Environmentally friendly synthesis of 2-aryl-2,3-dihydroquinazolin-4(1H)-ones by novel Co-CNTs as recoverable catalysts

The objective of this study is to investigate the possibility of using Co-CNTs as a green reaction medium and a catalyst for the cyclo-condensation of o-aminobenzamide with various aldehydes. This inexpensive, non-toxic, and readily available catalyst efficiently catalyzes the above condensation for the synthesis of 2-aryl-2,3-dihydroquinazolin-4(1H)-ones. Compared to the classical reaction, this is a simple, highly yielding, time saving, and environmentally friendly method.     

Fatty acid amide hydrolase inhibitors. 2. Novel synthesis of sterically hindered azabenzhydryl ethers and an improved synthesis of VER-156084

We report an improved synthesis of the fatty acid amide hydrolase (FAAH) inhibitor VER-156084. The key step is a novel, environmentally benign etherification to form an unusual, highly hindered azabenzhydryl ether. The method is applied to a variety of primary and secondary alcohols.     

Optimal Control of the Obstacle for an Elliptic Variational Inequality

An optimal control problem for an elliptic obstacle variational inequality is considered. The obstacle is taken to be the control and the solution to the obstacle problem is taken to be the state. The goal is to find the optimal obstacle from H ¹ ₀ (Ω) so that the state is close to the desired profile while the H ¹ (Ω) norm of the obstacle is not too large. Existence, uniqueness, and regularity as well as some characterizations of the optimal pairs are established. Accepted 11 September 1996     

含有各阶导数的高阶微分方程边值问题三个单调正解的存在性

利用五个泛函的不动点定理,研究一类含有各阶导数的2m阶微分方程边值问题的三个单调正解的存在性.     

Estimates on Green functions and Schrödinger-type equations for non-symmetric diffusions with measure-valued drifts

In this paper, we establish sharp two-sided estimates for the Green functions of non-symmetric diffusions with measure-valued drifts in bounded Lipschitz domains. As consequences of these estimates, we get a 3G type theorem and a conditional gauge theorem for these diffusions in bounded Lipschitz domains.Informally the Schrödinger-type operators we consider are of the form L+μ⋅∇+ν where L is a uniformly elliptic second order differential operator, μ is a vector-valued signed measure belonging to Kd,1 and ν is a signed measure belonging to Kd,2. In this paper, we establish two-sided estimates for the heat kernels of Schrödinger-type operators in bounded C1,1-domains and a scale invariant boundary Harnack principle for the positive harmonic functions with respect to Schrödinger-type operators in bounded Lipschitz domains.     

Revised Iterative Solution for Groundstate of Schrodinger Equation

A revised iterative method based on Green function defined by quadratures along a single trajectory is proposed to solve the low-lying quantum wave function for Schrodinger equation. Specially a new expression of the perturbed energy is obtained, which is much simpler than the traditional one. The method is applied to solve the unharmonic oscillator potential. The revised iteration procedure gives exactly the same result as those based on the single trajectory quadrature method. A comparison of the revised iteration method to the old one is made using the example of Stark effect. The obtained results are consistent to each other after making power expansion.     

An application of the capacitance matrix method to accommodate masked land areas and island circulations in a primitive equation ocean model

The capacitance matrix method has been implemented in a primitive equation ocean model to accommodate islands and portions of irregular coastal boundaries that cannot be treated adequately by boundary-fitted orthogonal curvilinear co-ordinates. The algorithm preserves the ability to solve the streamfunction equation using fast and accurate elliptic solvers that require a rectangular computational domain. By superposition of a set of island Green functions, the solution is adjusted to ensure continuity of pressure around each island. The implementation is tested by comparison with an analytic solution for wind-driven flow in a closed basin similar to the southwest Pacific Ocean.     

超收敛中的双P猜想续篇——离散格林函数的权模估计

探讨超收敛猜想中p=4的情形.为此目的我们推导了离散格林函数的权模估计.     

乔治·格林及格林函数法

乔治.格林是一位重要的数学物理学家.简要介绍了乔治.格林的生平和科学研究经历,揭示了帮助他取得重要科学研究成果的主要因素,介绍了格林函数法的建立过程及其重要性.     

Poisson Kernel and Green Function of the Ball in Real Hyperbolic Spaces

Let (X _t ) _t⩾0 be the n-dimensional hyperbolic Brownian motion, that is the diffusion on the real hyperbolic space having the Laplace–Beltrami operator as its generator. The aim of the paper is to derive the formulas for the Gegenbauer transform of the Poisson kernel and the Green function of the ball for the process (X _t ) _t⩾0. Under additional hypotheses we prove integral representations for the Poisson kernel. This yields explicit formulas in and spaces for the Poisson kernel and the Green function as well.