An in!nite word de!ned over a !nite alphabet A is balanced if for any pair (!;!′) of factors of the same length and for any letter a in the alphabet ‖!|a − |!|a|6 1; where |!|a denotes the number of occurrences of the letter a in the word !. In this paper, we generalize this notion and introduce a measure of balance for an in!nite sequence. In the case of !xed points of primitive substitutions,...

Let X be a smooth variety over an algebraically closed field k of characteristic p, and F : X → X the Frobenius morphism. We prove that if X is an incidence variety (a partial flag variety in type An) or a smooth quadric (in this case p is supposed to be odd) then H (X, End(F∗OX)) = 0 for i > 0. Using this vanishing result and the derived localization theorem for crystalline differential operat...

Homogeneous games were introduced by von Neumann and Morgenstern in the constantsum case. Peleg studied the kernel and the nucleolus within this framework. However, for the general nonconstant-sum case Ostmann invented the unique minimal representation, Rosenmiiller gave a second characterization and Sudhiilter discovered the “incidence vector”. Based on these results Peleg and Rosenmiiller tre...

Introduction Conclusions References

A geometric constraint problem, also known as a geometric constraint system, consists of a finite set of geometric objects, such as points, lines, circles, planes, spheres, etc., and constraints upon them, such as incidence, distance, tangency, and so on. A solution of a geometric constraint problem P is a coordinate assignment for each of the geometric objects of P that places them in relation...