共查询到20条相似文献,搜索用时 46 毫秒
1.
Wei Cao 《Discrete and Computational Geometry》2011,45(3):522-528
Let f(X) be a polynomial in n variables over the finite field
\mathbbFq\mathbb{F}_{q}. Its Newton polytope Δ(f) is the convex closure in ℝ
n
of the origin and the exponent vectors (viewed as points in ℝ
n
) of monomials in f(X). The minimal dilation of Δ(f) such that it contains at least one lattice point of $\mathbb{Z}_{>0}^{n}$\mathbb{Z}_{>0}^{n} plays a vital pole in the p-adic estimate of the number of zeros of f(X) in
\mathbbFq\mathbb{F}_{q}. Using this fact, we obtain several tight and computational bounds for the dilation which unify and improve a number of previous
results in this direction. 相似文献
2.
Victor Alexandru Angel Popescu Elena Liliana Popescu Sobia Sultana 《Monatshefte für Mathematik》2009,38(3):223-233
Let (K, v) be a perfect rank one valued field and let ([`(Kv)],[`(v)]){(\overline{K_{v}},\overline{v})} be the canonical valued field obtained from (K, v) by the unique extension of the valuation [(v)\tilde]{\widetilde{v}} of K
v
, the completion of K relative to v, to a fixed algebraic closure [`(Kv)]{\overline{K_{v}}} of K
v
. Let [`(K)]{\overline{K}} be the algebraic closure of K in [`(Kv)]{\overline {K_{v}}}. An algebraic extension L of K, L ì [`(K)]{L\subset\overline{K}}, is said to be a v-adic maximal extension, if [`(v)] | L{\overline{v}\mid_{L}} is the only extension of v to L and L is maximal with this property. In this paper we describe some basic properties of such extensions and we consider them in
connection with the v-adic spectral norm on [`(K)]{\overline{K}} and with the absolute Galois groups Gal([`(K)]/K){(\overline{K}/K)} and Gal([`(Kv)] /Kv){(\overline{K_{v}} /K_{v})}. Some other auxiliary results are given, which may be useful for other purposes. 相似文献
3.
A group G is said to be capable if it is isomorphic to the central factor group H/Z(H) for some group H. Let G be a nonabelian group of order p
2
q for distinct primes p and q. In this paper, we compute the nonabelian tensor square of the group G. It is also shown that G is capable if and only if either Z(G) = 1 or p < q and
Gab=\mathbbZp×\mathbbZp{G^{\rm ab}=\mathbb{Z}_{p}\times\mathbb{Z}_{p}} . 相似文献
4.
Amol Sasane 《Complex Analysis and Operator Theory》2012,6(2):465-475
Let
\mathbb Dn:={z=(z1,?, zn) ? \mathbb Cn:|zj| < 1, j=1,?, n}{\mathbb {D}^n:=\{z=(z_1,\ldots, z_n)\in \mathbb {C}^n:|z_j| < 1, \;j=1,\ldots, n\}}, and let
[`(\mathbbD)]n{\overline{\mathbb{D}}^n} denote its closure in
\mathbb Cn{\mathbb {C}^n}. Consider the ring
Cr([`(\mathbbD)]n;\mathbb C) = {f:[`(\mathbbD)]n? \mathbb C:f is continuous and f(z)=[`(f([`(z)]))] (z ? [`(\mathbbD)]n)}C_{\rm r}(\overline{\mathbb{D}}^n;\mathbb {C}) =\left\{f: \overline{\mathbb{D}}^n\rightarrow \mathbb {C}:f \,\, {\rm is \,\, continuous \,\, and}\,\, f(z)=\overline{f(\overline{z})} \;(z\in \overline{\mathbb{D}}^n)\right\} 相似文献
5.
Yu. S. Kolomoitsev 《Journal of Mathematical Sciences》2010,165(4):463-472
Let B be a set of integers with certain arithmetic properties. We obtain estimates of the best approximation of functions in the
space L
p
, 0 < p <1, by trigonometric polynomials that are constructed by the system
{eikx}k ? \mathbbZ\B \{e^{ikx}\}_{k\in \mathbb{Z}\backslash B} . Bibliography: 13 titles. 相似文献
6.
M. S. Vyazovs’ka 《Ukrainian Mathematical Journal》2009,61(12):2008-2015
We show that the derivative of an arbitrary rational function R of degree n that increases on the segment [−1, 1] satisfies the following equality for all 0 < ε < 1 and p, q > 1:
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