Sufficient conditions for functional-limit-theorem versions ofL = λW

The familiar queueing principle expressed by the formulaL=W can be interpreted as a relation among strong laws of large numbers. In a previous paper, we showed that this principle can be extended to include relations among other classical limit theorems such as central limit theorems and laws of the iterated logarithm. Here we provide sufficient conditions for these limit theorems using regenerative structure.Supported by the National Science Foundation under Grant No. ECS-8404809 and by the U.S. Army under Contract No. DAAG29-80-C-0041.     

Nonlocal symmetries,exact solutions and conservation laws of the coupled Hirota equations

Using the Lax pair, nonlocal symmetries of the coupled Hirota equations are obtained. By introducing an appropriate auxiliary dependent variable, the nonlocal symmetries are successfully localized to Lie point symmetries. With the help of Lie symmetries of the closed prolongation, exact solutions and nonlocal conservation laws of the coupled Hirota equations are studied.     

带斜楔相控声束偏转聚焦延时特性研究

带斜楔的相控阵超声检测广泛应用于低碳钢薄壁工件焊缝的检测,研究带斜楔的相控阵超声偏转聚焦检测延时法则和对应的声场将使检测可靠性进一步提高。本文利用费马原理探究了相控阵超声探头辐射声波至楔块中,在楔块-工件平面界面发生模式转换入射到工件中的横波聚焦时各阵元延时的计算方法,数值求解指定焦点时各阵元的延时,并利用计算得到的延时进行声场仿真和实验测量,发现声波能很好的聚焦在目标点,仿真和实验结果吻合。     

Polynomial viscosity methods for multispecies kinematic flow models

Multispecies kinematic flow models are defined by systems of strongly coupled, nonlinear first‐order conservation laws. They arise in various applications including sedimentation of polydisperse suspensions and multiclass vehicular traffic. Their numerical approximation is a challenge since the eigenvalues and eigenvectors of the corresponding flux Jacobian matrix have no closed algebraic form. It is demonstrated that a recently introduced class of fast first‐order finite volume solvers, called polynomial viscosity matrix (PVM) methods [M. J. Castro Díaz and E. Fernández‐Nieto, SIAM J Sci Comput 34 (2012), A2173–A2196], can be adapted to multispecies kinematic flows. PVM methods have the advantage that they only need some information about the eigenvalues of the flux Jacobian, and no spectral decomposition of a Roe matrix is needed. In fact, the so‐called interlacing property (of eigenvalues with known velocity functions), which holds for several important multispecies kinematic flow models, provides sufficient information for the implementation of PVM methods. Several variants of PVM methods (differing in polynomial degree and the underlying quadrature formula to approximate the Roe matrix) are compared by numerical experiments. It turns out that PVM methods are competitive in accuracy and efficiency with several existing methods, including the Harten, Lax, and van Leer method and a spectral weighted essentially non‐oscillatory scheme that is based on the same interlacing property. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1265–1288, 2016     

Self-consistent Sources and Conservation Laws for Sup er-Geng Equation Hierarchy

Based on the matrix Lie super algebra and supertrace identity, the integrable super-Geng hierarchy with self-consistent is established. Furthermore, we establish the in-finitely many conservation laws for the integrable super-Geng hierarchy. The methods de-rived by us can be generalized to other nonlinear equation hierarchies.     

Carbazole-Dendronized Luminescent Radicals

A series of carbazole-dendronized tris(2,4,6-trichlorophenyl)methyl (TTM) radicals have been synthesized. The photophysical properties of dendronized radicals up to the fourth generation were compared systematically to understand how structure–property relationships evolve with generation. The photoluminescence quantum yield (PLQY) was found to increase with the increasing generation, and the fourth generation (G4TTM) in cyclohexane solution showed a PLQY as high as 63 % at a wavelength of 627 nm (in the deep-red region) from the doublet state. The dendron modification strategy also showed a blue-shift of the emission on increasing the generation number, and the photostability was also increased compared to the bare TTM radical.     

Folate content in sea buckthorn berries and related products (Hippophaë rhamnoides L. ssp. rhamnoides): LC-MS/MS determination of folate vitamer stability influenced by processing and storage assessed by stable isotope dilution assay

A stable isotope dilution assay was adopted for quantitation of folate vitamers in sea buckthorn berries, juice, and concentrate using fourfold labeled folate isotopologues of the folate derivatives as the internal standards and reversed-phase liquid chromatography-tandem mass spectrometry with electrospray ionization (LC-ESI-MS/MS). Processing effects and storage stability were investigated during juice and concentrate production from sea buckthorn berries (Hippopha? rhamnoides). The technological processing of the berries caused a total degradation of tetrahydrofolate and 5-formyltetrahydrofolate in the generated juice. The content of the main folate vitamer 5-methyltetrahydrofolate remained approximately unchanged during the whole processing from the berries to the concentrate. Sea buckthorn juice was stored under two household storage conditions (6 degrees C, 25 degrees C), and also under accelerated aging conditions (40 degrees C) for up to 7 days to determine the effects of storage temperature on the stability of 5-methyltetrahydrofolate. The content of 5-methyltetrahydrofolate was nearly unchanged during the storage at 6 degrees C after 7 days. The juice showed almost identical degradation of 5-methyltetrahydrofolate of about 17-20% at 25 degrees C and 40 degrees C after 7 days of storage. [figure: see text]