Suppose $$\{\lambda _d\}$$ are Selberg’s sieve weights and $$1 \le w < y x$$ . Graham’s estimate on the Barban–Vehov problem shows that $$\sum _{1 n x} (\sum _{d|n} \lambda _d)^2 = \frac{x}{\log (y/w)} + O(\frac{x}{\log ^2(y/w)})$$ We prove an analogue of this for a sum over ideals arbitrary number field k. Our asymptotic remains same; only difference is effective error term may depend arithmet...

The boundedness on weighted local Hardy spaces h 1;p w of the oscil-latory singular integral Tf(x) = Z R n e iQ(x;y) K(x; y)f(y)dy is considered when Q(x; y) = P(x ? y) for some real-valued polynomial P with its degree not less than two. Also a suucient and necessary condition on polynomial Q on R n R n such that T maps h 1;p w to weighted integrable function spaces L 1 w is found. AMS subject ...

We prove two extensions of the Hales-Jewett coloring theorem. The first is a polynomial version of a finitary case of Furstenberg and Katznelson’s multiparameter elaboration of a theorem, due to Carlson, about variable words. The second is an “idempotent” version of a result of Carlson and Simpson. MSC2000: Primary 05D10; Secondary 22A15. For k,N ∈ N, let W k denote the set of length-N words on...

Let n be a positive integer or infinity (denote ∞). We denote by W ∗(n) the class of groups G such that, for every subset X of G of cardinality n + 1, there exist a positive integer k, and a subset X0 ⊆ X, with 2 ≤ |X0| ≤ n + 1 and a function f : {0, 1, 2, . . . , k} −→ X0, with f(0) 6= f(1) and non-zero integers t0, t1, . . . , tk such that [x0 0 , x t1 1 , . . . , x tk k ] = 1, where xi := f(...

K e y w o r d s K i n e t i c equations, Navier-Stokes system, Singularly perturbed problem, Hydrodynamic limit. The Boltzmann equation, in the hydrodynamic limit, as both the Knudsen number and the Mach number are of the same order and tend to 0, is consistent with the incompressible NavierStokes equation (set [1-a]). Our aim is to study the incompressible macroscopic limit for the Enskog kine...

Proof We give a detailed proof sketch. (Note that the proof we give here is different from the one in [1]; in particular, we do not rely on the existence of oblivious Turing machines.) Let L be a language in NP. This means there is a Turing machine M and a polynomial p such that (1) M(x,w) runs in time p(|x|), and (2) x ∈ L if and only if there exists a w for which M(x,w) = 1. Note that we may ...

and Applied Analysis 3 estimates in L2-norm under very general changes in the mesh in Section 4. In Section 5, we present results of numerical experiment, which confirm our theoretical results. Throughout the analysis, the symbol K will denote a generic constant, which is independent of mesh parameters Δt and h and not necessarily the same at different occurrences. 2. The Godunov-Mixed Method o...

We prove the following theorem. Let G be a graph of order n and let W V(G). If |W | 3 and dG(x)+dG( y) n for every pair of non-adjacent vertices x, y # W, then either G contains cycles C , C, ..., C |W | such that C i contains exactly i vertices from W (i=3, 4, ..., |W | ), or |W |=n and G=Kn 2, n 2 , or else |W |=4, G[W]=K2, 2 . This generalizes a result of J. A. Bondy (1971, J. Combin. Theory...

We study two families of orthogonal polynomials with respect to the weight function w(t)(t2−‖x‖2)μ−12, μ>−12, on cone {(x,t):‖x‖≤t,x∈Rd,t>0} in Rd+1. The first family consists monomial Vk,n(x,t)=tn−|k|xk+⋯ for k∈N0d |k|≤n, which has least L2 norm among all form tn−|k|xk+P deg⁡P≤n−1, and we will provide an explicit construction Vk,n. second defined by Rodrigues type formulas when w is either Lag...