Multiple-magnetic field 139La NMR and density functional theory investigation of the solid lanthanum(III) halides

Results from a solid-state ¹³⁹La NMR spectroscopic investigation of the anhydrous lanthanum(III) halides (LaX₃; X=F, Cl, Br, I) at applied magnetic fields of 7.0, 9.4, 11.7, 14.1, and 17.6 T are presented and highlight the advantages of working at high applied magnetic field strengths. The ¹³⁹La quadrupolar coupling constants are found to range from 15.55 to 24.0 MHz for LaCl₃ and LaI₃, respectively. The lanthanum isotropic chemical shifts exhibit an inverse halogen dependence with values ranging from −135 ppm for LaF₃ to 700 ppm for LaI₃, which represents nearly half of the total lanthanum chemical shift range. The spans of the magnetic shielding tensors also vary widely, from 35 to 650 ppm for the solid LaF₃ through LaI₃. DFT calculations of the ¹³⁹La electric field gradient and magnetic shielding tensors have been performed and provide a qualitative interpretation of the trends observed experimentally.     

Spectral Properties of Uperpositions of Ornstein-Uhlenbeck Type Processes

Stationary processes with prescribed one-dimensional marginal laws and long-range dependence are constructed. The asymptotic properties of the spectral densities are studied. The possibility of Mittag-Leffler decay in the autocorrelation function of superpositions of Ornstein-Uhlenbeck type processes is proved. AMS 2000 Subject Classification Primary 60E07, 60G10, 60G18 Secondary 62M10, 62P05 Supported by the Danish National Research Foundation and EPSRC grant RCMT091. Partially supported by the ARC grants DP 0345577, DP0559807 and EPSRC grant RCMT091.     

Partially dynamic maintenance of minimum weight hyperpaths

We address the problem of dynamically maintaining minimum weight hyperpaths in a directed hypergraph in a decremental setting. For such a problem, we provide a new efficient algorithm that works for a wide class of hyperpath weight measures. This algorithm explicitly updates minimum weight hyperpaths in

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worst case time under a sequence of L hyperarc weight increments and hyperarc deletions, where C is the maximum weight of minimum hyperpaths in and is the size of the representation of the hypergraph. Hyperpath weight measures are only required to belong to the class of strict weakly superior functions.     

Rotational spectrum of cyclohexyl sarin

The rotational spectrum of cyclohexyl sarin (also known as GF) has been measured in a jet-cooled expansion using Fourier transform microwave spectroscopy. Two spectra have been observed, each having splittings associated with the internal rotation of the CH₃P group. The observed V₃ barriers are similar in magnitude to those reported for other organophosphonate nerve agents. The two conformational structures of GF have been identified from comparisons of the observed rotational constants and dipole moment magnitudes with ab initio predictions at the MP2/6311G (d,p) level. These two structures are distinguished by the placement of the fluorophosphonate group at the equatorial and axial positions of the cyclohexane ring. The data also suggest that both conformers prefer a positioning of the FP group with the PO oxygen in an eclipsed orientation relative to the C₁ hydrogen on the ring.     

Perturbation approach to elastic constitutive relations of polycrystals

Herein we obtain a formula for the effective elastic stiffness tensor C^eff of an orthorhombic aggregate of cubic crystallites by the perturbation method. The effective elastic stiffness tensor of the polycrystal gives the relationship between volume average stress and volume average strain. Under Voigt's model, Reuss’ model and Man's theory, the elastic constitutive relation accounts for the effect of the orientation distribution function (ODF) up to terms linear in the texture coefficients. However, the formula derived in this paper delineates the effect of crystallographic texture on elastic response and shows quadratic texture dependence. The formula is very simple. We also consider the influence of grain shape to elastic constitutive relations of polycrystals. Some examples are given to compare computational results of the formula with those given by Voigt's model, Reuss's model, the finite element method, and the self-consistent method. In Section 3, we also present an expression of the perturbation displacement field, in which Green's function for an orthorhombic aggregate of cubic crystallites is included.     

Molecular dynamics simulation of peeling a DNA molecule on substrate

Molecular dynamics (MD) simulations are performed to study adhesion and peeling of a short fragment of single strand DNA (ssDNA) molecule from a graphite surface. The critical peel-off force is found to depend on both the peeling angle and the elasticity of ssDNA. For the short ssDNA strand under investigation, we show that the simulation results can be explained by a continuum model of an adhesive elastic band on substrate. The analysis suggests that it is often the peak value, rather than the mean value, of adhesion energy which determines the peeling of a nanoscale material.The project supported by the Distinguished Young Scholar Fund of NSFC (10225209) and key project from the Chinese Academy of Sciences (KJCX2-SW-L2)     

Extremum problems for entire functions of exponential spherical type

We consider extremum problems for entire functions of exponential spherical type related to important extremum problems on the optimal point (the Chernykh point) in the sharp jackson inequality in the spaceL ₂(ℝ ⁿ ) and the connection between codes and designs on the torusT ⁿ . Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 179–187, August, 2000.     

Molecular dynamics in solid pregnenolone studied by H spin–lattice relaxation

Spin–lattice relaxation times T₁ in solid pregnenolone have been studied over a wide range of temperatures, from 77 up to 417 K. The dynamic processes arising from C₃ motion of the three methyl substituents are separated, and their activation parameters are determined.     

Enhancement of nonlinear optical response of exciton–polaritons by controlling thickness of GaAs layer

We demonstrate a remarkable thickness dependence of nonlinear optical response of exciton–polaritons in GaAs thin films by degenerate four-wave mixing (DFWM) at low temperature (T=5 K). High-quality samples of layer thickness from 80 to 200 nm were grown by molecular beam epitaxy. Confined mode of the exciton–polariton dominantly contributed to the reflection spectra, which were examined by the calculation using a transfer matrix method. The DFWM intensity at exciton resonance was enhanced at a particular thickness (110 nm). This thickness dependence is in good agreement with the nonlocal theory, which shows a remarkable size dependence of the internal field relevant to the confined mode of the exciton–polaritons.