Contributions to the study of the comparative morphology of teeth and other relevant ichthyodorulites in living supra-specific taxa of Chondrichthyan fishes. Part B: Batomorphii. 4a: Order Rajiformes - Suborder Myliobatoidei - Superfamily Dasyatoidea - Family Dasyatidae - Subfamily Dasyatinae - Genera: <i>Amphotistius, Dasyatis, Himantura, Pastinachus, Pteroplatytrygon, Taeniura, Urogymnus</i> and <i>Urolophoides</i> (incl. supraspecific taxa of uncertain status and validity), Superfamily Myliobatoidea - Family Gymnuridae - Genera: <i>Aetoplatea</i> and <i>Gymnura</i>, Superfamily Plesiobatoidea - Family Hexatrigonidae - Genus: <i>Hexatrygon</i>

Part B of this series, comprising the Batomorphii is continued with taxa of the Myliobatoidei. The tooth morphology of representatives of eight genera (incl. supraspecific taxa of uncertain status and validity) of the family Dasyatidae, two of Gymnuridae and one of Hexatrygonidae is described and illustrated by SEM-photographs. A differential diagnosis for a final conclusions on myliobatoid odontology will be given in a forthcoming issue dealing with the last myliobatoid taxa

Chirality of wave functions for three coalescing levels

The coalescence of three levels has particular attractive features. Even though it may be difficult to realise such event in the laboratory (three additional real parameters must be adjusted), to take up the challenge seems worthwhile. In the same way as the chiral behaviour of a usual EP can give a direction on a line, the state vectors in the vicinity of an EP3 provide an orientation in the plane. The distinction between left and right handedness depends on the distribution of the widths of the three levels in the vicinity of the point of coalescence.Comment: Manuscript has been discussed in June 2007 with the experimental group under Professor Achim Richter at the TU Darmstadt. It has been presented at the 6th International Workshop on Pseudo Hermitian Hamiltonians, London, 16-18 July 2007. An expanded version is being prepared for publication. 3 Figures, 11 page

Influence of gas discharge parameters on emissions from a dielectric barrier discharge excited argon excimer lamp

The original publication is available at http://www.sajs.co.za/A dielectric barrier discharge excited neutral argon (Ar I) excimer lamp has been developed and characterised. The aim of this study was to develop an excimer lamp operating at atmospheric pressure that can replace mercury lamps and vacuum equipment used in the sterilisation of medical equipment and in the food industry. The effects of discharge gas pressure, flow rate, excitation frequency and pulse width on the intensity of the Ar I vacuum ultraviolet (VUV) emission at 126 nm and near infrared (NIR) lines at 750.4 nm and 811.5 nm have been investigated. These three lines were chosen as they represent emissions resulting from deexcitation of excimer states that emit energetic photons with an energy of 9.8 eV. We observed that the intensity of the VUV Ar2* excimer emission at 126 nm increased with increasing gas pressure, but decreased with increasing excitation pulse frequency and pulse width. In contrast, the intensities of the NIR lines decreased with increasing gas pressure and increased with increasing pulse frequency and pulse width. We have demonstrated that energetic VUV photons of 9.8 eV can be efficiently generated in a dielectric barrier discharge in Ar

Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation

The paper presents a new theory of unfolding of eigenvalue surfaces of real symmetric and Hermitian matrices due to an arbitrary complex perturbation near a diabolic point. General asymptotic formulae describing deformations of a conical surface for different kinds of perturbing matrices are derived. As a physical application, singularities of the surfaces of refractive indices in crystal optics are studied.Comment: 23 pages, 7 figure

Application of Pseudo-Hermitian Quantum Mechanics to a Complex Scattering Potential with Point Interactions

We present a generalization of the perturbative construction of the metric operator for non-Hermitian Hamiltonians with more than one perturbation parameter. We use this method to study the non-Hermitian scattering Hamiltonian: H=p^2/2m+\zeta_-\delta(x+a)+\zeta_+\delta(x-a), where \zeta_\pm and a are respectively complex and real parameters and \delta(x) is the Dirac delta function. For regions in the space of coupling constants \zeta_\pm where H is quasi-Hermitian and there are no complex bound states or spectral singularities, we construct a (positive-definite) metric operator \eta and the corresponding equivalent Hermitian Hamiltonian h. \eta turns out to be a (perturbatively) bounded operator for the cases that the imaginary part of the coupling constants have opposite sign, \Im(\zeta_+) = -\Im(\zeta_-). This in particular contains the PT-symmetric case: \zeta_+ = \zeta_-^*. We also calculate the energy expectation values for certain Gaussian wave packets to study the nonlocal nature of \rh or equivalently the non-Hermitian nature of \rH. We show that these physical quantities are not directly sensitive to the presence of PT-symmetry.Comment: 22 pages, 4 figure

Fermionic coherent states for pseudo-Hermitian two-level systems

We introduce creation and annihilation operators of pseudo-Hermitian fermions for two-level systems described by pseudo-Hermitian Hamiltonian with real eigenvalues. This allows the generalization of the fermionic coherent states approach to such systems. Pseudo-fermionic coherent states are constructed as eigenstates of two pseudo-fermion annihilation operators. These coherent states form a bi-normal and bi-overcomplete system, and their evolution governed by the pseudo-Hermitian Hamiltonian is temporally stable. In terms of the introduced pseudo-fermion operators the two-level system' Hamiltonian takes a factorized form similar to that of a harmonic oscillator.Comment: 13 pages (Latex, article class), no figures; v2: some amendments in section 2, seven new refs adde

Stochastic pump effect and geometric phases in dissipative and stochastic systems

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).Comment: Review. 35 pages. J. Phys. A: Math, Theor. (in press

Phylogenomic Discordance Suggests Polytomies Along the Backbone of the Large Genus Solanum

Premise of the study Evolutionary studies require solid phylogenetic frameworks, but increased volumes of phylogenomic data have revealed incongruent topologies among gene trees in many organisms both between and within genomes. Some of these incongruences indicate polytomies that may remain impossible to resolve. Here we investigate the degree of gene-tree discordance in Solanum, one of the largest flowering plant genera that includes the cultivated potato, tomato, and eggplant, as well as 24 minor crop plants. Methods A densely sampled species-level phylogeny of Solanum is built using unpublished and publicly available Sanger sequences comprising 60% of all accepted species (742 spp.) and nine regions (ITS, waxy, and seven plastid markers). The robustness of this topology is tested by examining a full plastome dataset with 140 species and a nuclear target-capture dataset with 39 species of Solanum (Angiosperms353 probe set). Key results While the taxonomic framework of Solanum remained stable, gene tree conflicts and discordance between phylogenetic trees generated from the target-capture and plastome datasets were observed. The latter correspond to regions with short internodal branches, and network analysis and polytomy tests suggest the backbone is composed of three polytomies found at different evolutionary depths. The strongest area of discordance, near the crown node of Solanum, could potentially represent a hard polytomy. Conclusions We argue that incomplete lineage sorting due to rapid diversification is the most likely cause for these polytomies, and that embracing the uncertainty that underlies them is crucial to understand the evolution of large and rapidly radiating lineages

Spectral Singularities of a General Point Interaction

We study the problem of locating spectral singularities of a general complex point interaction with a support at a single point. We also determine the bound states, examine the special cases where the point interaction is P-, T-, and PT-symmetric, and explore the issue of the coalescence of spectral singularities and bound states.Comment: 11 page