Determining a Magnetic Schrödinger Operator from Partial Cauchy Data

In this paper we show, in dimension n ≥ 3, that knowledge of the Cauchy data for the Schrödinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic field and the electric potential. We follow the general strategy of [7] using a richer set of solutions to the Dirichlet problem that has been used in previous works on this problem.     

Structures of vanadium(III)-ethylenediamine-N,N'-diacetato-N,N'-di-3-propionato complexes. Critical role of pπ-dπ donation in determining the coordination number

Li[V(eddadp)]·3H(2)O (1a) and Cs[V(eddadp)]·2H(2)O (1b) were characterized by X-ray crystallography. 1a crystallizes in the monoclinic space group Cc with a = 11.467(7) ?, b = 13.398(8) ?, c = 12.529(8) ?, β = 114.85(4)°; V = 1746.7(2) ?(3), and Z = 4; 1b crystallizes in the monoclinic space group P2(1)/n with a = 10.265(5) ?, b = 11.673(6) ?, c = 15.507(8) ?, β = 104.29(2)°, V = 1800.6(2) ?(3), and Z = 4. The solution structure of 1 has been ascertained to be predominantly six-coordinated with a hexadentate eddadp which is based on a comparison of the electronic and Raman spectra of aqueous solutions of 1 with those in the solid state.     

The role of oxidative etching in the synthesis of ultrathin single-crystalline Au nanowires

The fabrication of ultrathin single-crystal Au nanowires with high aspect ratio and that are stable in air is challenging. Recently, a simple wet-chemical approach using oleylamine has been reported for the synthesis of Au nanowires with micrometer length and 2 nm in diameter. Despite efforts to understand the mechanism of the reaction, an ultimate question about the role of oxygen (O(2)) during the synthesis remained unclear. Here we report that the synthesis of ultrathin Au nanowires employing oleylamine is strongly affected by the amount of O(2) absorbed in the reaction solution. Saturating the solution with O(2) leads to both a high-yield production of nanowires and an increase in their length. Nanowires with diameters of about 2 nm and lengths of 8 μm, which corresponds to an aspect ratio of approximately 4000, were produced. The role of oxygen is attributed to the enhanced oxidation of twin defects on Au nanoparticles formed in the first stage of the reaction. Understanding the role of oxidative etching is crucial to significantly increasing the yield and the length of ultrathin Au nanowires.     

Vortex quantum creation and winding number scaling in a quenched spinor Bose gas

Motivated by a recent experiment, we study nonequilibrium quantum phenomena taking place in the quench of a spinor Bose-Einstein condensate through the zero-temperature phase transition separating the polar paramagnetic and planar ferromagnetic phases. We derive the typical spin domain structure (correlations of the effective magnetization) created by the quench arising due to spin-mode quantum fluctuations, and we establish a sample-size scaling law for the creation of spin vortices, which are topological defects in the transverse magnetization.     

Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field

Partially supported by NSF Grant DMS-9123742     

Comparison of atmospheric pressure photoionization and electrospray ionization mass spectrometry for the analysis of UV filters

A comparison was made between the electrospray ionization (ESI) and atmospheric pressure photoionization (APPI) tandem mass spectrometric (MS/MS) responses of eleven ultraviolet (UV) filters. Four of the target compounds were favourably ionized in negative ion mode, and the other seven compounds in positive ion mode. For nine of the compounds APPI generated a similar response to that of ESI, but the APPI signal‐to‐noise (S/N) ratios were 1.3–60 times higher. The two most polar of the UV filter compounds (PBSA and BP‐4) were more efficiently ionized by ESI, offering higher signal intensities and lower detection limits. APPI was, however, less susceptible to ion suppression than ESI when real samples were injected. In order to optimize the APPI conditions different dopant solvents were examined to enhance the efficiency of the photoionization process. Among the evaluated dopants, toluene was selected as the best compromise. At a toluene flow rate of 10% of the solvent flow rates the ionization response increased by a factor of 40–50 over the use of no dopant for the compounds in positive ion mode and by more than 300 for the compounds in negative ion mode. Copyright © 2009 John Wiley & Sons, Ltd.     

Structure of glassy polymers. V. Small-angle x-ray scattering from polystyrene

Small-angle x-ray scattering (SAXS) from glassy atactic polystyrene has been measured using a Bonse–Hart system. After correcting for absorption, background, and beam divergence, the scattering has been placed on an absolute basis using a standard silica suspension as a reference.The desmeared absolute intensity decreases strongly with increasing scattering angle over the range between 20 sec and 20 min. At larger angles, the intensity decreases much more slowly with increasing angle and approaches the value expected for density fluctuations frozen-in at the glass transition. The angular variation of intensity is well described by the scattering from heterogeneities of various sizes and concentrations superimposed on the scattering from thermal density fluctuations. These heterogeneities range in radius from 10 to 4000 Å. The present SAXS results on glassy polystyrene seem inconsistent with the presence of nodular features as representative of the bulk polymer.     

Remarks on the relation between quantum and classical entropy as proposed by A. Wehrl

Using an inequality of Lieb one can compute a probability distribution which is less mixed than any (z|ωz)dz, where z labels the points of phase space, w is a density matrix, and (z| the appropriate coherent state.