On multiple integrals represented as a linear form in 1, ζ(3), ζ(5),..., ζ(2<Emphasis Type="Italic">k</Emphasis> − 1)

A theorem on the presentability of a multiple integral as a linear form in 1, ζ(3), ζ(5),..., ζ(2k − 1) over ℚ is proved. This theorem refines the results recently obtained by D. Vasiliev, V. Zudilin, and S. Zlobin. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 143–178, 2005.     

Weighted estimates of a solution to the linear problem connected with the one-phase Stefan problem in the case where the specific heat tends to zero

We prove estimates in weighted Hölder norms for a solution to the model linear problem related with the one-phase Stefan problem with a small multiplier ε at time derivative in the heat equation. These estimates are uniform with respect to parameter ε and are significant in justification of passage to the limit in the one-phase Stefan problem as the specific heat tends to zero. Bibliography: 8 titles.     

On <Emphasis Type="Italic">W</Emphasis>-geometry of Toda systems

We describe W-geometry of two-dimensional Toda systems associated with the Lie algebra C _n . __________ Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry, 2005.     

Cayley hypersurfaces

We exhibit a family of homogeneous hypersurfaces in affine space, one in each dimension, that generalize the Cayley surface.     

On the role of mechanical effects during dynamic fatigue of PbTiO3 single crystals

The details of the mechanical effects (twinning and microcracking) are clarified at various stages of dynamic fatigue of PbTiO₃ crystals using a polarization microscope and selective etching.     

Possibility of observing chiral-symmetry effects in ferromagnetic nanoparticles

The statistics of left-and right-handed vortical magnetization states in a system of submicron-sized ferromagnetic disks is studied experimentally. Lattices of elliptic cobalt particles with a planar size of 750 × 450 nm and a thickness of 25 nm were formed using high-resolution electronic lithography. To visualize the magnetization distributions in the disks, magnetic force microscopy was used. The experimental results indicate the conservation of magnetic chiral symmetry in cobalt ferromagnetic particles of the above size and shape.     

A note on scheduling to meet two min-sum objectives

We consider a single machine scheduling problem with two min-sum objective functions: the sum of completion times and the sum of weighted completion times. We propose a simple polynomial time (1+(1/γ),1+γ)-approximation algorithm, and show that for γ>1, there is no (x,y)-approximation with 1<x<1+(1/γ) and 1<y<1+(γ-1)/(2+γ).     

The Design of Single Mode Large Cross-section Glass-based Waveguides for Photonic Integrated Circuits

This paper presents our recent simulation results and novel designs of single mode large cross-section glass-based waveguides for photonic integrated circuits (PICs). Simulations were performed using an in-house Finite Difference (FD) based mode solver and the FD Beam propagation Method (FD-BPM). Our simulation results show that this innovative technology could provide a simplified means to couple optical energy efficiently between optical components in a single chip. This would provide the base for the future large-scale integration of optical components in PICs. The novel idea of using single mode large cross-section glass-based waveguides as an optical integration platform is an evolutionary innovative solution for the monolithic integration of optical components, in which the glass-based structures act both as waveguides and as an optical bench for integration. This allows easy and efficient optical coupling between optical components and optical fibres, removing costly and tedious alignment problems and considerably reducing optical coupling losses in PICs. We expect that the glass-based waveguide PICs technology will enable the emergence of a new generation of compact, reliable, high speed, and multifunctional devices.