The Caratheodory-Fejer extension theorem

A construction of Carathéodory and Fejér [1] produces a function which is bounded and analytic in the unit disk with specified initial coefficients. An operator generalization of the construction is now obtained for application to the invariant subspace problem. A formal proof [2] of the existence of invariant subspaces is given by the theory of square summable power series [3] in its vector formulation [4]. But the justification of the formal argument requires a determination of extreme points of a convex set [5]. A solution is now given to an extension problem for convex decompositions which arises in connection with the Carathéodory-Fejér theorem. A necessary condition for an extreme point is obtained as an application. The condition is conjectured to be sufficient.     

An inequality for the multivariate normal distribution

Herman Chernoff used Hermite polynomials to prove an inequality for the normal distribution. This inequality is useful in solving a variation of the classical isoperimetric problem which, in turn, is relevant to data compression in the theory of element identification. As the inequality is of interest in itself, we prove a multivariate generalization of it using a different argument.     

Vibrational energy relaxation of high density HCl fluid in the 150–345 K range

The vibrational lifetime of liquid hydrogen chloride alone the liquid—vapor coexistence curve and of high density hydrogen chloride above the critica anti-Stokes Raman scattering technique. The results obtained above the critical temperature show a gas-liKe behaviour with a larger relaxation rate con is consistent with a contribution of van der Waals dimers to vibrational relaxation. The results obtained along the liquid—vapor coexistence curve ar model.     

Near-edge X-ray absorption fine structure spectroscopy of diamondoid thiol monolayers on gold

Diamondoids, hydrocarbon molecules with cubic-diamond-cage structures, have unique properties with potential value for nanotechnology. The availability and ability to selectively functionalize this special class of nanodiamond materials opens new possibilities for surface modification, for high-efficiency field emitters in molecular electronics, as seed crystals for diamond growth, or as robust mechanical coatings. The properties of self-assembled monolayers (SAMs) of diamondoids are thus of fundamental interest for a variety of emerging applications. This paper presents the effects of thiol substitution position and polymantane order on diamondoid SAMs on gold using near-edge X-ray absorption fine structure spectroscopy (NEXAFS) and X-ray photoelectron spectroscopy (XPS). A framework to determine both molecular tilt and twist through NEXAFS is presented and reveals highly ordered diamondoid SAMs, with the molecular orientation controlled by the thiol location. C 1s and S 2p binding energies are lower in adamantane thiol than alkane thiols on gold by 0.67 +/- 0.05 and 0.16 +/- 0.04 eV, respectively. These binding energies vary with diamondoid monolayer structure and thiol substitution position, consistent with different degrees of steric strain and electronic interaction with the substrate. This work demonstrates control over the assembly, in particular the orientational and electronic structure, providing a flexible design of surface properties with this exciting new class of diamond nanoparticles.     

Software for the calculation of isotope patterns in tandem mass spectrometry

Software, available at no cost on the Internet, is described which uses polynomial expansion algorithms to calculate the isotope patterns for precursor ion, neutral loss, and MSn product ion tandem mass spectra. Such information is useful for determining product ion and neutral loss composition, identification of analytes in complex samples, deconvolution of overlapping spectra, and correction of peak heights or areas in quantitative analysis. The effect of less than unit mass resolution on the isotope patterns is described and experimental examples of the use of the software are presented.     

Synthesis of a stable radical anion via the one electron reduction of a 1,1-bis-phosphinosulfide alkene derivative

A new type of stable radical ligand featuring a 1,1-bis-phosphinosulfide alkene backbone has been prepared and characterized on the basis of X-ray diffraction, EPR and DFT studies.     

Bi5(dpd)6 within CH3CN](ClO4)3.3CH3CN: a supramolecular, tetrahedral pentabismuth cluster derived from a nonabismuth oxo/hydroxide

The novel tetrahedral [Bi(5)(dpd)(6) within CH(3)CN](ClO(4))(3).3CH(3)CN (dpd = di-2-pyridyl-gem-diolate) has been synthesized from [Bi(9)(mu(3)-O)(8)(mu(3)-OH)(6)](ClO(4))(5) and di-2-pyridyl ketone. The Bi(5) complex incorporates CH(3)CN via C-HO hydrogen bonding.     

Microcalorimetrics studies of the thermodynamics and binding mechanism between L-tyrosinamide and aptamer

In recent years, several high-resolution structures of aptamer complexes have shed light on the binding mode and recognition principles of aptamer complex interactions. In some cases, however, the aptamer complex binding behavior and mechanism are not clearly understood, especially with the absence of structural information. In this study, it was demonstrated that isothermal titration calorimetry (ITC) and circular dichroism (CD) were useful tools for studying the fundamental binding mechanism between a DNA aptamer and L-tyrosinamide (L-TyrNH2). To gain further insight into this behavior, thermodynamic and conformational measurements under different parameters such as salt concentration, temperature, pH value, analogue of L-TyrNH2, and metal ion were carried out. The thermodynamic signature along with the coupled CD spectral change suggest that this binding behavior is an enthalpy-driven process, and the aptamer has a conformational change from B-form to A-form. The results showed that the interaction is an induced fit binding, and the driving forces in this binding behavior may include electrostatic interactions, hydrophobic effects, hydrogen bonding, and the binding-linked protonation process. The amide group and phenolic hydroxyl group of the L-TyrNH2 play a vital role in this binding mechanism. In addition, it should be noted that Mg(2+) not only improves binding affinity but also helps change the structure of the DNA aptamer.