The modified $F(R)$ gravity theory with the function $F(R)=-(1/\beta)\ln(1-\beta R)$ is studied. action at small coupling $\beta$ becomes Einstein--Hilbert action. bound on parameter from local tests $\beta\leq 2\times 10^{-6}$ cm$^2$. We find constant curvature solutions and it was shown that de Sitter space unstable but a solution zero Ricci scalar stable. potential mass of field (scalaron) a...

We study the problem of stabilization for acoustic system with a spatially distributed damping. Without imposing any hypotheses on structural properties damping term, we identify logarithmic decay solutions growing time. Logarithmic rate is shown through new Carleman estimate which allows us to carry out special analysis resolvent.

We discuss recent results for the asymptotic behavior of fermion scattering amplitudes in the Sudakov limit. The results include next-to-next-to-leading logarithmic electroweak corrections and are used for the analysis of fermion-antifermion pair production in ee annihilation at high energy. The importance of the subleading logarithmic contributions is emphasized and the fermionic contributions...

provided that f : a, b → is a convex function 1, page 137 , 2, page 1 . This result for convex functions plays an important role in nonlinear analysis. These classical inequalities have been improved and generalized in a number of ways and applied for special means including Stolarsky type, logarithmic, and p-logarithmic means. A generalization of H.H inequalities was obtained in 3–5 , 2, page ...

We present a new method for solving the BFKL evolution applicable at both leading and next-to-leading logarithmic accuracy, and tailored to the study of QCD multijet events at colliders. We utilise this to discuss corrections to the standard analysis. There are known, large corrections from energy and momentum conservation. We show that, despite claims to the contrary in the literature, these a...