Facile formation of molybdenum(VI) monooxo aryloxides MoO(OAr)4-nCln from molybdenum dioxo dichloride

Molybdenum monooxo compoundsMoO(OAr)4-nCln (n=0-2, Ar=2,6-Me2C6H3 or 2,6-i-Pr2C6H3) have been synthesized starting from the dioxo precursor MoO2Cl2. The complexes are characterized spectroscopically and by X-ray diffraction. The formation mechanism likely involves phenol precoordination followed by addition across the Mo=O bond.     

Inside or outside a ligand cleft? Synthetic, structural, and kinetic inertness studies of zinc, cadmium, and mercury complexes of cross-bridged cyclam and cyclen

Ethylene cross-bridging of the popular tetraazamacrocyclic ligand cyclam has led to metal complexes with enhanced kinetic inertness. The synthesis and spectral characterization of zinc(II), cadmium(II), and mercury(II) complexes of cross-bridged cyclam (L1) as well as cross-bridged cyclen (L2) are reported along with the details of our synthetic route to L2. X-ray structural studies revealed that all Zn(II) and Cd(II) cations are fully kappa(4)N-coordinated inside the respective ligand's molecular cleft with L1 providing the better fit for Zn(II). While Hg(II) is similarly coordinated to L2, it has been found to complex L1 outside the ligand cleft in a novel exo-kappa(2)N-mode. Solution NMR data of the kappa(4)N complexes are consistent with the presence of only a single cis-folded isomer in each case. Ligand (1)H and (13)C coupling to both (111,113)Cd and (199)Hg in their complexes can be clearly discerned. The relative kinetic inertness of representative cross-bridged complexes in acidic aqueous solution has been assessed and found to be in the following order: Zn(II) > Cd(II)[dbl greater-than] Hg(II). The data also reaffirm that cross-bridged cyclam ligand L1 forms a substantially more inert complex with zinc(II) than either the smaller cyclen analogue L2 or the unbridged 1,4,8,11-tetramethyl-cyclam L3.     

"Eclipse" effect in the scattering of weakly bound helium clusters

The total cross sections of the helium dimer, trimer, and tetramer for scattering from Kr atoms have been measured for cluster beam velocities between 250 and 820 m/s. The dimer cross section is twice that of the atom within 5% indicating that the Kr atoms scatter from the He atoms independently, which is consistent with the large dimer bond distance of about 50 A. The trimer and tetramer cross sections are somewhat larger and can be described by an impulse approximation with a multiple "eclipse" correction, extending ideas of Glauber for high energy collisions with the deuteron.     

Wave interaction in acoustic resonators with and without hysteresis

Nonlinear interaction of counterpropagating waves in solids is considered by using a general approach taking into account only the cumulative (resonant) nonlinear perturbations giving a nonzero contribution over the period and, consecutively, potentially able to significantly modify the linear solution. Different stress-strain relations are addressed, including those with hysteresis which serve as basic models for the recent acoustic experiments with rock and metals. An important case of the interaction of counterpropagating waves with close amplitudes in a high-Q resonator (bar) with hysteresis is specially addressed and compared with the case of a ring resonator.     

Evidence for a bound HeH2 halo molecule by diffraction from a transmission grating

The HeH2 van der Waals complex has been identified in a molecular beam produced by a cryogenic (T0=24.7 K) free jet expansion of a 1% H2 mixture in 99% 4He gas. The weakly bound HeH2 complexes in the beam are identified via their first order diffraction angles after passing through a 100 nm period transmission grating. An electron impact mass spectrometer analysis of the diffraction patterns is used to discriminate against ion fragments of the constituent gas clusters.     

Pulsed ultrasound-modulated light tomography

Ultrasound-modulated light tomography is a new technique that combines laser light and ultrasound to provide a representation of the light density inside turbid media. We present a method that can produce two- or three-dimensional light density representations with standard ultrasonic pulses. This technique should allow simple, direct fusion of ultrasonic images with optical tomography.     

Lagrangian velocity statistics in turbulent flows: effects of dissipation

We use the multifractal formalism to describe the effects of dissipation on Lagrangian velocity statistics in turbulent flows. We analyze high Reynolds number experiments and direct numerical simulation data. We show that this approach reproduces the shape evolution of velocity increment probability density functions from Gaussian to stretched exponentials as the time lag decreases from integral to dissipative time scales. A quantitative understanding of the departure from scaling exhibited by the magnitude cumulants, early in the inertial range, is obtained with a free parameter function D(h) which plays the role of the singularity spectrum in the asymptotic limit of infinite Reynolds number. We observe that numerical and experimental data are accurately described by a unique quadratic D(h) spectrum which is found to extend from h(min) approximately 0.18 to h(max) approximately 1.     

Crystal structure in nematic emulsion

We describe the experimental observation of a crystal structure formed by glycerol droplets suspended in a nematic liquid crystal. The structure exhibits a high density hexagonal ordering. We have experimentally observed a noticeable interaction between droplets with tangential boundary conditions. Within the scope of known models we discuss the nature of appropriate mechanisms of the interaction.     

A Bohr Phenomenon For Elliptic Equations

In 1914 Bohr proved that there is an r (0,1) such that if apower series converges in the unit disk and its sum has modulusless than 1 then, for |z| < r, the sum of absolute valuesof its terms is again less than 1. Recently, analogous resultshave been obtained for functions of several variables. The aimof this paper is to place the theorem of Bohr in the contextof solutions to second-order elliptic equations satisfying themaximum principle. 2000 Mathematics Subject Classification: 35J15, 32A05, 46A35.     

Multidimensional analogues of Bohr's theorem on power series

Generalizing the classical result of Bohr, we show that if an -variable power series converges in -circular bounded complete domain and its sum has modulus less than 1, then the sum of the maximum of the modulii of the terms is less than 1 in the homothetic domain , where . This constant is near to the best one for the domain