Probabilistic Weyl laws for quantized tori

For the Toeplitz quantization of complex-valued functions on a $2n$-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law. In numerical experiments the same Weyl law also holds for ``false'' eigenvalues created by pseudospectral effects.Comment: 33 pages, 3 figures, v2 corrected listed titl

Ethyl 1-(4-chloro­phen­yl)-3-[1-(4-meth­oxy­phen­yl)-4-oxo-3-phenyl­azetidin-2-yl]-2-nitro-2,3,10,10a-tetra­hydro-1H,5H-pyr­rolo[1,2-b]isoquinoline-10a-carboxyl­ate

In the title compound, C37H34ClN3O6, the pyrrolidine and piperidine rings adopt envelope and boat conformations, respectively. The β-lactam ring is planar and forms dihedral angles of 21.3 (2) and 73.9 (2)°, respectively, with the attached methoxy­phenyl and phenyl rings. Intra­molecular C—H⋯O and C—H⋯N hydrogen bonds are observed. Centrosym­metrically related mol­ecules are linked together by weak C—H⋯O hydrogen bonds to form dimers

Toeplitz operators on symplectic manifolds

We study the Berezin-Toeplitz quantization on symplectic manifolds making use of the full off-diagonal asymptotic expansion of the Bergman kernel. We give also a characterization of Toeplitz operators in terms of their asymptotic expansion. The semi-classical limit properties of the Berezin-Toeplitz quantization for non-compact manifolds and orbifolds are also established.Comment: 40 page

Large N limit of SO(N) gauge theory of fermions and bosons

In this paper we study the large N_c limit of SO(N_c) gauge theory coupled to a Majorana field and a real scalar field in 1+1 dimensions extending ideas of Rajeev. We show that the phase space of the resulting classical theory of bilinears, which are the mesonic operators of this theory, is OSp_1(H|H )/U(H_+|H_+), where H|H refers to the underlying complex graded space of combined one-particle states of fermions and bosons and H_+|H_+ corresponds to the positive frequency subspace. In the begining to simplify our presentation we discuss in detail the case with Majorana fermions only (the purely bosonic case is treated in our earlier work). In the Majorana fermion case the phase space is given by O_1(H)/U(H_+), where H refers to the complex one-particle states and H_+ to its positive frequency subspace. The meson spectrum in the linear approximation again obeys a variant of the 't Hooft equation. The linear approximation to the boson/fermion coupled case brings an additonal bound state equation for mesons, which consists of one fermion and one boson, again of the same form as the well-known 't Hooft equation.Comment: 27 pages, no figure

Global syndromes induced by changes in solutes of the world’s large rivers

AbstractSolute-induced river syndromes have grown in intensity in recent years. Here we investigate seven such river syndromes (salinization, mineralization, desalinization, acidification, alkalization, hardening, and softening) associated with global trends in major solutes (Ca2+, Mg2+, Na+, K+, SO42−, Cl−, HCO3−) and dissolved silica in the world’s large rivers (basin areas ≥ 1000 km2). A comprehensive dataset from 600 gauge stations in 149 large rivers reveals nine binary patterns of co-varying trends in runoff and solute concentration. Solute-induced river syndromes are associated with remarkable increases in total dissolved solids (68%), chloride (81%), sodium (86%) and sulfate (142%) fluxes from rivers to oceans worldwide. The syndromes are most prevalent in temperate regions (30~50°N and 30~40°S based on the available data) where severe rock weathering and active human interferences such as urbanization and agricultural irrigation are concentrated. This study highlights the urgency to protect river health from extreme changes in solute contents.</jats:p

Experimental Study of Dispersion and Modulational Instability of Surface Gravity Waves on Constant Vorticity Currents

This paper examines experimentally the dispersion and stability of weakly nonlinear waves on opposing linearly vertically sheared current profiles (with constant vorticity). Measurements are compared against predictions from the unidirectional (1D + 1) constant vorticity nonlinear Schrödinger equation (the vor-NLSE) derived by Thomas et al. (Phys. Fluids, vol. 24, no. 12, 2012, 127102). The shear rate is negative in opposing currents when the magnitude of the current in the laboratory reference frame is negative (i.e. opposing the direction of wave propagation) and reduces with depth, as is most commonly encountered in nature. Compared to a uniform current with the same surface velocity, negative shear has the effect of increasing wavelength and enhancing stability. In experiments with a regular low-steepness wave, the dispersion relationship between wavelength and frequency is examined on five opposing current profiles with shear rates from 0 to −0.87 s−1. For all current profiles, the linear constant vorticity dispersion relation predicts the wavenumber to within the 95 % confidence bounds associated with estimates of shear rate and surface current velocity. The effect of shear on modulational instability was determined by the spectral evolution of a carrier wave seeded with spectral sidebands on opposing current profiles with shear rates between 0 and −0.48 s−1. Numerical solutions of the vor-NLSE are consistently found to predict sideband growth to within two standard deviations across repeated experiments, performing considerably better than its uniform-current NLSE counterpart. Similarly, the amplification of experimental wave envelopes is predicted well by numerical solutions of the vor-NLSE, and significantly over-predicted by the uniform-current NLSE

A local families index formula for d-bar operators on punctured Riemann surfaces

Using heat kernel methods developed by Vaillant, a local index formula is obtained for families of d-bar operators on the Teichmuller universal curve of Riemann surfaces of genus g with n punctures. The formula also holds on the moduli space M{g,n} in the sense of orbifolds where it can be written in terms of Mumford-Morita-Miller classes. The degree two part of the formula gives the curvature of the corresponding determinant line bundle equipped with the Quillen connection, a result originally obtained by Takhtajan and Zograf.Comment: 47 page