Superelectrophilic activation of polyfunctional organic compounds using zeolites and other solid acids

Zeolites and other available solid acids have been successfully applied to initiate reactions, which were earlier recognised to involve superelectrophilic intermediates and thus required excess of superacids to be carried out.     

Water and tris(5-acetyl-3-thienyl)methane (TATM) assemble into a one-dimensional channel compound

Tris(5-acetyl-3-thienyl)methane (TATM), a well known hydrophobic host compound, assembles with water molecules into a material with one-dimensional channels that also contain water.     

On a subspace perturbation problem

We discuss the problem of perturbation of spectral subspaces for linear self-adjoint operators on a separable Hilbert space. Let and be bounded self-adjoint operators. Assume that the spectrum of consists of two disjoint parts and such that 0$">. We show that the norm of the difference of the spectral projections

for and is less than one whenever either (i) or (ii) and certain assumptions on the mutual disposition of the sets and are satisfied.

     

(Modified) Fredholm Determinants for Operators with Matrix-Valued Semi-Separable Integral Kernels Revisited

We revisit the computation of (2-modified) Fredholm determinants for operators with matrix-valued semi-separable integral kernels. The latter occur, for instance, in the form of Greens functions associated with closed ordinary differential operators on arbitrary intervals on the real line. Our approach determines the (2-modified) Fredholm determinants in terms of solutions of closely associated Volterra integral equations, and as a result offers a natural way to compute such determinants.We illustrate our approach by identifying classical objects such as the Jost function for half-line Schrödinger operators and the inverse transmission coe.cient for Schrödinger operators on the real line as Fredholm determinants, and rederiving the well-known expressions for them in due course. We also apply our formalism to Floquet theory of Schrödinger operators, and upon identifying the connection between the Floquet discriminant and underlying Fredholm determinants, we derive new representations of the Floquet discriminant.Finally, we rederive the explicit formula for the 2-modified Fredholm determinant corresponding to a convolution integral operator, whose kernel is associated with a symbol given by a rational function, in a straghtforward manner. This determinant formula represents a Wiener-Hopf analog of Days formula for the determinant associated with finite Toeplitz matrices generated by the Laurent expansion of a rational function.     

Fluctuations of the phase difference across an array of Josephson junctions in superfluid 4He near the lambda Transition

We present a formal thermodynamic treatment of superfluid flow in a Josephson junction. We show that the current i(s) and the phase difference phi are thermodynamic conjugate variables. We derive quantitative expressions for the rms fluctuations of i(s) and phi. Also, we discuss the thermodynamic stability and the thermal activation to the phase-slip region. We apply the developed formalism to show why an array of apertures in 4He can exhibit the Josephson effect near the lambda transition despite strong thermal fluctuations.     

Photoinduced emission of cooper pairs from superconductors

Under certain conditions specified in this work, a Cooper pair can be emitted from a superconductor upon the absorption of one ultraviolet photon. The spectra of the excited electron pair carry direct information on the energy and angular pair correlation. These statements are concluded from a formal and numerical analysis based on the Bardeen-Cooper-Schrieffer theory for superconductivity.     

The structure and oscillational motion of Fe atoms in interstitial sites in Al as determined from interference of Mössbauer γ radiation

The first excited site of the ⁵⁷Fe atom entrapped in an interstitial site in aluminum, as reported by [1.]. from a Mössbauer spectroscopic study of a single crystal, is analyzed by consideration of the value of the Hooke's law constant of the Fe---Al bonds obtained from the values for elemental Fe and Al. The eight wavefunctions for the eightfold nearly degenerate excited state are described as 2s1p1d1f hybrids of three-dimensional harmonic oscillator wavefunctions relative to the center of the undistorted Al₆ octahedron or as localized 1s functions relative to the center of the distorted octahedron. These considerations provide a qualitative understanding of the observations on this system.     

Structure and dynamics of hydrogen molecules in the novel clathrate hydrate by high pressure neutron diffraction

The D2 clathrate hydrate crystal structure was determined as a function of temperature and pressure by neutron diffraction for the first time. The hydrogen occupancy in the (32+X)H2.136H(2)O, x=0-16 clathrate can be reversibly varied by changing the large (hexakaidecahedral) cage occupancy between two and four molecules, while remaining single occupancy of the small (dodecahedral) cage. Above 130-160 K, the guest D2 molecules were found in the delocalized state, rotating around the centers of the cages. Decrease of temperature results in rotation freezing followed by a complete localization below 50 K.