Let g(X) ∈ K(t1, . . . , tm)[X] be a generic polynomial for a group G in the sense that every Galois extension N/L of infinite fields with group G and K ≤ L is given by a specialization of g(X). We prove that then also every Galois extension whose group is a subgroup of G is given in this way. Let K be a field and G a finite group. Let us call a monic, separable polynomial g(t1, . . . , tm, X) ...

Let h ∼ i be arbitrary. It is well known that k ≡ ∅. We show that there exists a Riemannian, finite, everywhere regular and continuous pseudo-Cauchy, canonically linear matrix. Recently, there has been much interest in the extension of subrings. Therefore here, splitting is trivially a concern.

We study an obstruction to splitting a finitely generated group G as an amalagamated free product or HNN extension over a given subgroup H and show that when the obstruction is “small” G splits over a related subgroup. Applications are given which generalise decomposition theorems from low dimensional topology.

‎‎we exhibit an explicit construction for the second cohomology group‎ ‎$h^2(l‎, ‎a)$ for a lie ring $l$ and a trivial $l$-module $a$‎. ‎we show how the elements of $h^2(l‎, ‎a)$ correspond one-to-one to the‎ ‎equivalence classes of central extensions of $l$ by $a$‎, ‎where $a$‎ ‎now is considered as an abelian lie ring‎. ‎for a finite lie‎ ‎ring $l$ we also show that $h^2(l‎, ‎c^*) cong m(l)$‎...

In many cases a logic program can be divided into two parts so that one of them the bottom part does not refer to the predicates de ned in the top part The bottom rules can be used then for the evaluation of the predicates that they de ne and the computed values can be used to sim plify the top de nitions We discuss this idea of splitting a program in the context of the answer set semantics The...

PURPOSE To identify the risk factors for development of peripapillary retinal splitting (schisis) in patients with glaucoma or suspicion of glaucoma. SETTING Glaucoma Clinic, Department of Ophthalmology, Northwestern University Feinberg School of Medicine, Chicago, IL. METHODS In this institutional cross-sectional study, 495 patients (990 eyes) who had undergone spectral-domain optical cohe...

this study was done to evaluate the effects of harvest time on some factor of ‘ahmadaqaie’ pistachio nuts in rafsanjan. in three consecutive years (2009-2012) during three stages of friut ripening (40, 70 and 100 percent of hulling), fruit was harvested and physiological and biochemical parameters were measured. the experiments were conducted as randomized complete block design with compound an...

During development segmentation is a process that generates a spatial periodic pattern. Peak splitting of waves of gene expression is a mathematically predicted, simple strategy accounting for this type of process, but it has not been well characterized biologically. Here we show temporally repeated splitting of gene expression into stripes that is associated with head axis growth in the spider...

in this paper we consider the solutions of linear systems of saddle point problems‎. ‎by using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the hermitian and skew hermitian splitting method‎.

We present combinatorial rules (one theorem and two conjectures) concerning three bases of Z[x1, x2, ....]. First, we prove a ”splitting” rule for the basis of Key polynomials [Demazure ’74], thereby establishing a new positivity theorem about them. Second, we introduce an extension of [Kohnert ’90]’s ”moves” to conjecture the first combinatorial rule for a certain deformation [Lascoux ’01] of ...