Nondispersive two-electron wave packets in driven helium

We provide a detailed quantum treatment of the spectral characteristics and of the dynamics of nondispersive two-electron wave packets along the periodically driven, collinear frozen planet configuration of helium. These highly correlated, long-lived wave packets arise as a quantum manifestation of regular islands in a mixed classical phase space, which are induced by nonlinear resonances between the external driving and the unperturbed dynamics of the frozen-planet configuration. Particular emphasis is given to the dependence of the ionization rates of the wave packet states on the driving field parameters and on the quantum mechanical phase space resolution, preceded by a comparison of 1D and 3D life times of the unperturbed frozen planet. Furthermore, we study the effect of a superimposed static electric field component, which, on the grounds of classical considerations, is expected to stabilize the real 3D dynamics against large (and possibly ionizing) deviations from collinearity. Received 7 November 2002 / Received in final form 2 December 2002 Published online 28 January 2003     

Thermal conductance for single wall carbon nanotubes

We report a theoretical analysis of the phonon thermal conductance, κ(T), for single wall carbon nanotubes (SWCN). In a range of low temperatues up to 100 K, κ(T) of perfect SWCN is found to increase with temperature, approximately, in a parabolic fashion. This is qualitatively consistent with recent experimental measurements where the tube-tube interactions are negligibly weak. When the carbon-carbon bond length is slightly varied, κ(T) is found to be qualitatively unaltered which implies that the anharmonic effect does not change the qualitative behavior of κ(T). Received 12 June 2001     

The spectrum of BSA(v, 3, λ; α) with α = 2,3

In this article, a kind of auxiliary design BSA^* for constructing BSAs is introduced and studied. Two powerful recursive constructions on BSAs from 3‐IGDDs and BSA^*s are exploited. Finally, the necessary and sufficient conditions for the existence of a BSA(v, 3, λ; α) with α = 2, 3 are established. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 61–76, 2007     

Classical limit of relativistic quantal system with attractive Coulomb interaction

Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r ²〉 − 〈r〉²]^1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order, the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic quantal system, in general.     

On the properties of solutions to the Goursat-Darboux problem with boundary and distributed controls

We consider a control system described by the Goursat-Darboux equation. The system is controlled by distributed and boundary controls. The controls are subject to the constraints given as multivalued mappings with closed, possibly nonconvex, values depending on the phase variable. Alongside the initial constraints, we consider the convexified constraints and the constraints whose values are the extreme points of the convexified constraints. We study the questions of existence of solutions and establish connections between the solutions under various constraints.     

Nanometric Antimony Powder Synthesis by Activated Alkaline Hydride Reduction of Antimony Pentachloride

A novel chemical reduction method using an activated alkaline hydride (LiH or NaH-t-BuONa) in tetrahydrofuran solvent has been applied to antimony salt reduction. X-ray diffraction and transmission electron microscopy studies have been carried out to characterize the morphology and structure of the materials. Alkali hydride nature influence has been proved. In both cases the process allows to prepare antimony particles in nanometer range from few nanometers to about 20nm which could be used as anodic materials for lithium–ion batteries. With lithium hydride well-crystallized particles inclined to agglomeration were observed whereas finely dispersed amorphous particles were pointing out after activated sodium hydride reduction.     

Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln²-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e ⁴ appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω ₂ which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω ₁)^1/2exp(- Ω ₁/|ω|) at T = 0, where Ω ₁ is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments. Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002     

Generators of some Ramanujan formulas

In this paper we prove some Ramanujan type formulas for 1/π but without using the theory of modular forms. Instead we use the WZ—method created by H. Wilf and D. Zeilberger and find some hypergeometric functions in two variables which are second components of WZ—pairs than can be certified using Zeilberger's EKHAD package. These certificates have an additional property which allows us to get generalized Ramanujan's type series which are routinely proven by computer. We call these second hypergeometric components of the WZ—pairs generators. Finding generators seems a hard task but using a kind of experimental research (explained below), we have succeeded in finding some of them. Unfortunately we have not found yet generators for the most impressive Ramanujan's formulas. We also prove some interesting binomial sums for the constant 1/π². Finally we rewrite many of the obtained series using pochhammer symbols and study the rate of convergence. 2000 Mathematics Subject Classification Primary—33C20     

Deposition conditions in tailoring the morphology of highly porous reticular films prepared by electrostatic spray deposition (ESD) technique

Spongy-like reticular structure is a unique morphology fabricated by electrostatic spray deposition (ESD) technique. The effects of solvent, substrate temperature, precursor feeding rate, static electric field strength, and deposition time on tailoring the reticular structure were investigated. Scanning electron microscopy was used to observe the film morphology. MnO_x or LiMn₂O₄ were selected as the model materials. It is found that in addition to the conventional solvent butyl carbitol, other kinds of solvents such as ethylene glycol and propylene glycol can also be used to obtain reticular films at a suitable substrate temperature. Porous films with a low cross-linking degree pore structure can be prepared by increasing precursor feeding rate or decreasing substrate temperature. Increasing the deposition time or the electric field strength helps to obtain reticular films with more homogeneous pore size distribution. In addition, the addition of a high boiling-point solvent in mixed alcohol solvent results in the increase of proper substrate temperature. It is concluded that the fluidity of the spray droplets on the surface of a hot substrate is an important factor to form a reticular film.     

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.