Multivariate normal distributions,Fisher information and matrix inequalities

Using appropriately parameterized families of multivariate normal distributions and basic properties of the Fisher information matrix for normal random vectors, we provide statistical proofs of the monotonicity of the matrix function A ^-1 in the class of positive definite Hermitian matrices. Similarly, we prove that A ¹¹ < A ^-111, where A ₁₁ is the principal submatrix of A and A ¹¹ is the corresponding submatrix of A ^-1. These results in turn lead to statistical proofs that the the matrix function A ^-1 is convex in the class of positive definite Hermitian matrices and that A ² is convex in the class of all Hermitian matrices. (These results are based on the Loewner ordering of Hermitian matrices, under which A < B if A - B is non-negative definite.) The proofs demonstrate that the Fisher information matrix, a fundamental concept of statistics, deserves attention from a purely mathematical point of view.     

Chemically assisted directed assembly of carbon nanotubes for the fabrication of large-scale device arrays

We report the directed assembly of single-walled carbon nanotubes (SWCNTs) at lithographically defined positions on gate oxide surfaces, allowing for the high yield ( approximately 90%) and parallel fabrication of SWCNT device arrays. SWCNTs were first chemically functionalized through diazonium chemistry with a hydroxamic acid end group that both renders the SWCNTs water-soluble and discriminately binds the SWCNTs to basic metal oxide surfaces (i.e., hafnium oxide (HfO2)). The functionalized SWCNTs are then assembled from an aqueous solution into narrow trenches etched into SiO2 films with HfO2 at the bottom. The side walls of the patterned trenches induce alignment of the SWCNTs along the length of the trenches. Heating the structures to 600 degrees C removes the organic moieties, leaving pristine SWCNTs as evidenced by Raman spectroscopy and electrical measurements. Palladium source-drain electrodes deposited perpendicular to the trench length readily contact the ends of the aligned SWCNTs. The resultant devices exhibit the electrical performance expected for SWCNT devices, with no performance deterioration as a result of the placement process. This technique allows for the directed assembly and alignment of SWCNTs over a large area and results in a high yield of working devices, presenting a promising path toward large-scale SWCNT device integration.     

Asymmetric amplification in catalysis by trans-1,2-diaminocyclohexane bistriflamide

A strong asymmetric amplification is observed in the addition of diethylzinc on aromatic aldehydes in the presence of the bistriflamide of trans-1,2-diaminocyclohexane 3a. The asymmetric amplification originates from the insolubility of the catalyst precursor 3a of low enantiomeric excess (ee), with a concomitant large increase of ee for the minor soluble part of 3a. Controlled mono-N-acetylation of 3a (20% ee) at -78 degrees C allowed isolation of 4 possessing 90% ee. [reaction: see text].     

Characterization of dimeric chiral lithium amide structures derived from N-isopropyl-O- triisopropylsilyl valinol

The dimeric structure is characterized for a chiral amide base complex consisting of an (S)-N-isopropyl-O-triisopropylsilyl valinol ligand and lithium. The complex is characterized by a variety of NMR techniques, including multinuclear one- and two-dimensional NMR experiments and diffusion-ordered NMR spectroscopy (DOSY) as well as diffusion coefficient-formula weight (D-fw) correlation analyses. Spartan calculations are presented which support the structural assignment. This structural characterization leads to an explanation of the behavior and the reactivity of these complexes in solution.     

Synthesis, characterization, and reaction of a ketone-derived 1,4-dienolate compound

The tetrahydrofuran tetrasolvated dimeric lithium dienolate derived from 2,2,7,7-tetramethyloctan-3,6-dione is characterized in the solid state by X-ray diffraction analysis and in solution by diffusion NMR. This dienolate was reacted with tropanone to yield two new products that are also described.     

Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys

In this short review, we first discuss the results, which are mainly devoted to the generalizations of the famous Kohn–Luttinger mechanism of superconductivity in purely repulsive fermion systems at low electron densities. In the context of repulsive-U Hubbard model and Shubin–Vonsovsky model we consider briefly the superconducting phase diagrams and the symmetries of the order parameter in novel strongly correlated electron systems including idealized monolayer and bilayer graphene. We stress that purely repulsive fermion systems are mainly the subject of unconventional low-temperature superconductivity. To get the high temperature superconductivity in cuprates (with T_C of the order of 100 K) we should proceed to the t–J model with the van der Waals interaction potential and the competition between short-range repulsion and long-range attraction. Finally we note that to describe superconductivity in metallic hydrogen alloys under pressure (with T_C of the order of 200 K) it is reasonable to reexamine more conventional mechanisms connected with electron–phonon interaction. These mechanisms arise in the attractive-U Hubbard model with static onsite or intersite attractive potential or in more realistic theories (which include retardation effects) such as Migdal–Eliashberg strong coupling theory or even Fermi–Bose mixture theory of Ranninger et al. and its generalizations.