Gibbs energy of activation for thermal isomerization of (1Z)‐acetaldehyde hydrazone and (1Z)‐acetaldehyde N,N‐dimethylhydrazone by Gaussian‐4 theory and CCSD(T)/CBS computations

In this article, we examined the Gibbs energy of activation for the Z/E thermal isomerization reaction of (1Z)‐acetaldehyde hydrazone and (1Z)‐acetaldehyde N,N‐dimethylhydrazone, at 298.15 K in the solvent of cyclohexane. We carried out computations employing both the Gaussian‐4 (G4) theory and the coupled cluster method using both single and double substitutions and triple excitations noniteratively, CCSD(T). The CCSD(T) energy is extrapolated to the complete basis set (CBS). We compared the calculated results to the available experimental observation. It appeared that both G4 and CCSD(T)/CBS computations overestimated the experimental value by as much as about 6 and 12 kcal/mol in the present two cases. We discussed possible sources of error and proposed the experimental kinetic data could be questionable. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Riesz transforms for a non-symmetric Ornstein-Uhlenbeck semigroup

Let (ℋ _t ) _t≥0 be the Ornstein-Uhlenbeck semigroup on ℝ ^d with covariance matrix I and drift matrix −λ(I+R), where λ>0 and R is a skew-adjoint matrix and denote by γ _∞ the invariant measure for (ℋ _t ) _t≥0. Semigroups of this form are the basic building blocks of Ornstein-Uhlenbeck semigroups which are normal on L ²(γ _∞). We investigate the weak type 1 estimate of the Riesz transforms for (ℋ _t ) _t≥0. We prove that if the matrix R generates a one-parameter group of periodic rotations then the first order Riesz transforms are of weak type 1 with respect to the invariant measure γ _∞. We also prove that the Riesz transforms of any order associated to a general Ornstein-Uhlenbeck semigroup are bounded on L ^p (γ _∞) if 1<p<∞. The authors have received support by the Italian MIUR-PRIN 2005 project “Harmonic Analysis” and by the EU IHP 2002-2006 project “HARP”.     

On the Elliptic Equation △u ＋ K（x）e^2u -0 with K（x） Positive Somewhere

This paper considers the existence problem of an elliptic equation.which is equivalent to the prescribing conformal Gaussian curvature problem on R2.An existence result is pried.In particular,K(x)is allowed to be unbounded above.     

Skew-Gaussian random field

In this article, we introduce the concept of skewness to the Gaussian random field theory by defining a new two-dimensional non-Gaussian random field called skew-Gaussian random field. We derive the expected Euler characteristic of its excursion set. Moreover, an approximation to the size distribution of one connected component is derived. As an illustration, we present a simulation study to compare the approximation mechanism with the exact one.     

Error bounds for approximations of traces of products of truncated Toeplitz operators

The paper establishes error orders for integral limit approximations to the traces of products of truncated Toeplitz operators generated by integrable real symmetric functions defined on the real line. These approximations and the corresponding error bounds are of importance in the statistical analysis of continuous-time stationary processes (asymptotic distributions and large deviations of Toeplitz type quadratic functionals, estimation of the spectrum, etc.). The results improve the rates obtained by the authors (in an earlier paper). An explicit second-order asymptotic expansion is found for the trace of a product of two truncated Toeplitz operators generated by the spectral densities of continuous-time stationary fractional Riesz-Bessel motions. The order of magnitude of the second term in this expansion is shown to depend on the long-memory parameters of the processes. The second-order term provides a substantially better approximation to the original functional, as compared with the first-order approximation. M. Ginovyan research was partially supported by National Science Foundation Grant #DMS-0706786.     

A quadrature finite element Galerkin scheme for a biharmonic problem on a rectangular polygon

A quadrature Galerkin scheme with the Bogner–Fox–Schmit element for a biharmonic problem on a rectangular polygon is analyzed for existence, uniqueness, and convergence of the discrete solution. It is known that a product Gaussian quadrature with at least three‐points is required to guarantee optimal order convergence in Sobolev norms. In this article, optimal order error estimates are proved for a scheme based on the product two‐point Gaussian quadrature by establishing a relation with an underdetermined orthogonal spline collocation scheme. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

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.     

Weighted norm inequalities,off-diagonal estimates and elliptic operators. Part IV: Riesz transforms on manifolds and weights

This is the fourth article of our series. Here, we study weighted norm inequalities for the Riesz transform of the Laplace–Beltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Gaussian upper bounds.      

三维Minkowski空间中非类光曲线的双曲达布像和从切高斯曲面

本文主要给出了三维Minkowski空间中非类光曲线的双曲达布像和从切高斯曲面的奇点分类,并且建立了奇点和曲线几何不变量之间的联系,其中曲线几何不变量与曲线同螺线切触的阶数密切相关.