The basis of nonlocal curvature invariants in quantum gravity theory

A complete basis of nonlocal invariants in quantum gravity theory is built to third order in spacetime curvature and matter-field strengths. The nonlocal identities are obtained which reduce this basis for manifolds with dimensionality $2\omega<6$. The present results are used in heat-kernel theory, theory of gauge fields and serve as a basis for the model-independent approach to quantum gravity and, in particular, for the study of nonlocal vacuum effects in the gravitational collapse problem.Comment: 28 pages, REVTeX, Alberta Thy 14-9

Asymptotic behaviours of the heat kernel in covariant perturbation theory

The trace of the heat kernel is expanded in a basis of nonlocal curvature invariants of $N$th order. The coefficients of this expansion (the nonlocal form factors) are calculated to third order in the curvature inclusive. The early-time and late-time asymptotic behaviours of the trace of the heat kernel are presented with this accuracy. The late-time behaviour gives the criterion of analyticity of the effective action in quantum field theory. The latter point is exemplified by deriving the effective action in two dimensions.Comment: 22 pages, REVTeX, Alberta Thy 45-9

Classification of limit varieties of J\mathscr J-trivial monoids

A variety of algebras is called limit if it is non-finitely based but all its proper subvarieties are finitely based. We present a new pair of limit varieties of monoids and show that together with the five limit varieties of monoids previously discovered by Jackson, Zhang and Luo and the first-named author, there are exactly seven limit varieties of $\mathscr J$-trivial monoids.Comment: 26 page

Thermally activated intersubband scattering and oscillating magnetoresistance in quantum wells

Experimental studies of magnetoresistance in high-mobility wide quantum wells reveal oscillations which appear with an increase in temperature to 10 K and whose period is close to that of Shubnikov-de Haas oscillations. The observed phenomenon is identified as magnetointersubband oscillations caused by the scattering of electrons between two occupied subbands and the third subband which becomes occupied as a result of thermal activation. These small-period oscillations are less sensitive to thermal suppression than the largeperiod magnetointersubband oscillations caused by the scattering between the first and the second subbands. Theoretical study, based on consideration of electron scattering near the edge of the third subband, gives a reasonable explanation of our experimental findings.Comment: 9 pages, 5 figure

Meshed power system reliability estimation techniques

Electrical power system (EPS) reliability indices (RI) are calculated at both the operating and planning stages of power system operation. RI calculation is the key concern for power reserve estimating and dispatching, validating the new generation capacity and tie line installations, basic facility maintenance planning, selecting distribution substation key diagrams and local power system connecting diagrams and specifying the energy and power charges. The primary barrier to fast RI calculation is a meshed and hierarchical structure of a power system, the analysis of which is more of a challenge for an engineer. Additionally, there are a number of issues concerning the probabilistic nature of RI. This paper presents novel mathematical algorithms that have been developed at the department of automated power systems (DAPS) of the Ural Federal University. © 2014 WIT Press.International Journal of Safety and Security Engineering;International Journal of Sustainable Development and Planning;WIT Transactions on Ecology and the Environmen