On the riemann zeta-function and the divisor problem II

Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of . If E ^*(t)=E(t)-2πΔ^*(t/2π) with , then we obtain

A half-moment model for radiative transfer in a 3D gray medium and its reduction to a moment model for hot, opaque sources

We present in this paper a new 3D half-moment model for radiative transfer in a gray medium, called the model, which uses maximum entropy closure. This model is a generalization to 3D of the 1D version recently proposed in (J. Comp. Phys. 180 (2002) 584). The direction space Ω is divided into two pieces, Ω⁺ and Ω^-, in a dynamical way by the plane perpendicular to the total radiative flux, and the half moments are defined from these subspaces. The model closure and the integrations of the radiative transfer equation performed on the moving Ω^± spaces are detailed. 1D planar results, which have motivated the extension of the model of (J. Comp. Phys. 180 (2002) 584) to multi-dimensions, are shown. These results are very good. The model is thereafter derived for 3D spherically symmetric geometry, where the correctness of the non-trivial border terms can be checked. Two 3D spherically symmetric problems are numerically solved in order to show the accuracy of the closure and the role of the border terms. Once again, compared to the solution obtained with a ray tracing solver, results are very good. From the 3D half-moment model, a new moment model, called , is derived for the particular case of a 3D hot and opaque source radiating into a cold medium, for applications such as simulations of stellar atmospheres and fires. Two-dimensional numerical results are presented and compared to those obtained solving the RTE and with other moment models. They demonstrate the very good accuracy of the model, its good convergence properties, and better prediction compared to all other existing moment models in its domain of applicability.     

High-power continuous-wave operation of a diode-pumped laser at

The continuous-wave laser properties of an efficient diode-pumped Nd:GdVO₄ crystal operating at formed with a simple plane-concave cavity have been studied. With the incident pump power of 21 W, an output power of 6.9 W was obtained, giving an optical conversion efficiency of 32.8% and a slope efficiency of 35.3%. The laser characterization of two different Nd³⁺-doped concentration of Nd:GdVO₄ crystals were studied.     

A note on the fundamental solution for the Tricomi-type equation in the hyperbolic domain

Barros-Neto and Gelfand (Duke Math. J. 98 (3) (1999) 465; Duke Math. J. 117 (2) (2003) 561) constructed for the Tricomi operator on the plane the fundamental solutions with the supports in the regions related to the geometry of the characteristics of the Tricomi operator. We give for the Tricomi-type operator a fundamental solution relative to an arbitrary point of Rⁿ⁺¹ with the support in the region t?0, where the operator is hyperbolic. Our key observation is that the fundamental solution for the Tricomi-type operator can be written like an integral of the distributions generated by the fundamental solution of the Cauchy problem for the wave equation. The application of that fundamental solution to the L^p-L^q estimate for the forced Tricomi-type equation is given as well.     

Bacteriochlorin <Emphasis Type="Italic">e</Emphasis><Subscript>6</Subscript> as a sensitizer for photodynamic therapy

A simple scheme of modification of the native pigment bacteriochlorophyll a, extracted from the biomass of phototropic bacteria, for the purpose of obtaining a water-soluble derivative — bacteriochlorin e ₆ — which is similar in molecular structure to the effective sensitizer chlorin e ₆ and, in addition, has an intense longwave absorption band in the near-infrared region of the spectrum where biological tissues weakly absorb light — has been developed. The ease of production of bacteriochlorin e ₆ in combination with its physicochemical and spectral properties allow it to be considered as a promising sensitizer for photodynamic therapy.Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 71, No. 6, pp. 745–748, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Migration Effects in Reversible System [Fe(CN)6]3–/4– on a Microelectrode

Migration factors Y are determined for an [Fe(CN)₆]^3–/4– reversible system at a platinum microelectrode 10 m in radius by measuring anodic and cathodic limiting currents at different concentrations of the redox forms in solution, from which Y _a and Y _c are calculated. The obtained results agree with theory. The experimental error for the Y _a/Y _c ratio is smaller than for each factor taken separately.     

Lipase-mediated deracemization of secondary 1-phenyl-substituted propargylic alcohols of different topology

Acetylation of (±)-1-phenylnon-2-yn-1-ol, (±)-1-phenylhept-1-yn-3-ol, and (±)-1-phenylundec-4-yn-3-ol ((±)-5) in the presence of lipase from Candida cylindracea (CCL) proceeds slowly to give products with ee 20%. The acetates of these alcohols are hydrolyzed in the presence of porcine pancreatic lipase (PPL) equally unsatisfactorily. The (⁶-arene)tricarbonylchromium complex of alcohol (±)-5 is acetylated in the presence of CCL up to 22% conversion to give (R)-acetate whose oxidative decomplexation followed by saponification results in alcohol (R)-(–)-5 with ee 95%. The configuration of alcohols (–)-5 and (+)-5 was determined by NMR spectroscopy of their esters with (R)- and (S)-Mosher"s acids.     

Optimized pathway selection in intraresidual triple-resonance experiments

An optimized intraresidual pulse sequence element with better sensitivity and suppression of sequential cross peaks is presented. Concatenation of three magnetization transfer delays allows their independent setting, in accordance with the relaxation properties of the individual spins, without concomitantly prolonging the pulse sequence. Additionally, implementations of the scheme to HNCA, HNCACB, and the TROSY based triple-resonance experiments are proposed. The feasibility of the new element was verified by recording HNCA and HNCACB on the small 8.6 kDa protein ubiquitin. The corresponding HNCA-TROSY experiment was tested on a larger protein, the 30.4 kDa Cel6A from the thermophilic soil bacterium Thermobifida fusca at 800 (1)H MHz.     

Effects of phonon-phonon coupling on low-lying states in neutron-rich Sn isotopes

Starting from an effective Skyrme interaction we present a method to take into account the coupling between one- and two-phonon terms in the wave functions of excited states. The approach is a development of a finite rank separable approximation for the quasiparticle RPA calculations proposed in our previous work. The influence of the phonon-phonon coupling on energies and transition probabilities for the low-lying quadrupole and octupole states in the neutron-rich Sn isotopes is studied.     

Beta-decay of 71Co and 73Co

A decay spectroscopy study of the neutron-rich cobalt isotopes has been performed using fragmentation of a ⁸⁶Kr³⁶⁺ beam and the new LISE2000 spectrometer at GANIL. For ⁷¹Co and ⁷³Co, the -delayed radiation has been observed for the first time, and the half-lives were found to be 79(5) ms and 41(4) ms, respectively. Features of the decay are discussed qualitatively in terms of nuclear models.