On the torsion of Jacobians of principal modular curves of level 3<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

We demonstrate that the 3-power torsion points of the Jacobians of the principal modular curves X(3ⁿ) are fixed by the kernel of the canonical outer Galois representation of the pro-3 fundamental group of the projective line minus three points. The proof proceeds by demonstrating the curves in question satisfy a two-part criterion given by Anderson and Ihara. Two proofs of the second part of the criterion are provided; the first relies on a theorem of Shimura, while the second uses the moduli interpretation. Received: 30 September 2005     

Local algebras in the representation of MV-algebras

In this paper we present several results about local MV-algebras, extending existing results given for MV-chains. The role of local MV-algebras in sheaf representation and weak boolean product is stressed and the relationship of local MV-algebras with varieties of MV-algebras is analyzed. Presented by S. Pulmannova. Received November 11, 2005; accepted in final form December 20, 2005.     

Hardy type inequalities with exponential weights for a class of convolution operators

In this paper we consider operators of the form H=λ(-i∇), with λ analytic in a strip and with some specific growth conditions at infinity, and prove Hardy type estimates in L ²(ℝ ⁿ ) with exponential weights. In fact we extend our previous results [19] from bounded analytic functions on a strip to analytic functions with polynomial growth in that strip.     

Instability of Solitary Waves in Nonlinear Composite Media

In this paper,we investigate a class of Hamiltonian systems arising in nonlinear composite media.By detailed analysis and computation we obtain a decaying estimates on the semigroup and prove the orbitalinstability of two families of explicit solitary wave solutions (slow family in anisotropic case and solitary wavesin isotropic case),which theoretically verify the related guess and numerical results.     

A Note on the Kissing Numbers of Superballs

The lower bounds for the translative kissing numbers of superballs are studied in this note. We improve the bound given by Larman and Zong. Furthermore, we give a constructive bound based on algebraic-geometry codes that also improves the bound by Larman and Zong in almost all cases.     

A web-based workforce management system for Sainsburys Supermarkets Ltd

Labour scheduling plays an important and critical role in Sainsburys day to day operations and profitability. The integrated workforce management solution for Sainsburys is an intelligent solution for the operational deployment of human resources, integrated business forecasting, generation and calculation of workload and staff scheduling. The workforce management technology has provided Sainsburys with a fully web-based and centralised system that produces optimised schedules for all employees satisfying the forecasted demand of work with granularity of fifteen minutes. The system is configured to respect all operational and business requirements as well as employee contractual constraints. This paper introduces the workforce management solution system designed, developed and implemented for Sainsburys. We concentrate on two modelling structures, namely the work pattern model and optimisation model, and briefly discuss the optimisation process.     

Tail asymptotics for the fundamental period in the MAP/G/1 queue

This paper studies the tail behavior of the fundamental period in the MAP/G/1 queue. We prove that if the service time distribution has a regularly varying tail, then the fundamental period distribution in the MAP/G/1 queue has also regularly varying tail, and vice versa, by finding an explicit expression for the asymptotics of the tail of the fundamental period in terms of the tail of the service time distribution. Our main result with the matrix analytic proof is a natural extension of the result in (de Meyer and Teugels, J. Appl. Probab. 17: 802–813, 1980) on the M/G/1 queue where techniques rely heavily on analytic expressions of relevant functions. I.-S. Wee’s research was supported by the Korea Research Foundation Grant KRF 2003-070-00008.     

Dark matter annihilation in the Galaxy

The awaited dark matter (DM) neutralino annihilation signal from the galactic halo crucially depends on the presence of small-scale clumps. A mass function of the DM small-scale clumps is calculated in the standard cosmological scenario. The final distribution of clumps in the Galaxy is influenced by their tidal destruction. The basic sources of clump destruction are (i) clumps of larger scales, (ii) the gravitational field of the galactic disk, (iii) the stars in the galactic bulge, and (iv) the stars in the galactic halo. The destruction of clumps due to their mutual tidal interactions is important at earl stages of hierarchical clustering and the galactic halo formation. The clumps surviving through the hierarchical clustering are continuously destroyed by interactions with the galactic disk and stars. It is shown that, among the Moon or Earth mass DM clumps surviving through the hierarchical clustering, only 20% will further survive near the Sun’s position mainly because of the tidal destruction by the galactic disk. This reduction of DM clump density significantly diminishes the expected DM annihilation signal from the galactic halo. The text was submitted by the authors in English.     

Control of the temperature hysteresis and diffuse dielectric anomaly in the temperature range of the ferroelectric-antiferroelectric phase transition in PbZr1 − x TixO3 (0.03 ≤ x ≤ 0.05) ceramics

The magnitudes of the temperature hysteresis and diffuse dielectric anomaly corresponding to the transition from the antiferroelectric phase to the ferroelectric phase in PbZr_{1 ? x} Ti_xO₃ (0.03 ≤ x ≤ 0.05) ceramics can be reversibly changed by varying the temperatures of heating and cooling in the course of thermocycling. The results obtained indicate that the antiferroelectric-ferroelectric transition in the PbZr_{1 ? x} Ti_xO₃ ceramics materials is a smeared first-order phase transition.     

Experimental and theoretical investigation into the effect of the electron velocity distribution on chaotic oscillations in an electron beam under virtual cathode formation conditions

The effect of the electron transverse and longitudinal velocity spread at the entrance to the interaction space on wide-band chaotic oscillations in intense multiple-velocity beams is studied theoretically and numerically under the conditions of formation of a virtual cathode. It is found that an increase in the electron velocity spread causes chaotization of virtual cathode oscillations. An insight into physical processes taking place in a virtual-cathode multiple-velocity beam is gained by numerical simulation. The chaotization of the oscillations is shown to be associated with additional electron structures, which were separated out by constructing charged particle distribution functions.