A non-Hermitian circular billiard

A perturbative form of a circular billiard with an off-centre flux line yields a non-Hermitian Hamiltonian with real spectrum. The spacing among neighbouring levels deviates from Poisson distribution (expected for integrable systems). The eigenfunctions exhibit directional property due to broken parity and time-reversal symmetries.     

Sur quelques récents résultats dans la théorie des surfaces algébriques

Sans résumé     

Synthèse de l'oxo-7 7H cyclohepta[b] pyridine et de quelques dérivés

This communication describes the synthesis of 7-one (7H) cyclohepta[b]pyridine and some derivatives (6,8-dimethyl; 8-methyl; 8-ethyl….). These compounds have been obtained by condensation of ketones with 2,3-diformylpyridine.     

First principles study of lead free piezoelectric AgNbO3 and (Ag1−xKx)NbO3 solid solutions

We present an ab-initio study of structural, electronic and ferroic properties of lead-free orthorhombic AgNbO₃ in centrosymmetric Pbcm and recently proposed noncentrosymmetric Pmc2₁ space group symmetries. The calculated polarization of AgNbO₃ in Pmc2₁ phase is ～0.09 μC/cm², whereas it is 55.9 μC/cm² in the ideal cubic phase. The large polarization of AgNbO₃ in the ideal cubic structure is attributed to off-centering of Ag as well as Nb ions at the A and B sites, respectively. In our calculations both phases (Pmc2₁ and Pbcm) of AgNbO₃ show small relative energy difference (～0.1 meV/f.u), thus suggesting the coexistence of centrosymmetric and non-centrosymmetric phases and thereby antiferroelectric and ferroelctric order in room temperature AgNbO₃ polycrystals. We further study structural properties and spontaneous polarization in orthorhombic Pmc2₁ Ag_1?xK_xNbO₃ solid solutions. The calculated spontaneous polarization of AgNbO₃ is enhanced due to suppression of NbO₆ octahedral tilt angles as K ion is substituted at Ag sites. Our study suggests that appropriate cation substitution should indeed result in the improvement of ferroelectric properties of lead-free AgNbO₃.     

The effect of topical anesthesia on vocal fold motion

The objective of this study was to determine if topical anesthesia to the larynx and pharynx affects vocal fold motion during dynamic voice evaluation with transnasal flexible endoscopy. Transnasal dynamic laryngeal examinations of 10 patients with no voice complaints were evaluated by five blinded fellowship-trained laryngologists. Each patient was examined before and after application of topical anesthetic. Reviewers rated briskness of right and left vocal fold movement and longitudinal tension on a visual analogue scale. Statistical comparisons were made between individual subject scores before and after anesthetic application. Inter-rater reliability was also assessed. No statistical difference was observed between subject scores before and after anesthetic application. Average intraclass correlation coefficients were 0.643 and 0.591 for pre- and postanesthesia scores, respectively. Application of topical anesthesia to the larynx and pharynx does not affect vocal fold motion.     

Quadratic Upper Bounds on the Erdős–Pósa Property for a Generalization of Packing and Covering Cycles

According to the classical Erd?s–Pósa theorem, given a positive integer k, every graph G either contains k vertex disjoint cycles or a set of at most vertices that hits all its cycles. Robertson and Seymour (J Comb Theory Ser B 41 (1986), 92–114) generalized this result in the best possible way. More specifically, they showed that if is the class of all graphs that can be contracted to a fixed planar graph H, then every graph G either contains a set of k vertex‐disjoint subgraphs of G, such that each of these subgraphs is isomorphic to some graph in or there exists a set S of at most vertices such that contains no subgraph isomorphic to any graph in . However, the function f is exponential. In this note, we prove that this function becomes quadratic when consists all graphs that can be contracted to a fixed planar graph . For a fixed c, is the graph with two vertices and parallel edges. Observe that for this corresponds to the classical Erd?s–Pósa theorem.     

Efficient Hyperpolarization of U‐13C‐Glucose Using Narrow‐Line UV‐Generated Labile Free Radicals

Free radicals generated by UV‐light irradiation of a frozen solution containing a fraction of pyruvic acid (PA) have demonstrated their dissolution dynamic nuclear polarization (dDNP) potential, providing up to 30 % [1‐¹³C]PA liquid‐state polarization. Moreover, their labile nature has proven to pave a way to nuclear polarization storage and transport. Herein, differently from the case of PA, the issue of providing dDNP UV‐radical precursors (trimethylpyruvic acid and its methyl‐deuterated form) not involved in any metabolic pathway was investigated. The ¹³C dDNP performance was evaluated for hyperpolarization of [U‐¹³C₆,1,2,3,4,5,6,6‐d₇]‐d ‐glucose. The generated UV‐radicals proved to be versatile and highly efficient polarizing agents, providing, after dissolution and transfer (10 s), a ¹³C liquid‐state polarization of up to 32 %.     

Static charged spheres with anisotropic pressure in general relativity

We report a generalization of our earlier formalism [Pramana, 54, 663 (1998)] to obtain exact solutions of Einstein-Maxwell’s equations for static spheres filled with a charged fluid having anisotropic pressure and of null conductivity. Defining new variables: w=(4π/3)(ρ+ε)r ², u=4πξr ², v _r=4πp _r r ², v _⊥=4πp _⊥ r ²[ρ, ξ(=−(1/2)F ₁₄ F ¹⁴), p _r, p _⊥ being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas ε denotes the eigenvalue of the conformal Weyl tensor and interpreted as the energy density of the free gravitational field], we have recast Einstein’s field equations into a form easy to integrate. Since the system is underdetermined we make the following assumptions to solve the field equations (i) u=v _r=(a ²/2κ)r ⁿ⁺², v _⊥=k ₁ v _r, w=k ₂ v _r; a ², n(>0), k ₁, k ₂ being constants with κ=((k ₁+2)/3+k ₂) and (ii) w+u=(b ²/2)r ⁿ⁺², u=v _r, v _⊥−v _r=k, with b and k as constants. In both cases the field equations are integrated completely. The first solution is regular in the metric as well as physical variables for all values of n>0. Even though the second solution contains terms like k/r ² since Q(0)=0 it is argued that the pressure anisotropy, caused by the electric flux near the centre, can be made to vanish reducing it to the generalized Cooperstock-de la Cruz solution given in [14]. The interior solutions are shown to match with the exterior Reissner-Nordstrom solution over a fixed boundary. Dedicated to Prof. F A E Pirani.     

A short range many-body potential for modelling bcc metals

The problem considered is the fitting of a many-body interaction potential to bulk crystal data. A parameterisation of the potential is assumed which is based on physical considerations. The free parameters are determined by using global optimization to perform a least squares fit, to a large number of crystal properties. This has been achieved for body centered cubic (bcc) materials. The approach adopted here fits the bcc crystal structure, as the preferred minimum energy configuration for tungsten, and also fits the dimer energetics and the elastic properties of crystalline tungsten.     

Ion plated indium oxide : infrared and optical study

The high optical transparency of ion plated indium oxide combined with their mechanical hardness and good environmental stability have opened up numerous applications in the line of sophisticated optoelectronic devices. Indium is evaporated at a low oxygen pressure on to an ordinary glass substrate mounted under the cathode and biased by a r.f. generator at 13,6 M Hz. Infrared spectra are recorded in the range 5000–200 cm^?1 by A.T.R. and reflexion-absorption spectroscopy, and show between 800 and 200 cm^?1 bands due to stretching and bending modes predicted by a factor group analysis. A tentative assignment is made of the highest frequency. Last U.V. and visible spectra are discussed.