拉丁美洲国际移民现状研究

对20世纪60年代以来拉丁美洲国际移民方向发生逆转的原因进行了分析，阐述了目前该州国际移民的主要流向及其数量，对其已经和可能产生的后果做了评价，并在此基础上提出了相应的对策。     

20世纪美国州及地方政府官员的罢免机制

20世纪初，随着垄断资本对政治干预的加强，美国代议制自身的弊端暴露得更加明显，时代呼唤着罢免机制的产生，罢免先后在15个州的州法令及36个州的地方政府宪章中得到批准，在实践中有过两次应用高潮，对州及地方政府影响较大，波及至今。近一个世纪的发展表明，罢免机制虽存在诸多不足，但已成为代议制政府在地方一级不可或缺的补充工具。     

Balanced diagonals in frequency squares

We say that a diagonal in an array is $\lambda$-balanced if each entry occurs $\lambda$ times. Let $L$ be a frequency square of type $F(n;\lambda )$; that is, an $n\times n$ array in which each entry from $\{1,2,\dots ,m=n∕\lambda \}$ occurs $\lambda$ times per row and $\lambda$ times per column. We show that if $m?3$, $L$ contains a $\lambda$-balanced diagonal, with only one exception up to equivalence when $m=2$. We give partial results for $m?4$ and suggest a generalization of Ryser’s conjecture, that every Latin square of odd order has a transversal. Our method relies on first identifying a small substructure with the frequency square that facilitates the task of locating a balanced diagonal in the entire array.     

Transversals in completely reducible multiary quasigroups and in multiary quasigroups of order 4

An $n$-ary quasigroup $f$ of order $q$ is an $n$-ary operation over a set of cardinality $q$ such that the Cayley table of the operation is an $n$-dimensional latin hypercube of order $q$. A transversal in a quasigroup $f$ (or in the corresponding latin hypercube) is a collection of $q$$(n+1)$-tuples from the Cayley table of $f$, each pair of tuples differing at each position. The problem of transversals in latin hypercubes was posed by Wanless in 2011.An $n$-ary quasigroup $f$ is called reducible if it can be obtained as a composition of two quasigroups whose arity is at least 2, and it is completely reducible if it can be decomposed into binary quasigroups.In this paper we investigate transversals in reducible quasigroups and in quasigroups of order 4. We find a lower bound on the number of transversals for a vast class of completely reducible quasigroups. Next we prove that, except for the iterated group ${\mathbb{Z}}_4$ of even arity, every $n$-ary quasigroup of order 4 has a transversal. Also we obtain a lower bound on the number of transversals in quasigroups of order 4 and odd arity and count transversals in the iterated group ${\mathbb{Z}}_4$ of odd arity and in the iterated group ${\mathbb{Z}}_2^2.$All results of this paper can be regarded as those concerning latin hypercubes.     

Partial difference sets and amorphic Cayley schemes in non‐abelian 2‐groups

In this paper, we consider regular automorphism groups of graphs in the RT2 family and the Davis‐Xiang family and amorphic abelian Cayley schemes from these graphs. We derive general results on the existence of non‐abelian regular automorphism groups from abelian regular automorphism groups and apply them to the RT2 family and Davis‐Xiang family and their amorphic abelian Cayley schemes to produce amorphic non‐abelian Cayley schemes.     

Intercalates and discrepancy in random Latin squares

An intercalate in a Latin square is a 2 × 2 Latin subsquare. Let be the number of intercalates in a uniformly random n × n Latin square. We prove that asymptotically almost surely , and that (therefore asymptotically almost surely for any ). This significantly improves the previous best lower and upper bounds. We also give an upper tail bound for the number of intercalates in 2 fixed rows of a random Latin square. In addition, we discuss a problem of Linial and Luria on low‐discrepancy Latin squares.     

Existence of LSs

Let X be a ‐set and be a partition of X into n groups of size 2 and one group G₀ of size 4. A large‐set‐plus denoted by LS is a partition of all ‐transverse triples of X into block sets of 3‐GDD(2ⁿ4¹)s with group set , and two block sets of 3‐GDD(2ⁿ)s with group set . In this paper, we study the existence problem of LSs and give a nearly complete solution.     

Divisors of the number of Latin rectangles

A k×n Latin rectangle on the symbols {1,2,…,n} is called reduced if the first row is (1,2,…,n) and the first column is T(1,2,…,k). Let Rk,n be the number of reduced k×n Latin rectangles and m=⌊n/2⌋. We prove several results giving divisors of Rk,n. For example, (k−1)! divides Rk,n when k?m and m! divides Rk,n when m<k?n. We establish a recurrence which determines the congruence class of for a range of different t. We use this to show that Rk,n≡((−1)^k−1(k−1)!)ⁿ⁻¹. In particular, this means that if n is prime, then Rk,n≡1 for 1?k?n and if n is composite then if and only if k is larger than the greatest prime divisor of n.     

An enumeration of equilateral triangle dissections

We enumerate all dissections of an equilateral triangle into smaller equilateral triangles up to size 20, where each triangle has integer side lengths. A perfect dissection has no two triangles of the same side, counting up- and down-oriented triangles as different. We computationally prove Tutte’s conjecture that the smallest perfect dissection has size 15 and we find all perfect dissections up to size 20.     

美国空间科学的发展及其启示

 剖析了美国空间科学战略规划的模式、科学计划的布局、空间科学发展的体制保障和机制创新；提出在中国空间科学发展不断得到重视的大环境下，亟需重视战略规划研究、并强调规划的严肃性，要坚持重大科学任务的国家属性和国际合作开放性并举，要重视厚植和夯实空间科学发展的基础等3方面的建议。