共查询到20条相似文献,搜索用时 93 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.
Li-Chien Shen 《The Ramanujan Journal》2013,30(2):211-222
We study a class of elliptic functions associated with the hypergeometric function ${_{2}}F_{1}(\frac{1}{6},\frac{5}{6};1;z)$ . From the perspective of the properties of conformal mappings and differential equations, we provide new insight into a set of identities of Ramanujan associated with the above hypergeometric function. 相似文献
3.
\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
4.
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
5.
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
6.
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
7.
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
8.
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
9.
Compositions of generalized fractional integral operators involving Gauss hy-pergeometric function with power weights are studied.Com position formulas forsuch integrals which are the operators of the same type are obtained.In parti-cular,compositions of two identical operators are given. 相似文献
10.
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
11.
Dong Sheng WU Yi Min XIAO 《数学学报(英文版)》2007,23(4):613-622
Let B^α = {B^α(t),t E R^N} be an (N,d)-fractional Brownian motion with Hurst index α∈ (0, 1). By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension results for the images of B^α when N 〉 αd. Our results extend those of Kaufman for one-dimensional Brownian motion. 相似文献
12.
Some new factorizations of unitons into Lie groups are established via singular Darboux transformations. The factorization
processes for Grassmannian unitons are also considered. Furthermore, a purely algebraic method for constructing Grassmannian
unitons is presented. 相似文献
13.
A Constructive Proof of the Gelfand—Kolmogorov Theorem 总被引:1,自引:0,他引:1
He Wei 《Applied Categorical Structures》2004,12(2):197-202
A construction of the Stone—ech compactification of a locale L is presented in this paper as a quotient of the frame of radical ideals of the algebra C
*(L). As a corollary, a constructive, localic version of the Gelfand—Kolmogorov theorem is obtained. 相似文献
14.
The Fractional Derivatives of a Fractal Function 总被引:2,自引:0,他引:2
Kui YAO Wei Yi SU Song Ping ZHOU 《数学学报(英文版)》2006,22(3):719-722
The present paper investigates the fractional derivatives of Weierstrass function, proves that there exists some linear connection between the order of the fractional derivatives and the dimension of the graphs of Weierstrass function. 相似文献
15.
《Chaos, solitons, and fractals》2001,12(10):1929-1935
16.
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
17.
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
18.
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
19.
Kolmogorov (Dokl. Akad. Nauk USSR, 14(5):953–956, 1957) showed that any multivariate continuous function can be represented as a superposition of one-dimensional functions, i.e., $$f(x_{1},\ldots,x_{n})=\sum_{q=0}^{2n}\varPhi _{q}\Biggl(\sum_{p=1}^{n}\psi_{q,p}(x_{p})\Biggr).$$ The proof of this fact, however, was not constructive, and it was not clear how to choose the outer and inner functions Φ q and ψ q,p , respectively. Sprecher (Neural Netw. 9(5):765–772, 1996; Neural Netw. 10(3):447–457, 1997) gave a constructive proof of Kolmogorov’s superposition theorem in the form of a convergent algorithm which defines the inner functions explicitly via one inner function ψ by ψ p,q :=λ p ψ(x p +qa) with appropriate values λ p ,a∈?. Basic features of this function such as monotonicity and continuity were supposed to be true but were not explicitly proved and turned out to be not valid. Köppen (ICANN 2002, Lecture Notes in Computer Science, vol. 2415, pp. 474–479, 2002) suggested a corrected definition of the inner function ψ and claimed, without proof, its continuity and monotonicity. In this paper we now show that these properties indeed hold for Köppen’s ψ, and we present a correct constructive proof of Kolmogorov’s superposition theorem for continuous inner functions ψ similar to Sprecher’s approach. 相似文献
20.
(欧庆铃)FluctuationLimitofaFractionalBrownianParticleSystem¥OnQingling(Dept.ofAppliedMath.,SouthChinaUniv.ofTech.,Guangzhou,Guan... 相似文献