共查询到20条相似文献,搜索用时 859 毫秒
1.
设$m$为正整数, $F_{q^r}$是特征为$p$的有限域. 本文证明了如果$p>m^2-m$且$q\equiv 1\pmod{m}$, 则多项式$x^{1+\frac{q-1}{m}}+ax~(a\neq0)$不是$F_{q^r}~(r\geq2)$上的置换多项式. 本文还证明了$q\equiv 1\pmod{7}$且$p\neq 2, 3$时, $x^{1+\frac{q-1}{7}}+ax~(a\neq0)$不是$F_{q^r}~(r\geq2)$上的置换多项式 相似文献
2.
\small\zihao{-5}\begin{quote}{\heiti 摘要:} 设$M$为$n+1$维单位球面$S^{n+1}(1)$中的一个极小闭超曲面,如果 $ n \le S \le n+\frac{2}{3}$, 则有 $S=n$ 且 $M$ 与某一Clifford 环面 $S^m(\sqrt{m/n}) \times S^{n-m}(\sqrt{(n-m)/n})$等距. 相似文献
3.
若能将图$G$画在一个平面上,使得任何两条边仅在顶点处相交,则称$G$是平面图.本文刻画了第二大特征值小于$\frac{\sqrt{5}-1}{2}$的所有无孤立点的平面图. 相似文献
4.
Paul Levrie 《The Ramanujan Journal》2010,22(2):221-230
In this paper, we derive some series for $\frac{1}{\pi}$ and $\frac{1}{\pi^{2}}$ from the Fourier–Legendre expansions of odd powers of $\sqrt{1-x^{2}}$ . 相似文献
5.
Let B?=?(B 1(t), . . . ,B d (t)) be a d-dimensional fractional Brownian motion with Hurst index ???<?1/4, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals of B is a difficult task because of the low H?lder regularity index of its paths. Yet rough path theory shows it is the key to the construction of a stochastic calculus with respect to B, or to solving differential equations driven by B. We intend to show in a series of papers how to desingularize iterated integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using ??standard?? tools of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates and call for an extension of Gaussian tools such as, for instance, the Malliavin calculus. After a first introductory paper (Magnen and Unterberger in From constructive theory to fractional stochastic calculus. (I) An introduction: rough path theory and perturbative heuristics, 2011), this one concentrates on the details of the constructive proof of convergence for second-order iterated integrals, also known as Lévy area. A summary in French may be found in Unterberger (Mode d??emploi de la théorie constructive des champs bosoniques, avec une application aux chemins rugueux, 2011). 相似文献
6.
Daniel Grieser 《Mathematische Semesterberichte》2007,54(2):199-217
Zusammenfassung Ausgehend von der Tatsache, dass die Summe der Diagonal-Elemente einer quadratischen Matrix gleich
der Summe ihrer Eigenwerte ist, wird durch Analogie-Bildung eine analoge Formel (‚Spurformel‘)
für stetige symmetrische Funktionen
geraten.
Aus dieser wird dann die Identit?t
hergeleitet.
Konsequente Fortführung der Analogie führt zu einer Beweisskizze der Spurformel. Es folgen weitere
interessante Anwendungen der Spurformel. Dies ist die Ausarbeitung eines Vortrags, der sich an Mathematik-Studierende
im zweiten Semester richtete und neben der Heranführung an spannende Mathematik zum Ziel hatte, zu
zeigen, dass formale Analogiebildung und Raten fruchtbare Prozesse in der Mathematik sein k?nnen. 相似文献
7.
Eiichi Bannai Etsuko Bannai Masatake Hirao Masanori Sawa 《Journal of Algebraic Combinatorics》2012,35(1):109-119
In this paper we prove that there exists no minimum cubature formula of degree 4k and 4k+2 for Gaussian measure on ℝ2 supported by k+1 circles for any positive integer k, except for two formulas of degree 4. 相似文献
8.
Queueing Systems - We study a model of wireless networks where users move at speed $$\theta \ge 0$$, which has the original feature of being defined through a fixed-point equation. Namely, we start... 相似文献
9.
Houshang Behravesh 《Southeast Asian Bulletin of Mathematics》2002,25(4):577-580
By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. For a given finite group G, let c(G) denote the minimal degree of a faithful representation of G by complex quasi-permutation matrices and let r(G) denote the minimal degree of a faithful rational valued character of G. Also let G denote one of the symbols Al, Bl, Cl, Dl, E6, E7, E8, G2, F4, 2B2, 2E4, 2G2, and 3D4. Let G(q) denote simple group of type G over GF(q). Let c(q) = c(G(q)) and r(q) = r(G(q)). Then we will show that lim Limq
= 1. 相似文献
10.
Wilfried Herget 《manuscripta mathematica》1978,23(2):131-141
Functional equations of the type (1) $$f(x) = d^{m - 1} \sum\limits_{i = 0}^{d - 1} {f(\frac{{x + i}}{d})}$$ for functions f: ?n→?n have first been considered in [1] and [2] in the cases m ∈ {0,1} (?n=Z/n? means the ring of integers modulo n). In this note we give the complete solution of (1) in the case f: ?p→?p (p a prime) for each m ∈ ?∪{0}. 相似文献
11.
