An adaptive wavelet viscosity method for hyperbolic conservation laws

We extend the multiscale finite element viscosity method for hyperbolic conservation laws developed in terms of hierarchical finite element bases to a (pre‐orthogonal spline‐)wavelet basis. Depending on an appropriate error criterion, the multiscale framework allows for a controlled adaptive resolution of discontinuities of the solution. The nonlinearity in the weak form is treated by solving a least‐squares data fitting problem. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008     

Exploiting equalities in polynomial programming

We propose a novel approach for solving polynomial programs over compact domains with equality constraints. By means of a generic transformation, we show that existing solution schemes for the, typically simpler, problem without equalities can be used to address the problem with equalities.     

消错逻辑的增加转化词

定义了增加转化词的概念 ,说明了它的研究对象及在消除决策错误中的作用 ,研究了在消错逻辑变换中 ,这个转化词所具有的性质和规律 .     

Small deviation probability via chaining

We obtain several extensions of Talagrand’s lower bound for the small deviation probability using metric entropy. For Gaussian processes, our investigations are focused on processes with sub-polynomial and, respectively, exponential behaviour of covering numbers. The corresponding results are also proved for non-Gaussian symmetric stable processes, both for the cases of critically small and critically large entropy. The results extensively use the classical chaining technique; at the same time they are meant to explore the limits of this method.     

On strong and total Lagrange duality for convex optimization problems

We give some necessary and sufficient conditions which completely characterize the strong and total Lagrange duality, respectively, for convex optimization problems in separated locally convex spaces. We also prove similar statements for the problems obtained by perturbing the objective functions of the primal problems by arbitrary linear functionals. In the particular case when we deal with convex optimization problems having infinitely many convex inequalities as constraints the conditions we work with turn into the so-called Farkas-Minkowski and locally Farkas-Minkowski conditions for systems of convex inequalities, recently used in the literature. Moreover, we show that our new results extend some existing ones in the literature.     

时标动力方程的稳定性分析

近来，一种称之为时标动力系统的新理论得到了蓬勃的发展. 该文给出并建立了时标动力系统的各种稳定性概念和Lyapunov稳定性准则(稳定, 一致稳定, 渐近稳定, 指数渐近稳定等等).     

A novel method for the determination of diffusion coefficients in amorphous poly(3-hydroxybutyrate)

A novel approach is proposed for the determination of the diffusion coefficient of certain drugs in amorphous poly(hydroxybutyrate) (PHB), which can be a reliable alternative to the conventional permeation based measurements. The method requires the preparation of PHB films with various concentrations of the drug and if the latter absorbs in the visible wavelength range, its concentration gradient in the polymer film as well as the time dependence of the latter can be analyzed quantitatively by following changes in color. Color can be converted into concentration with the help of adequate calibration and thus the dependence of additive concentration on space (x) and time (t), i.e. the c(x,t) function, can be determined relatively easily. The fitting of the numerical solution of Fick's second law onto the measured values provides directly the targeted diffusion coefficient. The comparison of diffusion coefficients obtained by the proposed approach to values published in the literature proved that the new method provides reliable results and requires reasonable time and effort at the same time.     

Percolation theory approach to transport phenomena in porous media

The percolation theory approach to static and dynamic properties of the single- and two-phase fluid flow in porous media is described. Using percolation cluster scaling laws, one can obtain functional relations between the saturation fraction of a given phase and the capillary pressure, the relative permeability, and the dispersion coefficient, in drainage and imbibition processes. In addition, the scale dependency of the transport coefficient is shown to be an outcome of the fractal nature of pore space and of the random flow pattern of the fluids or contaminant.     

Triply bridged (1,3,5) cyclophanes from cystine and lanthionine linkers—a comparison

The condensation of benzene 1,3,5-tricarbonylchloride with cystine-di-Me [H₂N-CH(COOMe)-CH₂-S-S-CH₂-CH(COOMe)-NH₂] yielded triply bridged (1,3,5) cyclophane 1, which was shown by detailed spectral studies and molecular orbital calculations to have a D₃ symmetry with conformationally identical linkers and a spherical topology. In sharp contrast, the (1,3,5) cyclophane 2 from the rarely studied lanthionine di-Me [H₂N-CH(COOMe)-CH₂-S-CH₂-CH(COOMe)-NH₂], showed only a equatorial twofold symmetry. This work highlights the special properties of the -S-S- bridge in cystine, which makes it an exceptional synthon in nature and organic synthesis.     

An unexpected coupling reaction between isocyanides and carboxylic acids: a method for the synthesis of highly stable symmetrical and unsymmetrical alkylamidine and arylamidine carbocations

An unexpected coupling reaction between isocyanides and carboxylic acids which led to the synthesis of highly stable symmetrical and unsymmetrical alkylamidine and arylamidine carbocations under mild reaction conditions is described. The structures of these compounds were confirmed by IR, mass, ¹H NMR, ¹³C NMR, and single-crystal X-ray diffraction studies and a plausible mechanism is proposed.