We present a new algorithm to model the input uncertainty and its propagation in incompressible flow simulations. The stochastic input is represented spectrally by employing orthogonal polynomial functionals from the Askey scheme as trial basis to represent the random space. A standard Galerkin projection is applied in the random dimension to obtain the equations in the weak form. The resulting...

We give a procedure of solving the weighted minimax flow problem in a polynomial time. The procedure utilizes the capacity modification technique and the binary search method. 1 . I NTRODUCTI ON We have considered variants of the maximum flow problems [5,6]. [5] discusses a minimax flo1N, i.e., the flow which minimizes the maximum arc-flow value among all flows of maximum flow value. [6] treats...

Within the smooth category, an intertwining is exhibited between the global rigidity of irreducible higher-rank Z Anosov actions on T and the classification of equilibrium-free flows on T that possess nontrivial generalized symmetries.

We formulate a Belief Propagation (BP) algorithm in the context of the capacitated minimum-cost network flow problem (MCF). Unlike most of the instances of BP studied in the past, the messages of BP in the context of this problem are piecewise-linear functions. We prove that BP converges to the optimal solution in pseudo-polynomial time, provided that the optimal solution is unique and the prob...

With the goal of providing the first example of application of a recently proposed method, thus demonstrating its ability to give results in principle, global stability of a version of the rotating Couette flow is examined. The flow depends on the Reynolds number and a parameter characterizing the magnitude of the Coriolis force. By converting the original Navier-Stokes equations to a finite-di...

We prove a polynomial upper bound on the deviation of ergodic averages for almost all directional flows on every translation surface, in particular, for the generic directional flow of billiards in any Euclidean polygon with rational angles.

Consider a convex set P in IR and a piecewise polynomial concave function F :P → IR. Let A be an algorithm that given a point x ∈ IR computes F (x) if x ∈ P, or returns a concave polynomial p such that p(x) < 0 but for any y ∈ P, p(y) ≥ 0. We assume that d is fixed and that all comparisons in A depend on the sign of polynomial functions of the input point. We show that under these conditions, o...

The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane. This is the first density result for the zeros of the Tutte polynomial in a region of positive volume. Our res...

Cardinality Maximum Flow Network Interdiction Problem (CMFNIP) is known to be strongly NP-hard problem in the literature. A particular case of CMFNIP has been shown to have reduction from clique problem. In the present work,an effort is being made to solve this particular case of CMFNIP in polynomial time. Direct implication of this solution is that the clique problem gets solved in polynomial ...

In this paper we seek to provide greater automation for formal deductive verification tools working with continuous and hybrid dynamical systems. We present an efficient procedure to check invariance of conjunctions of polynomial equalities under the flow of polynomial ordinary differential equations. The procedure is based on a necessary and sufficient condition that characterizes invariant co...