The 1-2-3-conjecture holds for dense graphs

This paper confirms the 1-2-3-conjecture for graphs that can be edge-decomposed into cliques of order at least 3. Furthermore we combine this with a result by Barber, Kühn, Lo, and Osthus to show that there is a constants such that every graph with and , where is the minimum degree of satisfying the 1-2-3-conjecture.     

适合于图像压缩的7/5小波基的构造

通过利用提升算法和检验双正交小波稳定性的充分必要条件Cohen-Daubechies准则,构造了一个适合于图像压缩的7/5双正交小波基.为了便于小波变换的硬件实现,选取四个提升系数中的三个为二进制分数,而另一提升因子为1/10的倍数.本文中所构造的7/5小波基虽然在压缩性能上低于CDF9/7小波,但由于提升系数为二进制分数和1/10的倍数,所以该小波基的小波变换更易于采用硬件来实现,并且其小波变换速度比CDF9/7小波要快.实验的结果表明该小波的压缩性能优于Daubechies5/3小波,同时与[6]所构造的两组7/5小波基相比较,该小波变换不仅能方便于硬件的实现,而且其压缩性能优于或相当于[6]中的两组7/5小波基.     

The crossing number of C5 × Cn

We prove that the crossing number of C₅ × C_n is 3n, which is consistent with the general conjecture that the crossing number of C_m × C_n is (m − 2)n, for 3 ≤ m ≤ n. © 1996 John Wiley & Sons, Inc.     

The domination numbers of the 5 × n and 6 × n grid graphs

The k × n grid graph is the product P_k × P_n of a path of length k ? 1 and a path of length n ? 1. We prove here formulas found by E. O. Hare for the domination numbers of P₅ × P_n and P₆ × P_n. © 1993 John Wiley & Sons, Inc.     

Class number 5, 6 and 7

We outline the determination of all imaginary quadratic fields with class number 5, 6 or 7.

     

单位圆盘到自身的调和映照的傅立叶系数估计

利用函数论的一般方法给出单位圆盘到自身的调和映照的傅立叶系数的界限,改进并推广了P.Duren和王晓英的相关结果.     

A Hilbert -module not anti-isomorphic to itself

We study the complexification of real Hilbert -modules over real -algebras. We give an example of a Hilbert -module that is not the complexification of any Hilbert -module, where is a real -algebra.

     

The admissibility of A5

Examples are constructed of division rings finite-dimensional and central over the rational field Q having subfields with Galois group isomorphic to the alternating group A₅. Similar results are obtained for any number field k when √?1 ? k.     

Ramanujan-type congruences modulo powers of 5 and 7

Let b _? (n) denote the number of ?-regular partitions of n. In 2012, using the theory of modular forms, Furcy and Penniston presented several infinite families of congruences modulo 3 for some values of ?. In particular, they showed that for α, n ≥ 0, b ₂₅ (3^2α+3 n+2 · 3^2α+2-1) ≡ 0 (mod 3). Most recently, congruences modulo powers of 5 for c5(n) was proved by Wang, where c _N (n) counts the number of bipartitions (λ₁,λ₂) of n such that each part of λ₂ is divisible by N. In this paper, we prove some interesting Ramanujan-type congruences modulo powers of 5 for b25(n), B25(n), c25(n) and modulo powers of 7 for c49(n). For example, we prove that for j ≥ 1, \({c_{25}}\left( {{5^{2j}}n + \frac{{11 \cdot {5^{2j}} + 13}}{{12}}} \right) \equiv 0\) (mod 5 ^j+1), \({c_{49}}\left( {{7^{2j}}n + \frac{{11 \cdot {7^{_{2j}}} + 25}}{{12}}} \right) \equiv 0\) (mod 7 ^j+1) and b ₂₅ (3^2α+3 · n+2 · 3^2α+2-1) ≡ 0 (mod 3 · 5^2j-1).     

T_(5/2)LF拓扑空间和S_(5/2)LF拓扑空间的分离性

定义 ST2 12 L F拓扑空间的分离性 ,证明 T2 12 LF拓扑空间、ST2 12 LF拓扑空间与 LF拓扑空间的其他几个分离性是协调的 ,并考察它们的性质。     

The packing measure of the Cartesian product of the middle third Cantor set with itself

For the packing measure of the Cartesian product of the middle third Cantor set with itself, the exact value