Social paradoxes of majority rule voting and renormalization group

Real-space renormalization group ideas are used to study a voting problem in political science. A model to construct self-directed pyramidal structures from bottom up to the top is presented. Using majority rules, it is shown that a minority and even a majority can be systematically self-eliminated from top leadership, provided the hierarchy has a minimal number of levels. In some cases, 70% of the population is found to have zero representation after six hierarchical levels. Results are discussed with respect to the internal operation of political organizations.     

A mixed phase transition for a hierarchical spin glass

A proof of the existence of a mixed ferromagnetic (or antiferromagnetic)-spin-glass fixed point for an Ising spin-glass model on the diamond hierarchical lattice is given.     

A New Proof of the Mullineux Conjecture

Let S _d denote the symmetric group on d letters. In 1979 Mullineux conjectured a combinatorial algorithm for calculating the effect of tensoring with an irreducible S _d-module with the one dimensional sign module when the ground field has positive characteristic. Kleshchev proved the Mullineux conjecture in 1996. In the present article we provide a new proof of the Mullineux conjecture which is entirely independent of Kleshchev's approach. Applying the representation theory of the supergroup GL(m | n) and the supergroup analogue of Schur-Weyl Duality it becomes straightforward to calculate the combinatorial effect of tensoring with the sign representation and, hence, to verify Mullineux's conjecture. Similar techniques also allow us to classify the irreducible polynomial representations of GL(m | n) of degree d for arbitrary m, n, and d.     

Recovery of Band-Limited Functions on Locally Compact Abelian Groups from Irregular Samples

Using the techniques of approximation and factorization of convolution operators we study the problem of irregular sampling of band-limited functions on a locally compact Abelian group G. The results of this paper relate to earlier work by Feichtinger and Gröchenig in a similar way as Kluvánek's work published in 1969 relates to the classical Shannon Sampling Theorem. Generally speaking we claim that reconstruction is possible as long as there is sufficient high sampling density. Moreover, the iterative reconstruction algorithms apply simultaneously to families of Banach spaces.     

S_fS_(f-1)约化系数的解析表式

利用线性方程方法和解析延拓得到了导出置换群Sf Sf- 1约化系数解析表达式的一种简单的代数计算方法 .着重讨论了无重复度时Sf Sf- 1约化系数解析表达式的推导方法 .作为例子 ,给出了关于置换群内积 [f- 1,1]·[f- 1,1]和 [f - 1,1]·[f - 2 ,1,1]有关的所有Sf Sf- 1约化系数的解析表达式 .     

幂零群的若干充分条件

本文利用Ｃ－正规子群的性质，得到了若干有限群为幂零群的充分条件，推广了一些著名定理，如Ｔｈｏｍｐｓｏｎ定理及Ｉｔ＾ｏ定理。     

-symmetry for (r,s)-hypergeometric series

Contiguous operators for a two-parameter analogue of hypergeometric series are constructed. These represent a two-parameter quantum enveloping algebra introduced by Takeuchi.     

Further results on large sets of disjoint group‐divisible designs with block size three and type 2n41

Large sets of disjoint group‐divisible designs with block size three and type 2ⁿ4¹ were first studied by Schellenberg and Stinson because of their connection with perfect threshold schemes. It is known that such large sets can exist only for n ≡0 (mod 3) and do exist for all odd n ≡ (mod 3) and for even n=24m, where m odd ≥ 1. In this paper, we show that such large sets exist also for n=2^k(3m), where m odd≥ 1 and k≥ 5. To accomplish this, we present two quadrupling constructions and two tripling constructions for a special large set called ^*LS(2ⁿ). © 2002 Wiley Periodicals, Inc. J Combin Designs 11: 24–35, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10032