共查询到20条相似文献,搜索用时 15 毫秒
1.
Alexander Ostrowski 《Mathematische Annalen》1920,82(1-2):64-67
Ohne ZusammenfassungAus einem an Herrn G. Pólya in Zürich gerichteten Briefe. 相似文献
2.
3.
4.
It is well known that the two dimensional integer lattice mathbb{Z}^2 is recurrent, while the three dimensional integer lattice is transient. In this paper we show that the product graph mathbb{Z}^2times{0,1,ldots,l-1} is recurrent. The proof approach only utilizes the elementary methods in probability theory (without thewords of electric networks). 相似文献
5.
6.
Rudolf Kochendörffer 《Mathematische Zeitschrift》1955,63(1):507-513
Ohne ZusammenfassungZum Gedenken an den 80. Geburtstag meines verehrten LehrersI. Schur 相似文献
7.
8.
9.
10.
J. Thomae 《Mathematische Annalen》1870,2(3):427-444
11.
G. Molteni 《Acta Mathematica Hungarica》2007,117(1-2):61-76
Let ζ be a primitive q′-root of unity. We prove that the series $ \sum\nolimits_{n = 1}^\infty {{{\zeta ^{ \llcorner n\theta \lrcorner } } \mathord{\left/ {\vphantom {{\zeta ^{ \llcorner n\theta \lrcorner } } n}} \right. \kern-0em} n}} $ for θ ∈ Q converges if and only if θ = p/q with (p,q) = 1 and q′ ? p, and that there exists an uncountable set S of Liouville’s numbers such that the series does not converge when θ ∈ S. 相似文献
12.
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
13.
14.
Koichi Betsumiya T. Aaron Gulliver Masaaki Harada 《Designs, Codes and Cryptography》2003,28(2):171-186
In this paper, it is shown that extremal (Hermitian) self-dual codes over
2 ×
2 exist only for lengths 1, 2, 3, 4, 5, 8 and 10. All extremal self-dual codes over
2 ×
2 are found. In particular, it is shown that there is a unique extremal self-dual code up to equivalence for lengths 8 and 10. Optimal self-dual codes are also investigated. A classification is given for binary [12, 7, 4] codes with dual distance 4, binary [13, 7, 4] codes with dual distance 4 and binary [13, 8, 4] codes with dual distance 4. 相似文献
15.
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
16.
17.
Let \(a,\ b,\ c,\ m\) be positive integers such that \(a+b=c^2, 2\mid a, 2\not \mid c\) and \(m>1\). In this paper we prove that if \(c\mid m \) and \(m>36c^3 \log c\), then the equation \((am^2+1)^x+(bm^2-1)^y=(cm)^z\) has only the positive integer solution \((x,\ y,\ z)\)=\((1,\ 1,\ 2)\). 相似文献
18.
João Marcos do Ó Bernhard Ruf 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(2):167-192
The main purpose of this paper is to establish the existence of a solution of the semilinear Schr?dinger equation
where V is a 1-periodic function with respect to x, 0 lies in a gap of the spectrum of − Δ + V, and f(s) behaves like ± exp(α s2) when s → ± ∞. 相似文献
19.
20.
In this paper we determine the method of multi-parameter interpolation and the scales of Lebesgue spaces $B_{\vec p} \left[ {0,2\pi } \right)$ and Besov spaces $B_{\vec p}^{\vec \alpha } \left[ {0,2\pi } \right)$ , which are generalizations of the Lorentz spacesL pq [0, 2π) and Besov spacesB pq α [0, 2π). We also prove imbedding theorems. 相似文献