Generalized 3G theorem and application to relativistic stable process on non-smooth open sets

Let G(x,y) and GD(x,y) be the Green functions of rotationally invariant symmetric α-stable process in Rd and in an open set D, respectively, where 0<α<2. The inequality GD(x,y)GD(y,z)/GD(x,z)?c(G(x,y)+G(y,z)) is a very useful tool in studying (local) Schrödinger operators. When the above inequality is true with c=c(D)∈(0,∞), then we say that the 3G theorem holds in D. In this paper, we establish a generalized version of 3G theorem when D is a bounded κ-fat open set, which includes a bounded John domain. The 3G we consider is of the form GD(x,y)GD(z,w)/GD(x,w), where y may be different from z. When y=z, we recover the usual 3G. The 3G form GD(x,y)GD(z,w)/GD(x,w) appears in non-local Schrödinger operator theory. Using our generalized 3G theorem, we give a concrete class of functions belonging to the non-local Kato class, introduced by Chen and Song, on κ-fat open sets. As an application, we discuss relativistic α-stable processes (relativistic Hamiltonian when α=1) in κ-fat open sets. We identify the Martin boundary and the minimal Martin boundary with the Euclidean boundary for relativistic α-stable processes in κ-fat open sets. Furthermore, we show that relative Fatou type theorem is true for relativistic stable processes in κ-fat open sets. The main results of this paper hold for a large class of symmetric Markov processes, as are illustrated in the last section of this paper. We also discuss the generalized 3G theorem for a large class of symmetric stable Lévy processes.     

High power single-frequency continuous-wave Nd:YVO4 master-oscillator power amplifier

We report a highly-efficient, high-power, single-frequency Nd:YVO₄ master-oscillator power-amplifier with near-diffraction-limited output beam quality. A diode-pumped Nd:YVO₄ ring laser incorporating a passive method for suppressing axial-mode-hopping was employed as the master-oscillator, and was amplified by a three-stage diode-end-pumped Nd:YVO₄ amplifier, yielding 79 W of output with an extraction efficiency of 29%. The overall power gain was 15 dB for an input power from the master-oscillator of 2.4 W, and the M² parameter was less than 1.5 at the maximum power. The prospects for a further increase of power and brightness via this approach are considered. PACS 42.55.Xi; 42.60.Da; 42.60.Jf     

The effect of surface crystalline layers on asymmetric off-diagonal magnetoimpedance in field-annealed CoFeSiB amorphous ribbons

The off-diagonal magnetoimpedance in field-annealed CoFeSiB amorphous ribbons was measured using a pick-up coil wound around the sample. One side of a ribbon was etched in hydrofluoric acid solution during various times in order to change the thickness of the surface crystalline layer appearing after annealing. The asymmetric two-peak field dependence of the off-diagonal impedance was observed for all samples. The evolution of the off-diagonal magnetoimpedance with the change in the ribbon thickness is analyzed.     

Synthesis and magnetic properties of multilayer Ni/Cu and NiFe/Cu nanowires

Highly ordered composite nanowires with multilayer Ni/Cu and NiFe/Cu have been fabricated by pulsed electrodeposition into nanoporous alumina membrane. The diameter of wires can be easily varied by pore size of alumina, ranging from 30 to 100 nm. The applied potential and the duration of each potential square pulse determine the thickness of the metal layers. The nanowires have been characterized by transmission electron microscopy (TEM), magnetic force microscopy (MFM), and vibrating sample magnetometer (VSM) measurements. The MFM images indicate that every ferromagnetic layer separated by Cu layer was present as single isolated domain-like magnet. This technique has potential use in the measurement and application of magnetic nanodevices.     

Practical stopping criteria for validating safety-critical software by estimating impartial reliability

In this research, we investigate stopping rules for software testing and propose two stopping rules from the aspect of software reliability testing based on the impartial reliability model. The impartial reliability difference (IRD-MP) rule considers the difference between the impartial transition-probability reliabilities estimated for both software developer and consumers at their predetermined prior information levels. The empirical–impartial reliability difference (EIRD-MP) rule suggests stopping a software test when the computed empirical transition reliability is tending to its estimated impartial transition reliability. To insure the high-standard requirement for safety-critical software, both rules take the maximum probability (MP) of untested paths into account.     

