Fixed Point Theorems on Product Topological Spaces and Applications

A new collectively fixed point theorem for a family of set-valued mappings defined on product spaces of non-compact topological spaces without linear structure is proved and some special cases are also discussed. As applications, some non-empty intersection theorems of sets with convex sections and equilibrium existence theorem of abstract economies are obtained under much weaker assumptions. Our results includes a number of known results as many special cases.     

Recognizing the P4-structure of a tree

The P₄-structure of a graphG =(V,E) is a hypergraphH = (V,F) such that, for every hyperedgeA inF, the cardinality ofA is four and the subgraph of G induced byA is a path. It is proved in this paper that the P₄-structure of a tree can be recognized in polynomial time.     

Low-threshold, high-efficiency, high-repetition-rate optical parametric generator based on periodically poled LiNbO3

We report a high-repetition-rate optical parametric generator (OPG) with a periodically poled lithium niobate (PPLN) crystal pumped by an acousto-optically Q-switched CW-diode-end-pumped Nd:YVO_4 laser. For the maximum 1064nm pump power of 970mW, the maximum conversion efficiency is 32.9% under the conditions of 250℃, 1064nm pulse repetition rate of 22.6kHz and pulse width of 12ns, and the PPLN OPG threshold in the collinear case is less than 23.7μJ. The output power increases with the increase of the crystal temperature. The 1485－1553nm signal wave and 3383－3754nm idler wave are obtained by changing the temperature and the angle of the PPLN crystal.     

Decentered twisted Gaussian Schell-model beams and their propagation through a misaligned first-order optical system

The propagation properties of decentered twisted Gaussian Schell-model (DTGSM) beams passing through a misaligned first-order optical system are studied. The explicit expressions for the cross-spectral density function and Wigner distribution function of the output beam are derived, which retain their form unchanged. It is shown that the DTGSM beams preserve their closed property. The second-order moments matrix and the Wigner distribution function evolve with the usual laws, whereas the first-order moments matrix varies, as if a ray passes through such system. The propagation of DTGSM beams through an aligned first-order optical system is treated as the limiting case that corresponds to the vanishing misalignment parameters.     

Investigation of charge effects on poling and stability for corona-poled polymer films

The optimal corona-poling temperature of polymer films was accurately determined by measuring the temperature dependence of the in situ second-harmonic (SH) intensity profile under the applied poling electric field. The in situ SH intensity profile was first measured by probing both the surface voltages and the poling currents induced by surface/space charges for the corona-poled polymer films. Moreover, charge effects on the stability of the chromophore orientation were first studied by using the thermally stimulated discharge-current technique. PACS 72.20.Jv; 42.65.Ky; 73.61.Ph; 81.40.Tv     

MULTIPLICATION OF WEAK FUNCTIONS

This paper is a contionuation of [1] and is concerned with multiplication of weak functions. Here the weak functions are treated as generalized expansions in Hermite functions in [2].     

Imprinting by hot embossing in polymer substrates using a template of silica glass surface-structured by the ablation of LIBWE method

Laser-induced backside wet etching (LIBWE) of silica glass plates was performed to fabricate an imprinting template for hot embossing in polymer substrates such as polystyrene and silicone resin. Well-defined inverse surface-micropatterns of gratings and grid arrays on the substrates were produced by the hot embossing using a surface-structured silica glass as the template. These results indicate that the LIBWE method allows us to generate robust glass molding tools that exhibit the inverse shapes of the intended microstructures. PACS 52.38.Mf; 68.47.Mn; 81.05.Kf; 81.05.Lg; 83.50.Uv     

X-ray absorption spectra of plasmas

In this paper we present a theoretical method to calculate the absorption spectra of hot dense plasmas. Based on our fully relativistic treatment incorporated with the quantum defect theory to handle the huge number of transition arrays from many configurations with high principal quantum number, we can calculate the absorption spectra for any element or multi-element plasmas with little computational efforts. We calculate the absorption spectra of C10H1605 plasmas, which are in good agreement with the experimental spectra. We can then provide diagnostic analysis for plasmas in relevant inertial confinement fusion (lCF) experiments; namely not only to determine plasmas' temperatures and densities, but also to provide the population densities of various ionic stages. Our theoretical method verified by "benchmark experiments" will be a basic tool to provide "precise" opacity data for the ICF research.``