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Log-convexity

Witryna23 sty 2024 · 1 Answer. Convexity is important because it tells us that the curvature of a given function has the same sign. It gives us the ability to describe the shape of a function. From the practical point of view it is relevant because convex functions have a unique minimum. This property is used to minimize functions. Witryna23 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. …

2-Log-Concavity of the Boros–Moll Polynomials - Cambridge Core

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 … Witryna13 sie 2014 · This is termed log-convexity (log-concavity). Determining log-convexity (log-concavity) allows us to exploit the same convex optimization procedures. … hxt1 promoter https://poolconsp.com

Log-convexity and the overpartition function SpringerLink

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 Witryna13 wrz 2024 · This gives. f ( λ x + ( 1 − λ) y) ≤ f ( x) λ f ( y) 1 − λ. and that is exactly the convexity condition for log ∘ f. Remarks: The opposite conclusion holds as well: If f: R → ( 0, + ∞) is log-convex then x ↦ e a x f ( x) is convex for all a ∈ R. This characterization can be used to show that the sum of log-convex functions is ... WitrynaThe convexity of an equity security priced consis-tently with the constant growth model is, then, equal to [2/(k - g)2]. For ease of exposition, the "2" in the convexity measure is netted out against the "1/2" in the Taylor-series expansion, resulting in Equation (1) in the text, where Convexity refers to this "simplified convexity." hx sweetheart\u0027s

Log-concavity and strong q-log-convexity for Riordan arrays and ...

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Log-convexity

(PDF) On (log-) convexity of power mean - ResearchGate

Witryna13 sie 2013 · The. -log-convexity of Domb's polynomials. In this paper, we prove the -log-convexity of Domb's polynomials, which was conjectured by Sun in the study of Ramanujan-Sato type series for powers of . As a result, we obtain the log-convexity of Domb's numbers. Our proof is based on the -log-convexity of Narayana polynomials … Witryna13 sie 2013 · The. -log-convexity of Domb's polynomials. In this paper, we prove the -log-convexity of Domb's polynomials, which was conjectured by Sun in the study of …

Log-convexity

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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 … 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 …

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 … Witryna7 lis 2013 · That is, taking the function $\log:(0,\infty)\rightarrow \mathbb{R}$ is the matrix inequality $$ \log\left((1-t)A+tB \right)\geq (1-t)\log A+ t \log B $$ satisf... Stack …

Witryna14 lut 2024 · On the preservation of log convexity and log concavity under some classical Bernstein-type operators. Journal of Mathematical Analysis and Applications … WitrynaA note on log-convexity of power means József Sándor Babe³-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania [email protected]

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.

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 ... hxt2s506eh/aWitryna27 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. hx stomp youtubeWitryna1 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; hxt2s517eh/aWitrynaLet [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 … hxs.to priceWitrynaThe 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 hxt2s506ehWitrynaarXiv mashoko christian hospitalWitryna27 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 ? hxs.xpath