Spatial solitons in Kerr and Kerr-like media

This is a review paper of basic knowledge and recent advances in the area of spatial solitons in Kerr and Kerr-like media. We consider spatial bright and dark solitons, solitons in waveguide geometries, optical bullets, vortex solitons and, briefly, dissipative cases. In our treatment, we use a Hamiltonian approach when considering stability issues.     

Optical detection of NO3 and NO2 in “pure” HNO3 vapor,the liquid-phase decomposition of HNO3

Flowing and static gas-phase samples of HNO₃ in O₂ and N₂ were analyzed by long-path ultraviolet/visible (UV/VIS) spectroscopy to reveal the presence of both NO₂ and NO₃, the concentrations of which were calculated using differential absorption cross sections. NO₂ is produced predominantly by the heterogeneous decomposition of HNO₃, whereas NO₃ is generated in the gas phase by the thermal decomposition of N₂O₅, a product of the self-disproportionation of liquid HNO₃. © 1993 John Wiley & Sons, Inc.     

Enhanced electron emission from phosphorus-doped diamond-cladsilicon field emitter arrays

Undoped and phosphorus (P)-doped diamond-clad Si field emitter arrays have been successfully fabricated using microwave plasma chemical vapor deposition (MPCVD) technology. The electron emission from the blunt diamond-clad microtips are much higher than those for the pure Si tips with sharp curvature due to a lower work function. Furthermore, the characteristics of emission current against applied voltage for the P-doped diamond-clad tips show superior emission at lower field to the undoped ones. After the examination of Auger electron spectroscopy (AES) and electrical characteristics of as-grown diamond, such a significant enhancement of the electron emission from the P-doped diamond-clad tips is attributed to a higher electron conductivity and defect densities     

Modeling electromigration lifetime under bidirectional currentstress

Electromigration reliability of interconnect under bidirectional current stress has been studied in a wide frequency range (mHz to 200 MHz). Experimental results show that the AC lifetime rises with the stress current frequency. The current density exponent and the activation energy of AC lifetime are found to be twice that of DC lifetime. Pure AC current stress failure at extremely high current density is believed to result from thermal migration of metal at hot/cold transition points     

Computer-intensive methods in statistical analysis

As far back as the late 1970s, the impact of affordable, high-speed computers on the theory and practice of modern statistics was recognized by Efron (1979, 1982). As a result, the bootstrap and other computer-intensive statistical methods (such as subsampling and the jackknife) have been developed extensively since that time and now constitute very powerful (and intuitive) tools to do statistics with. This article provides a readable, self-contained introduction to the bootstrap and jackknife methodology for statistical inference; in particular, the focus is on the derivation of confidence intervals in general situations. A guide to the available bibliography on bootstrap methods is also offered     

On finite convolutions of singular distributions and a “singular analog” of the Jessen-Wintner theorem

We study the fractal properties of a convolution of two Cantor distributions. By using the method of characteristic functions, we establish sufficient conditions for the singularity of the convolution of an arbitrary finite number of distributions of random variables with independent s-adic digits. We disprove the hypothesis on the validity of a “singular analog” of the Jessen-Wintner theorem for anomalously fractal distributions. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 8, pp. 1082–1088, August, 1998. The present work was partially supported by the International Soros Program of Educational Support in Exact Sciences (grant No. APU 061086).     

Second Quantization of the Stueckelberg Relativistic Quantum Theory and Associated Gauge Fields

The gauge compensation fields induced by the differential operators of the Stueckelberg-Schrödinger equation are discussed, as well as the relation between these fields and the standard Maxwell fields; An action is constructed and the second quantization of the fields carried out using a constraint procedure. The properties of the second quantized matter fields are discussed.     

On finite-dimensional approximation of solutions of ill-posed problems

We show that the modified method for finite-dimensional approximation of solutions of Fredholm integral equations of the first kind presented in this paper is more economical than traditional methods for finite-dimensional approximation. Institute of Mathematies, Ukrainian Academy of Science, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 289–295, February, 1997.     

Vector algorithm for Reed-Muller expansions

A novel vector algorithm for Reed-Muller (RM) expansions is proposed which can save as many as a factor of 2^n-1 memory elements compared with previous matrix algorithms