A stochastic algorithm using one sample point per iteration and diminishing stepsizes

A stochastic algorithm for finding stationary points of real-valued functions defined on a Euclidean space is analyzed. It is based on the Robbins-Monro stochastic approximation procedure. Gradient evaluations are done by means of Monte Carlo simulations. At each iteratex _i , one sample point is drawn from an underlying probability space, based on which the gradient is approximated. The descent direction is against the approximation of the gradient, and the stepsize is 1/i. It is shown that, under broad conditions, w.p.1 if the sequence of iteratesx ₁,x ₂,...generated by the algorithm is bounded, then all of its accumulation points are stationary.     

瓣形均匀带电面在其直径处的电势分布

从点电荷的电势计算公式出发推导出了瓣形均匀带电面在其直径处的电势分布.进一步讨论了均匀带电半球面在其底面以及均匀带电球面内部和外部的电势分布.     

Observation of the nonlinear effect in relativistic Thomson scattering of electron and laser beams

Thomson scattering of high-power laser and electron beams is a good test of electrodynamics in the high-field region. We demonstrated production of high-intensity X-rays in the head-on collision of a CO₂ laser and 60-MeV electron beams at Brookhaven National Laboratory, Accelerator Test Facility. The energy of an X-ray photon was limited at 6.5 keV in the linear (lowest order) Thomson scattering, but the nonlinear (higher order) process produces higher energy X-rays. We measured the angular distribution of the high-energy X-rays and confirmed that it agrees with theoretical predictions.     

Asymptotic optimality of the bayes estimator in models differentiable in quadratic mean

We study the asymptotic properties of the Bayes estimator in models differentiable in quadratic mean (DQM) in the case of independent and identically distributed observations. The goal is to define weak assumptions on the model under which this estimator is asymptotically efficient, regular, and asymptotically of minimal risk. The results of the paper are applied to models based on a mixture distribution, the Cauchy distribution with location and scale parameter, and the Weibull distribution. Bibliography: 10 titles. Published in Zapiski Nauchnykh Seminarov POMI, Vol. 328, 2005, pp. 114–146.     

Observation of dielectronic satellites in the K-spectrum of argon ions in plasma produced by femtosecond laser pulses

The satellite structure of 1s2p ^1,3 P ₁-1s ²¹ S ₀ lines of the He-like argon ion in plasma produced by a 45-fs laser pulse in a gas-jet cluster target is measured with a high spectral resolution. Radiation transitions 2p → 1s from autoionizing states (AISs) are detected for ions ranging from Li-like to F-like. The spectrum observed is theoretically simulated with the use of the spectroscopic data for the AISs of multicharged ions obtained within the multiconfiguration relativistic Hartree-Fock method. Good agreement with experimental data is obtained when the main population channels of these states are taken into account for typical values of cluster-target plasma parameters.     

Structures and stability of Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>C and Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>N clusters

We report results of the atomic and electronic structures of Al₇C cluster using ab initio molecular dynamics with ultrasoft pseudopotentials and generalized gradient approximation. The lowest energy structure is found to be the one in which carbon atom occupies an interstitial position in Al₇ cluster. The electronic structure shows that the recent observation [Chem. Phys. Lett. 316, 31 (2000)] of magic behavior of Al₇C^- cluster is due to a large highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO) gap which makes Al₇C^- chemically inert. These results have further led us to the finding of a new neutral magic cluster Al₇N which has the same number of valence electrons as in Al₇C^- and a large HOMO-LUMO gap of 1.99 eV. Further, calculations have been carried out on (Al₇N)₂ to study interaction between magic clusters. Received 28 July 2001     

Binding position of azathioprine with bovine serum albumin determined by measuring nuclear magnetic resonance relaxation time.

The interaction between azathioprine (AZ) and bovine serum albumin (BSA) is mainly due to hydrophobic binding according to the dependence of the binding constant on the ionic strength obtained by equilibrium dialysis. The binding constant and partition coefficient of AZ were smaller than those of warfarin, phenylbutazone and ibuprofen. Little variation in the proton chemical shift of AZ was observed whether there was an absence or presence of BSA (7.25 x 10(-5) M). The spin-lattice relaxation time (T1) of AZ decreased in the presence of BSA to 6-22%. The spin-spin relaxation rate (1/T2) of AZ increased 16-24 times for the methyl group and the imidazole ring and 8-13 times for the purine ring in the presence of BSA. The ratio of the spin-spin relaxation rate of the free AZ to the bound AZ ((1/T2)b/(1/T2)f) of the methyl group and the imidazole ring was 2-3 times larger than that of the purine ring. The binding of AZ to BSA was concluded to be mainly at the methyl group on the imidazole ring of AZ.     

Syntactic characterization of closure under connected limits

Summary We give a syntactic characterization of (finitary) theories whose categories of models are closed under the formation of connected limits (respectively the formation of pullbacks and substructures) in the category of all structures. They are also those theories whose consistent extensions by new atomic facts admit in each component an initial structure (respectively an initial term structure), and also thoseT for whichM(T) is locally finitely multi-presentable in a canonical way. We also show that these two properties of theories are nonuniform.     

Molecular dynamics simulation of processing using AFM pin tool

A three-dimensional molecular dynamics (MD) model is utilized to investigate the effect of tool geometry on the deformation process of the workpiece and the nature of deformation process at the atomic-scale. Results show that different states exist between the atomic force microscope (AFM) pin tool and the workpiece surface, i.e. the non-wear state, the ploughing state, the state in which ploughing is dominant and the state in which cutting plays a key role. A relationship between the deformation process of the workpiece and the potential energy variation is presented. The potential energy variation of atoms in different deformed regions in the workpiece such as plastically deformed region, elastically deformed region and the mixed deformation region is different. The features of variations of potential energy are discussed.     

Khillah extract as inhibitor for acid corrosion of SX 316 steel

The inhibitive effect of the extract of khillah (Ammi visnaga) seeds, on the corrosion of SX 316 steel in HCl solution was determined using weight loss measurements as well as potentiostatic technique. It was found that the presence of the extract reduces markedly the corrosion rate of steel in the acid solution. The inhibition efficiency increases as the extract concentration is increased. The inhibitive effect of khillah extract was discussed on the basis of adsorption of its components on the metal surface. Negative values were calculated for the energy of adsorption indicating the spontaneity of the adsorption process. The formation of insoluble complexes as a result of interaction between iron cations and khellin, which present in the extract, was also discussed.