We show that f -vectors of matroid complexes of realizable matroids are strictly log-concave. This was conjectured by Mason in 1972. Our proof uses the recent result by Huh and Katz who showed that the coefficients of the characteristic polynomial of a realizable matroid form a log-concave sequence. We also prove a statement on log-concavity of h-vectors which strengthens a result by Brown and ...

We consider a skew product with the interval [0,a] as a fiber space and maps in fibers that are concave and fix 0. If the map in the base is an irrational rotation of a circle, then it has been known that under some additional conditions there exists a Strange Nonchaotic Attractor (SNA) for the system. The proofs involved Lyapunov exponents and Birkhoff Ergodic Theorem. We show that the existen...

Abstract In this work, we investigate blowup phenomena for nonlinearly damped viscoelastic equations with logarithmic source effect and time delay in the velocity. Owing to nonlinear damping term instead of strong or linear dissipation, cannot apply concavity method introduced by Levine. Thus, utilizing energy method, show that solutions not only non-positive initial but also some positive blow...

Tools from advanced real analysis and the Prékopa-Borell Theorem are combined to derive a tight sufficient condition for regularity (R. Myerson, Optimal auction design, Mathematics of Operations Research 6, 1981, pp. 58-73). The conventional log-concavity condition arises as a special case. The approach allows various generalizations, for instance to multidimensional types. Regularity is verifi...

Concave functions play a fundamental role in the structure of and minimization of badness-of-fit functions used in data analysis when extreme values of either parameters or data need to be penalized. This paper summarizes my findings about this role. I also describe three examples where concave functions are useful: building measures of badness-of-fit, building robust M -estimators, and buildin...

We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coefficients which allow us to characterise transport problems in a gradient flow setting, and form the basis of our introduction of a discrete version of the Benamou–Brenier formula. Further, we use these coefficients to state a new form of weighted log-concavity. These results a...