The main purpose of this paper is to prove a group-theoretic generalization of a theorem of Katz on isocrystals. Along the way we reprove the group-theoretic generalization of Mazur’s inequality for isocrystals due to Rapoport-Richartz, and generalize from split groups to unramified groups a result from [KR] which determines when the affine Deligne-Lusztig subset X μ (b) of G(L)/G(oL) is non-em...

There is a standard correspondence between elements of the cohomology group H(F, μn) (with the trivial action of ΓF = Gal(Fs/F ) on μn) and cyclic extensions of dimension n over F . We extend this to a correspondence between the cohomology groups H(F, μn) where the action of ΓF on μn varies, and the extensions of dimension n of K which are Galois over F , where K = F [μn] and [K :F ] is prime t...

The first aim of this note is to fill a gap in the literature by giving proof following refinement Shafarevich's theorem on solvable Galois groups: Given global field $k$, finite set $\mathcal{S}$ primes and group $G$, there extension $k$ $G$ which all are totally split. To that end, we prove that, given every split embedding problem $G \rightarrow {\rm{Gal}}(L/k)$ over with nilpotent kernel ha...

criticism of public extension services has resulted in various countries seeking alternative approaches for provision of these services. in all these approaches, extension personnel are the key factors to the success of the implementation. today, agricultural extension services in turkey bear the responsibility of the ministry of food, agriculture and livestock. a number of non-public extension...

Splitting off a pair of edges su; sv in a graph G means replacing these two edges by a new edge uv. This operation is well-known in graph theory. Let G = (V + s; E + F ) be a graph which is k-edge-connected in V and suppose that jF j is even. Here F denotes the set of edges incident with s. Lovász [12] proved that if k 2 then the edges in F can be split off in pairs preserving the k-edge-connec...

Gaussian split Ewald (GSE) is a versatile Ewald mesh method that is fast and accurate when used with both real-space and k-space Poisson solvers. While real-space methods are known to be asymptotically superior to k-space methods in terms of both computational cost and parallelization efficiency, k-space methods such as smooth particle-mesh Ewald (SPME) have thus far remained dominant because t...

The paper deals with ring extensions $$R\subseteq S$$ and their lattices [R, S] of subextensions is mainly devoted to FCP (extensions whose are Artinian Noetherian). object the introduction study elements that split in some sense extensions. reason why this splitting was used earlier without common nature being recognized. There favorable cases allowing build splitters, when we dealing $${\math...

A powerful way to detect selection in a population is by modeling local allele frequency changes in a 7 particular region of the genome under scenarios of selection and neutrality, and finding which model is 8 most compatible with the data. Chen et al. [1] developed a composite likelihood method called XP-CLR 9 that uses an outgroup population to detect departures from neutrality which could be...

For m≥2, we study derivations on symbol algebras of degree m over fields with characteristic not dividing m. A differential central simple algebra a field k is split by finitely generated extension k. certain algebras, provide explicit construction splitting and give bounds their algebraic transcendence degrees. We further analyze maximal subfields that algebras.

In this work, we consider extensions of solvable Lie algebras with naturally graded filiform nilradicals. Note that there exist two [Formula: see text] and We find all one-dimensional nilradical text]. prove exists a unique non-split central extension maximal codimension. Moreover, whose codimension is equal to one are found compared these the nilradicals algebra