The drops are used to control the descents,  stabilize the bed level, and control the upstream water level in sloping channels with less slope than the ground slope. The current study presents a numerical analysis of hydraulic characteristics in the vertical drop using computational fluid dynamics. At first, the laboratory models were used for verification and choosing the best model of turbule...

In this paper we extend the study of bipartite graphs with the induced ε-density property introduced by Frankl, Rödl, and the author. For a given kpartite k-uniform hypergraph G we say that a k-partite k-uniform hypergraph R = (W1, . . . ,Wk,F) has the induced ε-density property if every subhypergraph ofR with at least ε|F| edges contains a copy of G which is an induced subhypergraph of R. We s...

We explore a number of problems related to learning and covering structured distributions. Hypothesis Selection: We provide an improved and generalized algorithm for selecting a good candidate distribution from among competing hypotheses. Namely, given a collection of N hypotheses containing at least one candidate that is ε-close to an unknown distribution, our algorithm outputs a candidate whi...

We prove that for any positive integer k and for ε = 1/((k + 2)(3k2 + 1)), the edges of any graph whose fractional arboricity is at most k + ε can be decomposed into k forests and a matching.

We consider the boundary value problem ∆u+ε k(x) e = 0 in a bounded, smooth domain Ω in R with homogeneous Dirichlet boundary conditions. Here ε > 0, k(x) is a non-negative, not identically zero function. We find conditions under which there exists a solution uε which blows up at exactly m points as ε→ 0 and satisfies ε ∫ Ω keε → 8mπ. In particular, we find that if k ∈ C(Ω̄), infΩ k > 0 and Ω is...

Let k[ε]2 := k[ε]/(ε2). The single valued real analytic n-polylogarithm Ln : C → R is fundamental in the study of weight n motivic cohomology over a field k, of characteristic 0. In this paper, we extend the construction in Ünver (Algebra Number Theory 3:1–34, 2009) to define additive n-polylogarithms lin:k[ε]2 → k and prove that they satisfy functional equations analogous to those of Ln . Unde...

We consider a second order damped-vibration equation Mẍ + D(ε)ẋ + Kx = 0, where M, D(ε), K are real, symmetric matrices of order n. The damping matrix D(ε) is defined by D(ε) = Cu + C(ε), where Cu presents internal damping and rank(C(ε)) = r, where ε is dampers’ viscosity. We present an algorithm which derives a formula for the trace of the solution X of the Lyapunov equation AX + XA = −B, as a...

k-Anonymity and ε-differential privacy are two mainstream privacy models, the former introduced to anonymize data sets and the latter to limit the knowledge gain that results from the inclusion of one individual in the data set. Whereas basic k-anonymity only protects against identity disclosure, t-closeness was presented as an extension of k-anonymity that also protects against attribute discl...