On a Delay Reaction-Diffusion Difference Equation of Neutral Type

In this paper, we first consider a delay difference equation of neutral type of the form: Δ(y _n + py _n−k + q _n y _n−l = 0 for n∈ℤ⁺(0) (1*) and give a different condition from that of Yu and Wang (Funkcial Ekvac, 1994, 37(2): 241–248) to guarantee that every non-oscillatory solution of (1*) with p = 1 tends to zero as n→∞. Moreover, we consider a delay reaction-diffusion difference equation of neutral type of the form: Δ₁(u _n,m + pu _n−k,m ) + q _n,m u _n−l,m = a ²Δ² ₂ u _{n +1, m−1} for (n,m) ∈ℤ⁺ (0) ×Ω, (2*) study various cases of p in the neutral term and obtain that if p≥−1 then every non-oscillatory solution of (2*) tends uniformly in m∈Ω to zero as n→∞; if p = −1 then every solution of (2*) oscillates and if p < −1 then every non-oscillatory solution of (2*) goes uniformly in m∈Ω to infinity or minus infinity as n→∞ under some hypotheses. Received July 14, 1999, Revised August 10, 2000, Accepted September 30, 2000     

Thermal Analysis of the Ferromagnetic Materials in the Region of Curie Temperature by Temperature-Modulated DTA

Thermal analysis has been employed to measure changes of the heat capacity of ferromagnetic materials such as alloys in the region of the Curie temperature. Thermal response for these materials is usually small in this region. The necessary increase in sensitivity was achieved by applying temperature modulation. Results obtained by this technique including temperature-modulated differential thermal analysis simultaneously with A.C. thermomagnetometry are presented.     

Accelerated Poisson-Boltzmann calculations for static and dynamic systems

We report here an efficient implementation of the finite difference Poisson-Boltzmann solvent model based on the Modified Incomplete Cholsky Conjugate Gradient algorithm, which gives rather impressive performance for both static and dynamic systems. This is achieved by implementing the algorithm with Eisenstat's two optimizations, utilizing the electrostatic update in simulations, and applying prudent approximations, including: relaxing the convergence criterion, not updating Poisson-Boltzmann-related forces every step, and using electrostatic focusing. It is also possible to markedly accelerate the supporting routines that are used to set up the calculations and to obtain energies and forces. The resulting finite difference Poisson-Boltzmann method delivers efficiency comparable to the distance-dependent dielectric model for a system tested, HIV Protease, making it a strong candidate for solution-phase molecular dynamics simulations. Further, the finite difference method includes all intrasolute electrostatic interactions, whereas the distance dependent dielectric calculations use a 15-A cutoff. The speed of our numerical finite difference method is comparable to that of the pair-wise Generalized Born approximation to the Poisson-Boltzmann method.     

Global Attractivity of the Equilibrium of a Nonlinear Difference Equation

The authors consider the nonlinear difference equation x_n+1=x_n+x_n-kf(x_n-k),n=0,1,(0.1) where (0,1), k 0,1, and f C¹[[0,), [0,)] with f(x) < 0.They give sufficient conditions for the unique positive equilibrium of (0.1) to be a global attractor of all positive solutions. The results here are somewhat easier to apply than those of other authors. An application to a model of blood cell production is given.     

Temperature Dependence of the Mössbauer Effect on Prussian Blue Nanowires

Highly ordered Prussian blue nanowires with diameter of about 50 nm and length up to 4 m have been fabricated by an electrodepositing technology with two-step anodizing anodic aluminum oxide films. The Mössbauer spectra taken between 15 and 300 K indicate that the hyperfine parameters decrease as the temperature increases. The temperature dependence of the quadrupole splitting, the isomer shift and the spectra area are discussed. A decrease of Debye temperature for Prussian blue nanowires was found with respect to that of Prussian blue bulk.     

