共查询到20条相似文献,搜索用时 46 毫秒
1.
Piotr Migus 《Archiv der Mathematik》2019,112(4):395-405
Let
$$f,g:({\mathbb {R}}^n,0)\rightarrow ({\mathbb {R}}^m,0)$$
be
$$C^{r+1}$$
mappings and let
$$Z=\{x\in \mathbf {\mathbb {R}}^n:\nu (df (x))=0\}$$
,
$$0\in Z$$
,
$$m\le n$$
. We will show that if there exist a neighbourhood U of
$$0\in {\mathbb {R}}^n$$
and constants
$$C,C'>0$$
and
$$k>1$$
such that for
$$x\in U$$
$$\begin{aligned}&\nu (df(x))\ge C{\text {dist}}(x,Z)^{k-1}, \\&\left| \partial ^{s} (f_i-g_i)(x) \right| \le C'\nu (df(x))^{r+k-|s|}, \end{aligned}$$
for any
$$i\in \{1,\dots , m\}$$
and for any
$$s \in \mathbf {\mathbb {N}}^n_0$$
such that
$$|s|\le r$$
, then there exists a
$$C^r$$
diffeomorphism
$$\varphi :({\mathbb {R}}^n,0)\rightarrow ({\mathbb {R}}^n,0)$$
such that
$$f=g\circ \varphi $$
in a neighbourhood of
$$0\in {\mathbb {R}}^n$$
. By
$$\nu (df)$$
we denote the Rabier function. 相似文献
2.
Periodica Mathematica Hungarica - Let N be a positive integer, $${\mathbb {A}}$$ be a nonempty subset of $${\mathbb {Q}}$$ and $$\alpha =\dfrac{\alpha _{1}}{\alpha _{2}}\in {\mathbb {A}}{\setminus... 相似文献
3.
Semigroup Forum - Let $${\mathbb {F}}$$ be a field. The set $$M_{n}({\mathbb {F}})$$ of all $$n \times n$$ matrices over $${\mathbb {F}}$$ forms a monoid under usual matrix multiplication. We... 相似文献
4.
Mathematical Programming - Given a polynomial function $$f :{\mathbb {R}}^n \rightarrow {\mathbb {R}}$$ and an unbounded closed semi-algebraic set $$S \subset {\mathbb {R}}^n,$$ we show that the... 相似文献
5.
Bhunia Dipak K. Fernndez-Crdoba Cristina Villanueva Merc 《Designs, Codes and Cryptography》2022,90(4):1037-1058
Designs, Codes and Cryptography - $${\mathbb {Z}}_{p^s}$$ -additive codes of length n are subgroups of $${\mathbb {Z}}_{p^s}^n$$ , and can be seen as a generalization of linear codes over... 相似文献
6.
Let $$W(z_1, \ldots , z_n): ({\mathbb {C}}^*)^n \rightarrow {\mathbb {C}}$$ be a Laurent polynomial in n variables, and let $${\mathcal {H}}$$ be a generic smooth fiber of W. Ruddat et al. (Geom Topol 18:1343–1395, 2014) give a combinatorial recipe for a skeleton for $${\mathcal {H}}$$. In this paper, we show that for a suitable exact symplectic structure on $${\mathcal {H}}$$, the RSTZ-skeleton can be realized as the Liouville Lagrangian skeleton. 相似文献
7.
Doklady Mathematics - Let $${{V}_{r}}({{\mathbb{R}}^{n}})$$, n ≥ 2, be the set of functions $$f \in {{L}_{{{\text{loc}}}}}({{\mathbb{R}}^{n}})$$ with zero integrals over all balls in... 相似文献
8.
Periodica Mathematica Hungarica - Let $${\mathbb {N}}$$ be the set of all nonnegative integers. For a given set $$S\subset {\mathbb {N}}$$ the representation function $$R_S(n)$$ is defined as the... 相似文献
9.
10.
11.
Archiv der Mathematik - In this note, we prove a Trudinger–Moser inequality for a conical metric in the unit ball. Precisely, let $${\mathbb {B}}$$ be the unit ball in $${\mathbb {R}}^N$$... 相似文献
12.
Mathematical Programming - Given $$P\subset {\mathbb {R}}^n$$, a mixed-integer set $$P^I=P\cap ({\mathbb {Z}}^{t}\times {\mathbb {R}}^{n-t}$$), and a k-tuple of n-dimensional integral vectors... 相似文献
13.
Journal of Algebraic Combinatorics - The fact that the groups $${\mathbb {Z}}_{2^m} \times {\mathbb {Z}}_{2^m}$$ contain difference sets was first established by induction by Jim Davis in his... 相似文献
14.
Aequationes mathematicae - Let $$I\subset {\mathbb {R}}$$ be an interval that is closed under addition, and $$ k\in {\mathbb {N}}$$ , $$k\ge 2\,$$ . For a function $$f:I\rightarrow \left( 0,\infty... 相似文献
15.
Statistical Inference for Stochastic Processes - We propose a randomized approach to the consistent statistical analysis of random processes and fields on $${\mathbb {R}}^m$$ and $${\mathbb {Z}}^m,... 相似文献
16.
The universal minimal one parameter system will be characterized as the space $$\Gamma ^{\infty }$$, in which $$\Gamma$$ is the Bohr compactification of the additive group $${\mathbb {R}}$$ of real numbers. In this way, we need to show that $$\Gamma ^\infty$$ is isomorphic to the spectrum of $$W({\mathbb {R}})$$, the norm closure of the invariant algebra generated by the maps $$\exp q(t)$$, where q(t) is a real polynomial on $${\mathbb {R}}$$. 相似文献
17.
Given a prime p, an integer $$H\in [1,p)$$, and an arbitrary set $${\mathcal {M}} \subseteq {\mathbb {F}} _p^*$$, where $${\mathbb {F}} _p$$ is the finite field with p elements, let $$J(H,{\mathcal {M}} )$$ denote the number of solutions to the congruence $$\begin{aligned} xm\equiv yn~\mathrm{mod}~ p \end{aligned}$$for which $$x,y\in [1,H]$$ and $$m,n\in {\mathcal {M}} $$. In this paper, we bound $$J(H,{\mathcal {M}} )$$ in terms of p, H, and the cardinality of $${\mathcal {M}} $$. In a wide range of parameters, this bound is optimal. We give two applications of this bound: to new estimates of trilinear character sums and to bilinear sums with Kloosterman sums, complementing some recent results of Kowalski et al. (Stratification and averaging for exponential sums: bilinear forms with generalized Kloosterman sums, 2018, arXiv:1802.09849). 相似文献
18.
Archiv der Mathematik - For an integer $$p\ge 2$$ , let $$\{x_n\}_{n\in {\mathbb {N}}}\subset {\mathbb {T}}$$ be the p-adic van der Corput sequence. For intervals $$[0,\alpha )\subset {\mathbb... 相似文献
19.
The Ramanujan Journal - Let $$k\in \mathbb {N}_{\ge 2}$$ and for given $$m\in \mathbb {Z}{\setminus }\{0\}$$ consider the sequence $$(S_{k,m}(n))_{n\in \mathbb {N}}$$ defined by the power series... 相似文献
20.
Covert David Koh Doowon Pi Youngjin 《Journal of Fourier Analysis and Applications》2019,25(3):1026-1052
Journal of Fourier Analysis and Applications - Let $${\mathbb {F}}_q^d$$ be the d-dimensional vector space over the finite field $${\mathbb {F}}_q$$ with q elements. Given k sets $$E_j\subset... 相似文献