Log-convexity

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August undefined, 2024

http://chandra.ie.cuhk.edu.hk/pub/papers/NIT/Log-cvx.pdf 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.

Chords through a convex body generated from within an …

Witryna21 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 … 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 … builders wirral merseyside

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

http://www.kurims.kyoto-u.ac.jp/EMIS/journals/SMA/v06/p15.pdf 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 ? Witryna14 lut 2024 · On the preservation of log convexity and log concavity under some classical Bernstein-type operators. Journal of Mathematical Analysis and Applications … crossword to print

LOG-CONCAVITY PROPERTY FOR SOME WELL-KNOWN DISTRIBUTIONS

A Criterion for the Log-Convexity of Combinatorial Sequences

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 ... In convex analysis, a non-negative function f : R → R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it satisfies the inequality for all x,y ∈ dom f and 0 < θ < 1. If f is strictly positive, this is equivalent to saying that the logarithm of the function, log ∘ f, is concave; that is, for all x,y ∈ dom f and 0 < θ < 1. crossword to print freeWitryna1 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 … builders wire mesh

"WitrynaA note on log-convexity of power means József Sándor Babe³-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania [email protected] " - Log-convexity

Log-convexity

Logarithmic convexity and geometric programming - ScienceDirect

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 ( … 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 …

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Witryna13 sie 2014 · This is termed log-convexity (log-concavity). Determining log-convexity (log-concavity) allows us to exploit the same convex optimization procedures. … 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 Witryna1 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 ...

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 … 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

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 ...

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." crossword top storyWitryna27 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. crossword to print out or solve on lineWitryna1. 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.) builders wirral area