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Free quotients and the first betti number of some hyperbolic manifolds
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In this note we present a very simple method of proving that some hyperbolic manifoldsM have finite sheeted covers with positive first Betti number.
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The first one is a conjecture of Ian Hughes which states that iff1, ..., fn are primary invariants of a finite linear groupG, then the least common multiple of the degrees of thefi is a multiple of the exponent ofG.
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First appeared in passing in the basic paper of O.
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To prove this, we first state and prove a general result which gives a criterion for checking whether a variety of dimensionN≥3 is a (compactification of a) ball quotient.
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The theory is applied to the case of cubic hypersurfaces, which is the one most relevant to special geometry, obtaining the solution of the two classification problems and the description of the corresponding homogeneous special K?hler manifolds.
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Well known wonderfulG-varieties are those of rank zero, namely the generalized flag varietiesG/P, those of rank one, classified in [A], and certain complete symmetric varieties described in [DP] such as the famous space of complete conics.
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[M]) for the symplectic case and Berndt and Vanhecke [BV1] for the rank-one case.
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In the present article we propose a more detailed proof of this fact than the one given by Varagnolo and Vasserot.
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The first one is a conjecture of Ian Hughes which states that iff1, ..., fn are primary invariants of a finite linear groupG, then the least common multiple of the degrees of thefi is a multiple of the exponent ofG.
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Once the above equality is proved, Lp-estimates for g*(f) are obviously equivalent to Lp/2-estimates for h(f).
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Boundedness for the general bilinear operator then follows once the corresponding Lp-boundedness of time-frequency paraproducts has been established.
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The system is subject to failure and it fails once the total cumulative damage level first exceeds a fixed threshold.
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The relict genera once occupied huge areas in the northern hemisphere in the Tertiary or the late Cretaceous, while neo-endemism mostly originated in the late Tertiary.
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Among them, the embryos of three seeds were hit at least once, and mutants with significant changes in agronomic traits were only found in later generations of these seeds.
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The first one is a conjecture of Ian Hughes which states that iff1, ..., fn are primary invariants of a finite linear groupG, then the least common multiple of the degrees of thefi is a multiple of the exponent ofG.
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The condition, which is expressed in terms of the intertwining operators of each primary summand of the quasi-regular representation, is then interpreted in the case of the compact Heisenberg manifolds.
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A method of algebraic operation of special matrices involved in the problem is given in this paper for obtaining a new solution for the m + 1 experiments based upon the old solution for the primary m experiments.
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Primary customers get in the system according to a Poisson process, and they will receive service immediately if the server is available upon arrival.
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The resulting average value of the Avrami exponent at n = 3.34 suggests that primary crystallization may correspond to a three-dimensional spherulitic growth.
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