Traces of Intertwiners for Quantum Groups and Difference Equations

In this Letter we study twisted traces of products of intertwining operators for quantum affine algebras. They are interesting special functions, depending on two weights ,, three scalar parameters q,,k, and spectral parameters z ₁,...,z _N , which may be regarded as q-analogs of conformal blocks of the Wess–Zumino–Witten model on an elliptic curve. It is expected that in the rank 1 case they essentially coincide with the elliptic hypergeometric functions defined by Felder and Varchenko. Our main result is that after a suitable renormalization the traces satisfy four systems of difference equations – the Macdonald–Ruijsenaars equation, the q-Knizhnik–Zamolodchikov–Bernard equation, and their dual versions. We also show that in the case when the twisting automorphism is trivial, the trace functions are symmetric under the permutation , k . Thus, our results generalize those of Etingof and Schiffmann, dealing with the case q=1, and Etingof, Varchenko, and Schiffmann, dealing with the finite-dimensional case.     

Far infrared sub-nanosecond pulse generation in GaP with a time-synchronized mode-locked double-frequency Nd: Glass laser system

Light pulses of 149 m wavelength and 700 ps duration are generated by non-collinear phase-matched difference frequency mixing of laser pulses at 1053.5 and 1061 nm in a (110) cut GaP crystal. The pump laser pulses are generated in a time-synchronized mode-locked double-frequency Nd:glass laser system consisting of a silicate glass branch and a phosphate glass branch. A photon conversion efficiency of 4 × 10^–6 is achieved. The non-linear susceptibility constant of GaP is determined to be d ₁₄ = (10 ± 1) pm V^–1.     

Quiesent Crystallization Kinetics of Nucleated Metallocene and ZN Isotactic Polypropylenes

Crystallization kinetics and thermodynamic properties of nucleated isotactic polypropylene (PP) are analyzed using Hoffman—Lauritzen crystallization theory to determine the mechanistic effects of the nucleators. Calorimetric data provides quantitative comparisons between nucleating efficiences of the (Millad) and (NJSTAR) nucleator in Metallocene (M) and Ziegler—Natta (ZN) PP. The two types of PP without nucleators showed similar crystallization behavior though the T°_m for ZN-iPP was about 10°C higher than M-iPP. Both nucleators show significant improvement in crystallization rate in both types of PP. In addition, Millad outperforms NJSTAR. The magnitude of the kinetic response is,however, different and both the nucleators appear to function better in ZN than in Metallocene PP. nucleated PP shows predominantly the form. The amount of the form is thermal history dependent and changes with supercooling (T=T°_m–T_c). Similar equilibrium melting temperature (T°_m) in the nucleated and control PPs indicates the lack of any thermodynamic effect of the nucleator. All nucleated PPs show a much lower secondary nucleation rate constant, K_g.This revised version was published online in November 2005 with corrections to the Cover Date.     

Electron irradiation effects in doped high temperature superconductors YBa2Cu3? x M x O y (M = Fe, Ni; x=0; x =0:01)

The influence of irradiation by electrons with an energy of 8 MeV, at dose intervals between 10¹³ and 2×10¹⁸el/cm², on the properties of impurity doped, high-temperature superconductor YBa₂Cu_3−x M _x O _y (M = Fe, Ni; x=0; x=0:01) ceramics has been studied. It has been established that, as the irradiation dose is increased, the onset temperature of the transition to the superconducting state (T _c ^on ), and the intergranular weak link coupling temperature between granules (T _m ^J ), exhibit an oscillation around their initial values of approximately about 1–1.5 K. This oscillation indicates that the process of radiation defect formation in HTSC occurs in multiple stages. It was also found that the critical current (J _c )decreases with an increase of the irradiation dose, and exhibits a local minimum at a dose of 8×10¹⁶el/cm²coinciding with minima for T _c ^on and T _m ^J at this dose. It was found that the introduction of Fe atoms to the ceramic decreases T _m ^J , while introducing Ni atoms decreases both T _c ^on and T _m ^J ; it is suggested that this is a result of Ni substitution of Cu both in Cu2 plane sites and Cu1 chain sites. The introduction of Ni causes a large change in the intergranular critical current density, J _c . A critical irradiation dose is obtained (2×10¹⁸)after which all HTSC parameters strongly decrease, i. e. the superconductivity of HTSC is destroyed.