An alternative construction of the positive inner product for pseudo-Hermitian Hamiltonians: Examples

This paper builds on our earlier proposal for construction of a positive inner product for pseudo-Hermitian Hamiltonians and we give several examples to clarify our method. We show through the example of the harmonic oscillator how our construction applies equally well to Hermitian Hamiltonians which form a subset of pseudo-Hermitian systems. For finite dimensional pseudo-Hermitian matrix Hamiltonians we construct the positive inner product (in the case of $2\times 2$ matrices for both real as well as complex eigenvalues). When the quantum mechanical system cannot be diagonalized exactly, our construction can be carried out perturbatively and we develop the general formalism for such a perturbative calculation systematically (for real eigenvalues). We illustrate how this general formalism works out in practice by calculating the inner product for a couple of ${\cal PT}$ symmetric quantum mechanical theories.Comment: 9 pages, revte

Torque vectoring based drive assistance system for turning an electric narrow tilting vehicle

The increasing number of cars leads to traffic congestion and limits parking issue in urban area. The narrow tilting vehicles therefore can potentially become the next generation of city cars due to its narrow width. However, due to the difficulty in leaning a narrow tilting vehicle, a drive assistance strategy is required to maintain its roll stability during a turn. This article presents an effective approach using torque vectoring method to assist the rider in balancing the narrow tilting vehicles, thus reducing the counter-steering requirements. The proposed approach is designed as the combination of two torque controllers: steer angle–based torque vectoring controller and tilting compensator–based torque vectoring controller. The steer angle–based torque vectoring controller reduces the counter-steering process via adjusting the vectoring torque based on the steering angle from the rider. Meanwhile, the tilting compensator–based torque vectoring controller develops the steer angle–based torque vectoring with an additional tilting compensator to help balancing the leaning behaviour of narrow tilting vehicles. Numerical simulations with a number of case studies have been carried out to verify the performance of designed controllers. The results imply that the counter-steering process can be eliminated and the roll stability performance can be improved with the usage of the presented approach

Comparisons of elastic and creep deformation linearly dependent upon stress

The theory of linear elasticity provides a complete description of reversible deformation under small stresses for both isotropic and anisotropic solids. At elevated temperatures, creep deformation sometimes occurs at a rate that is linearly dependent upon stress. When this form of creep arises from vacancy movement, there is possibility of anisotropic behaviour through the orientational dependence of average grain dimensions. This indicates that the elasticity theory may be utilised to provide comparable descriptions of such creep deformation, with creep strain built up of equal increments of strain occurring in equal intervals of time. The extent of this analogy is explored with the conclusion that its usefulness is substantial when grains are small in relation to geometrical features of the component but it is no longer applicable when the grains approach the size of these features and where there is a high gradient of stress

A new CH carbonaceous chondrite from Acfer, Algeria

A single stone weighing 1456 g was found in November 2002 in the Acfer area, Algeria. Oxygen isotope, chondrules-matrix ratio as well as other petrographic features point to a classification as CH carbonaceous chondrite

Characterization of Mauritius parakeet (Psittacula eques) microsatellite loci and their cross-utility in other parrots (Psittacidae, Aves).

We characterized 21 polymorphic microsatellite loci in the endangered Mauritius parakeet (Psittacula eques). Loci were isolated from a Mauritius parakeet genomic library that had been enriched separately for eight different repeat motifs. Loci were characterized in up to 43 putatively unrelated Mauritius parakeets from a single population inhabiting the Black River Gorges National Park, Mauritius. Each locus displayed between three and nine alleles, with the observed heterozygosity ranging between 0.39 and 0.96. All loci were tested in 10 other parrot species. Despite testing few individuals, between seven and 21 loci were polymorphic in each of seven species tested

A new CO carbonaceous chondrite from Acfer, Algeria

Many small fragments, totally weighing 118 g were found in the Acfer area by an Italian dealer. Chondrules size and types (predominance of granular olivine type), occurrence of twinned clinoenstatite and absence of plagioclase suggested a classification as CO carbonaceous chondrite