Almost sure exponential stability of numerical solutions for stochastic delay differential equations

Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (SDDEs). The important feature of this technique is that it enables us to study the almost sure exponential stability of numerical solutions of SDDEs directly. This is significantly different from most traditional methods by which the almost sure exponential stability is derived from the moment stability by the Chebyshev inequality and the Borel–Cantelli lemma

Finite Density of States in a Mixed State of d_x^2-y^2+id_xy Superconductor

We have calculated the density of states of quasiparticles in a d_x^2-y^2+id_xy superconductor, and show that in the mixed state the quasiparticle spectrum remains gapless because of the Doppler shift by superflow. It was found that if the d_{xy} order gap $\Delta_1\propto \sqrt{H}$ as suggested by experiments, then thermal conductivity $\kappa \propto \sqrt{H}$ in accord with experimental data at lowest temperatures. This is an appended version of the paper published in Phys. Rev. {\bf B 59}, 6024, (1999). We now also discuss the disorder effects and analyze the H log H crossover at small fields. We argue that H log H regime is present and disorder effect is dominant as the field-induced seconary gap is small at small fields.Comment: This is an appended version of the paper published in Phys. Rev. {\bf B 59}, 6024, (1999). We now also discuss the disorder effects and analyze the H log H crossover at small fields. 3 pages, Latex file with 2 eps figure file

Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations

A discrete stochastic Razumikhin-type theorem is established to investigate whether the Euler--Maruyama (EM) scheme can reproduce the moment exponential stability of exact solutions of stochastic functional differential equations (SFDEs). In addition, the Chebyshev inequality and the Borel-Cantelli lemma are applied to show the almost sure stability of the EM approximate solutions of SFDEs. To show our idea clearly, these results are used to discuss stability of numerical solutions of two classes of special SFDEs, including stochastic delay differential equations (SDDEs) with variable delay and stochastically perturbed equations

Field-Orientation Dependent Heat Capacity Measurements at Low Temperatures with a Vector Magnet System

We describe a heat capacity measurement system for the study of the field-orientation dependence for temperatures down to 50 mK. A "Vector Magnet" combined with a mechanical rotator for the dewar enables the rotation of the magnetic field without mechanical heating in the cryostat by friction. High reproducibility of the field direction, as well as an angular resolution of better than 0.01 degree, is obtained. This system is applicable to other kinds of measurements which require a large sample space or an adiabatic sample environment, and can also be used with multiple refrigerator inserts interchangeably.Comment: 7 pages, 8 figure

The Distinct Roles of Prior IT Use and Habit Strength in Predicting Continued Sporadic Use of IT

This article studies prediction of continued IT use in conditions where individuals use the technology sporadically. Our study augments the unified theory of acceptance and use of technology (UTAUT) model [Venkatesh et al., 2003] with measures of prior IT use frequency and habit strength. We find these two factors provide distinct predictions which explain most of the effects that occur within the model under sporadic use conditions

Predicting Continuing Acceptance of IT in Conditions of Sporadic Use

This paper tests a new predictive model of IT acceptance in conditions where use is characteristically sporadic. The model utilizes cognitive constructs from the well-known technology acceptance model (TAM) [8] in combination with habit and a new construct measuring perceived regularity of use. Initial tests indicate that the model explains several important effects of regularity and predicts substantially more of the variance in continuing acceptance than alternative models

Liquid-like behavior of supercritical fluids

The high frequency dynamics of fluid oxygen have been investigated by Inelastic X-ray Scattering. In spite of the markedly supercritical conditions ($T\approx 2 T_c$, $P>10^2 P_c$), the sound velocity exceeds the hydrodynamic value of about 20%, a feature which is the fingerprint of liquid-like dynamics. The comparison of the present results with literature data obtained in several fluids allow us to identify the extrapolation of the liquid vapor-coexistence line in the ($P/P_c$, $T/T_c$) plane as the relevant edge between liquid- and gas-like dynamics. More interestingly, this extrapolation is very close to the non metal-metal transition in hot dense fluids, at pressure and temperature values as obtained by shock wave experiments. This result points to the existence of a connection between structural modifications and transport properties in dense fluids.Comment: 4 pages, 3 figures, accepted by Phys. Rev. Let

Orbital-dependent metamagnetic response in Sr4Ru3O10

We show that the metamagnetic transition in Sr$_4$Ru$_3$O$_{10}$ bifurcates into two transitions as the field is rotated away from the conducting planes. This two-step process comprises partial or total alignment of moments in ferromagnetic bands followed by an itinerant metamagnetic transition whose critical field increases with rotation. Evidence for itinerant metamagnetism is provided by the Shubnikov-de Hass effect which shows a non-trivial evolution of the geometry of the Fermi surface and an enhancement of the quasiparticles effective-mass across the transition. The metamagnetic response of Sr$_4$Ru$_3$O$_{10}$ is orbital-dependent and involves ferromagnetic and metamagnetic bands.Comment: Physical Review B (in press