Seiji Nishioka 《Aequationes Mathematicae》2011,81(1-2):121-134
In this paper we prove the transcendence of the solutions of the q-Painlevé equation of type ${A_6^{(1)}}$ . The q-Painlevé equation of type ${A_6^{(1)}}$ is also called d-P II or q-P II and has a continuous limit to the Painlevé equation of type II. Its symmetry is (A 1?+?A 1)(1). 相似文献
12.
设 $p\geq 7$ 为任意奇素数. 证明了当 $3\leq s
相似文献
13.
本文中, 我们主要刻画了Toeplitz算子$T=M_{z^k}+M^*_{z^l}$的约化子空间, 其中 $k_i, l_i$ ($i=1,2$) 均是正整数, $k=(k_1,k_2), l=(l_1,l_2)$ 且 $k\neq l$, $M_{z^k}$, $M_{z^l}$ 是双圆盘加权Hardy空间$\mathcal{H}_\omega^2(\mathbb{D}^2)$上的乘法算子. 对权系数 $\omega$ 适当限制, 我们证明了由 $z^m$ 生成的 $T$ 的约化子空间均是极小的. 特别地, Bergman 空间和加权 Dirichlet 空间 $\mathcal{D}_\delta(\mathbb{D}^2)(\delta>0)$ 均是满足该限制条件的加权Hardy空间. 作为应用, 我们刻画了 $\mathcal{D}_\delta(\mathbb{D}^2)(\delta>0)$ 上 Toeplitz 算子 $T_{z^k+\bar{z}^l}$ 的约化子空间, 该结论是对双圆盘Bergman 空间上相关结论的推广. 相似文献
14.
G. Lomadze 《Georgian Mathematical Journal》1996,3(5):485-500
Entire modular forms of weights $\tfrac{7}{2}$ and $\tfrac{9}{2}$ for the congruence group Γ0(4N) are constructed, which will be useful for revealing the arithmetical sense of additional terms in formulas for the number of representations of positive integers by quadratic forms in 7 and 9 variables. 相似文献
15.
涉及无限族非扩张映象$\{T_n\}_{n=1}^\infty$的迭代算法$x_{n 1}=\alpha_{n 1}f(x_n) (1-\alpha_{n 1})T_{n 1}x_n$ 总被引:1,自引:0,他引:1
Under the framework of uniformly smooth Banach spaces, Chang proved in 2006 that the sequence {xn} generated by the iteration xn+1 =αn+1f(xn) + (1 - αn+1)Tn+1xn converges strongly to a common fixed point of a finite family of nonexpansive maps {Tn}, where f : C → C is a contraction. However, in this paper, the author considers the iteration in more general case that {Tn} is an infinite family of nonexpansive maps, and proves that Chang's result holds still in the setting of reflexive Banach spaces with the weakly sequentially continuous duality mapping. 相似文献
16.
本文探讨模同态广义逆在环模理论中的应用.利用模同态的{1}-逆与{2}-逆,分别给出了一类环及一类重要模的特征刻画. 相似文献
17.
证明了对于q≥17,当4q~5-5q~4-2q+1≤d≤4q~5-5q~4-q时,不存在达到Griesmer界的[n,k,d]_q码.此结果推广了Cheon等人在2005年和2008年的非存在性定理. 相似文献
18.
Luigi Merli 《Annali di Matematica Pura ed Applicata》1958,46(1):97-107
19.
In this paper, by using the “twisting technique” we obtain a class of new modules A b over the Witt algebras \(\mathcal {W}_{n}\) from modules A over the Weyl algebras \(\mathcal {K}_{n}\) (of Laurent polynomials) for any \(b\in \mathbb {C}\). We give necessary and sufficient conditions for A b to be irreducible, and determine necessary and sufficient conditions for two such irreducible \(\mathcal {W}_{n}\)-modules to be isomorphic. Since \(\mathfrak {sl}_{n+1}(\mathbb {C})\) is a subalgebra of \(\mathcal {W}_{n}\), all the above irreducible \(\mathcal {W}_{n}\)-modules A b can be considered as \(\mathfrak {sl}_{n+1}(\mathbb {C})\)-modules. For a class of such \(\mathfrak {sl}_{n+1}(\mathbb {C})\)-modules, denoted by Ω1?a (λ 1, λ 2, ? ,λ n ) where \(a\in \mathbb {C}, \lambda _{1},\lambda _{2},\cdots ,\lambda _{n} \in \mathbb {C}^{*}\), we determine necessary and sufficient conditions for these \(\mathfrak {sl}_{n+1}(\mathbb {C})\)-modules to be irreducible. If the \(\mathfrak {sl}_{n+1}(\mathbb {C})\)-module Ω1?a (λ 1, λ 2,? ,λ n ) is reducible, we prove that it has a unique nontrivial submodule W 1?a (λ 1, λ 2,...λ n ) and the quotient module is the finite dimensional \(\mathfrak {sl}_{n+1}(\mathbb {C})\)-module with highest weight mΛ n for some non-negative integer \(m\in \mathbb {Z}_{+}\). We also determine necessary and sufficient conditions for two \(\mathfrak {sl}_{n+1}(\mathbb {C})\)-modules of the form Ω1?a (λ 1, λ 2,? ,λ n ) or of the form W 1?a (λ 1, λ 2,...λ n ) to be isomorphic. 相似文献
20.
N. V. Krylov 《Probability Theory and Related Fields》2010,147(3-4):583-605
We prove Itô’s formula for the L p -norm of a stochastic ${W^{1}_{p}}$ -valued processes appearing in the theory of SPDEs in divergence form. 相似文献