In this paper it is established that the remainders in asymptotic expansions of the logarithm of Barnes double gamma function and Euler’s gamma function are (up to a sign) completely monotonic functions of order comparable with the decay of the remainder in the expansion. We first recall some definitions and give some preliminary results. A function f : (0, ∞) → R is called completely monotonic...

In this paper we prove a unique continuation theorem for second order strictly hyperbolic differential operators. Results also hold for higher order operators if the hyperbolic cones are strictly convex. These results are proved via certain Carleman inequalities. Unlike [6], the paramétrées involved only have real phase functions, but they also have Gaussian factors. We estimate the parametrice...

We prove that the following statement follows from the Open Colouring Axiom (OCA): if X is locally compact σ-compact but not compact and if itš Cech-Stone remainder X * is a continuous image of ω * then X is the union of ω and a compact set. It follows that the remainders of familiar spaces like the real line or the sum of countably many Cantor sets need not be continuous images of ω * .

In this article, we derived new information inequalities on Jain-Saraswat's functional coefficient of distance (2013) for 3-convex functions. Further, evaluated some important relations among Relative Jensen Shannon distance, Arithmetic Geometric Triangular discrimination, Chi-square and many more. Moreover, explained the series version by using Taylor's with both Lagrange's Cauchy's form remai...

Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these expansions can be used in deriving uniform asymptotic expansions of integrals. The method is also used for obtaining Lau...

In the present work the approach-density matrix deformation-earlier developed by the author to study a quantum theory of the Early Universe (Planck's scales) is applied to study a quantum theory of black holes. On this basis the author investigates the information paradox problem, entropy of the black hole remainders after evaporation, and consistency with the holographic principle. The possibi...