Abstract Let K/k be an extension of number fields. We describe theoretical results and computational methods for calculating the obstruction to Hasse norm principle defect weak approximation one torus \[R_{K/k}^1{\mathbb{G}_m}\] . apply our techniques give explicit computable formulae when normal closure has symmetric or alternating Galois group.

foliar analysis of natural deciduous tree species of basswood (tilia americana l.) (ba), american beech (acer grandifolia enrh) (be), and white ash (fraxinus americana l.) (wa) was carried out in 1994 in southern quebec. the diagnosis and recommendation integrated system (dris) was developed from the traditional method to find the preliminary norm and indices of n, p, k, ca, and mg for the ...

We prove the Simons-Johnson theorem for the sums Sn of m-dependent random variables, with exponential weights and limiting compound Poisson distribution CP(s, λ). More precisely, we give sufficient conditions for ∑ ∞ k=0 ehk|P (Sn = k)−CP(s, λ){k}| → 0 and provide an estimate on the rate of convergence. It is shown that the Simons-Johnson theorem holds for weighted Wasserstein norm as well. The...

We obtain a quantitative version of the classical Chevalley-Weil theorem for curves. Let φ : C̃ → C be an unramified morphism of non-singular plane projective curves defined over a number field K. We calculate an effective upper bound for the norm of the relative discriminant of the number field K(Q) over K for any point P ∈ C(K) and Q ∈ φ(P ). 2000 MCS: 14G25, 14H25, 11G30.

Let K be a p-adic field. We give an explicit characterization of the abelian extensions of K of degree p by relating the coefficients of the generating polynomials of extensions L/K of degree p to the exponents of generators of the norm group NL/K(L ∗). This is applied in an algorithm for the construction of class fields of degree pm, which yields an algorithm for the computation of class field...

for any positive integer k is bounded above by a quantity that is independent of k. Hence, whenever A(x) is divisible by a cylcotomic polynomial and N is su ciently large, there will be Q(x) 2 Z[x] with arbitrarily large Euclidean norm and with kAQk N . It is reasonable, however, to expect that the Euclidean norm of Q(x) is bounded whenever A(x) is free of cyclotomic factors. This in fact is th...

We consider the operator T = m k=1 A 1k ⊗ A 2k (1 ≤ m < ∞), where A lk are n l × n l matrices (k = 1,. .. , m; l = 1, 2), ⊗ means the tensor product. Norm estimates for the resolvent of that operator are derived. By these estimates, we obtain bounds for a solution X of the equation m k=1 A 1k X A 2k = C and explore perturbations of that equation. The norm estimates for the resolvent of T enable...

Based on the analysis of Cockburn et. al. [Math. Comp. 78 (2009), pp. 1-24] for a selfadjoint linear elliptic equation, we first discuss superconvergence results for nonselfadjoint linear elliptic problems using discontinuous Galerkin methods. Further, we have extended our analysis to derive superconvergence results for quasilinear elliptic problems. When piecewise polynomials of degree k ≥ 1 a...

It has been observed from the authors’ numerical experiments (2007) that the Local Discontinuous Galerkin (LDG) method converges uniformly under the Shishkin mesh for singularly perturbed two-point boundary problems of the convection-diffusion type. Especially when using a piecewise polynomial space of degree k, the LDG solution achieves the optimal convergence rate k+1 under the L2-norm, and a...

Reconstruction of signals or images from a few discrete Fourier transform (DFT) values has applications in MRI and SAR. Many real-world signals can be sparsified by an invertible transformation, such as wavelets, into a sparse (mostly zero, with K nonzero values at unknown locations) signal. This Ksparse signal can be reconstructed using the K lowestfrequency DFT values using Prony’s method or ...