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Using a natural representation of a $1/s$-concave function on $\mathbb{R}^d$ as a convex set in $\mathbb{R}^{d+1},$ we derive a simple formula for the integral of its $s$-polar. This leads to convexity properties of the integral of the…

A systematic derivation of Boltzmann equation is presented in the framework of closed-time-path formalism. Introducing a new type of probe, the expectation value of number operator is calculated as a functional of source. Then solving for…

We will prove a reverse Rogers-Shephard inequality for log-concave functions. In some particular cases, the method used for general log-concave functions can be slightly improved, allowing us to prove volume estimates for polars of…

We obtain necessary and sufficient conditions on a function in order that it be the Laplace transform of an absolutely monotonic function. Several closely related results are also given.

We define the concept of weighted lattice polynomial functions as lattice polynomial functions constructed from both variables and parameters. We provide equivalent forms of these functions in an arbitrary bounded distributive lattice. We…

We consider an inverse problem of recovering the non-linearity in the one dimensional variable exponent $p(x)$-Laplace equation from the Dirichlet-to-Neumann map. The variable exponent can be recovered up to the natural obstruction of…

We recast homogeneous linear recurrence sequences with fixed coefficients in terms of partial Bell polynomials, and use their properties to obtain various combinatorial identities and multifold convolution formulas. Our approach relies on a…

We study the error of the number of points of a unimodular lattice that fall in a strictly convex and analytic set having the origin and that is dilated by a factor $t$. The aim is to generalize the result of a previous article. We first…

We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.

We find auto-Backlund transformation for the r-th double modified dispersionless Kadomtsev--Petviashvili equation.

We prove an exact formula for the second moment of Rankin-Selberg $L$-functions $L(1/2,f \times g)$ twisted by $\lambda_f(p)$, where $g$ is a fixed holomorphic cusp form and $f$ is summed over automorphic forms of a given level $q$. The…

The Laplace transform of partial sums of the square of a non-centered Gauss-Markov process, conditioning on its starting point, is explicitly computed. The parameters of multiplicative ergodicity are deduced.

We deal with a class of one-parameter family of integral transforms of Bargmann type arising as dual transforms of fractional Hankel transform. Their ranges are identified to be special subspaces of the weighted hyperholomorphic left…

We use the so called resolvent transform method to study the cyclicity of the one point mass singular inner function in weighted Bergman type spaces.

Recent lattice calculations of hadron structure functions are described.

In this paper, using the Bregman distance, we introduce a new projection-type algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points. Then the strong convergence of the sequence…

Watson proved Kirkman's hypothesis (partially solved by Cayley). Using Lagrange Inversion, we drastically shorten Watson's computations and generalize his results at the same time.

We show that methods developed in the context of perturbative calculations can be transferred to non-perturbative calculations. We demonstrate that correlation functions on the lattice can be computed with the method of differential…

The inverse problem of the calculus of variations consists in determining if the solutions of a given system of second order differential equations correspond with the solutions of the Euler-Lagrange equations for some regular Lagrangian.…

Using results from spectral theory of Eisenstein series, we prove a formula for the second moment of the Siegel transform when averaged over the subspace of symplectic lattices. This generalizes the classical formula of Rogers for the…