Multiple nontrivial solutions for nonlinear periodic problems with the p-Laplacian

We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential (hemivariational inequality). Using the degree theory for multivalued perturbations of (S)₊-operators and the spectrum of a class of weighted eigenvalue problems for the scalar p-Laplacian, we prove the existence of at least three distinct nontrivial solutions, two of which have constant sign.     

Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries

We consider nonnegative solutions of a parabolic equation in a cylinder D×(0,T), where D is a noncompact domain of a Riemannian manifold. Under the assumption [IU] (i.e., the associated heat kernel is intrinsically ultracontractive), we establish an integral representation theorem: any nonnegative solution is represented uniquely by an integral on (D×{0})∪(M_∂D×[0,T)), where M_∂D is the Martin boundary of D for the associated elliptic operator. We apply it in a unified way to several concrete examples to explicitly represent nonnegative solutions. We also show that [IU] implies the condition [SP] (i.e., the constant function 1 is a small perturbation of the elliptic operator on D).     

Maximum-norm error analysis of a non-monotone FEM for a singularly perturbed reaction-diffusion problem

A non-monotone FEM discretization of a singularly perturbed one-dimensional reaction-diffusion problem whose solution exhibits strong layers is considered. The method is shown to be maximum-norm stable although it is not inverse monotone. Both a priori and a posteriori error bounds in the maximum norm are derived. The a priori result can be used to deduce uniform convergence of various layer-adapted meshes proposed in the literature. Numerical experiments complement the theoretical results. AMS subject classification (2000)  65L10, 65L50, 65L60     

圆柱型正交各向异性圆形薄板的非线性非对称弯曲问题（Ⅱ）

本文利用“正则摄动法”［２］研究文献［１］中由“两变量法”［３］所得到的关于Ｗｎｍ，和的递推方程和递推边界条件的求解问题。求得了本问题的一致有效渐近解，最后作为实例，我们利用“混合摄动法”［４］研究了轴对称线性弯曲问题，并将所得结果与文献［５］中给出的精确解相比较，两者基本上是一致的。     

两种群竞争模型的奇摄动群

本文应用多重尺度法构造出非线性微分方程组的解的渐近展开式。并用微分不等式的技巧，证明原问题的解的存在性，且给出解的一致有效渐近估计．     

Interval parameter perturbation method for evaluating the bounds on natural frequencies of structures with interval parameters

For structural parameters with uncertainties, interval mathematics can, in the case where the probabilistic distribution density of uncertain variables is unavailable, deal with the influence of uncertainties in structural parameters on the response of structures. In order to evaluate the region containing natural frequencies of structures with interval parameters, the interval parameter perturbation method is presented in this paper. The advantage of the present method is its computational efficiency in evaluating the region containing natural frequencies. A numerical example is used to illustrate the efficiency of the method proposed. The project is supported by National Youth Natural Science Foundation of China and National Outstanding Youth Science Foundation of China.     

On the spectrum of the Heisenberg Hamiltonian

The quantum, antiferromagnetic, spin-1/2 Heisenberg Hamiltonian on thed-dimensional cubic lattice ^d is considered for any dimensiond. First the anisotropic case is considered for small transversal coupling and a convergent expansion is given for a family of eigenprojections which is complete in all finite-volume truncations. Then the general case is considered, for which an upper bound to the ground-state energy is given which is optimal for strong enough anisotropy. This bound is expressed through a functional involving the statistical expectation value at finite temperature of a certain correlation function of an Ising model defined on the lattice ^d itself.     

Relativistic atomic natural orbital type basis sets for the alkaline and alkaline-earth atoms applied to the ground-state potentials for the corresponding dimers

New basis sets of the atomic natural orbital (ANO) type have been developed for the atoms Li–Fr and Be–Ra. The ANOs have been obtained from the average density matrix of the ground states and the lowest excited states of the atom, the positive ion, and the dimer at its equilibirium geometry. Scalar realtivisitc effects are included through the use of a Douglas–Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of the ground-state potentials for the dimers. Computed bond energies are accurate to within 0.05 eV for the alkaline dimers and 0.02 eV for the alkaline-earth dimers (except for Be₂).Acknowledgments.ensp;B.O.R. would like to express his gratitude to Prof. Jacopo Tomasi for all the inspiration that his scientific work has given him through the years and continues to do in particular through the work on solvent effects on molecular properties. This work has been supported by a grant from the Swedish Science Research Council, VR.Contribution to the Jacopo Tomasi Honorary Issue     

Free energy perturbation approach to the critical assessment of selective cyclooxygenase-2 inhibitors

The discovery of selective cyclooxygenase-2 (COX-2) inhibitors represents a major achievement of the efforts over the past few decades to develop therapeutic treatments for inflammation. To gain insights into designing new COX-2-selective inhibitors, we address the energetic and structural basis for the selective inhibition of COX isozymes by means of a combined computational protocol involving docking experiment, force field design for the heme prothetic group, and free energy perturbation (FEP) simulation. We consider both COX-2- and COX-1-selective inhibitors taking the V523I mutant of COX-2 to be a relevant structural model for COX-1 as confirmed by a variety of experimental and theoretical evidences. For all COX-2-selective inhibitors under consideration, we find that free energies of binding become less favorable as the receptor changes from COX-2 to COX-1, due to the weakening and/or loss of hydrogen bond and hydrophobic interactions that stabilize the inhibitors in the COX-2 active site. On the other hand, COX-1-selective oxicam inhibitors gain extra stabilization energy with the change of residue 523 from valine to isoleucine because of the formations of new hydrogen bonds in the enzyme-inhibitor complexes. The utility of the combined computational approach, as a valuable tool for in silico screening of COX-2-selective inhibitors, is further exemplified by identifying the physicochemical origins of the enantiospecific selective inhibition of COX-2 by -substituted indomethacin ethanolamide inhibitors.     

琼脂凝胶中形成铬酸铅周期性沉淀的机理研究

选择硝酸铅和铬酸钾作为相互扩散的反应物以形成铬酸铅在琼脂凝胶中的周期性沉淀．分别在光照和黑暗中对六种不同浓度的硝酸铅溶液进行了实验．根据实验现象对周期性沉淀的形成提出了可能的机理．认为光辐射可使铬酸铅部分电离，从而减慢了胶核成长速率，有利于汇聚成带．