where Ω is an open connected subset of R with a sufficiently smooth boundary, ρ and θ are sufficiently smooth scalar functions on Ω bounded below by a positive number, and u is a function on Ω that does not vanish uniformly. This eigenvalue PDE is the standard idealization of finding the vibrational modes of a thin plate clamped at the edges, in which the stiffness of the plate is given by θ, t...

A vertex|matching-partition (V |M) of a simple graph G is a spanning collection of vertices and independent edges of G. Let vertex v ∈ V have weight wv and edge e ∈ M have weight we. Then the weight of V |M is w(V |M) = ∏ v∈V wv · ∏ e∈M we. Define the vertex|matching-partition function of G as W(G) = ∑ V |M w(V |M). In this paper we study this function when G is a path and a cycle. We generate ...

We prove that a class of one-loop partition functions found by Dienes, giving rise to a vanishing cosmological constant to one-loop, cannot be realized by a consistent lattice string. The construction of non-supersymmetric string with a vanishing cosmological constant therefore remains as elusive as ever. We also discuss a new test that any one-loop partition function for a lattice string must ...

A new recursive procedure of the calculation of a restricted partition function is suggested. An explicit combinatorial formula for the restricted partition function is found based on this procedure.

We obtain large N asymptotics for the random matrix partition function

The color-flavor transformation for the unitary group (Zirnbauer 1996) is extended to the special unitary group. The resulting partition function is represented as sum over disconnected sectors characterized by a U(1)-charge. Application to low energy QCD on a lattice leads to a theory where the inverse number of colors appears as expansion parameter. We use a saddle point approximation to esti...

In general partition function form games, the recursive core coalition structure may be either coarser or finer than the one that maximizes the social surplus. Moreover, the recursive core structure is typically different from the one predicted by the α-core. We fully implement the recursive core for general games, including non-superadditive games where the grand coalition does not form in equ...

We present the construction of the partition function of 3-dimensional gravity in the Lorentzian regime as a state sum model over a triangulation. This generalize the work of Ponzano and Regge to the case of Lorentzian signature.

The Nekrasov conjecture predicts a relation between the partition function for N = 2 supersymmetric Yang–Mills theory and the Seiberg-Witten prepotential. For instantons on R, the conjecture was proved, independently and using different methods, by Nekrasov-Okounkov, Nakajima-Yoshioka, and Braverman-Etingof. We prove a generalized version of the conjecture for instantons on noncompact toric sur...

Abstract We study the form of the Turaev-Viro partition function Z(M) for different 3-manifolds with boundary. We show that for S2 boundaries Z(M) factorizes into a term which contains the boundary dependence and another which depends only on the topology of the underlying manifold. From this follows easily the formula for the connected sum of two manifolds Z(M#N ). For general Tg boundaries th...