The electrical properties of doped silicon,grown by Molecular-Beam-Epitaxy (MBE)

Measurements of the Hall coefficients and of the resistivity of MBE-grown Si, doped with P, As, Sb, B, and Ga in the concentration range 10¹⁴ to 10²⁰ cm^–3, were carried out at 77 K and at 300 K. With the exception of Ga-doped Si, the measured mobilities were close to or higher than those of bulk materials at both temperatures. The Mott metal/non-metal transition has been observed in the present epitaxial materials and the measured values for the critical impurity concentration at which the transition occurs, agree with values reported by other workers for bulk silicon.     

A note on Cesàro-Orlicz sequence spaces

The condition δ₂ in Cesàro-Orlicz sequence spaces equipped with the Luxemburg norm is discussed. The comparison theorem for these spaces is presented. Some counterexamples are provided.     

End-point detection in potentiometric titration by continuous wavelet transform

The aim of this work was construction of the new wavelet function and verification that a continuous wavelet transform with a specially defined dedicated mother wavelet is a useful tool for precise detection of end-point in a potentiometric titration. The proposed algorithm does not require any initial information about the nature or the type of analyte and/or the shape of the titration curve. The signal imperfection, as well as random noise or spikes has no influence on the operation of the procedure.The optimization of the new algorithm was done using simulated curves and next experimental data were considered. In the case of well-shaped and noise-free titration data, the proposed method gives the same accuracy and precision as commonly used algorithms. But, in the case of noisy or badly shaped curves, the presented approach works good (relative error mainly below 2% and coefficients of variability below 5%) while traditional procedures fail. Therefore, the proposed algorithm may be useful in interpretation of the experimental data and also in automation of the typical titration analysis, specially in the case when random noise interfere with analytical signal.     

Dispersion relation in the limit of high frequency for a hyperbolic system with multiple eigenvalues

The results of a previous paper (Muracchini et al., 1992) are generalized by considering a hyperbolic system in one space dimension with multiple eigenvalues. The dispersion relation for linear plane waves in the high-frequency limit is analyzed and the recurrence formulas for the phase velocity and the attenuation factor are derived in terms of the coefficients of a formal series expansion in powers of the reciprocal of frequency. In the case of multiple eigenvalues, it is also verified that linear stability implies λ$\lambda$-stability for the waves of weak discontinuity. Moreover, for the linearized system, the relationship between entropy and stability is studied. When the nonzero eigenvalue is simple, the results of the paper mentioned above are recovered. In order to illustrate the procedure, an example of the linear hyperbolic system is presented in which, depending on the values of parameters, the multiplicity of nonzero eigenvalues is either one or two. This example describes the dynamics of a mixture of two interacting phonon gases.     

[Phthalocyaninato(2–)]­antimony(III) chloride

The title antimony(III) complex, [Sb(C₃₂H₁₆N₈)]Cl or [SbPc]Cl (where Pc = C₃₂H₁₆N₈²⁻), has been obtained from the reaction of pure powdered antimony with 1,2-di­cyano­benzene under a stream of ICl vapour. The asymmetric unit of this complex consists of an [SbPc]⁺ cation and a Cl⁻ anion. The phthalocyaninate residue [SbPc]⁺ is not planar. The Sb atom lies 1.057 (3) Å from the plane defined by the four iso­indole N atoms. A combination of ionic and donor–acceptor interactions links the [SbPc]Cl mol­ecules to form centrosymmetric [(SbPc)Cl]₂ pseudo-dimers in the crystal. The Sb—Cl distances in the pseudo-dimer are not equivalent [3.043 (2) and 3.201 (2) Å]. The pseudo-dimers are weakly linked through Cl⃛H—C_benzo interactions to form a three-dimensional network. As a result of these interactions, the four Sn—N_isoindole bond lengths in the [SbPc]⁺ residue are not equivalent and the symmetry of the Sb—N core is only close to C_s.     

Mixed symbolic–numerical computations with general DAEs II: An applications case study

A variety of theorems and properties of nonlinear DAEs were discussed in part I. This paper illustrates many of these ideas within the context of analyzing a specific nonlinear system that exhibits a variety of interesting features. This revised version was published online in June 2006 with corrections to the Cover Date.     

An efficient algorithm for a job shop problem

We study the problem of minimizing makespan in a two-machine job shop with unit processing time operations. An efficient algorithm with respect to a succinct encoding of the problem instances is proposed. The algorithm is an improvement of earlier algorithms proposed for the problem by Brucker [1,2], Hefetz and Adiri [7], and Timkovskiy [15]. The idea behind the algorithm has the potential of extension to job shops with parallel machines.This research is supported in part by NSERC Grants A4619, OGP0105675, OGP0104900, General Motors of Canada, and the Manufacturing Research Corporation of Ontario.