共查询到20条相似文献,搜索用时 15 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.
Acta Mathematica Hungarica - For any positive integer m, let $$\mathbb{Z}_{m}$$ be the set of residue classes modulo m. For $$A\subseteq \mathbb{Z}_{m}$$ and $$\overline{n}\in \mathbb{Z}_{m}$$ ,... 相似文献
3.
Let $$K:=\mathbb {Q}(G)$$ be the number field generated by the complex character values of a finite group G. Let $$\mathbb {Z}_K$$ be the ring of integers of K. In this paper we investigate the suborder $$\mathbb {Z}[G]$$ of $$\mathbb {Z}_K$$ generated by the character values of G. We prove that every prime divisor of the order of the finite abelian group $$\mathbb {Z}_K/\mathbb {Z}[G]$$ divides |G|. Moreover, if G is nilpotent, we show that the exponent of $$\mathbb {Z}_K/\mathbb {Z}[G]$$ is a proper divisor of |G| unless $$G=1$$. We conjecture that this holds for arbitrary finite groups G. 相似文献
4.
Periodica Mathematica Hungarica - For any positive integer m, let $$\mathbb {Z}_{m}$$ be the set of residue classes modulo m. For $$A\subseteq \mathbb {Z}_{m}$$ and $$\overline{n}\in \mathbb... 相似文献
5.
The Ramanujan Journal - Let $$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}}$$ defined by the power series... 相似文献
6.
7.
Mathematical Notes - Let $$\mathbb{F}_{q}$$ be a finite field, let $$\mathbb{X}$$ be a subset of the projective space ?s?1 over $$\mathbb{F}_{q}$$ parametrized by rational functions,... 相似文献
8.
Let T 1 be an integer, T = {0, 1, 2,..., T- 1}. This paper is concerned with the existence of periodic solutions of the discrete first-order periodic boundary value problems△u(t)- a(t)u(t) = λu(t) + f(u(t- τ(t)))- h(t), t ∈ T,u(0) = u(T),where △u(t) = u(t + 1)- u(t), a : T → R and satisfies∏T-1t=0(1 + a(t)) = 1, τ : T → Z t- τ(t) ∈ T for t ∈ T, f : R → R is continuous and satisfies Landesman-Lazer type condition and h : T → R. The proofs of our main results are based on the Rabinowitz's global bifurcation theorem and Leray-Schauder degree. 相似文献
9.
Aequationes mathematicae - Let $$\mathbb {N}$$ be the set of nonnegative integer numbers. A plane monoid is a submonoid of $$(\mathbb {N}^2,+)$$ . Let M be a plane monoid and $$p,q\in \mathbb {N}$$... 相似文献
10.
The Ramanujan Journal - Let $$G\cong {\mathbb {Z}}/m_1{\mathbb {Z}}\times \cdots \times {\mathbb {Z}}/m_r{\mathbb {Z}}$$ be a finite abelian group with $$m_1\mid \cdots \mid m_r=\exp (G)$$ . The... 相似文献
11.
Qian Jin Luo 《数学学报(英文版)》2020,36(6):711-722
Let B be the unit disc in R~2, H be the completion of C_0∞(B) under the norm■ .By the method of blow-up analysis and an argument of rearrangement with respect to the standard hyperbolic metric ■, we prove that, for any fixed■ ,the supremum■ .This is an analog of early results of Lu–Yang(Discrete Contin. Dyn. Syst., 2009) and Yang(Trans.Amer. Math. Soc., 2007), and extends those of Wang–Ye(Adv. Math., 2012) and Yang–Zhu(Ann.Global Anal. Geom., 2016). 相似文献
12.
The purpose of this paper is to give characterizations for uniform exponential dichotomy of evolution families on the real
line. We consider a general class of Banach function spaces denoted
and we prove that if
with
and the pair
is admissible for an evolution family
then
is uniformly exponentially dichotomic. By an example we show that the admissibility of the pair
for an evolution family is not a sufficient condition for uniform exponential dichotomy. As applications, we deduce necessary
and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pairs
and
with
相似文献
13.
Acta Mathematica Hungarica - We deal with isomorphic Banach–Stone type theorems for closed subspaces of vectorvalued continuous functions. Let $$\mathbb{F}=\mathbb{R}$$ or $$\mathbb{C}$$ .... 相似文献
14.
The universal minimal one parameter system will be characterized as the space $$\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}}$$. 相似文献
15.
Archiv der Mathematik - For an integer $$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
16.
Results in Mathematics - We consider continuous solutions $${f : \mathbb{R}_{+} \rightarrow \mathbb{R}_{+}=(0,\infty )}$$ of the functional equation $${f(xf(x))=\varphi (f(x))}$$ where... 相似文献
17.
Let $$\Omega \subset {\mathbb {R}}^N$$ be an arbitrary open set, $$0<s<1$$ and denote by $$(e^{-t(-\Delta )_{{{\mathbb {R}}}^N}^s})_{t\ge 0}$$ the semigroup on $$L^2({{\mathbb {R}}}^N)$$ generated by the fractional Laplace operator. In the first part of the paper, we show that if T is a self-adjoint semigroup on $$L^2(\Omega )$$ satisfying a fractional Gaussian estimate in the sense that $$|T(t)f|\le Me^{-bt(-\Delta )_{{{\mathbb {R}}}^N}^s}|f|$$, $$0\le t \le 1$$, $$f\in L^2(\Omega )$$, for some constants $$M\ge 1$$ and $$b\ge 0$$, then T defines a bounded holomorphic semigroup of angle $$\frac{\pi }{2}$$ that interpolates on $$L^p(\Omega )$$, $$1\le p<\infty $$. Using a duality argument, we prove that the same result also holds on the space of continuous functions. In the second part, we apply the above results to the realization of fractional order operators with the exterior Dirichlet conditions. 相似文献
18.
Geometriae Dedicata - Let X be a genus two double covering surface of the standard flat torus $$({\mathbb {C}}/{\mathbb {Z}}[i],dz)$$ with two ramified values $$0\ mod\ {\mathbb {Z}}[i]$$ and... 相似文献
19.
Archiv der Mathematik - We analyze certain compositions of rational inner functions in the unit polydisk $$\mathbb {D}^{d}$$ with polydegree (n, 1), $$n\in \mathbb {N}^{d-1}$$ , and... 相似文献
20.
Periodica Mathematica Hungarica - For a given set $$S\subseteq \mathbb {Z}_m$$ and $$\overline{n}\in \mathbb {Z}_m$$ , $$R_S(\overline{n})$$ is defined as the number of solutions of the equation... 相似文献