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On an arbitrary compact Riemann surface, necessary and sufficient conditions are found for the existence of semistable vector bundles with slope between zero and one and a prescribed number of linearl...
A vector minmax problem for controlled Markov chains
A vector minmax problem controlled Markov chains
2010/11/9
The problem of controlling a finite state Markov chain in the presence of an adversary so as to ensure desired performance levels for a vector of objectives is cast in the framework of Blackwell appro...
Parametrix techniques and martingale problem for some degenerate Kolmogorov's equations
Parametrix techniques martingale problem degenerate Kolmogorov's equations
2010/11/15
We prove the uniqueness of the martingale problem associated to some degenerate operators. The key point is to exploit the strong parallel between the new technique introduced by Bass and Perkins (Fr...
A Note on a Problem of J. Galambos
Oppenheim series expansion Restricted Oppenheim series expansion Lüroth series Hausdorff dimension
2010/2/25
For any x\in (0,1], letx = \frac{1}{d1} + \frac{a1}{b1} \frac{1}{d2} + ··· + \frac{a1a2 ··· an}{b1b2 ··· bn} \frac{1}{dn+1} + ··· be the Oppenheim series expansion of x. In this paper, we investigate ...
On a Problem of Mahler Concerning the Approximation of Exponentials and Logarithms
Mahler Concerning Approximation of Exponentials Logarithms
2010/11/1
We first propose two conjectural estimates on Diophantine approximation of logarithms of algebraic numbers. Next we discuss the state of the art and we give further partial results on this topic.