Log-convexity

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August undefined, 2024

WitrynaIn general, a log-convex function is a function $x\mapsto f(x)>0$ such that $x\mapsto\log f(x)$ is convex (as stated in the question). Instead, the log-convexity … Witryna1 paź 2007 · Hence the log-convexity of {c(n)} ngreaterorequalslant0 follows from Proposition 4.6. 4.2. Linear transformations preserving log-convexity In [46], Wang …

Convexity for Equity Securities: Does Curvature Matter?

Witryna1 sty 2013 · In this short note we prove that the power mean M p (a,b) is convex in p for p≤0, log-convex for p≤0 and log-concave for p≥0. Discover the world's research. 20+ million members; Witryna31 gru 2003 · In many applications, assumptions about the log-concavity of a probability distribution allow just enough special structure to yield a workable theory. This paper … dragon 32k

A note on log-convexity of power means - CORE

Witryna27 lip 2009 · A sequel to this paper will further consider the critical case and other ramifications of the log-convexity of the extinction time distribution. Type Research Article. Information Probability in the Engineering and Informational Sciences, Volume 1, Issue 3, July 1987, pp. 265 - 278. Witryna27 mar 2015 · The graph of convex function is : In a book it is written that g ( x) = log x is strictly convex function. So i searched for graph of g ( x) = log x and found that. Though it has been said that g ( x) = log x is strictly convex function, comparing these two graph it seems to me g ( x) = log x is concave function . Where am i doing mistake ? dragon 3308

Log-convexity and log-concavity of hypergeometric-like functions

WitrynaA note on log-convexity of power means József Sándor Babe³-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania [email protected] Witryna1 gru 2024 · The log–log convex properties of state matrices of positive systems, like the log–log convexity of the spectral r of a positive matrix in any of its entries ( … dragon 3301Witryna23 lut 2016 · $\begingroup$ @YulInn: The most natural and elemenary definition of the natural logarithm---or its inverse, the exponential---is via calculus, or at least as a limit. … radio kfyi 550 phoenix arizona

"Witryna13 paź 2013 · TL;DR: A criterion for the log-convexity of some combinatorial sequences is presented and it suffices to compute a constant number of terms at the beginning of the sequence. Abstract: Recently, Do s li c , and Liu and Wang developed techniques for dealing with the log-convexity of sequences. In this paper, we present a criterion for … " - Log-convexity

Log-convexity

Witryna14 lut 2024 · On the preservation of log convexity and log concavity under some classical Bernstein-type operators. Journal of Mathematical Analysis and Applications … Witryna4 lut 2024 · 1 定义. 如果函数 f:R^n\rightarrow R ，定义域内满足 f(x)>0 的点构成的 \mathrm{log}f 是凸的，那么称函数 f 为对数凸函数。相应的，如果 log(f) 是凹的的，那么称函数 f 为对数凹函数。. 我们还可以不用对数描述对数凹凸性。设一函数 f:R^n\rightarrow R ，其定义域为一凸集且定义域内所有点都满足 f(x)>0 ，那么 ...

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WitrynaLOGARITHMIC CONVEXITY AND GEOMETRIC PROGRAMMING 395 It has been shown [14] that every lower (upper) semicontinuous strictly quasiconvex (concave) is … WitrynaThe log-concavity and log-convexity property have an important role in economics, social sciences, information theory and optimization. Most of the time logarithm of cumulative function of a random variable is concave. In papers such as La ont and

http://chandra.ie.cuhk.edu.hk/pub/papers/NIT/Log-cvx.pdf Witryna在上一节中，我们提到了一个log-convex的函数一定是一个convex函数，一个log-concave的函数一定是一个concave函数。因此如果一个函数是二阶可微的，那么我 …

Witryna13 maj 2024 · 1 Introduction. An overpartition of n is a non-increasing sequence of natural numbers whose sum is n in which the first occurrence of a number may be … WitrynaThis paper establishes the log-convexity of Fisher information for scalar random variables along the heat ﬂow, thus resolving a conjecture posed in [1]. The convexity result can also be interpreted along similar lines as the convexity of H 2(p H 1 2 (u)) in u, established in [2], where H 2(x) = xlog 2 (x) (1 x)log 2

Witryna14 lip 2016 · A body E is completely embedded within a convex body G. A line segment is generated by a measure depending only on E or on both E and G . This line segment is then projected to the surface of G in one or both directions.

Witryna18 lut 2009 · Log-convexity and log-concavity of hypergeometric-like functions. D.Karp, S.M. Sitnik. We find sufficient conditions for log-convexity and log-concavity for the … dragon333A logarithmically convex function f is a convex function since it is the composite of the increasing convex function $${\displaystyle \exp }$$ and the function $${\displaystyle \log \circ f}$$, which is by definition convex. However, being logarithmically convex is a strictly stronger property than … Zobacz więcej In mathematics, a function f is logarithmically convex or superconvex if $${\displaystyle {\log }\circ f}$$, the composition of the logarithm with f, is itself a convex function. Zobacz więcej • $${\displaystyle f(x)=\exp( x ^{p})}$$ is logarithmically convex when $${\displaystyle p\geq 1}$$ and strictly logarithmically convex when • Zobacz więcej Let X be a convex subset of a real vector space, and let f : X → R be a function taking non-negative values. Then f is: • Logarithmically convex if $${\displaystyle {\log }\circ f}$$ is … Zobacz więcej • Logarithmically concave function Zobacz więcej dragon 3315Witryna1 sie 2024 · This paper focuses on the log-convexity of various combinatorial sequences. We mainly discuss several kinds of recurrence sequences, which include two three-term linear recurrence sequences, a ... radio khana en vivoWitryna23 sie 2024 · 4. (Log-)convex functions do not need to be twice differentiable, so any proof through d 2 d x 2 lacks generality. On the other hand e x is both a convex and log-convex function, and we may wonder when the composition of two convex functions is convex. Assume that f ( x) is convex . Then g ( x) = e f ( x) is convex iff. dragon3388Witryna1. DEFINITION. A positive function 0 (x) defined on a convex set r C E" is called logarithmic convex, log convex, or L-convex (logarithmic concave, log concave, orL-concave) on F if log 8 (x) is a convex (concave) function on r. (For brevity we write L-convex or L-concave below.) dragon 3313WitrynaLet [A n,k] n,k ⩾0 be an infinite lower triangular array satisfying the recurrencefor n ⩾ 1 and k ⩾ 0, where A 0,0 = 1, A 0, k = A k,–1 = 0 for k > 0. We present some criteria for … radio kfzWitryna21 sie 2013 · It has been conjectured by Boros and Moll that these polynomials are infinitely log-concave. In this paper, we show that P m (a) is 2-log-concave for any m ≥ 2. Let d i (m) be the coefficient of a i in P m (a). We … dragon 3302