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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Asymptotic log-concavity of dominant lower Bruhat intervals
显性 Bruhat区间 渐近对数凹性
2023/11/13
The unimodality of lower Bruhat intervals for the “upper half” remains as an open problem. For affine Weyl group W with corresponding finite Weyl group W_f, we prove that lower W_f-parabolic Bruhat in...
The Boros-Moll polynomials Pm(a) arise in the evaluation of a quartic integral. It has been conjectured by Boros and Moll that these polynomials are infinitely log-concave. In this paper, we show that...
The Interlacing Log-concavity of the Boros-Moll Polynomials
interlacing log-concavity log-concavity the Boros-Moll polynomials
2014/6/3
We introduce the notion of interlacing log-concavity of a polynomial sequence {Pm(x)}m≥0, where Pm(x) is a polynomial of degree m with positive coefficients. This sequence is said to be interlacingly ...
Higher Order Log-Concavity in Euler's Difference Table
log-concavity 2-log-concavity reverse ultra log-concavity Euler's difference table
2014/6/3
For 0 ≤ k ≤ n, let ekn be the entries in Euler's difference table and let dkn = ekn/k!. Dumont and Randrianarivony showed ekn equals the number of permutations on [n] whose fixed points are contained ...
On Log-concavity of the Generalized Marcum Q Function
increasing failure rate log-concavity modified Bessel function noncentral chi square
2011/6/20
It is shown that, if 1/2 then the generalized
Marcum Q function Q(a, b) is log-concave in b 2 [0,1). This
proves a conjecture of Sun, Baricz and Zhou (2010). We also
point out relevant results...
Relative log-concavity and a pair of triangle inequalities
Bernoulli sum binomial approximation Hoeffding’s inequality maximum entropy
2010/10/19
The relative log-concavity ordering $\leq_{\mathrm{lc}}$ between probability mass functions (pmf's) on non-negative integers is studied. Given three pmf's $f,g,h$ that satisfy $f\leq_{\mathrm{lc}}g\le...
The Reverse Ultra Log-Concavity of the Boros-Moll Polynomials
log-concavity reverse ultra log-concavity Boros-Moll polynomials
2014/6/3
We prove the reverse ultra log-concavity of the Boros-Moll polynomials. We further establish an inequality which implies the log-concavity of the sequence {i!di(m)} for any m ≥ 2, where di(m) are the ...
On some properties of life distributions with increasing elasticity and log-concavity
Life distributions Log-concavity Closure property
2010/9/14
The purpose of this paper is to extend and systematize known results in log-concave and log-convex properties of life distributions. Also, to discuss the closure property of increasing generalized fai...