Log-convexity
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 … 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 and Yeh established the connection between linear transformations preserving the log-concavity and the q-log-concavity. This method is also effective for the log-convexity.
Log-convexity
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A 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 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 ...
WitrynaA note on log-convexity of power means József Sándor Babe³-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania [email protected] Witryna23 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.
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. 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 …
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 …
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 ... brand lanceWitrynaLet {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 … brand korean buildWitryna31 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 … brandland norwichWitryna21 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 … brand lampertheim hofheimWitrynaThe 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." haikyu touch the dreamWitryna1 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 … haikyu to the top vostfrWitryna18 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 … haikyu to the top bd batch sub indo