共查询到20条相似文献,搜索用时 171 毫秒
1.
A. S. Morozov 《Algebra and Logic》2012,51(1):66-88
It is proved that every two Σ-presentations of an ordered field \mathbbR \mathbb{R} of reals over \mathbbH\mathbbF ( \mathbbR ) \mathbb{H}\mathbb{F}\,\left( \mathbb{R} \right) , whose universes are subsets of \mathbbR \mathbb{R} , are mutually Σ-isomorphic. As a consequence, for a series of functions f:\mathbbR ? \mathbbR f:\mathbb{R} \to \mathbb{R} (e.g., exp, sin, cos, ln), it is stated that the structure \mathbbR \mathbb{R} = 〈R, +, ×, <, 0, 1, f〉 lacks such Σ-presentations over \mathbbH\mathbbF ( \mathbbR ) \mathbb{H}\mathbb{F}\,\left( \mathbb{R} \right) . 相似文献
2.
E. A. Sevost’yanov 《Ukrainian Mathematical Journal》2011,63(1):84-97
For open discrete mappings
f:D\{ b } ? \mathbbR3 f:D\backslash \left\{ b \right\} \to {\mathbb{R}^3} of a domain
D ì \mathbbR3 D \subset {\mathbb{R}^3} satisfying relatively general geometric conditions in D \ {b} and having an essential singularity at a point
b ? \mathbbR3 b \in {\mathbb{R}^3} , we prove the following statement: Let a point y
0 belong to
[`(\mathbbR3)] \f( D\{ b } ) \overline {{\mathbb{R}^3}} \backslash f\left( {D\backslash \left\{ b \right\}} \right) and let the inner dilatation K
I
(x, f) and outer dilatation K
O
(x, f) of the mapping f at the point x satisfy certain conditions. Let B
f
denote the set of branch points of the mapping f. Then, for an arbitrary neighborhood V of the point y
0, the set V ∩ f(B
f
) cannot be contained in a set A such that g(A) = I, where
I = { t ? \mathbbR:| t | < 1 } I = \left\{ {t \in \mathbb{R}:\left| t \right| < 1} \right\} and
g:U ? \mathbbRn g:U \to {\mathbb{R}^n} is a quasiconformal mapping of a domain
U ì \mathbbRn U \subset {\mathbb{R}^n} such that A ⊂ U. 相似文献
3.
Affine extractors over prime fields 总被引:1,自引:0,他引:1
Amir Yehudayoff 《Combinatorica》2011,31(2):245-256
An affine extractor is a map that is balanced on every affine subspace of large enough dimension. We construct an explicit
affine extractor AE from
\mathbbFn \mathbb{F}^n to
\mathbbF\mathbb{F},
\mathbbF\mathbb{F} a prime field, so that AE(x) is exponentially close to uniform when x is chosen uniformly at random from an arbitrary affine subspace of
\mathbbFn \mathbb{F}^n of dimension at least δn, 0<δ≤1 a constant. Previously, Bourgain constructed such affine extractors when the size of
\mathbbF\mathbb{F} is two. Our construction is in the spirit of but different than Bourgain’s construction. This allows for simpler analysis
and better quantitative results. 相似文献
4.
Swan (Pac. J. Math. 12:1099–1106, 1962) gives conditions under which the trinomial x
n
+ x
k
+ 1 over
\mathbbF2{\mathbb{F}_{2}} is reducible. Vishne (Finite Fields Appl. 3:370–377, 1997) extends this result to trinomials over extensions of
\mathbbF2{\mathbb{F}_{2}}. In this work we determine the parity of the number of irreducible factors of all binomials and some trinomials over the
finite field
\mathbbFq{\mathbb{F}_{q}}, where q is a power of an odd prime. 相似文献
5.
A. Arkhipova 《Journal of Mathematical Sciences》2011,176(6):732-758
We prove the existence of a global heat flow u : Ω ×
\mathbbR+ ? \mathbbRN {\mathbb{R}^{+}} \to {\mathbb{R}^{N}}, N > 1, satisfying a Signorini type boundary condition u(∂Ω ×
\mathbbR+ {\mathbb{R}^{+}}) ⊂
\mathbbRn {\mathbb{R}^{n}}),
n \geqslant 2 n \geqslant 2 , and
\mathbbRN {\mathbb{R}^{N}}) with boundary ∂
[`(W)] \bar{\Omega } such that φ(∂Ω) ⊂
\mathbbRN {\mathbb{R}^{N}} is given by a smooth noncompact hypersurface S. Bibliography: 30 titles. 相似文献
6.
In this paper we study the problem of explicitly constructing a dimension expander raised by [3]: Let
\mathbbFn \mathbb{F}^n be the n dimensional linear space over the field
\mathbbF\mathbb{F}. Find a small (ideally constant) set of linear transformations from
\mathbbFn \mathbb{F}^n to itself {A
i
}
i∈I
such that for every linear subspace V ⊂
\mathbbFn \mathbb{F}^n of dimension dim(V)<n/2 we have
dim( ?i ? I Ai (V) ) \geqslant (1 + a) ·dim(V),\dim \left( {\sum\limits_{i \in I} {A_i (V)} } \right) \geqslant (1 + \alpha ) \cdot \dim (V), 相似文献
7.
Consider a random smooth Gaussian field G(x):
F ? \mathbbR F \to \mathbb{R} , where F is a compact set in
\mathbbRd {\mathbb{R}^d} . We derive a formula for the average area of a surface determined by the equation G(x) = 0 and give some applications. As
an auxiliary result, we obtain an integral expression for the area of a surface determined by zeros of a nonrandom smooth
field. Bibliography: 13 titles. 相似文献
8.
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
9.
O. Yu. Dashkova 《Ukrainian Mathematical Journal》2012,63(9):1379-1389
We study a
\mathbbZG \mathbb{Z}G -module A such that
\mathbbZ \mathbb{Z} is the ring of integer numbers, the group G has an infinite sectional p-rank (or an infinite 0-rank), C
G
(A) = 1, A is not a minimax
\mathbbZ \mathbb{Z} -module, and, for any proper subgroup H of infinite sectional p-rank (or infinite 0-rank, respectively), the quotient module A/C
A
(H) is a minimax
\mathbbZ \mathbb{Z} -module. It is shown that if the group G is locally soluble, then it is soluble. Some properties of soluble groups of this kind are discussed. 相似文献
10.
Let X, X
1, X
2,… be i.i.d.
\mathbbRd {\mathbb{R}^d} -valued real random vectors. Assume that E
X = 0 and that X has a nondegenerate distribution. Let G be a mean zero Gaussian random vector with the same covariance operator as that of X. We study the distributions of nondegenerate quadratic forms
\mathbbQ[ SN ] \mathbb{Q}\left[ {{S_N}} \right] of the normalized sums S
N
= N
−1/2 (X
1 + ⋯ + X
N
) and show that, without any additional conditions,
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