Numerical flow visualization of first cycle and cyclic motion of a rigid fling-clapping wing

A flow visualization of the two-dimensional rigid fling-clap motions of the flat-plate wing is performed to get the knowledge of fling-clapping mechanism that might be employed by insects during flight. In this numerical visualization, the time-dependent Navier-Stokes equations are solved for two types of wing motion; ‘fling followed by clap and pause motion’ and ‘cyclic fling-clapping motion’. The result is observed regarding the main flow features such as the sequential development of the two families of separation vortex pairs and their movement. For the ‘fling followed by clap and pause motion’, a strong separation vortex pair of counterrotation develops in the opening between the wings in the fling phase and they then move out from the opening in the following clap phase. For ‘the cyclic fling-clapping motion’, the separation vortex pair developed in the outside space in the clap phase move into the opening in the following fling phase. The separation vortex pair in the opening developed in the fling phase of the cyclic motion is observed to be stronger than those of the ‘fling followed by clap and pause motion’. Regarding the strong fling separation vortex and the weak clap separation vortex above it in the opening, the flow pattern of the fling phase of the cyclic fling and clap motion is different to that of the fling phase of the first cycle. The flow pattern of the third cycle of the cyclic fling-clapping motion is observed to be almost same as that of the second cycle. Therefore, a periodicity of the flow pattern is established after the second cycle.     

A Reverse of bessel’s inequality in 2-inner product spaces and some grüss type related results with applications

A reverse of Bessel’s inequality in 2-inner product spaces and companions of Grüss inequality with applications for determinantal integral inequalities are given.     

Photoemission studies of oxygen adsorbed on a LiAl(1 1 0) alloy surface: Role of Li segregation

We investigated that the effect of the number of segregated Li atoms on the rate of oxidation on a LiAl alloy surface. Oxygen molecules adsorbed on the LiAl alloy react with the surface atoms to form stable oxides. The segregated Li atoms at reconstructed surfaces (c(2×2) and (2×1)) enhance the oxidation rate and form stable LiAlO_x and Li₂O. The degree of enhancement of oxidation by segregated Li atoms varies as a function of O₂ exposure and annealing temperature, where the latter is directly related to the mode of surface reconstruction by Li segregation.     

Allocating unfunded liability in pension valuation under uncertainty

This paper studied the cost allocation for the unfunded liability in a defined benefit pension scheme incorporating the stochastic phenomenon of its returns. In the recent literature represented by Cairns and Parker [Insurance: Mathematics and Economics 21 (1997) 43], Haberman [Insurance: Mathematics and Economics 11 (1992) 179; Insurance: Mathematics and Economics 13 (1993) 45; Insurance: Mathematics and Economics 14 (1994) 219; Insurance: Mathematics and Economics 14 (1997) 127], Owadally and Haberman [North American Actuarial Journal 3 (1999) 105], the fund level is modeled based on the plan dynamics and the returns are generated through several stochastic processes to reflect the current realistic economic perspective to see how the contribution changed as the cost allocation period increased. In this study, we generalize the previous constant value assumption in cost amortization by modeling the returns and valuation rates simultaneously. Taylor series expansion is employed to approximate the unconditional and conditional moments of the plan contribution and fund level. Hence the stability of the plan contribution and the fund size under different allocation periods could be estimated, which provide valuable information adding to the previous works.     

Anchoring Properties of Nematic Liquid Crystals Studied Using the Attenuated Total Reflection Method

By using the attenuated total reflection method associated with the excitation of surface plasmons, the tilt angle of the liquid crystal director and its gradient at the surface are measured in a planar nematic cell as a function of the applied voltage. The surface anchoring anisotropy δπ of the liquid crystal and the surface elastic constant k_s, are found to be δπ = 0.288 erg/cm and k_s, = 9·12 × 10^-11 erg, respectively, when the boundary condition suggested by Barbero et al is used. The theoretical and experimental values obtained with this boundary condition and that of Mada are discussed. The results show that the boundary condition proposed by Barbero et al is in better agreement with the experiment.