Related papers: A note on generating functions
We present an approach to Gromov-Witten invariants that works on arbitrary (closed) symplectic manifolds. We avoid genericity arguments and take into account singular curves in the very formulation. The method is by first endowing mapping…
We uncover the lowest order differential invariants of Lagrangian submanifolds under affine symplectic maps, and find out what happens when they are constant.
We introduce the notion centre of a convex set and study the space of continuous affine functions on a compact convex set with a centre. We show that these spaces are precisely the dual of a base normed space in which the underlying base…
The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically…
A function which is analytic and bounded in the Unit disk is called a generator for the Hardy space or the Bergman space if polynomials in that function are dense in the corresponding space. We characterize generators in terms of sub-spaces…
We present an overview of the role of generating functions in quantum mechanical contexts, mainly in the modern theory of polarization and in the study of quantum phase transitions. Generating functions enable the derivation of moments and…
These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.
This paper deals with certain fundamental results about affine hulls and simplices in a real normed linear space. The framework of the paper is Bishop's constructive mathematics, which, with its characteristic interpretation of existence as…
We give asymptotic expressions for the number of commuting matrices over finite fields. For this, we use product expansions for the corresponding generating functions.
We construct harmonic functions in the quarter plane for discrete Laplace operators. In particular, the functions are conditioned to vanish on the boundary and the Laplacians admit coefficients associated with transition probabilities of…
Let $\sum_{\beta\in\nats^d} F_\beta x^\beta$ be a multivariate power series. For example $\sum F_\beta x^\beta$ could be a generating function for a combinatorial class. Assume that in a neighbourhood of the origin this series represents a…
In the Hilbert space of n qubits, we introduce the symplectic space (n odd) and the orthogonal space (n even) via the spin-flip operator. Under this mathematical structure we discuss some properties of n qubits, including homomorphically…
The recently developed theory of extended generating functions of symplectic maps are combined with methods to prove invertibility via high-order Taylor model methods to obtain rigorous lower bounds for the domains of definition of…
By the simple finite element method, we study the symplectic, multisymplectic structures and relevant preserving properties in some semi-linear elliptic boundary value problem in one-dimensional and two-dimensional spaces respectively. We…
A simple permutation is one that does not map a nontrivial interval onto an interval. It was recently proved by Albert and Atkinson that a permutation class with only finitely simple permutations has an algebraic generating function. We…
Symplectic invariants introduced in math-ph/0702045 can be computed for an arbitrary spectral curve. For some examples of spectral curves, those invariants can solve loop equations of matrix integrals, and many problems of enumerative…
We describe the extent to which Ionel-Parker's proposed refinement of the standard relative Gromov-Witten invariants sharpens the usual symplectic sum formula. The key product operation on the target spaces for the refined invariants is…
I study flux groups of compact symplectic manifolds. Under some topological assumptions, I give a new estimate of the rank of flux groups and give a method of construcion of compact symplectic aspherical manifolds.
Motivated by relations with a symplectic invariant known as the "cylindrical symplectic capacity", in this note we study the expectation of the area of a minimal projection to a complex line for a randomly rotated cube.
The main aim of this paper is twofold: (1) Suggesting a statistical mechanical approach to the calculation of the generating function of restricted integer partition functions which count the number of partitions --- a way of writing an…