Stereocontrolled synthesis of enantiopure anticancer cyclopentenone prostaglandin analogues: (−)- and (+)-TEI-9826

The synthesis of both enantiomers of TEI-9826 has been accomplished in seven steps with an overall yield of 44% starting from diastereomeric camphor protected 3-[(dimethoxyphosphoryl)methyl]-4,5-dihydroxycyclopent-2-enones. The key steps include a fully diastereoselective hydrogenation of the endocyclic carbon–carbon double bond in the cyclopentenone ring controlled with a chiral diol moiety and the conversion of the latter into a new transposed olefinic bond.     

Integers without divisors in a given progression

An asymptotic formula is given for the number of integers n ≤ x which do not have divisors in a fixed arithmetical progression. This extends a previous result of Banks et al. (Forum Math 20:1005–1037, 2008) who considered the case of progressions with prime difference.     

Optimal partitioning of a measurable space into countably many sets

Summary A notion of an optimal partition of a measurable space into countably many sets according to given nonatomic probability measures is defined. It is shown that the set of optimal partitions is nonempty. Bounds for the optimal value are given and the set of optimal partitions is characterized. Finally, an example related to statistical decision theory is presented.     

Scattering matrix in conformal geometry

Inventiones mathematicae -     

Harmonic functions of polynomial growth on certain complete manifolds

Given a complete manifold with a particular structure at infinity, we give the dimension of the space of harmonic functions with prescribed polynomial growth.     

Metal nanowires fabricated by means of magnetostrictive actuator

A new method of fabricating nanowires for electric conductance quantization studies is proposed as an alternative to the method based on converse piezoelectric effect. Commonly used for nanowire fabrication, piezoelectric actuators are expensive and require high-level voltage control signal. The method presented in this paper is based on the use of magnetostrictive actuator. Both the actuator structure and the method of the conversion factor measurement are discussed. The results of the tests of the magnetostrictive actuator are also reported. The parameters of the proposed actuator are compared with those of its piezoelectric counterpart used to date. The results of measurement confirm that the proposed actuator can be used for studying electric conductance quantization in nanowires. Presented at the X-th Symposium on Surface Physics, Prague, Czech Republic, July 11–15, 2005     

Differential equation for the generalized Bell function

The generalized Bell function is introduced and an ordinary differential equation which it obeys is derived.