THE OSCILLATION OF THE POISSON SEMIGROUP ASSOCIATED TO PARABOLIC HERMITE OPERATOR

Let O（PτL be the oscillation of the Possion semigroup associated with the parabolic Hermite operator = t-△＋｜x｜2. We show that O（PτL） is bounded from LP （Rn＋1） into itself for 1 〈 p 〈 ∞, bounded from L1（Rn＋l） into weak-L1（Rn＋1） and bounded from Lc∞（Rn＋1） into BMO（Rn＋1）. In the case p = ∞ we show that the range of the image of the operator O（PτL） is strictly smaller than the range of a general singular operator.

Effects of Rotor Solidity on the Performance of Impulse Turbine for OWC Wave Energy Converter

Impulse turbine, working as a typical self-rectifying turbine, is recently utilized for the oscillating water column（OWC） wave energy converters, which can rotate in the same direction under the bi-directional air flows. A numerical model established in Fluent is validated by the corresponding experimental results. The flow fields, pressure distribution and dimensionless evaluating coefficients can be calculated and analyzed. Effects of the rotor solidity varying with the change of blade number are investigated and the suitable solidity value is recommended for different flow coefficients.

Oscillation and variation for Riesz transform in setting of Bessel operators on H1 and BMO

Letλ〉0,and let the Bessel operator△λ:=-d2/dx2-2λ/x d/dx defined on R+:=(0,∞).We show that the oscillation andρ-variation operators of the Riesz transform R△λassociated with△λare bounded on BMO(R+,dmλ),whereρ>2 and dmλ=x2λdx.Moreover,we construct a(1,∞)△λ-atom as a counterexample to show that the oscillation andρ-variation operators of R△λare not bounded from to L1(R+,dmλ).Finally,we prove that the oscillation and theρ-variation operators for the smooth truncations associated with Bessel operators R~△λare bounded from H1(R+:dmλ)to L1(R+,dmλ).

Operators Related to Truncated Hilbert Transforms on H1

Abstract In this paper, we give counterexamples to show that variation and oscillation operators related to rough truncations of the Hilbert transform are not bounded from H1 to L1, and prove variation, oscillation and A-jump operators related to smooth truncations are bounded from H1 to L1.

Barut–Girardello Coherent States for Nonlinear Oscillator with Position-Dependent Mass

Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut–Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover,it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.

Performance of a monolithic Tm:YLF micro laser

We report a monolithic Tm：YLF micro laser in this Letter. In order to improve the relaxation oscillation of the laser, both ends of the crystal are coated, making the Tm：YLF crystal itself a resonant cavity. The micro laser is pumped by a 792 nm laser diode operated in the continuous wave（CW） mode. We obtain maximum output powers of 7.78 and 10.4 W at the total incident power of 43.6 W with focus lenses of 37.5 and 40 mm, respectively,corresponding to the slope efficiencies of 25.6% and 40.0% and the optical–optical conversion efficiencies of 17.8%and 23.8%. It is clear that the amplitude of the relaxation oscillation is smaller and the beam quality is better with the focus length of 37.5 mm; however, the laser with the focus length of 40 mm produces a higher output power and a more stable wavelength centering at 1878.44 nm.

Generalized Coherent States for Position-Dependent Effective Mass Systems

A generalized scheme for the construction of coherent states in the context of position-dependent effective mass systems has been presented. This formalism is based on the ladder operators and associated algebra of the system which are obtained using the concepts of supersymmetric quantum mechanics and the property of shape invariance. In order to exemplify the general results and to analyze the properties of the coherent states, several examples have been considered.