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It is proved in this note that the analogues of the Bennequin inequality which provide an upper bound for the Bennequin invariant of a Legendrian knot in the standard contact three dimensional space in terms of the lower degree in the framing variable of the HOMFLY and the Kauffman polynomials are not sharp. Furthermore, the relationships between these(More)
We consider the finite binary words Z(n), n ∈ N defined by the following self-similar process: Z(0) := 0, Z(1) := 01, and Z(n + 1) := Z(n) · Z(n − 1), where the dot · denotes word concatenation, and w the word obtained from w by exchanging the zeros and the ones. Denote by Z(∞) = 01110100. .. the limiting word of this process, and by z(n) the n th bit of(More)
  • Lenhard Lee, Ng A B, +15 authors Joe Gallian
  • 2011
We introduce new, readily computable invariants of Legendrian knots and links in standard contact three-space, allowing us to answer many previously open questions in contact knot theory. The origin of these invariants is the powerful Chekanov-Eliashberg diierential graded algebra, which we reformulate and generalize. We give applications to Legendrian(More)
Given a sequence x = {x n , n ∈ N} with integer values, or more generally with values in a ring of polynomials with integer coefficients, one can form the generalized binomial coefficients associated with x, n m x = m l=1 x n−l+1 x l. In this note we introduce several sequences that possess the following remarkable feature: the fractions n m x are in fact(More)
Zirconium (Zr) is a transition metal that has both stable and radioactive isotopes.This metal has gained significant attention as a major pollutant of concern, partly because it has been prominent in the debate concerning the growing anthropogenic pressure on the environment. Its numerous past and present uses have induced significant soil and water(More)
We show that there is no positive loop inside the component of a fiber in the space of Legendrian embeddings in the contact manifold ST * M , provided that the universal cover of M is R n. We consider some related results in the space of one-jets of functions on a compact manifold. We give an application to the positive isotopies in homogeneous(More)
Editor—Approximately 10% of all critically ill patients in the USA and in Europe are denied intensive care unit (ICU) admission because of bed shortage. 1 Such a refusal may be associated with a modification of patient care objectives and increased mortality. 2 The post-anaesthesia care unit (PACU) is an alternative setting for the care of critically ill(More)
This paper analyzes the relationship between bank sediment storage and radionuclide content in six alluvial sites located in different geomorphic contexts along the lower Rhône River. The 137Cs, 238Pu, 239+240Pu, 241Am and 210Pb profiles show different patterns, which indicates a differential storage of contaminated sediment in the banks. Three sites record(More)
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