The complexity of the visibility region formed by a point light source after k diffuse reflections in a simple n-sided polygon is O(n), which is the first result polynomial in n, with no dependence on k. This bound is an exponential improvement over the previous bound of O(n2d(k+1)/2e+1) due to Prasad et al. [8].

We consider the equations of an incompressible, homogeneous fluid, occupying a bounded domain in R. The stress tensor has a general polynomial dependence on the symmetric velocity gradient. Our goal is to estimate the dimension of the global attractor in terms of the relevant physical constants.

We present exact calculations of the chromatic polynomial and resultant ground state entropy of the q-state Potts antiferromagnet on lattice strips that are homeomorphic expansions of a strip of the kagomé lattice. The dependence of the ground state entropy on the form of homeomorphic expansion is elucidated.

A derivative expansion of the Wegner-Houghton equation is derived for a scalar theory. The corresponding full non-perturbative renormalization group equations for the potential and the wavefunction renormalization function are presented. We also show that the two loop perturbative anomalous dimension for the O(N) theory can be obtained by means of a polynomial truncation in the field dependence...

In this paper we consider polynomial cointegrating relationships among stationary processes with long range dependence. We express the regression functions in terms of Hermite polynomials and we consider a form of spectral regression around frequency zero. For these estimates, we establish consistency by means of a more general result on continuously averaged estimates of the spectral density m...

A priori and a posteriori error estimates are derived for the numerical approximation of scalar and complex valued phase field models. Particular attention is devoted to the dependence of the estimates on a small parameter. For typical singularities the estimates depend on the inverse of the parameter in a polynomial as opposed to exponential dependence of estimates resulting from a straightfor...

This paper presents a new approach for computing the transitive closure of a union of relations describing all the dependences in both uniform and quasi-uniform perfectly-nested parameterized loops. This approach is based on calculating the basis of a dependence distance vectors set. The procedure has polynomial time complexity for most steps of calculations. This allows us to effectively extra...

To construct actions for describing superbranes propagating in AdS×S superbackgrounds we propose a coset space realization of these superbackgrounds which results in a short polynomial fermionic dependence (up to a six power in Grassmann coordinates) of target superspace supervielbeins and superconnections. Gauge fixing κ–symmetry in a way compatible with a static brane solution further reduces...

‎This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE)‎. ‎We are going to calculate polynomial and non-polynomial exact solutions by using Lie point symmetry‎. ‎We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎A generalized procedure for polynomial solution is pr...

In this paper we prove that a polynomial system can be always mapped by some rational mapping into a general quadratic system. This result is useful for studies of systems with a complex dynamics. One generalization is discussed. Our approach is based on theorems on algebraic dependent polynomials. Key-Words:Polynomial, polynomial system, quadratic system, rational mapping, algebraic dependence...