In this note we introduce a new family of entropy powers which are related to generalized entropies, called Sharma-Mittal and prove their concavity along diffusion processes generated by $L^{2}$ -Wasserstein gradient flows correspondi...

We discuss interplays between log-concave functions and log-concave sequences. We prove a Bernstein-type theorem, which characterizes the Laplace transform of logconcave measures on the half-line in terms of log-concavity of the alternating Taylor coefficients. We establish concavity inequalities for sequences inspired by the PrékopaLeindler and the Walkup theorems. One of our main tools is a s...

We prove two conjectures of Brändén on the real-rootedness of the polynomials Qn(x) and Rn(x) which are related to the Boros-Moll polynomials Pn(x). In fact, we show that both Qn(x) and Rn(x) form Sturm sequences. The first conjecture implies the 2-log-concavity of Pn(x), and the second conjecture implies the 3-log-concavity of Pn(x). AMS Classification 2010: Primary 26C10; Secondary 05A20, 30C15.

In their study of a quartic integral, Boros and Moll discovered a special class of Jacobi polynomials, which we call the Boros-Moll polynomials. Kauers and Paule proved the conjecture of Moll that these polynomials are logconcave. In this paper, we show that the Boros-Moll polynomials possess the ratio monotone property which implies the log-concavity and the spiral property. We conclude with a...