In this paper we prove an asymptotically tight bound (asymptotic with respect to the number of polynomials for fixed degrees and number of variables) on the number of connected components of the realizations of all realizable sign conditions of a family of real polynomials. More precisely, we prove that the number of connected components of the realizations of all realizable sign conditions of ...

We prove an asymptotically tight bound (asymptotic with respect to the number of polynomials for fixed degrees and number of variables) on the number of semi-algebraically connected components of the realizations of all realizable sign conditions of a family of real polynomials. More precisely, we prove that the number of semi-algebraically connected components of the realizations of all realiz...

The impact of secondary flows on the flow velocity in open channel bends and confluences was simulated using three-dimensional (3D) numerical models. Reynolds-averaged Navier–Stokes equation system utilized as governing equations two different turbulence models were employed this study: standard k-? model realizable k–? model. In a recent study by authors, rigid lid approach used, which does no...

A k-digraph is an orientation of a multi-graph that is without loops and contains at most k edges between any pair of distinct vertices. We obtain necessary and sufficient conditions for a sequence of non-negative integers in non-decreasing order to be a sequence of numbers, called marks (k-scores), attached to vertices of a k-digraph. We characterize irreducible and uniquely realizable mark se...

In a recent paper, we gave a generalization of extremal problems involving certain graphtheoretic invariants. In that work, we defined a (p, A, 8, A) graph as a graph having p points, maximum degree A, minimum degree 6, and line-connectivity A. An arbitrary quadruple of integers (a, b, c, d) was called (p, A, & A) realizable if there is a (p, A, 8, A) graph with p = a, A = b, 8 = c, and A = d. ...

Numerical simulations have been undertaken for the benchmark problem in a Square cavity by using computational fluid dynamics software. This work aims at discussing the fundamental numerical and computational fluid dynamic aspects which can lead to the definition of the following meshing methods and turbulence models. The meshes used for the simulation are hexahedral, hexahedral cell with near ...

A generalization of the well-known shu f l e network i s proposed f o r multihop lightwave communication. In the classical definition of 4 shu f l e network, i.e., N = kpk where N i s the number of nodes and k i s the n u m ber of stages w i th base p , the realizable values of N are veay discrete and m a n y of the intermediate values of N are no t ,realizable. In this paper, we propose 4 new ...