Unboundedness of adjacency matrices of locally finite graphs

Given a locally finite simple graph so that its degree is not bounded, every self-adjoint realization of the adjacency matrix is unbounded from above. In this note we give an optimal condition to ensure it is also unbounded from below. We also consider the case of weighted graphs. We discuss the question of self-adjoint extensions and prove an optimal criterium.Comment: Typos corrected. Examples added. Cute drawings. Simplification of the main condition. Case of the weight tending to zero more discussed

Hidden symmetry of the quantum Calogero-Moser system

Hidden symmetry of the quantum Calogero-Moser system with the inverse-square potential is explicitly demonstrated in algebraic sense. We find the underlying algebra explaining the super-integrability phenomenon for this system. Applications to related multi-variable Bessel functions are also discussed.Comment: 16 pages, latex, no figure

Additional Constants of Motion for a Discretization of the Calogero--Moser Model

The maximal super-integrability of a discretization of the Calogero--Moser model introduced by Nijhoff and Pang is presented. An explicit formula for the additional constants of motion is given.Comment: 7 pages, no figure

Exactly Solvable Pairing Model Using an Extension of Richardson-Gaudin Approach

We introduce a new class of exactly solvable boson pairing models using the technique of Richardson and Gaudin. Analytical expressions for all energy eigenvalues and first few energy eigenstates are given. In addition, another solution to Gaudin's equation is also mentioned. A relation with the Calogero-Sutherland model is suggested.Comment: 9 pages of Latex. In the proceedings of Blueprints for the Nucleus: From First Principles to Collective Motion: A Festschrift in Honor of Professor Bruce Barrett, Istanbul, Turkey, 17-23 May 200

Nitrogen-Vacancy Ensemble Magnetometry Based on Pump Absorption

We demonstrate magnetic field sensing using an ensemble of nitrogen-vacancy centers by recording the variation in the pump-light absorption due to the spin-polarization dependence of the total ground state population. Using a 532 nm pump laser, we measure the absorption of native nitrogen-vacancy centers in a chemical vapor deposited diamond placed in a resonant optical cavity. For a laser pump power of 0.4 W and a cavity finesse of 45, we obtain a noise floor of $\sim$ 100 nT/$\sqrt{\textrm{Hz}}$ spanning a bandwidth up to 125 Hz. We project a photon shot-noise-limited sensitivity of $\sim$ 1 pT/$\sqrt{\textrm{Hz}}$ by optimizing the nitrogen-vacancy concentration and the detection method.Comment: 7 pages and 5 figure

Sense of taste in patients after cochlear implantation-preliminary study

Background: Taste is the leading sense in how we determine the quality of consumed food. Proper gustatory sensation largely determines the well-being and health of an organism, and this affects their quality of life.Objectives: The aim of the present study was to estimate the risk of early taste disorders following implantation surgery. Methods: Twenty patients underwent a taste test before, 1 day after, and 1 month after cochlear implantation. The taste sensations of sweet, sour, salty, and bitter were determined. Results: Statistical analysis showed no significant differences (p > 0.05) between individual tests among the entire study group. After dividing the respondents into smoking (n=6) and non-smoking (n=14) groups, only a weak correlation (p =0.043) was found between the results of the first and second examination in the smoker group. However, a statistically significant decrease in the number of saline-sensitive (p<0.001) and acid-sensitive (p = 0.042) subjects was observed. Conclusion: These findings suggest that people after a cochlear implant may have transient taste disorders. Taste disorder called dysgeusia may be an early complication after the implantation procedure contributing to deterioration of patients quality of life. Keywords: Sense of taste; taste disorders; cochlear implant surgery; quality of life, partial deafness treatment

Dyson's Brownian Motion and Universal Dynamics of Quantum Systems

We establish a correspondence between the evolution of the distribution of eigenvalues of a $N\times N$ matrix subject to a random Gaussian perturbing matrix, and a Fokker-Planck equation postulated by Dyson. Within this model, we prove the equivalence conjectured by Altshuler et al between the space-time correlations of the Sutherland-Calogero-Moser system in the thermodynamic limit and a set of two-variable correlations for disordered quantum systems calculated by them. Multiple variable correlation functions are, however, shown to be inequivalent for the two cases.Comment: 10 pages, revte

From bi-Hamiltonian geometry to separation of variables: stationary Harry-Dym and the KdV dressing chain

Separability theory of one-Casimir Poisson pencils, written down in arbitrary coordinates, is presented. Separation of variables for stationary Harry-Dym and the KdV dressing chain illustrates the theory.Comment: LaTex 14 pages, Proceedings of the Special Session on Integrable Systems of the First Joint Meeting of the American Mathematical Society and the Hong Kong Mathematical Society, to appear in J. Nonl. Math. Phy

Microcrystalline Bi2ZnB2O7-polymer composites with silver nanoparticles as materials for laser operated devices

A novel type of composite for optoelectronic which is operated by second harmonic generation in the Bi2ZnB2O7 crystallites (with sizes varying within 1–30 μm) and Ag nanoparticles (NP) embedded in PMMA polymer composites is proposed. The substantial influence of the Ag NP on the bicolor induced second harmonic generation was established. The phototreatment was performed by bicolor beams of nanosecond Nd:YAG laser (1,064/532 nm) at angles between the fundamental and photoinducing beams varying within the 19°–21° range. The studies of the corresponding dependences of the SHG during illumination by the two coherent beams at 1,064/532 nm showed a maximal enhancement of the output SHG for the Ag NP average sizes equal to about 40 nm. The role of the excited plasmons may be here crucial. Additionally the time shift between the fundamental and the doubled frequency beam maxima was found, which shows strong sensitivity to illumination. The established time shift is sensitive to the pumping power

Elliptic operators in even subspaces

In the paper we consider the theory of elliptic operators acting in subspaces defined by pseudodifferential projections. This theory on closed manifolds is connected with the theory of boundary value problems for operators violating Atiyah-Bott condition. We prove an index formula for elliptic operators in subspaces defined by even projections on odd-dimensional manifolds and for boundary value problems, generalizing the classical result of Atiyah-Bott. Besides a topological contribution of Atiyah-Singer type, the index formulas contain an invariant of subspaces defined by even projections. This homotopy invariant can be expressed in terms of the eta-invariant. The results also shed new light on P.Gilkey's work on eta-invariants of even-order operators.Comment: 39 pages, 2 figure