The problem of nonperturbative description of stationary flames with arbitrary gas expansion is considered. On the basis of the Thomson circulation theorem an implicit integral of the flow equations is constructed. With the help of this integral, a simple explicit expression for the vortex mode of the burnt gas flow near the flame front is obtained. Furthermore, a dispersion relation for the potential mode at the flame front is written down, thus reducing the initial system of bulk equations and jump conditions for the flow variables to a set of integrodifferential equations for the flame front position and the flow velocity at the front. The developed approach is applied to the case of thin flames. Finally, an asymptotic expansion of the derived equations is carried out in the case → 1 where is the gas expansion coefficient, and a single equation for the front position is obtained in the second post-Sivashinsky approximation. It is demonstrated, in particular, how the well-known problem of correct normalization of the front velocity is resolved in our approach. It is verified also that in the first post-Sivashinsky approximation, the equation reduces to the Sivashinsky-Clavin equation corrected according to Cambray and Joulin. Analytical solutions of the derived equations are found, and compared with the results of numerical simulations.

The structure of counterterms in higher derivative quantum gravity is reexamined. Nontrivial dependence of charges on the gauge and parametrization is established. Explicit calculations of two-loop contributions are carried out with the help of the generalized renormgroup method demonstrating consistency of the results obtained. 1.IntroductionAs well known, not all of the problems of the quantum eld theory are exhausted by the construction of S-matrix. Investigation of evolution of the Universe, behavior of quarks in quantum chromodynamics etc. require the introduction of more general object the so called eective action. Besides that, the program of renormalization of the S-matrix itself has not yet been carried out in terms of the S-matrix alone. Renormalization of the Green functions, therefore, is the central point of the whole theory. Given these functions one can obtain the S-matrix elements with the help of the reduction formulas. In this respect those properties of the generating functionals which remain valid after the transition to the S-matrix is made are of special importance.We mean rst of all the properties of the so called "essential" coupling constants in the sense of S.Weinberg [1]. They are dened as those independent from any redenition of the elds. In the context of the quantum theory one can say that the renormalization of "essential" charges is independent from renormalizations of the elds. Separation of quantities into "essential" and "inessential" ones is convenient and we use it below.In this paper we shall consider the problem of gauge and parametrization dependence of the eective action of R 2 -gravity.There are two general and powerful methods of investigation of gauge dependence in quantum eld theory. The rst of them [2] uses the Batalin-Vilkovisky formalism [3,4,5] and is based on the fact that any change of gauge condition can bepresented

An exact equation describing freely propagating stationary flames with arbitrary values of the gas expansion coefficient is obtained. This equation respects all conservation laws at the flame front, and provides a consistent nonperturbative account of the effect of vorticity produced by the curved flame on the front structure. It is verified that the new equation is in agreement with the approximate equations derived previously in the case of weak gas expansion.

A nonlinear equation describing curved stationary flames with arbitrary gas expansion θ = ρ fuel /ρ burnt , subject to the Landau-Darrieus instability, is obtained in a closed form without an assumption of weak nonlinearity. It is proved that in the scope of the asymptotic expansion for θ → 1, the new equation gives the true solution to the problem of stationary flame propagation with the accuracy of the sixth order in θ − 1. In particular, it reproduces the stationary version of the well-known Sivashinsky equation at the second order corresponding to the approximation of zero vorticity production. At higher orders, the new equation describes influence of the vorticity drift behind the flame front on the front structure. Its asymptotic expansion is carried out explicitly, and the resulting equation is solved analytically at the third order. For arbitrary values of θ, the highly nonlinear regime of fast flow burning is investigated, for which case a large flame velocity expansion of the nonlinear equation is proposed.

The power spectrum of quantum fluctuations of the electromagnetic field produced by an elementary particle is determined. It is found that in a wide range of practically important frequencies the power spectrum of fluctuations exhibits an inverse frequency dependence. The magnitude of fluctuations produced by a conducting sample is shown to have a Gaussian distribution around its mean value, and its dependence on the sample geometry is determined. In particular, it is demonstrated that for geometrically similar samples the power spectrum is inversely proportional to the sample volume. It is argued also that the magnitude of fluctuations induced by external electric field is proportional to the field strength squared. A comparison with experimental data on flicker noise measurements in continuous metal films is made.