On a two variable class of Bernstein-Szego measures

The one variable Bernstein-Szego theory for orthogonal polynomials on the real line is extended to a class of two variable measures. The polynomials orthonormal in the total degree ordering and the lexicographical ordering are constructed and their recurrence coefficients discussed.Comment: minor change

First principle study of intrinsic defects in hexagonal tungsten carbide

The characteristics of intrinsic defects are important for the understanding of self-diffusion processes, mechanical strength, brittleness, and plasticity of tungsten carbide, which present in the divertor of fusion reactors. Here, we use first-principles calculations to investigate the stability of point defects and their complexes in WC. Our calculation results confirm that the formation energies of carbon defects are much lower than that of tungsten defects. The outward relaxations around vacancy are found. Both interstitial carbon and interstitial tungsten atom prefer to occupy the carbon basal plane projection of octahedral interstitial site. The results of isolated carbon defect diffusion show that the carbon vacancy stay for a wide range of temperature because of extremely high diffusion barriers, while carbon interstitial migration is activated at lower temperatures for its considerable lower activation energy. These results provide evidence for the presumption that the 800K stage is attributed by the annealing out of carbon vacancies by long-range migration.Comment: Submitted to Journal of Nuclear Material

Higher analogues of the discrete-time Toda equation and the quotient-difference algorithm

The discrete-time Toda equation arises as a universal equation for the relevant Hankel determinants associated with one-variable orthogonal polynomials through the mechanism of adjacency, which amounts to the inclusion of shifted weight functions in the orthogonality condition. In this paper we extend this mechanism to a new class of two-variable orthogonal polynomials where the variables are related via an elliptic curve. This leads to a `Higher order Analogue of the Discrete-time Toda' (HADT) equation for the associated Hankel determinants, together with its Lax pair, which is derived from the relevant recurrence relations for the orthogonal polynomials. In a similar way as the quotient-difference (QD) algorithm is related to the discrete-time Toda equation, a novel quotient-quotient-difference (QQD) scheme is presented for the HADT equation. We show that for both the HADT equation and the QQD scheme, there exists well-posed $s$-periodic initial value problems, for almost all \s\in\Z^2. From the Lax-pairs we furthermore derive invariants for corresponding reductions to dynamical mappings for some explicit examples.Comment: 38 page

Crystal and Electronic Structures of Alluaudite-Type Double Molybdates of Scandium and Indium

Double molybdates of indium and scandium with alluaudite structure are prepared by the solid-phase synthesis method. The crystal structure of the indium containing compound is refined and optical characteristics of Na5R(Mo04)4(R = Sc, In) are determined. Electronic structures of Na5R(Mo04)4(R = Sc, In) molybdates are studied within the ab initio method taking account of Na/Sc(In) positional disordering. Calculations of the imaginary part of dielectric function predict the optical gap of ~3.8 eV, in accordance with absorption spectroscopy data. It is established that formation energy of sodium vacancies strongly depends on sodium position and Sc(In) concentration. As a result, various diffusion mechanisms may be activated in alluaudite-type compounds with high and low contents of metal R. © 2019, Pleiades Publishing, Ltd

An expansion for polynomials orthogonal over an analytic Jordan curve

We consider polynomials that are orthogonal over an analytic Jordan curve L with respect to a positive analytic weight, and show that each such polynomial of sufficiently large degree can be expanded in a series of certain integral transforms that converges uniformly in the whole complex plane. This expansion yields, in particular and simultaneously, Szego's classical strong asymptotic formula and a new integral representation for the polynomials inside L. We further exploit such a representation to derive finer asymptotic results for weights having finitely many singularities (all of algebraic type) on a thin neighborhood of the orthogonality curve. Our results are a generalization of those previously obtained in [7] for the case of L being the unit circle.Comment: 15 pages, 1 figur

A New Dolphin Species, the Burrunan Dolphin Tursiops australis sp. nov., Endemic to Southern Australian Coastal Waters

Small coastal dolphins endemic to south-eastern Australia have variously been assigned to described species Tursiops truncatus, T. aduncus or T. maugeanus; however the specific affinities of these animals is controversial and have recently been questioned. Historically ‘the southern Australian Tursiops’ was identified as unique and was formally named Tursiops maugeanus but was later synonymised with T. truncatus. Morphologically, these coastal dolphins share some characters with both aforementioned recognised Tursiops species, but they also possess unique characters not found in either. Recent mtDNA and microsatellite genetic evidence indicates deep evolutionary divergence between this dolphin and the two currently recognised Tursiops species. However, in accordance with the recommendations of the Workshop on Cetacean Systematics, and the Unified Species Concept the use of molecular evidence alone is inadequate for describing new species. Here we describe the macro-morphological, colouration and cranial characters of these animals, assess the available and new genetic data, and conclude that multiple lines of evidence clearly indicate a new species of dolphin. We demonstrate that the syntype material of T. maugeanus comprises two different species, one of which is the historical ‘southern form of Tursiops’ most similar to T. truncatus, and the other is representative of the new species and requires formal classification. These dolphins are here described as Tursiops australis sp. nov., with the common name of ‘Burrunan Dolphin’ following Australian aboriginal narrative. The recognition of T. australis sp. nov. is particularly significant given the endemism of this new species to a small geographic region of southern and south-eastern Australia, where only two small resident populations in close proximity to a major urban and agricultural centre are known, giving them a high conservation value and making them susceptible to numerous anthropogenic threats