Results 31 to 40 of about 2,291,183 (283)

Evaluation of the real parts of polylogarithm expressions containing complex arguments via certain logarithmic integrals [PDF]

Notes on Number Theory and Discrete Mathematics
We consider a polylogarithm expression containing complex arguments, namely 𝓟±(n)=ℜ(Liₙ((1±i)/2)). The central notion of the present paper is to evaluate the real parts of 𝓟±(n) for first four orders, specifically n = 1,2,3, and 4, by constructing ...
Narendra Bhandari
doaj   +1 more source

Generalized Extended Matrix Variate Beta and Gamma Functions and Their Applications

Ingeniería y Ciencia, 2016
In this article, we define and study generalized forms of extended matrix variate gamma and beta functions. By using a number of results from matrix algebra, special functions of matrix arguments and zonal polynomials we derive a number of properties of ...
Daya K. Nagar, Sergio Alexander Gómez-Noguera, Arjun K Gupta   +2 more
doaj   +1 more source

Integral Representations of the Catalan Numbers and Their Applications

Mathematics, 2017
In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations ...
Feng Qi, Bai-Ni Guo
doaj   +1 more source

Explicit Expressions for Most Common Entropies

Entropy, 2023
Entropies are useful measures of variation. However, explicit expressions for entropies available in the literature are limited. In this paper, we provide a comprehensive collection of explicit expressions for four of the most common entropies for over ...
Saralees Nadarajah, Malick Kebe
doaj   +1 more source

Perturbation of an Eigen-Value from a Dense Point Spectrum : An Example [PDF]

, 1997
We study a perturbed Floquet Hamiltonian $K+\beta V$ depending on a coupling constant $\beta$. The spectrum $\sigma(K)$ is assumed to be pure point and dense.
Ao P, Bellissard J, Bellissard J, Benvenuto F, Bleher P M, Combescure M, Eliasson L H, Howland J S, Howland J S, Howland J S, Joye A, Kato T, M Vittot, Nenciu G, P Duclos, P Stovicek, Rellich F, Simon B, Stein E M, Ulam S, Yajima K   +20 more
core   +2 more sources

Beta-functions and superstring compactifications

Physics Letters B, 1986
It is shown that quartic curvature modifications to the gravitational effective action derived from superstrings agree on Ricci-flat Kahler backgrounds with a recently-proposed four-loop counterterm in N = 2 Ricci-flat σ-models. These results seem to suggest that Calabi-Yau manifolds may not provide consistent compactifications of the superstring.
M.D. FREEMAN, C.N. POPE
openaire   +1 more source

The incomplete beta function and its ratio to the complete beta function [PDF]

Mathematics of Computation, 1968
The incomplete beta function, B x ( p , q ) = ∫ 0 x y p − 1 ( 1
Osborn, D., Madey, R.
openaire   +2 more sources

Compositional Data Modeling through Dirichlet Innovations

Mathematics, 2021
The Dirichlet distribution is a well-known candidate in modeling compositional data sets. However, in the presence of outliers, the Dirichlet distribution fails to model such data sets, making other model extensions necessary.
Seitebaleng Makgai, Andriette Bekker, Mohammad Arashi   +2 more
doaj   +1 more source

Beta Function Quintessence Cosmological Parameters and Fundamental Constants I: Power and Inverse Power Law Dark Energy Potentials

, 2018
This investigation explores using the beta function formalism to calculate analytic solutions for the observable parameters in rolling scalar field cosmologies.
Thompson, Rodger I.
core   +1 more source

Infrared Zero of $\beta$ and Value of $\gamma_m$ for an SU(3) Gauge Theory at the Five-Loop Level [PDF]

, 2016
We calculate the value of the coupling at the infrared zero of the beta function of an asymptotically free SU(3) gauge theory at the five-loop level as a function of the number of fermions. Both a direct analysis of the beta function and analyses of Pad\'
Ryttov, Thomas A., Shrock, Robert
core   +2 more sources