35 research outputs found
Chromatic Ramsey number of acyclic hypergraphs
Suppose that is an acyclic -uniform hypergraph, with . We
define the (-color) chromatic Ramsey number as the smallest
with the following property: if the edges of any -chromatic -uniform
hypergraph are colored with colors in any manner, there is a monochromatic
copy of . We observe that is well defined and where
is the -color Ramsey number of . We give linear upper bounds
for when T is a matching or star, proving that for , and where
and are, respectively, the -uniform matching and star with
edges.
The general bounds are improved for -uniform hypergraphs. We prove that
, extending a special case of Alon-Frankl-Lov\'asz' theorem.
We also prove that , which is sharp for . This is
a corollary of a more general result. We define as the 1-intersection
graph of , whose vertices represent hyperedges and whose edges represent
intersections of hyperedges in exactly one vertex. We prove that for any -uniform hypergraph (assuming ). The proof uses the list coloring version of Brooks' theorem.Comment: 10 page
Peasant settlers and the ‘civilizing mission’ in Russian Turkestan, 1865-1917
This article provides an introduction to one of the lesser-known examples of European settler colonialism, the settlement of European (mainly Russian and Ukrainian) peasants in Southern Central Asia (Turkestan) in the late nineteenth and early twentieth centuries. It establishes the legal background and demographic impact of peasant settlement, and the role played by the state in organising and encouraging it. It explores official attitudes towards the settlers (which were often very negative), and their relations with the local Kazakh and Kyrgyz population. The article adopts a comparative framework, looking at Turkestan alongside Algeria and Southern Africa, and seeking to establish whether paradigms developed in the study of other settler societies (such as the ‘poor white’) are of any relevance in understanding Slavic peasant settlement in Turkestan. It concludes that there are many close parallels with European settlement in other regions with large indigenous populations, but that racial ideology played a much less important role in the Russian case compared to religious divisions and fears of cultural backsliding. This did not prevent relations between settlers and the ‘native’ population deteriorating markedly in the years before the First World War, resulting in large-scale rebellion in 1916
Moments of the weighted Cantor measures
Based on the seminal work of Hutchinson, we investigate properties of α-weighted Cantor measures whose support is a fractal contained in the unit interval. Here, α is a vector of nonnegative weights summing to 1, and the corresponding weighted Cantor measure μα is the unique Borel probability measure on [0, 1] satisfying
μα(E)=∑n=0N-1αnμα(ϕn-1(E)){\mu ^\alpha }(E) = \sum\nolimits_{n = 0}^{N - 1} {{\alpha _n}{\mu ^\alpha }(\varphi _n^{ - 1}(E))}
where ϕn : x ↦ (x + n)/N. In Sections 1 and 2 we examine several general properties of the measure μα and the associated Legendre polynomials in
Lμα2L_{{\mu ^\alpha }}^2
[0, 1]. In Section 3, we (1) compute the Laplacian and moment generating function of μα, (2) characterize precisely when the moments Im = ∫[0,1]xm dμα exhibit either polynomial or exponential decay, and (3) describe an algorithm which estimates the first m moments within uniform error ε in O((log log(1/ε)) · m log m). We also state analogous results in the natural case where α is palindromic for the measure να attained by shifting μα to [−1/2, 1/2]