Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

Structural characterization of polypyrrole in the solid state by high resolution 15N NMR spectroscopy [II]

The solid-state ¹⁵N CP/MAS NMR spectra and ¹⁵N spin-lattice relaxation times (T₁) of doped and dedoped ¹⁵N-labeled polypyrroles prepared by electrochemical polymerization, have been measured by means of high-resolution solid-state ¹⁵N NMR. The ¹⁵N signal of polypyrrole consists of four peaks decomposed by line shape analysis. The four peaks obtained have been assigned to the various structures of polypyrrole. Further, the half-width of the ¹⁵N NMR spectra of polypyrroles is discussed as related to the electrical conductivity. © 1995 John Wiley & Sons, Inc.     

Some geometrical aspects of semidefinite linear complementarity problems

This article studies some geometrical aspects of the semidefinite linear complementarity problem (SDLCP), which can be viewed as a generalization of the well-known linear complementarity problem (LCP). SDLCP is a special case of a complementarity problem over a closed convex cone, where the cone considered is the closed convex cone of positive semidefinite matrices. It arises naturally in the unified formulation of a pair of primal-dual semidefinite programming problems. In this article, we introduce the notion of complementary cones in the semidefinite setting using the faces of the cone of positive semidefinite matrices and show that unlike complementary cones induced by an LCP, semidefinite complementary cones need not be closed. However, under R₀-property of the linear transformation, closedness of all the semidefinite complementary cones induced by L is ensured. We also introduce the notion of a principal subtransformation with respect to a face of the cone of positive semidefinite matrices and show that for a self-adjoint linear transformation, strict copositivity is equivalent to strict semimonotonicity of each principal subtransformation. Besides the above, various other solution properties of SDLCP will be interpreted and studied geometrically.     

Characterization of supercommuting matrices

For a given n-by-n matrix A, we consider the set of matrices which commute with A and all of whose principal submatrices commute with the corresponding principal submatrices of A. The properties of this set are examined, with particular attention to its dimension.     

Matrices that preserve vectors of fixed sign variation

For each k≥ 0, those nonsingular matrices that transform the set of totally nonzero vectors with k sign variations into (respectively, onto) itself are studied. Necessary and sufficient conditions are provided. The cases k=0,1,2,n-3,n-2,n-1 are completely characterized.     

Enlarged symmetry groups of finite-size clusters with periodic noundary conditions

Any system that approximates an infinite lattice by a family of finite clusters (with periodic boundary conditions) passes through an intermediate region with enlarged (hidden) symmetry as the system size is increased. The hidden symmetry allows for extra degeneracies and level crossings and has application to exact-diagonalization studies, Monte Carlo simulations, lattice gauge theories, and renormalization group calculations.     

111In–L–LDL and 153Gd–L–LDL as radiotracers for detection of AR4‐2J rat pancreatic tumors

Pancreatic cancer has an extremely poor prognosis, due, in part, to lack of methods for early diagnosis. The present study was designed to evaluate the potential of labeling low‐density lipoprotein (LDL) with a radionuclide using a lipid chelating agent, bis(stearylamide) of diethylenetriaminepentaacetic acid (L), to detect pancreatic tumors by gamma‐scintigraphy. Previous studies indicated that the difficulty of visualization of pancreatic tumors was due to their poor vascularization. This study compares the ability of two radiotracers, ¹¹¹In–L–LDL and ¹⁵³Gd–L–LDL to target highly vascularized rat pancreatic tumors (AR4‐2J) implanted in nude mice. Biodistribution studies showed that the tumor uptake of ¹¹¹In–L–LDL and ¹⁵³Gd–L–LDL tracers was twofold and fivefold higher respectively than with the controls (¹¹¹In citrate and ¹⁵³Gd citrate respectively). These tracers would thus be suitable for scintigraphic imaging. We show here that LDL could be employed as a delivery system for tracers such as ¹¹¹In or ¹⁵³Gd when these two radionuclides are complexed by a lipid‐chelating anchor, and that ¹¹¹In–L–LDL and ¹⁵³Gd–L–LDL enabled better visualization of the pancreatic tumor tissues, with a better result with ¹⁵³Gd–L–LDL. Copyright © 2004 John Wiley & Sons, Ltd.     

Assignment of chemical shifts in benzohydroxamic acid and structure of its silylated derivatives by 15N enrichment

¹⁵N isotopic enrichment was necessary for the unequivocal assignment of the ¹H NMR lines to the protons in the NH–OH fragment of benzohydroxamic acid, BHXA, C₆H₅CONHOH, in dry dimethyl sulfoxide solutions. The assignment [δ(NH) = 11.21, δ(OH) = 9.01, ¹J(¹⁵N,¹H) = 102.2 Hz, ²J(¹⁵N,¹H) <1.5 Hz], which is opposite to that used by other authors, confirms the assignment extended to BHXA by Brown and co‐workers from the spectra of acetohydroxamic acid. The enrichment allowed also assignment of the ²⁹Si lines in the spectra of disilylated benzohydroxamic acid, (Z)‐tert‐butyldimethylsilyl N‐tert‐butyldimethylsilyloxybenzoimidate (2) and (Z)‐tert‐butyldiphenylsilyl N‐tert‐butyldiphenylsilyloxybenzoimidate (3), and confirmed structure of the monosilylated products, N‐tert‐butyldiphenylsilyloxybenzamide (4) and N‐tert‐butyldiphenylsilyloxy benzoimidic acid (5). Copyright © 2003 John Wiley & Sons, Ltd.     

Bounds on the inverses of nonnegative triangular matrices with monotonicity properties

Some bounds on the entries and on the norm of the inverse of triangular matrices with nonnegative and monotone entries are found. All the results are obtained by exploiting the properties of the fundamental matrix of the recurrence relation which generates the sequence of the entries of the inverse matrix. One of the results generalizes a theorem contained in a recent article of one of the authors about Toeplitz matrices.