Metric fluctuations,entropy, and the Wheeler-deWitt equation

Quantization using quantum potentials is described in terms of momentum fluctuations, and it is related to Fisher information and entropy. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 32–44, July, 2007.     

Object-oriented representation of hierarchical graphs

We introduce the concept of C₀-systems, which can be used to represent syntactic objects of graph-based formal systems with inheritance. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 4, pp. 159–170, 2004.     

Simplified analytic solutions and a novel fast algorithm for Yb-doped double-clad fiber lasers

In this paper, continuous wave Yb³⁺-doped double-clad fiber lasers (DCFLs) with linear-cavity are investigated theoretically and numerically using the rate equations. Under the steady state conditions, the simplified analytic solutions of Yb³⁺-doped DCFLs under considering the scattering loss are deduced in the strongly pump condition. Compared with the known analytic solutions in published literatures, our analytic solutions are more accurate, especially, at higher reflectivity of output mirror. In addition, a fast and stable algorithm based on the Newton-Raphson method is proposed to simulate numerically Yb³⁺-doped DCFLs. The results by simplified analytic solutions are in good agreement with those by the numerical simulation. Moreover, we have performed the optimization of an Yb³⁺-doped DCFL using the simplified analytic solutions and the numerical simulations, respectively.     

Differential equations uniquely determined by algebras of point symmetries

We continue to investigate strongly and weakly Lie remarkable equations, which we defined in a recent paper. We consider some relevant algebras of vector fields on ℝ^k (such as the isometric, affine, projective, or conformal algebras) and characterize strongly Lie remarkable equations admitted by the considered Lie algebras. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 486–494, June, 2007.     

Runge–Kutta Methods for Itô Stochastic Differential Equations with Scalar Noise

A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation systems w.r.t. a one-dimensional Wiener process is introduced. The colored rooted tree analysis is applied to derive conditions for the coefficients of the stochastic Runge–Kutta method assuring convergence in the weak sense with a prescribed order. Some coefficients for new stochastic Runge–Kutta schemes of order two are calculated explicitly and a simulation study reveals their good performance.     

One-pot diastereoselective synthesis of α-aminonitriles from aldehydes, chiral amines, and trimethylsilyl cyanide under solvent-free conditions

Treatment of aliphatic and aromatic aldehydes with chiral amines and trimethylsilyl cyanide in the absence or in the presence of Lewis acids (including lithium perchlorate) under solvent-free conditions afforded the corresponding α-aminonitriles in good yields and with a diastereoselectivity of 68 to 86%. Published in Russian in Zhurnal Organicheskoi Khimii, 2006, Vol. 42, No. 1, pp. 56–59. The text was submitted by the authors in English.     

Hydrogen-induced metallization on Ge(1 1 1) c(2 × 8)

We have studied hydrogen adsorption on the Ge(1 1 1) c(2 × 8) surface using scanning tunneling microscopy (STM) and angle-resolved photoelectron spectroscopy (ARPES). We find that atomic hydrogen preferentially adsorbs on rest atom sites. The neighbouring adatoms appear higher in STM images, which clearly indicates a charge transfer from the rest atom states to the adatom states. The surface states near the Fermi-level have been followed by ARPES as function of H exposure. Initially, there is strong emission from the rest atom states but no emission at the Fermi-level which confirms the semiconducting character of the c(2 × 8) surface. With increasing H exposure a structure develops in the close vicinity of the Fermi-level. The energy position clearly indicates a metallic character of the H-adsorbed surface. Since the only change in the STM images is the increased brightness of the adatoms neighbouring a H-terminated rest atom, we identify the emission at the Fermi-level with these adatom states.