Abstract We expand upon the notion of equivariant log concavity and make conjectures for Orlik–Solomon algebras matroids, Cordovil oriented Orlik–Terao hyperplane arrangements. In case Coxeter arrangement Lie algebra $\mathfrak{s}\mathfrak{l}_n$, we exploit theory representation stability to give computer-assisted proofs these in low degree.

We give a sufficient condition for the strict parabolic power concavity of convolution in space variable function defined on \(\mathbb {R}^n \times (0,+\infty )\) and {R}^n\). Since naturally implies {R}^n\), our two functions As applications, we show Gauss–Weierstrass integral Poisson upper half-space.

This paper studies a parabolic equation with exponential nonlinearity, which has several applications, for example the self-trapped beams in plasma. Based on modified concavity method we prove blow-up of solution initial data high energy. We also proposed solution’s lower and upper bound time equation. Our results complement existing results.

The ratio monotonicity of a polynomial is a stronger property than log-concavity. Let P (x) be a polynomial with nonnegative and nondecreasing coefficients. We prove the ratio monotone property of P (x+ 1), which leads to the log-concavity of P (x+ c) for any c ≥ 1 due to Llamas and Mart́ınez-Bernal. As a consequence, we obtain the ratio monotonicity of the Boros-Moll polynomials obtained by Che...

Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured in On the similarity of the entropy power inequality and the BrunnMinkowski inequality (IEEE Trans. Inform. Theory 30 (1984), no. 6, 837-839) the 1 n -concavity of the outer parallel volume of measurable sets as an analogue of the concavity of entropy power. We inve...

Lattice gauge theory (LGT) results denote to the confinement for quark potential in various Yang–Mills theories. This property can also be obtained G(2) theory. LGT calculations show that should have downward concavity behavior. Confinement properties explained using thick center vortex model. However this model, an upward is seen some intervals of potential. Considering reason concavity, it sh...

We investigate stability of invariant measures diffusion processes with respect to $L^p$ distances on the coefficients, under an assumption log-concavity. The method is a variant technique introduced by Crippa and De Lellis study transport equations. As application, we prove partial extension inequality Ledoux, Nourdin Peccati relating Stein discrepancies non-Gaussian setting via moment map con...

This paper provides some results on different types of convexity and concavity in the class of multivariate copulas. We also study their properties and provide several examples to illustrate our results.