Spatial characterization of the transversal structure of rotationally symmetric pulsed beams

A simple analytical model is proposed to describe the transversal spatial structure of a tridimensional rotationally symmetric pulsed beam. The spatial behaviour of the pulse amplitude is shown to be linked to its (measurable) second- and higher-order intensity moments, namely, beam width, quality parameter and kurtosis. As an illustrative experimental example, this model has been applied to high-quality TEA CO2 laser pulses. This revised version was published online in November 2006 with corrections to the Cover Date.     

Synthesis, characterization and thermal analysis of some new transition metal complexes of a polydentate Schiff base

A new polydentate Schiff base (H3L) was synthesized from the condensation of 2,6-diformyl-4-methylphenol and S-methylhydrazine-carbodithionate. The 1:1 metal complexes were obtained from the interaction of H3L and the metal ions Cr(III), Co(II), Ni(II), Cu(II), Cd(II) and Hg(II). The complexes were characterized by elemental analysis and IR spectroscopy. Detailed studies of the thermal properties of the complexes were investigated by thermogravimetry techniques.     

Differences Between Consecutive Primes

Let p_n be the nth prime. Then this paper is concerned with provingthe following result on the distribution of consecutive primes. The exponent of x in this theorem improves on the work of Heath-Brownwho proved (1) with exponent . Under the Riemann hypothesisone can prove (1) with exponent .The proof of the theorem startswith the Heath-Brown–Linnik identity which leads to aformula giving the number of primes in an interval in termsof coefficients of certain Dirichlet series. I then estimatethe coefficients by using, among other things, the informationwhich can be gained from Montgomery's mean value theorem andHuxley's version of the Hal' asz lemma. Furthermore, by usingfamiliar sieve arguments I am able to discard some of the coefficientsallowing us to gain an improvement over the previous resultof Heath-Brown. 1991 Mathematics Subject Classification: 11N05.     

Quantum superarrivals and information transfer through a time-varying boundary

The time-dependent Schrödinger equation is solved numerically for the case of a Gaussian wave packet incident on a time-varying potential barrier. The time evolving reflection and transmission probabilities of the wave packet are computed for several different time-dependent boundary conditions obtained by reducing or increasing the height of the potential barrier. We show that in the case when the barrier height is reduced to zero, a time interval is found during which the reflection probability is larger (superarrivals) compared to the unperturbed case. We further show that the transmission probability exhibits superarrivals when the barrier is raised from zero to a finite value of its height. Superarrivals could be understood by ascribing the features of a real physical field to the Schrödinger wave function which acts as a carrier through which a disturbance, resulting from the boundary condition being perturbed, prpagates from the barrier to the detectors measuring reflected and transmitted probabilities. The speed of propagation of this effect depends upon the rate of reducing or raising the barrier height, thus suggesting an application for secure information transfer using superarrivals.     

Kinetics and mechanism of oxidation of (aqua-2-aminomethyl-pyridine) chromium(III) by N-bromosuccinimide

Summary The kinetics of oxidation of (aqua-2-aminomethyl-pyridine) Cr^III by N-bromosuccinimide (NBS) in aqueous solution to yield chromium(VI) has been studied spectrophotometrically over the 25–40 °C range. The reaction rate is first order with respect to both [NBS] and [Cr^III], and increases with increasing pH between 7.6 and 8.6. The thermodynamic activation parameters were calculated. The experimental rate law is consistent with a mechanism in which the deprotonated [Cr(L)₂(OH)]²⁺ was considered to be the most reactive form compared to its conjugate acid. It is assumed that electron transfer takes place via an inner-sphere mechanism.