On some degenerate quasilinear equations involving variable exponents

In the present paper, we are concerned with some degenerate quasilinear equations involving variable exponents. Using various (variational and nonvariational) techniques, we prove existence, nonexistence and multiplicity results.     

Prediction of a bcc-hcp phase transition for Sn: A first-principles study

The high-pressure structural transformation of elemental Sn is studied using an ab initio density functional theory implementation of the metadynamics method that predicts with sufficient compression, Sn will transform from the bcc structure into an hcp structure. The low-free-energy pathway associated with this phase transition is characterized as the Burgers transition mechanism. The superconducting properties of Sn under pressure are also investigated. Both bcc and hcp structures of Sn exhibit very weak electron-phonon coupling and therefore would not sustain superconductivity at high pressure.     

The Katětov dimension of proximity spaces

An analogue of Kattov's theorem on the equality between the dimension of a Tychonov space and the analytic dimension of its ring of bounded real-valued continuous maps is established for proximity spaces and proximally continuous maps by an internal method of proof. A new kind of filter, called proximally prime filter, arises naturally as a tool in this theory.     

Comprehensive research about the cooperative up-conversion luminescence of the ytterbium-doped oxyfluoride vitroceramics

The cooperative up-conversion blue luminescence of Yb^{3+} ion-doped oxyfluoride vitroceramic material (Yb:FOV) and the influence of co-doped Ho^{3+} ion, when excited by a 960 nm diode-laser, are studied in this paper. A strong blue 479.1 nm up-conversion luminescence of the Yb:FOV material is discovered. It is found that the 479.1 nm luminescence results from the cooperative up-conversion of the coupled states of the Yb^{3+}－Yb^{3+} clusters formed by two adjacent Yb^{3+} ions. The measured cooperative up-conversion luminescence main peak 479.1 nm of this paper is different from the characteristic fluorescence main peak of the Tb^{3+} ion positioned at about 495－504 nm wave-range. Our result coincides with all the published correct papers, whose cooperative up-conversion luminescence main peaks of the direct Yb^{3+}－Yb^{3+} clusters are all positioned at about 476－480 nm wave-range. All of these indicate that the large cooperative up-conversion blue luminescence of the direct Yb^{3+}－Yb^{3+} clusters discovered in this paper is stable. It further proves that the cooperative up-conversion green luminescence may result from the Yb^{3+}-Tb^{3+} cooperative effect. In particular, the original work of this paper improves considerably on the traditional concept by the experimental facts that the blue 479.1 nm cooperative up-conversion luminescence strength of Yb(5):FOV is 230 times greater than that of fluoride glass Yb(3):ZBLAN. This is a great development to meet the practical requirements for blue up-conversion luminescence strength. This result indicates that the large cooperative up-conversion blue luminescence could be achieved excellently by using a suitable material, such as oxyfluoride vitroceramic, which provides a better chance to form better Yb^{3+}－Yb^{3+} clusters and has less relaxation to keep the more efficient up-conversion luminescence. It is also found that impurities seriously reduce the cooperative up-conversion luminescence intensity due to the cross-relaxation from the Yb^{3+}－Yb^{3+} clusters, which means that the cooperative up-conversion blue luminescence could be further improved by pure Yb^{3+} ion-doped materials that have as few impurities as possible to reduce the cross-relaxation. The large cooperative up-conversion blue luminescence of Yb(5):FOV also comes from its higher concentration (5 mol%) of activator Yb^{3+} ion which acts well because the cooperative up-conversion blue luminescence intensity varies linearly against the square of the concentration of Yb^{3+} ions in the range of 0.5－5 mol%. In summary, the great improvement of our work on cooperative up-conversion blue luminescence results from the comprehensive enhancement of the factors of better-coupled chance of the Yb^{3+}－Yb^{3+} clusters, less cross-relaxation, better concentration contribution of Yb^{3+} activator, non-saturation, and better up-conversion luminescence efficiency.     

Structural, electrical and optical properties of ZnS films deposited by close-spaced evaporation

ZnS films have been deposited on glass substrates by close-spaced evaporation (CSE) technique. The films were grown at different temperatures in the range, 200-350 °C. The layers have been characterized with X-ray diffractometer (XRD), atomic force microscope (AFM), energy dispersive analysis of X-rays (EDAX) and optical spectrophotometer to evaluate the quality of the layers for photovoltaic applications. The studies showed that the optimum substrate temperature for the growth of ZnS layers was 300 °C. The films grown at these temperatures exhibited cubic structure with nearly stoichiometric composition. The AFM data revealed that the films had nano-sized grains with a grain size of ∼40 nm. The optical studies exhibited direct allowed transition with an energy band gap of 3.61 eV. The other structural and optical parameters such as lattice stress, dislocation density, refractive index and extinction coefficient were also evaluated. The temperature-dependent conductivity measured in the range, 303-523 K showed a change in the conduction mechanism at 120 °C. The activation energy values evaluated using the temperature dependence of electrical conductivity are 7 and 29 meV at low and high temperature regions, respectively.     

Proof of chiral symmetry breaking in lattice gauge theory

Using the method of infrared bounds and partial-integration formulas, we prove that there is a chiral phase transition in four-dimensional strongly coupled lattice gauge theory with gauge group U(N) and staggered fermions for all N5.     

On constant mean curvature hypersurfaces with finite index

We discuss the non-existence of complete noncompact constant mean curvature hypersurfaces with finite index in a 4- or 5-dimensional manifold. As a consequence, we obtain that a complete noncompact constant mean curvature hypersurface in with finite index must be minimal. Received: 30 May 2005     

On some bilinear problems on weighted Hardy‐Sobolev spaces

In this paper we study the bilinear problem of characterizing the positive Borel measures μ on S ⁿ, satisfying where $H_s^2(w)$ and $H_t^2(w)$ are weighted Hardy‐Sobolev spaces, under adequate conditions on the weight w.     

Pressure Effects on Spectra of Tunable Laser Crystal GSGG:Cr3+ Ⅳ:Pressure-Induced Shifts of R1 Line, R2 Line, and U Band at 300 K

By means of both a theory for pressure-induced shifts (PS) of energy spectra and a theory for shifts of R2 line, and U band of GSGG:Cr3+ at 300 K have been calculated, respectively. The calculated results are in good agreement with all the experimental data. Their physical origins have also been explained. It is found that the mixingdegree of \t22(3T1)e4T2> and \t322E> base-wavefunctions in the wavefunctions of R1 level of GSGG:Cr3+ at 300 K is remarkable under normal pressure, and the mixing-degree rapidly decreases with increasing pressure. The change of the and the PS of R1 line (or R2 line) due to EPI are quite different. It is the combined effect of them that gives rise to the total PS ofR1 line (or R2 line). In the range of about 15 kbar ～ 45 kbar, the mergence and/or order-reversal between t22(3T1)e4T2 levels and t32 2 T1 levels take place, which cause the fluctuation of the rate of PS for t22(3T1)e4T2 (or t3 2 2T1)with pressure. At 300 K, both the temperature-dependent contribution to R1 line (or R2 line or U band) from EPI and the temperature-independent one are important.