Results 71 to 80 of about 525,503 (229)

The generating function of the $σ_1$ function [PDF]

open access: yesarXiv, 2011
In this paper, we give a generate function for the $\sigma_1$ function. Then we find some connections between the $\sigma_1$ function and the Ramanujan's tau function. We hope this connection will give some insights into the unsolved problems in classical number theory.
arxiv  

The predictive value of masticatory function for adverse health outcomes in older adults: a systematic review

open access: yesThe Journal of Nutrition, Health and Aging
Masticatory function is associated with a variety of health outcomes. The aim of this systematic review is to clarify the predictive value of masticatory function for adverse health outcomes, such as frailty, sarcopenia and malnutrition, in older adults ...
Menke J. de Smit   +3 more
doaj  

Sharp Estimates for Norms of Functions from Conjugate Classes in Metrics C and L [PDF]

open access: yesarXiv, 2014
Sharp estimates for C - and L - norms of functions that are conjugate with functions from the classes W^rH_\omega of periodic functions having prescribed concave majorant of moduli of continuity, as well as sharp estimates for the differences of such functions are obtained.
arxiv  

Non-commutative Functional Calculus and Spectral Theory [PDF]

open access: yesarXiv, 2015
We develop a functional calculus for $d$-tuples of non-commuting elements in a Banach algebra. The functions we apply are free analytic functions, that is nc functions that are bounded on certain polynomial polyhedra.
arxiv  

New generalizations of Zeta-Function and Tricomi function [PDF]

open access: yesarXiv, 2017
In this paper we introduce new generalizations of the zeta function, the Tricomi functions; their main properties are studied. This opens the way to a deeper, better application of these functions both in the theory of special functions, and in many applied sciences.
arxiv  

$\,_{3}F_{4}$ hypergeometric functions as a sum of a product of $\,_{2}F_{3}$ functions [PDF]

open access: yesarXiv
This paper shows that certain $\,_{3}F_{4}$ hypergeometric functions can be expanded in sums of pair products of $\,_{1}F_{2}$ functions. In special cases, the $\,_{3}F_{4}$ hypergeometric functions reduce to $\,_{2}F_{3}$ functions. Further special cases allow one to reduce the $\,_{2}F_{3}$ functions to $\,_{1}F_{2}$ functions, and the sums to ...
arxiv  

Conjugates of integral functionals on continuous functions [PDF]

open access: yesarXiv, 2017
This article gives necessary and sufficient conditions for the dual representation of Rockafellar in (Integrals which are convex functionals. II, Pacific J. Math., 39:439--469, 1971) for integral functionals on the space of continuous functions.
arxiv  

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