We study quasi–Monte Carlo algorithms based on low discrepancy sequences for multivariate integration. We consider the problem of how the minimal number of function evaluations needed to reduce the worst-case error from its initial error by a factor of ε depends on ε−1 and the dimension s. Strong tractability means that it does not depend on s and is bounded by a polynomial in ε−1. The least po...

The number of lattice bond trees in the square lattice (counted modulo translations), t(n), is a basic quantity in lattice statistical mechanical models of branched polymers. This number is believed to have asymptotic behavior given by t(n) approximately Alambda(n)n(-theta), where A is an amplitude, lambda is the growth constant, and theta the entropic exponent. In this paper, we show that lamb...

We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation $ \begin{equation*} u_{t} = \Delta u + |u|^{p} \end{equation*} $ on complete Riemannian manifolds dimension n \geq 5 with nonnegative Ricci tensor, when p is smaller than critical Sobolev exponent \frac{n+2}{n-2} $.

It is proved that the free m-generated Burnside groups B(m, n) of exponent n are infinite provided that m > 1 , n > 248 . In 1902 William Burnside posed the following problem [2]. Does a group G have to be finite provided that G has a finite set of generators and its elements satisfy the identity x" — 1 ? In other words, must a finitely generated group G of exponent n be finite? In the same pap...

A number of results for reactions involving subdiffusive species, all with the same anomalous exponent , have recently appeared in the literature and can often be understood in terms of a subordination principle whereby time in ordinary diffusion is replaced by tgamma. However, very few results are known for reactions involving different species characterized by different anomalous diffusion ex...

We show that if G is any p-group of class at most two and exponent p, then there exist groups G1 and G2 of class two and exponent p that contain G, neither of which can be expressed as a central product, and with G1 capable and G2 not capable. We provide upper bounds for rank(Gi ) in terms of rank(G) in each case.

We obtained the global persistence exponent for a continuous spin model on the simple cubic lattice with double-exchange interaction by using two different methods. First, we estimated the exponent theta(g) by following the time evolution of probability P(t) that the order parameter of the model does not change its sign up to time t[P(t) approximately t(-theta(g)]. Afterwards, that exponent was...

We present a novel method for exactly solving (in fact, counting solutions to) general constraint satisfaction optimization with at most two variables per constraint (e.g. MAX-2-CSP and MIN-2-CSP), which gives the first exponential improvement over the trivial algorithm; more precisely, it is a constant factor improvement in the base of the runtime exponent. In the case where constraints have a...