Log-convexity

Author: bdtd

August undefined, 2024

Witryna14 lut 2024 · On the preservation of log convexity and log concavity under some classical Bernstein-type operators. Journal of Mathematical Analysis and Applications … 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 …

Convexity for Equity Securities: Does Curvature Matter?

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 ( … 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. henry 8th tv series

ca.classical analysis and odes - What does log convexity …

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." 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. WitrynaThis 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. henry 8th six wives names

Proof of concavity of log function - Mathematics Stack Exchange

Logarithmically concave function - Wikipedia

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 … 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. henry 8th wives fact fileWitryna14 sie 2014 · This is termed log-convexity (log-concavity). Determining log-convexity (log-concavity) allows us to exploit the same convex optimization procedures. $\underline{\mathrm{Question}}$ I want to know if the idea of log-convexity can be extended further. In particular, can we describe a function as being log-log-convex … henry 8th wives rhyme words

"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 … " - Log-convexity

Log-convexity

Logarithmically convex function - Wikipedia

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

Did you know?

Witryna1 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; 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

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

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 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 …

Witryna31 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 …

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. henry 8th wives in order of deathWitryna13 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 … henry 8 wife catherineWitryna1. 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.) henry 8th wives and childrenWitryna13 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 ... henry 8th reinWitryna13 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 … henry 8th wives in order of marriageWitrynaIn 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 … henry 8 weightWitryna1 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. henry 8th wife song