The present article focuses on the evaluation of a first-moment closure model applicable to film cooling flow and heat transfer computations. The present first-moment closure model consists of a higher level of turbulent heat flux modeling in which two additional transport equations for temperature variance kθ and its dissipation rate εθ are ...

A. (Forgive my choice of) Notation. Let G be a complex, connected, semisimple (or reductive) Lie group, T a maximal torus in G, and K the identity component of the fixed points of an involution in G. Equivalently, K is the complexification of a maximal compact subgroup of the identity component of a real form of G. Of course we assume T ⊂ K. We let ΛG denote the lattice of T -characters (the we...

The area of distributed monitoring requires tracking the value of a function of distributed data as new observations are made. An important case is when attention is restricted to only a recent time period, such as the last hour of readings—the sliding window case. In this announcement, we outline a novel paradigm for handling such monitoring problems, which we dub the “forward/backward” approa...

Let P be a set of n points in Euclidean space and let 0< ε< 1. A wellknown result of Johnson and Lindenstrauss states that there is a projection of P onto a subspace of dimension O(ε−2 logn) such that distances change by at most a factor of 1+ ε. We consider an extension of this result. Our goal is to find an analogous dimension reduction where not only pairs but all subsets of at most k points...

An (α, β)-spanner of a graph G is a subgraph H that approximates distances in G within a multiplicative factor α and an additive error β, ensuring that for any two nodes u, v, dH(u, v) ≤ α ·dG(u, v)+β. This paper concerns algorithms for the distributed deterministic construction of a sparse (α, β)-spanner H for a given graph G and distortion parameters α and β. It first presents a generic distr...

Let X be a smooth projective variety defined over field k of characteristic 0 and let L nef line bundle k. We prove that if x∈X is k-rational point then the Seshadri constant ε(X,L,x) k‾ same as show, by constructing families examples, there are varieties whose global ε(X) zero. also result on existence curve with natural (and necessary) hypothesis.

The class FORMULA[s]∘G consists of Boolean functions computable by size- s De Morgan formulas whose leaves are any from a G. We give lower bounds and (SAT, Learning, pseudorandom generators ( PRG )) algorithms for FORMULA[n 1.99 ]∘G, classes G with low communication complexity . Let R (k) be the maximum k -party number-on-forehead randomized function in Among other results, we show following: •...

We prove that for every k and every ε > 0, there exists g such that every graph with tree-width at most k and odd-girth at least g has circular chromatic number at most 2 + ε.

Let’s quickly review some results from previous lectures. Definition 1 Let (Enc,Dec) denote an encryption scheme where Enc : {0, 1}m×{0, 1}n → {0, 1}λ and Dec : {0, 1}m × {0, 1}λ → {0, 1}n are functions. A correct encryption scheme satisfies ∀r, x Decr(Encr(x)) = x. Let R and X denote distributions on r and x respectively. (Enc,Dec) is said to be (k, ε)-secure if it is (R, ε)-secure for every k...