Zeldovich's regularization method in the theory of quasistationary states

The complex quasienergy, including the level width Γ, is calculated for a loosely bound atomic state in an intense monochromatic laser field of circular polarization. The method proposed by Zeldovich for regularizing divergent integrals that involve the Gamow wave function is employed in this calculation. The convergence of the method is demonstrated, and the conditions of its applicability are indicated.     

Structure of carbon nanoparticles synthesized by adiabatic compression of acetylene and their application in supercapacitors

The work reports the study of the structure of carbon nanoparticles prepared by the pyrolysis of heliumdiluted acetylene under adiabatic compression in a piston reactor. At a pushing gas pressure of 0.5 MPa, 0.7 MPa, and 0.9 MPa the reaction gas was heated to temperatures of 400 °C, 600 °C, and 750 °C. By transmission electron microscopy it is found that carbon nanoparticles have a spherical shape and their size varies from 20 nm to 60 nm. The structural features of carbon nanoparticles are determined from the X-ray photoelectron spectroscopy data and the analysis of the near-edge X-ray absorption fine structure spectroscopy. Carbon nanoparticles prepared at a pushing gas pressure of 0.5 MPa have an amorphous structure and consist of hydrogenated carbon with impurities of polycyclic aromatic fragments. At a stronger compression ratio, carbon nanoparticles with a layered structure consisting mainly of sp² hybridized carbon atoms are formed. The capacitance behavior and electrochemical impedance of carbon nanoparticle-based supercapacitors are compared.     

A test for self-exciting clustering mechanism

In this paper, we propose a test to distinguish between data with cluster pattern where the variables are dependent in a self-exciting fashion versus independently identically distributed random variables. We also developed asymptotic distribution of the test statistic with closed-form covariance structure. Comparisons with scan statistics are discussed in the context of simulated earthquake data. Applications to two data sets are discussed.     

Relativistic theory of tunnel and multiphoton ionization of atoms in a strong laser field

Relativistic generalization is developed for the semiclassical theory of tunnel and multiphoton ionization of atoms and ions in the field of an intense electromagnetic wave (Keldysh theory). The cases of linear, circular, and elliptic polarizations of radiation are considered. For arbitrary values of the adiabaticity parameter γ, the exponential factor in the ionization rate for a relativistic bound state is calculated. For low-frequency laser radiation , an asymptotically exact formula for the tunnel ionization rate for the atomic s level is obtained including the Coulomb, spin, and adiabatic corrections and the preexponential factor. The ionization rate for the ground level of a hydrogen-like atom (ion) with Z ? 100 is calculated as a function of the laser radiation intensity. The range of applicability is determined for nonrelativistic ionization theory. The imaginary time method is used in the calculations.     

A martingale approach to scan statistics

Scan statistics are commonly used in biology, medicine, engineering and other fields where interest is in the probability of observing clusters of events in a window at an unknown location. Due to the dependent nature of the number of events in a large number of overlapping window locations, even approximate solutions for the simplest scan statistics may require elaborate calculations. We propose a new martingale method which allows one to approximate the distribution for a wide variety of scan statistics, including some for which analytical results are computationally infeasible.     

Generalized size-dependent structural states of materials with an ultrafine structure

The necessity of introduction of boundary and surface (crystalline, quasicrystalline, and amorphous) structural states at different scale levels is justified for micro-and nanocrystalline materials. The bulk and boundary size-dependent structural states of solids with an ultrafine structure are considered in a unified approach. The generalized structural states of nanostructured and nanomicrostructured materials are determined and systematized.     

Comparison of the mass spectra of the volatile products liberated from polymers in the course of mechanical destruction and thermal degradation

The compositions of the volatile products liberated from polymers in the course of mechanical destruction and thermal degradation have been studied and compared by means of mass spectrometry. For those polymers in which in both cases breakdown of the macromolecules begins with the basic chain, the volatile products are the same. For polymers in which breakdown of the molecules in thermal degradation begins with the stripping of side groups, the volatile products of thermal and mechanical degradation are different. This confirms and extends the ideas of the kinetic theory of fracture concerning the relationship between the processes of mechanical fracture and thermal degradation of polymers.Mekhanika Polimerov, Vol. 3, No. 1, pp. 80–88, 1967     

Mathematical equations for potentiometric analysis by the multiple addition method

Equations are proposed to process the results of potentiometric analysis by the methods of two and multiple standard additions in the case when the slope of the electrode response is known. In the analysis of 1 × 10^?3 to 1 × 10^?5 M bromide ion model solutions, RSD is within 7–8% when the method of two additions is used and within 3–7% when the method of multiple additions is used. The error of determinations is at most 5%.     

Silver nanocomposites based on a copolymer of 1-vinyl-1,2,4-triazole with crotonaldehyde

New polymer silver nanocomposites were synthesized using a copolymer of 1-vinyl-1,2,4-triazole with crotonaldehyde as the silver ion reducing agent and stabilizer of metal nanoparticles. The formation of the metallic phase in the nanoscale state was confirmed by UV spectroscopy and X-ray phase analysis. According to the transmission electron microscopy, nanoparticles have sizes of 2—14 nm and are uniformly distributed in the volume of the polymeric matrix.     

Evidence of the hydroxyl radical formation upon the photolysis of an iron-rich clay in aqueous solutions

With the use of laser flash photolysis, the formation of hydroxyl radicals upon the photolysis of an iron-rich clay (montmorillonite KSF) was demonstrated. The ^•OH radical was shown to be formed by the photolysis of the Fe(OH)_aq ²⁺ complex that escaped from the clay into the solution bulk.