The usual geometrical-optics expansion of the solution for the Helmholtz equation of a point source in an inhomogeneous medium yields two equations: an eikonal equation for the traveltime function, and a transport equation for the amplitude function. However, two difficulties arise immediately: one is how to initialize the amplitude at the point source as the wavefield is singular there; the ot...

The full asymptotic expansion of the trace of the heat semi–group, tr(e−∆Ωt),where −∆Ω is the Dirichlet Laplace-Beltrami operator acting on L2(Ω) for geodesic spherical polygons Ω ⊂ S2, is derived in half–powers of t, and the coefficients determined explicitly. Let Ω be a non-empty open connected set in S = {x ∈ R : |x| = 1} with a piecewise geodesic boundary ∂Ω and interior angles γ1, · · · , ...

We discuss -expansion in curved space-time for asymptotically free and asymptotically non-free theories. The existence of stable and unstable xed points is investigated for f 4 theory and SU(2) gauge theory. It is shown that -expansion maybe compatible with asymptotic freedom on special solutions of the RG equations in a special case (supersymmetric theory). Using -expansion RG technique the e ...

We study string theory duals of the expanding boost invariant conformal gauge theory plasmas at strong coupling. The dual supergravity background is constructed as an asymptotic latetime expansion, corresponding to equilibration of the gauge theory plasma. The absence of curvature singularities in the first few orders of the late-time expansion of the dual gravitational background unambiguously...

We consider the approximation of the convolution product of not necessarily identical probability distributions qj I + pjF , (j = 1, . . . , n), where, for all j , pj = 1 − qj ∈ [0, 1], I is the Dirac measure at point zero, and F is a probability distribution on the real line. As an approximation, we use a compound binomial distribution, which is defined in a one-parametric way: the number of t...

We consider the approximation of the convolution product of not necessarily identical probability distributions qjI+pjF , (j = 1, . . . , n), where, for all j, pj = 1− qj ∈ [0, 1], I is the Dirac measure at point zero, and F is a probability distribution on the real line. As an approximation, we use a compound binomial distribution, which is defined in a one-parametric way: the number of trials...

We study string theory duals of the expanding boost invariant conformal gauge theory plasmas at strong coupling. The dual supergravity background is constructed as an asymptotic latetime expansion, corresponding to equilibration of the gauge theory plasma. The absence of curvature singularities in the first few orders of the late-time expansion of the dual gravitational background unambiguously...

We discuss ǫ-expansion in curved space-time for asymptotically free and asymptotically non-free theories. The existence of stable and unstable fixed points is investigated for fφ4 theory and SU(2) gauge theory. It is shown that ǫ-expansion maybe compatible with asymptotic freedom on special solutions of the RG equations in a special case (supersymmetric theory). Using ǫ-expansion RG technique t...