Let D be the open unit disk in the complex plane. For ε > 0 we consider the sector Σε = {z ∈ C : | arg z| < ε}. We prove that for every α ≥ 0 and for each ε > 0 there is a constant K > 0 depending only on α and ε such that for any function f in the weighted Bergman space Aα univalent on D, and f(0) = 0, then ∫ f−1(Σε) |f(z)|dAα(z) > K‖f‖1,α. This result extends a theorem of Marshall and Smith i...

Let H be a given (possibly empty) family of connected graphs, each containing a cycle, and let G be a arbitrary finite H-free graph with minimum degree at least k. For p ∈ [0, 1], we form the p-random subgraph Gp of G by independently keeping each edge of G with probability p. Extending a classical result of Ajtai, Komlós, and Szemerédi, we prove that for every positive ε, there exists a positi...

Different variants for buoyancy-affected terms in k-ε turbulence model have been utilized to predict the flow parameters more accurately, and investigate applicability of alternative k-ε turbulence buoyant closures in numerical simulation of a horizontal gravity current. The additional non-isotropic turbulent stress due to buoyancy has been considered in production term, based on Algebraic Stre...

We extend a result of Ramaré and Rumely, 1996, about the Chebyshev function θ in arithmetic progressions. We find a map ε(x) such that | θ(x; k, l)− x/φ(k) |< xε(x) and ε(x) = O ( 1 lna x ) (∀a > 0), whereas ε(x) is a constant. Now we are able to show that, for x > 1531, | θ(x; 3, l)− x/2 |< 0.262 x lnx and, for x > 151, π(x; 3, l) > x 2 lnx .

We extend a result of Ramaré and Rumely, 1996, about the Chebyshev function θ in arithmetic progressions. We find a map ε(x) such that | θ(x; k, l)− x/φ(k) |< xε(x) and ε(x) = O ( 1 lna x ) (∀a > 0), whereas ε(x) is a constant. Now we are able to show that, for x > 1531, | θ(x; 3, l)− x/2 |< 0.262 x lnx and, for x > 151, π(x; 3, l) > x 2 lnx .

Hub labeling schemes are popular methods for computing distances on road networks and other large complex networks, often answering to a query within few microseconds graphs with millions of edges. In this work, we study their algorithmic applications beyond distance queries. Indeed, several implementations hub labels were reported have good practical performances, both in terms pre-processing ...

Nitriding of Fe-1 wt.% Cu and Fe-5 alloys at 813 K leads to the formation predominantly γ′-iron nitride phase (γ′-Fe4N) when using nitriding conditions, which lead pronounced ε-iron (ε-Fe3N1+x) upon pure α-Fe. Energy dispersive X-ray analysis reveals that developing γ′ can attain a content corresponding base material. In contrast, tiny amounts ε-nitride eventually develop contain considerably l...

We show that AC0 circuits on n variables with depth d and sizem have at most 2−Ω(k/ logd−1 m) of their Fourier mass at level k or above. Our proof builds on a previous result by Håstad (SICOMP, 2014) who proved this bound for the special case k = n. Our result improves the seminal result of Linial, Mansour and Nisan (JACM, 1993) and is tight up to the constants hidden in the Ω notation. As an a...