In the paper, author presents bounds for completely monotonic degree of a remainder an asymptotic expansion trigamma function. This result partially confirms one in series conjectures on degrees remainders expansions logarithm gamma function and polygamma functions.

1. ‘Part’ and Parthood 2. Basic Principles 2.1. Parthood as a Partial Ordering 2.2. Other Mereological Concepts 3. Supplementation Principles 3.1. Parts and Remainders 3.2. Identity and Extensionality 4. Closure Principles 4.1. Finitary Operations 4.2. Unrestricted Fusions 4.3. Composition, Existence, and Identity 5. Atomismistic and Atomless Mereologies Bibliography Historical Surveys Monograp...

The properties of two families of s-orthogonal polynomials, which are connected with Chebyshev polynomials of third and fourth kind, are studied. Evaluations of the remainders are given and asymptotic formulae are calculated for the corresponding hyper-Gaussian formulae used for an approximate estimation of integrals. 2000 Mathematics Subject Classification: 33C45, 65D32.

ABSTRACT A scheme for systematically separating ultraviolet divergences of Feynrnan amplitudes in parametric space is developed. It is summarized by an explicit formula which enables us to incorporate readily the ultraviolet-finite remainders thus constructed into the usual renormalization s theme . It is shown further that infrared divergences can be treated in a very similar way. Our method i...

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...