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Partition relations for cardinal numbers
1. INTRODUCTION In this paper our main object is the study of relations between cardinal numbers which are written in the form a-(b o , b,,. . .) r or a-(b)C ~° or (b) (b o b,) Such relations wereExpand
On sums and products of integers
Let 1 ≦ a 1 <... <a n be a sequence of integers Consider the integers of the form $$a_i + a_j ,\,a_i a_j ,\,1 \leqq i \leqq j \leqq n.$$ (1)
On a property of families of sets
1. Introduction. In this paper we are going to generalize a problem solved by MILLER in his paper [l] and prove several results concerning this new problem and some related questions. We mention hereExpand
Cube-Supersaturated Graphs and Related Problems
In this paper we shall consider ordinary graphs, that is, graphs without loops and multiple edges . Given a graph L, ex(n , L) will denote the maximum number of edges a graph G" of order n can haveExpand
On Ramsey Like Theorems , Problems and Results
(1) n → (k1, . . . , k`)` means that if we split the r-tuples of a set, S, |S| = n into ` classes, than for some i, 1 ≤ i ≤ ` there is a subset Si ⊆ S, |Si| ≥ ki all of whose r-tuples are in the i-thExpand
Have oil and gas prices got separated
This paper applies vector error correction models that show that oil and natural gas prices decoupled around 2009. Before 2009, US and UK gas prices had a long-term equilibrium with crude prices toExpand
On the structure of set-mappings
1 . Introduction. Let S be a set and f(x) a function which makes correspond to every x E S a subset fix) of S so that x(f (x) . Such a function f(x) we shall call a set-mapping defined on S. A subsetExpand
Random Walk Theory and the Weak-Form Efficiency of the US Art Auction Prices
We perform variance ratio tests based on non-parametric methods to detect the size of the random walk component of the US art auction prices. The past 134 years of the US art prices exhibit largeExpand