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.     

On local optima in multiobjective combinatorial optimization problems

In this article, local optimality in multiobjective combinatorial optimization is used as a baseline for the design and analysis of two iterative improvement algorithms. Both algorithms search in a neighborhood that is defined on a collection of sets of feasible solutions and their acceptance criterion is based on outperformance relations. Proofs of the soundness and completeness of these algorithms are given.     

Branched polymers in a wedge geometry in three dimensions

We investigate the statistical and dimensional properties of uniform star polymers attached by the branching vertex of degreef in a wedge geometry in three dimensions and described by the wedge angles and. We show that the growth constant is equal to ^f , where is the self-avoiding walk limit. Thef and (, ) dependences of the corresponding critical exponent _f (, ) are studied using Monte Carlo techniques. In the casef=1, our results are compared with existing predictions obtained from series expansion and renormalization group methods. We have also estimated the amplitudes for the mean square radius of gyration and the mean square end-to-end branch length. Our results for the ratio of the mean square radius of gyration of anf-star to that of a linear polymer of the same degree of polymerization attached in a similar wedge, and the analogous ratio for the mean square end-to-end branch length, are consistent with these ratios being lattice-independent quantities.     

Fe/Zn双金属氰化物催化剂催化环氧丙烷聚合的活性结构研究

以氯化锌、铁氰化钾（含有整合剂）的水溶液为原料，合成了铁锌双金属氰化物（DMC）催化剂。为获得高活性的DMC催化剂，需将叔丁醇 、多元醇螯合剂螯合至其结构中，用XRD、XPS等分析手段，对铁锌DMC催化剂的结构与活性进行分析表征。实验发现，DMC催化剂的晶体结构与螯合剂密切相关，螯合剂能显著降低DMC催化剂的结晶程度，从而提高DMC催化剂的活性。同时，氯化锌过量也有利于DMC催化剂活性的提高。并表征了相关DMC催化剂的活性中心。     

Static atomic displacements of Sn in disordered NiAs/Ni2In type HT-Ni1+δSn

The crystal structures of the intermediate solid solution HT (high temperature) Ni_1+δSn with δ=0.28, 0.52 and 0.61 (refined Ni contents) have been analyzed in detail by X-ray diffraction on single crystals. The previously reported basic atomic arrangement, i.e., a NiAs/Ni₂In structure type (P6₃/mmc, Ni(1) on 2a, 0 0 0, Ni(2) with an occupancy δ on 2d, and Sn on 2c, ), is confirmed. However, strong anisotropic atomic displacements occur for Sn within the a-b plane of the hexagonal unit cell, which require a Gram-Charlier expansion of the probability density function of Sn in order to obtain a good fit to the diffraction data. Direction, magnitude and the concentration dependence of the displacements can be interpreted in terms of the geometrical requirements of the different local atomic configurations in the planes z=±1/4, so that the displacements can be identified as static ones.     

Local polarizabilities in molecules,based on ab initio Hartree-Fock calculations

A method to separate the total molecular polarizability, calculated in the uncoupled Hartree-Fock approximations, into local contributions is proposed. The method is tested for H₂, H₂O, H₂CO and C₆H₆ and the results are discussed. It is found that the ratio of the polarizability contributions for two atoms in a molecule almost only depends on the type of atoms and is almost independant of molecule.     

Weighted local polynomial estimations of a non-parametric function with censoring indicators missing at random and their applications

In this paper, we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random, and establish the asymptotic normality of these estimators. As their applications, we derive the weighted local linear calibration estimators and imputation estimations of the conditional distribution function, the conditional density function and the conditional quantile function, and investigate the asymptotic normality of these estimators. Finally, the simulation studies are conducted to illustrate the finite sample performance of the estimators.     

Realization of fixed point sets

Letf:XX be a selfmap of a compact connected polyhedron, andA a nonempty closed subset ofX. In this paper, we shall deal with the question whether or not there is a mapg:XX homotopic tof such that the fixed point set Fixg ofg equalsA. We introduce a necessary condition for the existence of such a mapg. It is shown that this condition is easy to check, and hence some sufficient conditions are obtained.Partially supported by the Natural Science Foundation of Liaoning University.     

Multi-element Saha–Boltzmann and Boltzmann plots in laser-induced plasmas

A multi-element Saha–Boltzmann plot method is proposed for the determination of the temperature and the relative number density in laser-induced plasmas, assuming local thermodynamic equilibrium and stoichiometry conservation. The method has been applied to the characterization of a plasma generated with a Cu–Fe–Ni–Mn alloy, using a Nd:YAG laser in air at atmospheric pressure. Spectra of the local emissivity have been obtained by spatial deconvolution of the intensity spectra, obtained with spatial resolution. Saha–Boltzmann plots obtained from the emissivities of 58 spectral lines of Fe I, Fe II, Ni I, Ni II, Mn I and Mn II have been fitted to linear behavior with high correlation, which shows the validity of the equation proposed. Radial distributions of the temperature and number densities of neutral atoms and ions have been determined. The results obtained reinforce the initial considerations of local thermodynamic equilibrium and conservation of stoichiometry. The proposed equation can also be applied to only one ionization species (multi-element Boltzmann plot). Spatially-integrated measurements of the plasma emission have also been performed to show that, in this case, the application of the method to the line intensities provides the two different apparent temperatures for neutral atoms and ions.