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Log-convexity

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 … 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 ...

optimization - Why is "Convexity" Important in Mathematics ...

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

Chords through a convex body generated from within an …

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. The handicap of not using calculus is artificial; so it is not surprising that the above proof is circuitous. If only rational numbers featured as base and index, then limits would … 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 ... 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 … des fakes news

The Time to Extinction of Branching Processes and Log-Convexity…

Category:A Criterion for the Log-Convexity of Combinatorial Sequences

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Log-convexity

Logarithmic convexity and geometric programming

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 … 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.

Log-convexity

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WitrynaLet {b k (n)} n=0 ∞ be the Bell numbers of order k. It is proved that the sequence {b k (n)/n!} n=0 ∞ is log-concave and the sequence {b k (n)} n=0 ∞ is log-convex, or … WitrynaLet [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 the log-concavity of rows and strong q-log-convexity of generating functions of rows.Our results can be applied to many well-known triangular arrays, such as the Pascal …

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 … WitrynaLet [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 …

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 ... WitrynaLOGARITHMIC CONVEXITY AND GEOMETRIC PROGRAMMING 395 It has been shown [14] that every lower (upper) semicontinuous strictly quasiconvex (concave) is …

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WitrynaarXiv chubb edwards emailWitryna21 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 … chubb e learningWitryna31 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 … chub beer