reduced integral quadratic forms with a condition of divisibility of the first coefficients

For the quadratic forms mentioned in the title, we use the discrete ergodic method to obtain asymptotic formulas with remainders depending on the L-Dirichlet function L(s, χ) and its behavior under some hypotheses.     

脉动压力脉动速度变形平均项的表达式

脉动压力脉动速度变形平均项,最初是Rotta[21]改写压力梯度做功项得来的.但是,这项处理起来都很困难,从Rotta开始,以后Launder等人都对这项做过一些假定.本文根据脉动速度所满足的方程解出脉动压力,然后进而求出脉动压力乘上脉动速度变形的平均值,得到了脉动压力脉动速度变形平均项的完整表达式.这个表达式说明了Rotta和Launder等人的有限表达式是有一定道理的.本文所得的完整表达式分为两种情形加以讨论.一种是几种涡旋不分开的情形,另一种是三种涡旋分开考虑的情形.由此,本文为雷诺应力模式和三涡旋模式等湍流模式提供了完整的脉动压力脉动速度变形平均项的表达式.     

H4GeMo12-nWnO40·mH2O（n=0, 9, 11, 12)和N-甲基吡咯烷酮电荷转移盐的合成、表征和非线性光学性质研究

由Ｈ４ＧｅＭｏ１２－ｎＷｎＯ４０·ｍ Ｈ２Ｏ（ｎ＝ ０, ９, １１, １２）和Ｎ－甲基吡咯烷酮合成,随后在ＣＨ３ＣＮ 和水中结晶,制成了一系列分子组成为［ＮＭＰＨ］４ＧｅＭｏ１２－ｎＷｎＯ４０·ＣＨ３ＣＮ的电荷转移化合物。并用元素分析、红外光谱、电子光谱进行了表征。结果表明在该系列化合物中, Ｎ－甲基吡咯烷酮通过Ｎ原子与酸中的质子结合成阳离子而与阴离子成盐;固体中阴离子和阳离子之间存在强的相互作用;化合物在光照下发生分子内电荷转移, 导致阳离子的氧化和阴离子的还原;ＥＳＲ结果表明阴离子还原反应处于单电子阶段; 非线性光学性质研究表明, 随着化合物分子内钨取代数的增多, 化合物倍频效应增强,三阶非线性系数增大