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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...
Measuring, simulating and exploiting the head concavity phenomenon in BKZ
BKZ algorithm simulator
2018/11/14
The Blockwise-Korkine-Zolotarev (BKZ) lattice reduction algorithm is central in cryptanalysis, in particular for lattice-based cryptography. A precise understanding of its practical behavior in terms ...
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...
Monotonicity and Concavity Properties of Some Functions Involving the Gamma Function with Applications
Gamma function Monotonicity Concavity Equivalence
2008/6/30
In this article, we give the monotonicity and concavity properties of some
functions involving the gamma function and some equivalence sequences to the
sequence n! with exact equivalence constants...