Volume comparison and the σk-Yamabe problem

In this paper we study the problem of finding a conformal metric with the property that the kth elementary symmetric polynomial of the eigenvalues of its Weyl-Schouten tensor is constant. A new conformal invariant involving maximal volumes is defined, and this invariant is then used in several cases to prove existence of a solution, and compactness of the space of solutions (provided the conformal class admits an admissible metric). In particular, the problem is completely solved in dimension four, and in dimension three if the manifold is not simply connected.     

The primary investigation of optical-limiting effects of optical active phthalocyanine derivative TMBO-SiPc

The optical-limiting property of an optically active phthalocyanine derivative with different configuration in chloroform solution was measured at 532 nm with 10 ns pulses. The excited state absorption cross-section σ_ex of the derivative was determined with the Z-scan technique. The results showed that the phthalocyanine derivative possesses larger σ_ex than the ground state absorption cross-section σ₀, indicating that it is a material for reverse saturable absorption. And it is specially noticed that the change in the optically active configuration affects its optical-limiting property significantly.     

Yb2.75C60价带光电子能谱

用角积分紫外光电子能谱技术测量了Yb2 75C6 0 薄膜的价带电子态密度分布 .相纯Yb2 75C6 0 样品通过C1s芯态x射线电子谱峰的位移表征 .结果表明Yb2 75C6 0 是半导体 ,在费米能级处几乎没有电子态分布 .Yb 6s电子态和C6 0 LU MO能带的杂化效应不可忽略 ,有部分Yb 6s电子分布在Yb C6 0 杂化能带上 .     

Discontinuous Galerkin method with a posterioriL_p(0,t_i) error estimate for second-kind Volterra problems

Summary. We consider a discontinuous Galerkin finite element method applied in time to a model Volterra equation of the second kind. A residual-based computable Galerkin-error estimate is derived for . This estimate does not explicitly contain the time step and therefore the time step control must be based on a heuristic criterion, the estimate can then be used to demonstrate the integrity, or otherwise, of the finite element solution. After performing some numerical experiments we conclude that this approach is at least competetive with classical discretizations since it is computationally simple to implement, but has the added advantage of reliable error feedback. Received June 25, 1995     

On the free boundary of surfaces with bounded mean curvature: the non-perpendicular case

H?lder continuity up to the free boundary is proved for minimizing solutions if they meet the supporting surface in an angle which is bounded away from zero. The problem is localized by proving the continuity of the distance function, a result which is also true for stationary points. Received: 14 April 1998     

Weighted Sobolev embedding with unbounded and decaying radial potentials

We prove embedding results of weighted W1,p(RN) spaces of radially symmetric functions. The results then are used to obtain ground and bound state solutions of quasilinear equations with unbounded or decaying radial potentials.     

The proportional hazards regression model with staggered entries: A strong martingale approach

The proportional hazards regression model, when subjects enter the study in a staggered fashion, is studied. A strong martingale approach is used to model the two-time parameter counting processes. It is shown that well-known univariate results such as weak convergence and martingale inequalities can be extended to this two-dimensional model. Strong martingale theory is also used to prove weight convergence of a general weighted goodness-of-fit process and its weighted bootstrap counterpart.     

FULL DISCRETE NONLINEAR GALERKIN METHOD FOR THE NAVIER-STOKES EQUATIONS

This paper deals with the inertial manifold and the approximate inertial manifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore, we provide the error estimates of the approximate solutions of the Navier-Stokes Equations.     

Coupling and Poisson approximation

We give an overview of the Stein-Chen method for establishing Poisson approximations of various random variables. Couplings of certain variables are used to gives explicit bounds for the total variation distance between the distribution of a random variable and a Poisson variable. Some applications are given. In some cases, explicit couplings may be used to obtain good estimates; in other applications it suffices to show the existence of couplings with certain monotonicity properties.Supported by the Göran Gustafsson Foundation for Research in Natural Sciences and Medicine.     

Synthesis of the D-Galactopyranoside Derivative of C_(60)

ThefascinatingsbocturesandpropertiesoffullereneshaveoPeneduPanewfieldofchendstry.Inparticular,F.Wudletal.l'2haveshownthatwatersofubleC6ocomPoundsinhibittheHITVen-zymesprotease(HIVP)andreversetranscriPtase(HIVRT).IthasbeenafocusofstUdytoinvestigatethebiologicalactivitiesofthesenovelsubstances.Fortheirpossiblemedicaluses,tolinkC6omoleculetonaturalProductssuchassugars,pephdes,amioacides,andsoonisanimPortantmethodinthisfield.Vasella3reportedthefirstglucosidederivativeofC6o'InthispaPer,w…