Related papers: Maximal Hamiltonian tori for polygon spaces
With any integer convex polytope $P\subset\midR^n$ we associate a multivariate hypergeometric polynomial whose set of exponents is $\midZ^{n}\cap P.$ This polynomial is defined uniquely up to a constant multiple and satisfies a holonomic…
Explicit expressions are given for the actions and radial matrix elements of basic radial observables on multi-dimensional spaces in a continuous sequence of orthonormal bases for unitary SU(1,1) irreps. Explicit expressions are also given…
We discuss the Hardy-Littlewood maximal operator on discrete Morrey spaces of arbitrary dimension. In particular, we obtain its boundedness on the discrete Morrey spaces using a discrete version of the Fefferman-Stein inequality. As a…
We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in…
Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable one-dimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported…
Given a lattice polygon $P$ with $g$ interior lattice points, we associate to it the moduli space of tropical curves of genus $g$ with Newton polygon $P$. We completely classify the possible dimensions such a moduli space can have. For…
We prove that if a subset of the d-dimensional vector space over a finite field is large enough, then it contains many k-tuples of mutually orthogonal vectors.
The main goal of this paper is to construct Mather measures for space-time periodical nonconvex Hamiltonians.
We characterize componentwise linear monomial ideals with minimal Taylor resolution and consider the lower bound for the Betti numbers of componentwise linear ideals.
Under the assumption that orthogonal polynomials of several variables admit an addition formula, we can define a convolution structure and use it to study the Fourier orthogonal expansions on a homogeneous space. We define a maximal…
We study the supremum of the volume of hyperbolic polyhedra with some fixed combinatorics and with vertices of any kind (real, ideal or hyperideal). We find that the supremum is always equal to the volume of the rectification of the…
We consider a problem posed by Erd\H{o}s, Herzog and Piranian on the maximum product of distances of a point set of order $n$ with a given diameter. We prove that it is sufficient to consider convex polygons and obtain results on the…
In this paper we find exact formulas for the numbers of partitions and compositions of an element into $m$ parts over a finite field, i.e. we find the number of nonzero solutions of the equation $x_1+x_2+...+x_m=z$ over a finite field when…
We establish some bounds on the number of higher-dimensional partitions by volume. In particular, we give bounds via vector partitions and MacMahon's numbers.
We study torus actions on symplectic manifolds with proper moment maps in the case that each reduced space is two-dimensional. We provide a complete set of invariants for such spaces. Our proof uses sheaves of groupoids of Hamiltonian…
We investigate the finite subgroups that occur in the Hamiltonian quaternion algebra over the real subfield of cyclotomic fields. When possible, we investigate their distribution among the maximal orders.
We summarise the procedure used to find the classical masses of Higgs particle, massive gauge boson and t'Hooft-Polyakov monopole in non-Hermitian gauge field theory. Their physical regions are explored, and the mechanism of the real value…
We study the existence of infinite-dimensional invariant tori in a mechanical system of infinitely many rotators weakly interacting with each other. We consider explicitly interactions depending only on the angles, with the aim of…
We generalize to some PDEs a theorem by Nekhoroshev on the persistence of invariant tori in Hamiltonian systems with $r$ integrals of motion and $n$ degrees of freedom, $r\leq n$. The result we get ensures the persistence of an…
We review in detail the Hamiltonian dynamics for constrained systems. Emphasis is put on the total Hamiltonian system rather than on the extended Hamiltonian system. We provide a systematic analysis of (global and local) symmetries in total…