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 … 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 …
Log-convexity
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WitrynaarXiv 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.
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. 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. …
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 ... Witryna1. 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.)
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 …
Witryna2 maj 2010 · Log convexity can be effectively used in derivation of various inequalities involving the gamma function (particularly, two-sided estimates of products of gamma functions). It is linked with the notion of Schur convexity which is itself used in many applications. An appetizer. Let m = max x i, s = ∑ x i, x i > 0, i = 1, …, n, then. city pass empire state buildingWitryna23 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. city pass explorer chicagoWitryna13 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 … city pass for 5 members offerWitryna13 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 … city pass for charleston scWitryna31 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 … city passes in atlanta gaWitryna7 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 … city pass for nashvilleWitrynaThis paper focuses on the log-convexity of the sequence $\{D_r(n)\}_{n\ge r}$ of $r$-derangement numbers, where $r\ge 2$ is a positive integer. dot sand rail headlights