Cesàro Asymptotics for Orthogonal Polynomials on the Unit Circle and Classes of Measures

The convergence in L²( ) of the even approximants of the Wall continued fractions is extended to the Cesàro–Nevai class CN, which is defined as the class of probability measures σ with lim_n→∞ ∑ⁿ⁻¹_k=0 |a_k|=0, {a_n}_n0 being the Geronimus parameters of σ. We show that CN contains universal measures, that is, probability measures for which the sequence {|_n|² dσ}_n0 is dense in the set of all probability measures equipped with the weak-* topology. We also consider the “opposite” Szeg class which consists of measures with ∑^∞_n=0 (1−|a_n|²)^1/2<∞ and describe it in terms of Hessenberg matrices.     

Multiple stochastic integrals constructed by special expansions of products of the integrating stochastic processes

The paper deals with problems of constructing multiple stochastic integrals in the case when the product of increments of the integrating stochastic process admits an expansion as a finite sum of series with random coefficients. This expansion was obtained for a sufficiently wide class including centered Gaussian processes. In the paper, some necessary and sufficient conditions are obtained for the existence of multiple stochastic integrals defined by an expansion of the product of Wiener processes. It was obtained a recurrent representation for the Wiener stochastic integral as an analog of the Hu–Meyer formula.     

Szegő’s theorem for matrix orthogonal polynomials

We extend some classical theorems in the theory of orthogonal polynomials on the unit circle to the matrix case. In particular, we prove a matrix analogue of Szeg?’s theorem. As a by-product, we also obtain an elementary proof of the distance formula by Helson and Lowdenslager.     

Superconducting 119-pole wiggler with a 2.1-T field and 30-mm period length for the ALBA storage ring

A superconducting 119-pole wiggler with a 2.1-T operating field and 30-mm period length, which is intended for use at the ALBA Synchrotron Light Facility (SLF), Barcelona, Spain, has been designed and manufactured at the Budker Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia. The interpole gap and aperture of the beam are 12.6 and 8.5 mm respectively. The total radiation power reaches 16 kW when the current of the 3-GeV electron beam is 0.4 A. In May 2010, after successful testing in Novosibirsk, the wiggler was transported to the ALBA SLF and was retested outside of the storage ring. The maximum field achieved by training of the magnet is 2.26 T. Owing to the improved cryostat structure, the equilibrium operating temperature of the magnet is brought down to 3.5 K, guaranteeing reliable operation of the device and zero liquid helium consumption. The basic parameters of the wiggler??s magnetic and cryogenic systems, as well as the results of their tests, are presented.     

Depressed cladding, buried waveguide laser formed in a YAG:Nd3+ crystal by femtosecond laser writing

Depressed cladding waveguides have been formed in laser crystals by a tightly focused beam of a femtosecond laser. A laser based on a depressed cladding waveguide in a neodymium-doped YAG crystal has been demonstrated for what is believed to be the first time.     

Superconducting Multipole Wigglers for Generating Synchrotron Radiation at the Budker Institute of Nuclear Physics

Physics of Particles and Nuclei Letters - Superconducting multipole insertion devices (wigglers and undulators) used to generate synchrotron radiation significantly increase the photon flux,...