Über die asymptotische Verteilungsfunktion rekurrenter Winkelvariablen

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Über die automorphen Transformationen beschränkter nicht-singulärer hermitescher Formen

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Compact eye-safe laser sources based on OPOs with KTP or PPKTP crystals

We report on compact eye-safe nanosecond laser sources emitting in the 1.5 μm wavelength range based on non-critically phase-matched parametric interaction in optical parametric oscillators (OPOs) with KTP and periodically poled KTP (PPKTP) crystals, pumped by the fundamental frequency of Nd:YAG lasers. As much as 250 μJ signal pulse energy at 1.5 μm wavelength, 6.5 ns FWHM pulse-width, has been obtained in a PPKTP-OPO, extracavity pumped by a Nd:YAG microlaser oscillator–amplifier at 650 μJ pump pulse energy, 8 ns pulse-width. A single signal pulse of 2.7-mJ output energy at 1.57 μm wavelength, less than 5 ns pulse-width, was generated in a KTP-OPO, intracavity pumped by a passively Q-switched Nd:YAG laser.     

The influence of finite aperture and frequency response of ultrasonic hydrophone probes on the determination of acoustic output

The influence of finite aperture and frequency response of piezoelectric ultrasonic hydrophone probes on the Thermal and Mechanical Indices was investigated using a comprehensive acoustic wave propagation model. The experimental verification of the model was obtained using a commercially available, 8 MHz, dynamically focused linear array and a single element, 5 MHz, focused rectangular source. The pressure-time waveforms were recorded using piezoelectric polymer hydrophone probes of different active element diameters and bandwidths. The nominal diameters of the probes ranged from 50 to 500 microm and their usable bandwidths varied between 55 and 100 MHz. The Pulse Intensity Integral (PII), used to calculate the Thermal Index (TI), was found to increase with increasing bandwidth and decreasing effective aperture of the probes. The Mechanical Index (MI), another safety indicator, was also affected, but to a lesser extent. The corrections needed were predicted using the model and successfully reduced the discrepancy as large as 30% in the determination of PII. The results of this work indicate that by accounting for hydrophones' finite aperture and correcting the value of PII, all intensities derived from the PII can be corrected for spatial averaging error. The results also point out that a caution should be exercised when comparing acoustic output data. In particular, hydrophone's frequency characteristics of the effective diameter and sensitivity are needed to correctly determine the MI, TI, and the total acoustic output power produced by an imaging transducer.     

Specific heat of a fermionic atomic cloud in the unitary regime

In the unitary regime, when the scattering amplitude greatly exceeds in magnitude the average interparticle separation, and below the critical temperature thermal properties of an atomic fermionic cloud are governed by the collective modes, specifically the Bogoliubov-Anderson sound modes. The specific heat of an atomic cloud in an elongated trap, in particular, has a rather complex temperature dependence, which changes from an exponential behavior at very low temperatures (T < h omega(parallel)), to proportional T for h omega(parallel) < T < h omega(perpendicular) and then continuously to proportional T4 at temperatures just below the critical temperature, when the surface modes play a dominant role. Only the low (h omega(parallel) < T < h omega(perpendicular)) and high (h omega(perpendicular) < T < T(c)) temperature power laws are well defined. For the intermediate temperatures one can introduce at most a gradually increasing with temperature exponent.     

Finite generation properties for fuchsian group von Neumann algebras tensor

We prove that the algebra , a free group with finitely many generators, contains a subnormal operator such that the linear span of the set is weakly dense in . This is the analogue for the factor , finite, of a well known fact about the unilateral shift on a Hilbert space : the linear span of all the monomials is weakly dense in .

We also show that for a suitable space of square summable analytic functions, if is the projection from the Hilbert space of all square summable functions onto and is the unbounded operator of multiplication by on , then the (unbounded) operator is nonzero (with nonzero domain).

     

On the process of successive approximation in initial value problems

Summary The convergence of the process of the successive approximations for the initial value problem dw/dz=f(z, w), w(0)=0, is studied in the complex field. The resulting z-domains of convergence are more favorable than those supplied by the classical approach. The improvement is made possible by the use of a ? principle of subordination ?, which allows a ? comparison test ? relative to the real field.