The exponential power law: partial wetting kinetics and dynamic contact angles

An equation for the kinetics of partial drop spreading is proposed. This equation was empirically derived from experimental data for the spreading kinetics of partially wetting liquids in terms of the wet area versus time. The equation has the form of an exponential power law (EPL), and transforms into the well-known power law for complete wetting, when the equilibrium contact angle approaches zero. The EPL fits very well available experimental data. To lend additional support to the validity of this generalized equation, it will be demonstrated that when it is transformed to present the dynamic contact angle (DCA), it fits very well DCA experimental data for other wetting processes, such as capillary flow and tape coating.     

Effects of tributyltin(IV) chloride on the gametes and fertilization of Ascidia malaca (Ascidiacea: Tunicata)

Ascidia malaca gametes before fertilization incubated in 10^?5 or 10^?7 M solutions of tributyltin(IV) chloride, TBTCl, for 3 h appear highly damaged under transmission electron microscopy observation. Also, the fertilization process is affected by the compound: the damaged spermatozoa are present in the vitelline coat and the egg does not cleave. An increase of microbodies, structurally similar to peroxisomes, have been detected in the egg peripheral cytoplasm, probably in relation to their role in alleviating damage to some cellular components. The results have shown that the reproduction of ascidians under unfavourable environmental conditions is prevented. Copyright © 2003 John Wiley & Sons, Ltd.     

The LEM exponential integrator for advection–diffusion–reaction equations

We implement a second-order exponential integrator for semidiscretized advection–diffusion–reaction equations, obtained by coupling exponential-like Euler and Midpoint integrators, and computing the relevant matrix exponentials by polynomial interpolation at Leja points. Numerical tests on 2D models discretized in space by finite differences or finite elements, show that the Leja–Euler–Midpoint (LEM) exponential integrator can be up to 5 times faster than a classical second-order implicit solver.     

Global smooth solutions to the multi-dimensional hydrodynamic model for two-carrier plasmas

The existence of global smooth solutions to the multi-dimensional hydrodynamic model for plasmas of electrons and positively charged ions is shown under the assumption that the initial densities are close to a constant. The model consists of the conservation laws for the particle densities and the current densities, coupled to the Poisson equation for the electrostatic potential. Furthermore, it is proved that the particle densities converge exponentially fast to the (constant) steady state. The proof uses a higher-order energy method inspired from extended thermodynamics.     

Research on exponential regularization approach for nonnegative Tucker3 decomposition

Methods of nonnegative tensor factorization (NTF), such as NTF1, NTF2, etc., are extension of nonnegative matrix factorization (NMF) for multi-way data analysis. As an existing NTF method, nonnegative Tucker3 decomposition (NTD) is researched for three-way decomposition in this paper. Firstly, an approach utilizing matrix exponentials built on Tikhonov-type regularization to enforce sparseness is proposed to extract image features instead of exclusively using Tucker tensor decomposition. Meanwhile, updating algorithms, derived from updating rules of NMF, are allowed to efficiently implement updating of mode matrices and core tensors alternatively for accuracy. Then, experimental cases of alternating least squares (ALS) and conjugate nonnegative constraints, called nonnegative alternating least squares (NALS), are studied to remedy data overfitting in computing procedures. Lastly, the proposed method exhibits more advantageous results than other algorithms of Tucker3 for feature extraction, thanks to computer simulations performed in the context of data analysis.     

The number of ideals in a quadratic field

LetK be a quadratic Geld, and letR(N) be the number of integer ideals inK with norm at most AT. Letx with conductork be the quadratic character associated withK. Then |R(N)−NL(1,x)|⩽Bk ^50/73 N ^23/73(logN)^461/146 forN ≥Ak, whereA andB are constants. ForN ≥Ak ^c,C sufficiently large, the factork ^50/73 may be replaced by (d(k))^4/73 k ^46/73. Dedicated to the memory of Professor K G Ramanathan     

Exponential distributions on semigroups

Three fundamental characterizations of the standard exponential distribution on [0, ) are the remaining life, memoryless and constant failure properties. Analogs of these properties are studied for distributions on a class of semigroups in which the semigroup operation replaces addition, a compatible partial order replaces the ordinary order, and a left-invariant measure replaces Lebesgue measure. Partial characterizations of exponential distributions on such semigroups are obtained and the semigroup formulation provides new characterizations of certain aging properties studied in reliability-increasing failure rate, new better than used, and increasing failure rate average.     

HOMOCLINIC SOLUTIONS FOR AUTONOMOUS DIFFERENTIAL EQUATIONS

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Network analysis of eigenvalue problem for multilayer dielectric waveguide consisting of arbitrary number of layers

In this paper, the eigenvalue problem of a multilayer dielectric waveguide consisting of arbitrary number of layers is solved by the microwave network method. A general program with the function of computer graphics has been developed for analyzing the dispersion characteristics and the electromagnetic field distributions of an N layer dielectric waveguide. As examples of practical applications of the program, first, the dispersions and field patterns for the planar waveguides with refractive index of parabolic and exponential profiles are analyzed. Secondly, the procedure of mode conversion and mode separation in dielectric branching waveguides is vividly demonstrated through analyzing the field distributions of asymmetric multilayer dielectric structures and the general rules of mode conversion are discussed. The examples show that the present method possesses the advantages of versatility, rapidity, simplicity and accuracy.     

基于模式识别技术的色貌模型评价研究

选用Munsell新标数据集,采用基于模式识别技术的圆度、色相角偏差、明度线性度与空间投影点聚集度四个指标来分别评价目前八个典型色貌模型在彩度均匀性、色相预测准确性、明度均匀性、颜色的空间再现的能力。结果表明,不同的色貌模型在四个方面的颜色再现性上表现出不同的优势。八个色貌模型对彩度预测最好的是RLAB,每个色貌模型对红色和绿色预测比较好,CAM02在色相预测整体上占优势;明度的均匀性预测都比较好,尤其是CIELAB;LLAB的颜色的空间再现能力最好。