Asymptotic behavior of solutions to scalar conservation laws and optimal convergence orders to N-waves

The goal of this article is to develop a new technique to obtain better asymptotic estimates for scalar conservation laws. General convex flux, f″(u)?0, is considered with an assumption . We show that, under suitable conditions on the initial value, its solution converges to an N-wave in L¹ norm with the optimal convergence order of O(1/t). The technique we use in this article is to enclose the solution with two rarefaction waves. We also show a uniform convergence order in the sense of graphs. A numerical example of this phenomenon is included.     

Invariant manifolds and the stability of traveling waves in scalar viscous conservation laws

The stability of traveling wave solutions of scalar viscous conservation laws is investigated by decomposing perturbations into three components: two far-field components and one near-field component. The linear operators associated to the far-field components are the constant coefficient operators determined by the asymptotic spatial limits of the original operator. Scaling variables can be applied to study the evolution of these components, allowing for the construction of invariant manifolds and the determination of their temporal decay rate. The large time evolution of the near-field component is shown to be governed by that of the far-field components, thus giving it the same temporal decay rate. We also give a discussion of the relationship between this geometric approach and previous results, which demonstrate that the decay rate of perturbations can be increased by requiring that initial data lie in appropriate algebraically weighted spaces.     

Similarity degrees for the crossed product of von Neumann algebras

In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve some upper bounds for similarity degrees of some finite von Neumann algebras.     

Study of spectral analytical data using fingerprints and scaled similarity measurements

A new chemoinformatic model has been developed for enlarging the differences between spectra and applied to differentiation of wines according to the criteria grape origin and variety and ageing process. The model is based on generation of fingerprints from normalised spectra, using empirical parameters and a set of 120 samples. After generation of the fingerprints, similarity matrixes were built on the basis of the Tanimoto similarity index between the fingerprints of the samples. Calculation of the Tanimoto index was modified to adapt the index to the characteristics of the analytical measurements. Thus, scaling factors taking into account pattern fingerprints generated from a group of samples with common characteristics were used. In addition, a modified expression for calculating the Tanimoto index was employed. Principal-components analysis (PCA) and soft independent modelling of class analogy (SIMCA) were applied to the similarity matrixes. The results obtained are discussed as a function of the normalisation method employed, the empirical factor used in generation of the fingerprints, and selection of samples for building the pattern fingerprint, etc. Finally, results from differentiation of wines are compared with those obtained by applying PCA to the unprocessed spectra as stated by the proposed model.     

Capillarity driven spreading of power-law fluids

We investigate the spreading of thin liquid films of power-law rheology. We construct an explicit travelling wave solution and source-type similarity solutions. We show that when the nonlinearity exponent λ for the rheology is larger than one, the governing dimensionless equation h_t + (h^λ+2|h_xxx|^λ−1h_xxx)_x=0 admits solutions with compact support and moving fronts. We also show that the solutions have bounded energy dissipation rate.     

计量逻辑学的基本思想和研究综述

介绍计量逻辑学的形成、特点及其与模糊逻辑的异同。关于命题逻辑的计量化理论,针对不同的系统论述了真度理论和相似度理论,特别是介绍了作者提出的命题逻辑系统L*以及与其配套的R0代数理论和完备性定理。介绍了逻辑理论在逻辑度量空间中的发散度和相容的理论以及三种近似推理模式。回顾了谓词逻辑计量化的进程和有待解决的问题。提出了模态逻辑和模型检验的计量化问题以及有待进一步探讨的几个研究课题。     

基于模糊聚类分析和曲线拟合的FTIR不同产地鸡骨草、毛鸡骨草鉴别分析

利用傅里叶变换红外光谱技术结合模糊聚类分析法和曲线拟合对鸡骨草、毛鸡骨草进行产地鉴别。选用曼哈顿距离单位计算的相异度聚类分析结果最优,5个产地鸡骨草都可完全区分开来,毛鸡骨草则只能鉴别出3个产地,南宁和钦州2个产地发生重叠;为了进一步鉴别不同产地鸡骨草和毛鸡骨草,对鸡骨草和毛鸡骨草平均红外谱图中1 034 cm-1吸收峰进行曲线拟合,野生鸡骨草拟合出11个子峰,其他各产地鸡骨草均只能拟合出9个子峰,上林产毛鸡骨草拟合出9个子峰,其他各产地毛鸡骨草均只能拟合出8个子峰,而且不同产地鸡骨草和毛鸡骨草拟合出的子峰位置和归一化强度都不完全相同;模糊聚类分析法和曲线拟合法有机结合能够使产地鉴别结果更加准确。     

Similarity Solutions for Thawing Processes with a Heat Flux Condition at the Fixed Boundary

Similarity solutions for a mathematical model for thawing in a saturated semi-infinite porous medium is considered when change of phase induces a density jump and a heat flux condition of the type is imposed on the fixed face x=0. Different cases depending on physical parameters are analysed and the explicit solution is obtained if and only if an inequality for the thermal coefficient q ₀ is verified. An improvement for the existence of a similarity solution for the same free boundary problem with a constant temperature on the fixed face x=0 is also obtained. Sommario. Vengono considerate soluzioni di similarità per un modello matematico di disgelo di un mezzo poroso saturo semi-infinito allorquando il cambiamento di fase induce un salto di densità ed una condizione di flusso di calore del tipo viene imposta sulla faccia fissa x=0. Si analizzano differenti casi dipendenti da parametri fisici e la soluzione esplicita viene ottenuta se e solo se risulta verificata una diseguaglianzo per il coefficiente termico q ₀. Si ottiene altresi un miglioramento della condizione di esistenza di una soluzione di similarità per lo stesso problema al contorno libero con temperatura costante sulla faccia fissa x=0.     

Significance of hydrophobic interactions in water–organic binary solvents

A LFE (Linear Free Energy) analysis of kinetic data for different organic reactions in various organic aqueous solutions was carried out. The rate constants of these reactions were compared with those for the solvolysis of tert-butyl chloride in the same solvents in terms of the LFE Relationships, and linear plots were observed in a wide range of the co-solvent content. This similarity points to a common nature of the solvent effect in these reactions in variety of water–organic mixtures, regardless of largely different reaction mechanisms. We explain these results by the prevalence of hydrophobic stabilization of the initial state of these reactions in water-rich solvent mixtures. Recently the same conclusion was also made on the basis of investigations into sonication effects in kinetics of organic reactions. A considerable contribution of hydrophobic effects to the Y scale by Grunwald and Winstein was deduced.     

Biologically-inspired stochastic vector matching for noise-robust information processing

“End of Moore’s Law” has recently become a topic. Keeping the signal-to-noise ratio (SNR) at the same level in the future will surely increase the energy density of smaller-sized transistors. Lowering the operating voltage will prevent this, but the SNR would inevitably degrade. Meanwhile, biological systems such as cells and brains possess robustness against noise in their information processing in spite of the strong influence of stochastic thermal noise. Inspired by the information processing of organisms, we propose a stochastic computing model to acquire information from noisy signals. Our model is based on vector matching, in which the similarities between the input vector carrying external noisy signals and the reference vectors prepared in advance as memorized templates are evaluated in a stochastic manner. This model exhibited robustness against the noise strength and its performance was improved by addition of noise with an appropriate strength, which is similar to a phenomenon observed in stochastic resonance. Because the stochastic vector matching we propose here has robustness against noise, it is a candidate for noisy information processing that is driven by stochastically-operating devices with low energy consumption in future. Moreover, the stochastic vector matching may be applied to memory-based information processing like that of the brain.