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Energy-Efficient Hierarchical Federated Learning in UAV Networks with Partial AI Model Upload Under Non-Convex Loss. [PDF]
Sensors (Basel)Li H, Wang S, Du Y, Li R, Fan X, Luo C.
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Journal of Mathematical Analysis and Applications, 2009 We introduce completely monotonic functions of order r>0 and show that the remainders in asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function give rise to completely monotonic functions of any positive integer
Stamatis Koumandos
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Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function [PDF]
Applied Mathematics and Computation, 2015 In this paper, we present some completely monotonic functions and asymptotic expansions related to the gamma function. Based on the obtained expansions, we provide new bounds for Γ(x + 1)/Γ(x + 1/2) and Γ(x + 1/2)
Chao-Ping Chen, Richard B Paris
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APPROXIMATION OF AND BY COMPLETELY MONOTONE FUNCTIONS
The ANZIAM Journal, 2019We investigate convergence in the cone of completely monotone functions. Particular attention is paid to the approximation of and by exponentials and stretched exponentials. The need for such an analysis is a consequence of the fact that although stretched exponentials can be approximated by sums of exponentials, exponentials cannot in general be ...
R. J. LOY, R. S. ANDERSSEN
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Some Absolutely Monotonic and Completely Monotonic Functions
SIAM Journal on Mathematical Analysis, 1974The functions $(1 - r)^{ - 2|\lambda |} (1 - 2xr + r^2 )^{ - \lambda } $ are shown to be absolutely monotonic, or equivalently, that their power series have nonnegative coefficients for $ - 1 \leqq x \leqq 1$. One consequence is a simple proof of Kogbetliantz’s theorem on positive Cesaro summability for ultraspherical series, [7].
Askey, Richard, Pollard, Harry
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Logarithmically completely monotonic functions concerning gamma and digamma functions
Integral Transforms and Special Functions, 2007 For given real numbers a0, b and c, let Fa, b, c(x)=[(x+1)]1/x(1+a/x)x+b/xc and a, b, c(x)=''(x)+[2+(b+c)x-2x2]/x3+[3a(2a-b)+(6a-b)x+2x2]/(x+a)3 with x(0, ), where (x) and (x) are the well-known Euler gamma function and the psi or digamma function ...
Feng Qi, Wing-Sum Cheung
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Completely monotonic functions
Integral Transforms and Special Functions, 2001In this expository article we survey some properties of completely monotonic functions and give various examples, including some famous special functions. Such function are useful, for example, in probability theory. It is known, [1, p.450], for example, that a function w is the Laplace transform of an infinitely divisible probability distribution on ...
K.S. Miller, S.G. Samko
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A Property of completely monotonic functions
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1987AbstractA non-negative function f(t), t > 0, is said to be completely monotonic if its derivatives satisfy (-1)n fn (t) ≥ 0 for all t and n = 1, 2, …, For such a function, either f(t + δ) / f(t) is strictly increasing in t for each δ > 0, or f(t) = ce-dt for some constants c and d, and for all t. An application of this result is given.
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A Note on Completely and Absolutely Monotone Functions
Canadian Mathematical Bulletin, 1982AbstractThe solutions of a certain class of first order linear differential equations are shown to be either completely or absolutely monotone depending on the nature of its coefficients. This is a simple theorem which is used to deduce a number of new and interesting results dealing with the complete and absolute monotonicity of functions.
Mahajan, Arvind, Ross, Dieter K.
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