Related papers: Multilinear singular integral forms of Christ-Jour…
We prove the existence of infinitely many solutions to a fractional Choquard type equation \[ (-\Delta)^s_p u+V(x)|u|^{p-2}u=(K\ast g(u))g'(u)+\varepsilon_W W(x)f'(u)\quad\text{in }\mathbb{R}^N \] involving fractional $p$-Laplacian and a…
We show that for fixed $d>3$ and $n$ growing to infinity there are at least $(n!)^{d-2 \pm o(1)}$ different labeled combinatorial types of $d$-polytopes with $n$ vertices. This is about the square of the previous best lower bounds. As an…
In this talk we discuss the solution for the sunrise integral around two and four space-time dimensions in terms of a generalised elliptic version of the multiple polylogarithms. In two space-time dimensions we obtain a sum of three…
We give an explicit combinatorial formula for the Schur expansion of Macdonald polynomials indexed by partitions with second part at most two. This gives a uniform formula for both hook and two column partitions. The proof comes as a…
In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…
In this paper we develop a new weak convergence and compact embedding method to study the existence and uniqueness of the $L_{\rho}^2({\mathbb{R}^{d}};{\mathbb{R}^{1}})\otimes L_{\rho}^2({\mathbb{R}^{d}};{\mathbb{R}^{d}})$ valued solution…
We show that given a positive integer $m$, a real number $p\in\left[ 2,\infty\right)$ and $1\leq s<p^{\ast}$ the set of non--multiple $\left( r;s\right)$--summing $m$--linear forms on $\ell_{p}\times\cdots\times \ell_{p}$ contains, except…
We classify polynomial models for real hypersurfaces in $\mathbb C^N$, which admit nonlinearizable infinitesimal CR automorphisms. As a consequence, this provides an optimal 1-jet determination result in the general case. Further we prove…
In this expository paper, we illustrate two explicit methods which lead to special $L$-values of certain modular forms admitting complex multiplication (CM), motivated in part by properties of $L$-functions obtained from Calabi-Yau…
The purpose of this note is to introduce a multiplication on the set of homogeneous polynomials of fixed degree d, in a way to provide a duality theory between monomial ideals of K[x_1,\ldots,x_d] generated in degrees \leq n and block…
We study properties of relative types of plurisubharmonic functions with respect to maximal plurisubharmonic weights. It is shown that they give a general form for upper semicontinuous, tropically additive functionals on plurisubharmonic…
We consider a special class of the multi-linear forms studied by Brascamp and Lieb. For these forms, we are able to characterize the L^p spaces for which the form is bounded. We use this characterization to study a non-linear map that…
We give criteria for Morin singularities into higher dimensions. As an application, we study the number of A-isotopy classes of Morin singularities.
Systems with singular higher order- Lagrangians are investigated by using the extended form of the canonical method. Besides, the canonical path integral formulation is generalized using the Hamilton- jacobi formulation to investigate…
Closed form expressions for a multivector exponential and logarithm are presented in real Clifford geometric algebras Cl(p,q)when n=p+q=1 (complex and hyperbolic numbers) and n=2 (Hamilton, split and conectorine quaternions). Starting from…
A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…
In this article, we study the local behaviour of the multiple polylogarithm functions at integer points, in the $s$-aspect. This is done by writing a Laurent type expansion at integer points, involving certain power series and rational…
We present results on the existence of long arithmetic progressions in the Thue-Morse word and in a class of generalised Thue-Morse words. Our arguments are inspired by van der Waerden's proof for the existence of arbitrary long…
There has been recent interest in the conditional central limit question for (strictly) stationary, ergodic processes $...,X_{-1},X_0,X_1,...$ whose partial sums $S_n=X_1+...+X_n$ are of the form $S_n=M_n+R_n$, where $M_n$ is a square…
Pairwise non isomorphic semigroups obtained from the semigroup PT_n of all partial transformations by the deformed multiplication proposed by Ljapin are classified.