Ergodicity of a Class of Cocycles Over Irrational Rotations

It is proved that if is irrational and L²(S¹) with o(l/n)then for each mZ\{0} the corresponding skew product is ergodic. The rigidity of specialflows over irrational rotations with roof functions whose Fouriercoefficients are in o(l/n) is also shown.     

On the distribution of the sum of digits of sums $$a+b$$ a + b

The Ramanujan Journal - Let $${\mathcal {A}}$$ , $${\mathcal {B}}$$ be large subsets of $$\{1,\ldots ,N\}$$ . We study the distribution of the sum of binary digits of the sums $$a+b$$ with...     

Construction of Pseudorandom Binary Sequences Using Additive Characters

In earlier papers the authors studied finite pseudorandom binary sequences, and they constructed sequences with strong pseudorandom properties. In these earlier constructions multiplicative characters were used. In this paper a new construction is presented which utilizes properties of additive characters. These new sequences can be computed fast, they are well-distributed relative to arithmetic progressions and their correlations of small order are small, but the price paid for the fast computation is that the correlations of large order can be large.     

Extended defects in shallow implants

Extended defects are often found after ion implantation and annealing of silicon and they are known to affect dopant diffusion. The article reviews the structure and energetics of the most often found extended defects and describes the mechanisms by which all these defects grow in size and transform during annealing. Defects grow by interchanging the Si atoms they are composed of and thus maintain large supersaturations of free Si interstitials in the region. A model has been developped to describe such an evolution in presence of a free surface. It is shown that after low energy implantation, the surface of the wafer may recombine large amounts of these free Si interstitials, driving defects into dissolution before transformation into more stable forms. Received: 21 August 2002 / Accepted: 21 August 2002 / Published online: 12 February 2003 RID="*" ID="*"Corresponding author. Fax: +33-56/2257-999, E-mail: claverie@cemes.fr     

La somme des chiffres des carrés

In this article we answer a question proposed by Gelfond in 1968. We prove that the sum of digits of squares written in a basis q ⩾ 2 is equidistributed in arithmetic progressions.     

On the Distribution in Residue Classes of Integers with a Fixed Sum of Digits

We give an asymptotic formula for the distribution of those integers n in a residue class, such that n has a fixed sum of base-g digits, with some uniformity over the choice of the modulus and g. We then use this formula to solve the problem of I. Niven of giving an asymptotic formula for the distribution of those integers n divisible by the sum of their base-g digits. Our results also allow us to give a stronger form of a result of M. Olivier dealing with the distribution of integers with a given gcd with their sum of base-g digits.For our friend Jean-Louis Nicolas on his sixtieth birthdayResearch partially supported by the Hungarian National Foundation for Scientific Research, Grant No. T029759, and “Balaton” French-Hungarian exchange program F-18/00.2000 Mathematics Subject Classification: Primary—11A63     

Sommes des chiffres et nombres presque premiers

Sans résumé

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Highly enantioselective and regioselective copper-catalyzed 1,4 addition of grignard reagents to cyclic enynones

In this letter we describe an unusual result in terms of regioselectivity with respect to copper-catalyzed conjugate additions of various Grignard reagents to cyclic enynones. The use of Cu(OTf)(2) and NHC ligand L1 as the catalyst combination in CH(2)Cl(2) led to the unique formation of the 1,4 adduct. This selectivity does not follow the general trend previously observed in the literature using extended Michael acceptors. Moreover these reactions allowed for the creation of a quarternary stereogenic center with enantioselectivities up to 97% ee.     

A complexity measure for families of binary sequences

In earlier papers finite pseudorandom binary sequences were studied, quantitative measures of pseudorandomness of them were introduced and studied, and large families of “good” pseudorandom sequences were constructed. In certain applications (cryptography) it is not enough to know that a family of “good” pseudorandom binary sequences is large, it is a more important property if it has a “rich”, “complex” structure. Correspondingly, the notion of “f-complexity” of a family of binary sequences is introduced. It is shown that the family of “good” pseudorandom binary sequences constructed earlier is also of high f-complexity. Finally, the cardinality of the smallest family achieving a prescibed f-complexity and multiplicity is estimated. This revised version was published online in August 2006 with corrections to the Cover Date.     

Sustainable concepts in olefin metathesis

Ruthenium-catalyzed olefin metathesis reactions represent an attractive and powerful transformation for the formation of new carbon-carbon double bonds. This area is now quite familiar to most chemists as numerous catalysts are available that enable a plethora of olefin metathesis reactions. Nevertheless, with the exception of uses in polymerization reactions, only a limited number of industrial processes use olefin metathesis. This is mainly due to difficulties associated with removing ruthenium from the final products. In this context, a number of studies have been carried out to develop procedures for the removal of the catalyst or the products of catalyst decomposition, however, none are universally attractive so far. This situation has resulted in tremendous activity in the area dealing with supported or tagged versions of homogeneous catalysts. This Review summarizes the numerous studies focused on developing cleaner ruthenium-catalyzed metathesis processes.