A co‐ordinate system independent streamwise upwind method for fluid flow computation

A new co‐ordinate invariant streamwise upwind formulation for convection dominated flows is developed. The eddy diffusivity/viscosity is added directly to the equations in order to remove the oscillations in the solution. The equations then can be solved by any high‐order scheme and the solution retains the accuracy of the high‐order scheme. The accuracy and reduced lateral thickness growth rate are demonstrated with several numerical examples, including pure convective flows and lid‐driven cavity flow. The lateral spreading due to the numerical diffusion is controlled by the anisotropic tensor. Copyright © 2004 John Wiley & Sons, Ltd.     

General constructions of biquandles and their symmetries

Biquandles are algebraic objects with two binary operations whose axioms encode the generalized Reidemeister moves for virtual knots and links. These objects also provide set theoretic solutions of the well-known Yang-Baxter equation. The first half of this paper proposes some natural constructions of biquandles from groups and from their simpler counterparts, namely, quandles. We completely determine all words in the free group on two generators that give rise to (bi)quandle structures on all groups. We give some novel constructions of biquandles on unions and products of quandles, including what we refer as the holomorph biquandle of a quandle. These constructions give a wealth of solutions of the Yang-Baxter equation. We also show that for nice quandle coverings a biquandle structure on the base can be lifted to a biquandle structure on the covering. In the second half of the paper, we determine automorphism groups of these biquandles in terms of associated quandles showing elegant relationships between the symmetries of the underlying structures.     

Conjectures on the Quotient Ring by Diagonal Invariants

We formulate a series of conjectures (and a few theorems) on the quotient of the polynomial ring in two sets of variables by the ideal generated by all S _n invariant polynomials without constant term. The theory of the corresponding ring in a single set of variables X = {x ₁, ..., x _n} is classical. Introducing the second set of variables leads to a ring about which little is yet understood, but for which there is strong evidence of deep connections with many fundamental results of enumerative combinatorics, as well as with algebraic geometry and Lie theory.     

高阶色散下啁啾孤子的演化特性

本文解析地研究初始注入光纤的带啁啾Sech形脉冲(1≠N<3/2)的演化特性。在文献5的基础上,主要利用变分原理,同时把高阶色散项作为摄动项,近似求解了脉冲振幅、脉宽以及频率啁啾参数随传输距离的演化方程。结果表明,高阶色散有助于光纤中渐近孤子的形成。     

ΛΛ 6 hypernucleus in α + 2Λ cluster model

The binding energy of the double hypernucleus _ΛΛ ⁶ is calculated in α + 2Λ cluster model using the method of translation invariant basis TIMO. As regards the required interaction potentials we use a density dependent effective ΛN force and a gaussian form for ΛΛ potential. With these interactions a very reasonable value ofB _ΛΛ is obtained if the oscillator states up to the excitation quantum numberN=12 are taken into account in the expansion of wavefunction of the hypernucleus. This value ofN is much smaller than that obtained in an earlier study. This lowering inN value is attributed to a much better choice of ΛN potential used in the present study.     

用于单载波频域均衡水声通信的可分近似稀疏信道估计

针对单载波频域均衡水声通信中信道估计易受噪声干扰的问题,提出了一种低复杂度的信道估计方法。考虑水声信道的时域稀疏特性,导出频域输入、输出信号与信道冲激响应的关系式,并引入稀疏正则项,构造稀疏信道估计的目标函数。然后利用可分近似对目标函数进行迭代优化,再经过稀疏化与去偏处理,得到信道传递函数的最终估计。最后,利用数值仿真和海试数据对所提出方法的性能和运算效率进行评估。较之传统信道估计方法,所提出的方法在估计精度和计算复杂度方面具有一定的优势。     

A novel MI-insensitive and filterless frequency octupling scheme based on two parallel dual-parallel Mach–Zehnder modulators

A novel MI-insensitive and filterless frequency octupling scheme based on two parallel dual-parallel Mach–Zehnder modulators (DP-MZMs) is proposed. The proposed scheme is not sensitive to modulation index and relatively strong MMW signal with good radio frequency spurious suppression ratio (RFSSR) can be obtained without strict requirement on modulation index. Filterless feature makes the scheme quite suitable for wavelength division multiplexing (WDM) applications. For verification, a 60 GHz millimeter wave with 44 dB RFSSR is generated from a 7.5 GHz radio frequency wave by simulation. Performance of the proposed scheme has been characterized under different conditions including DC-bias drifts of MZMs, different amplitudes of RF inputs and different extinction ratios of MZMs.     

Singularity spectrum of fractal signals from wavelet analysis: Exact results

The multifractal formalism for singular measures is revisited using the wavelet transform. For Bernoulli invariant measures of some expanding Markov maps, the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima. The generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures. It is demonstrated that the Hausdorff dimensionD(h) of the set of singularities of Hölder exponenth can be directly determined from the wavelet transform modulus maxima. The singularity spectrum so obtained is shown to be not disturbed by the presence, in the signal, of a superimposed polynomial behavior of ordern, provided one uses an analyzing wavelet that possesses at leastN>n vanishing moments. However, it is shown that aC behavior generally induces a phase transition in theD(h) singularity spectrum that somewhat masks the weakest singularities. This phase transition actually depends on the numberN of vanishing moments of the analyzing wavelet; its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal. These theoretical results are illustrated with numerical examples. They are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional Brownian motions and turbulent velocity signals.