A non-singular equation for the three-body scattering problem

This paper derives a non-singular integral equation for the three-body problem. Starting from the three-body equations obtained by Karlsson and Zeiger we introduce a set of algebraic transformations that remove all the Green function pole singularities. For scattering energies on the real axis we find a singularity-free momentum-space integral equation. This equation requires only a finite range of momentum values for its solution. In the case of well-behaved two-body interactions, such as the superposition of Yukawa interactions, we prove that the kernels of this equation have a finite Hilbert-Schmidt norm. This same norm provides a general criteria for establishing when the impulse approximation is accurate.     

Two-color cross-correlation of fs-laser pulses by two-photon induced photoconductivity for near and far field optical measurements

Two-color two-photon induced photoconductivity in a GaAsP diffusion type photodiode is demonstrated by measuring femtosecond cross-correlation functions for widely separated wavelength pairs of 775 and 1300 nm. Results are obtained for a range of tunable wavelengths and average powers of the incident lasers by measuring the two-photon induced photocurrent as a function of the optical delay between the pulses. The temporal autocorrelation of femtosecond laser pulses in the near-field of a small diameter aluminum coated optical fiber tip is also obtained with the same photodiode method for single colors.     

Electric dipole moment for supersymmetric monopoles

The electric dipole moment for the monopoles that can be present in N = 2 and N = 4 supersymmetric SU(2) gauge theories, spontaneously broken by imposing a non-zero expectation value of a scalar field at infinity, is determined by considering the response to a weak external electric field. The magnetic g factor g_M = 2 which is in accord with the duality conjecture of Montonen and Olive.     

Synoptic airflow and UK daily precipitation extremes

We develop a vector generalised linear model to describe the influence of the atmospheric circulation on extreme daily precipitation across the UK. The atmospheric circulation is represented by three covariates, namely synoptic scale airflow strength, direction and vorticity; the extremes are represented by the monthly maxima of daily precipitation, modelled by the generalised extreme value distribution (GEV). The model parameters for data from 689 rain gauges across the UK are estimated using a maximum likelihood estimator. Within the framework of vector generalised linear models, various plausible models exist to describe the influence of the individual covariates, possible nonlinearities in the covariates and seasonality. We selected the final model based on the Akaike information criterion (AIC), and evaluated the predictive power of individual covariates by means of quantile verification scores and leave-one-out cross validation. The final model conditions the location and scale parameter of the GEV on all three covariates; the shape parameter is modelled as a constant. The relationships between strength and vorticity on the one hand, and the GEV location and scale parameters on the other hand are modelled as natural cubic splines with two degrees of freedom. The influence of direction is parameterised as a sine with amplitude and phase. The final model has a common parameterisation for the whole year. Seasonality is partly captured by the covariates themselves, but mostly by an additional annual cycle that is parameterised as a phase-shifted sine and accounts for physical influences that we have not attempted to explicitly model, such as humidity.     

Generalized cartan type k lie algebras in characteristic 0

The Lie algebra of Cartan type K which occurs as a subalgebra of the Lie algebra of derivations of the polynomial algebra F[x₀, x₁,…, x_n,x_n?1,…,x_?n], where F is a field of characteristic 0, was generalized by the first author to a class which included a subalgebra of the derivations of the Laurent polynomials F[x₀,x₁,…, x_n,x_?1,…,x_?n,X₀ ^?1x₁ ^-1,…,x_n ^?1,…,x_?1 ^?1…,x_?n ^?1]A further generalization of these algebras is the main topic of this paper. We show when these algebras are simple, determine all possible     

A simple method for extracting both active oily and water soluble extract (WSE) from Nigella sativa (L.) seeds using a single solvent system

The current study provides a way of extraction for both active NSO and WSE from Nigella sativa seeds using 98% methanol. About 1?kg of ground seeds was macerated by 1:2.5 w/v (g/mL) for 72?hours. After rotary evaporation and 7 days of continuous drying and chilling at 50 and 4?°C, NSO and WSE were obtained at the same instant. Solubility tests of 24 solvents and 11 thin layer chromatographic analyses while 2, 2-diphenyl-1-picrylhydrazyl free radical scavenging assay of NSO (73.66) , WSE (33.32) and NSO?+?WSE (78.22) against ascorbic acid (IC50?=?4.28?mg/mL) was performed. WSE was found to be highly soluble in water and 5% NaOH exhibiting the same Rf value of 0.95 for EtOH:DMSO (9:1) against the honey. WSE has revealed more than twofold higher anti-oxidant activity than others. Formulation of WSE with Tualang honey may provide better targeted hydrophilic drug delivery systems.     

Direct detection of polyynes formation from the reaction of ethynyl radical (C2H) with propyne (CH3-C[triple bond]CH) and allene (CH2=C=CH2)

The reactions of the ethynyl radical (C(2)H) with propyne and allene are studied at room temperature using an apparatus that combines the tunability of the vacuum ultraviolet radiation of the Advanced Light Source at Lawrence Berkeley National Laboratory with time-resolved mass spectrometry. The C(2)H radical is prepared by 193-nm photolysis of CF(3)CCH and the mass spectrum of the reacting mixture is monitored in time using synchrotron-photoionization with a dual-sector mass spectrometer. Analysis using photoionization efficiency curves allows the isomer-specific detection of individual polyynes of chemical formula C(5)H(4) produced by both reactions. The product branching ratios are estimated for each isomer. The reaction of propyne with ethynyl gives 50-70% diacetylene (H-C[triple bond]C-C[triple bond]C-H) and 50-30% C(5)H(4), with a C(5)H(4)-isomer distribution of 15-20% ethynylallene (CH(2)=C=CH-C[triple bond]CH) and 85-80% methyldiacetylene (CH(3)-C[triple bond]C-C[triple bond]CH). The reaction of allene with ethynyl gives 35-45% ethynylallene, 20-25% methyldiacetylene and 45-30% 1,4-pentadiyne (HC[triple bond]C-CH(2)-C[triple bond]CH). Diacetylene is most likely not produced by this reaction; an upper limit of 30% on the branching fraction to diacetylene can be derived from the present experiment. The mechanisms of polyynes formation by these reactions as well as the implications for Titan's atmospheric chemistry are discussed.