Response of a SINIS Detector with Electron Cooling to Submillimeter-Wave Radiation

JETP Letters - The response of a detector fabricated on a silicon substrate in the form of a metamaterial that is a 10 × 10 matrix of split rings containing superconductor-insulator-normal...     

On the largest principal angle between random subspaces

Formulas are derived for the probability density function and the probability distribution function of the largest canonical angle between two p-dimensional subspaces of Rⁿ chosen from the uniform distribution on the Grassmann manifold (which is the unique distribution invariant by orthogonal transformations of Rⁿ). The formulas involve the gamma function and the hypergeometric function of a matrix argument.     

The efficient evaluation of the hypergeometric function of a matrix argument

We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions. Our algorithms exploit the combinatorial properties of the Jack function, and have complexity that is only linear in the size of the matrix.

     

On the complete pivoting conjecture for a hadamard matrix of order 12

This paper settles a conjecture by Day and Peterson that if Gaussian elimination with complete pivoting is performed on a 12 by 12 Hadamard matrix, then (1,2,2,4,3,10/3,18/5,4,3,6,6,12) must be the (absolute) pivots. Our proof uses the idea of symmetric block designs to reduce the complexity that would be found in enumerating cases.

In contrast, at least 30 patterns for the absolute values of the pivots have been observed for 16 by 16 Hadamard matrices. This problem is non-trivial because row and column permutations do not preserve pivots. A naive computer search would require (12!)² trials.     

Wave Dynamics of Saturated Porous Media and Evolutionary Equations

Nonlinear wave dynamics of an elastically deformed saturated porous media is investigated following the Biot approach. Mathematical models under research are the Biot model and its generalization by consideration of viscous stresses inside liquids. Using two-scales and linear WKB methods, the classical Biot system is transformed to a first-order wave equation. To construct the solution of the other system, an asymptotic modified two-scales method is developed. Initial system of equations is transformed to a nonlinear generalized Korteweg–de Vries–Burgers equation for quick elastic wave. Distinctions of wave propagation in the context of the Biot model and its generalization are shown.     

CHARACTERIZATION OF THE 32,000 DALTON MEMBRANE PROTEIN—I. EARLY SYNTHESIS DURING PHOTOINDUCED PLASTID DEVELOPMENT OF SPIRODELA

The kinetics of ³⁵S methionine incorporation into soluble and membrane proteins during the transition from steady state dark growth to greening was studied in Spirodela. A sharp increase in the rate of incorporation occurred at 3 h, which was several h before major increases in chlorophyll were apparent. Part of this enhanced incorporation was due to enhanced synthesis of a 32 ,000 dalton membrane protein. This synthesis was paralleled by a temporal increase in in uitro template capacity for this protein and an increase in 0.5 × 10⁶ dalton plastid messenger RNA.     

Faraday effect and aggregation of paramagnetic ions in borate glasses

The magneto-optical Faraday effect and electron spin resonance (ESR) in a potassium-aluminum borate glass containing small amounts of impurities of Fe and Mn oxides have been investigated. The Faraday effect measurements and ESR data made it possible to reveal the formation of clusters of paramagnetic ions interacting via oxygen even in the stage of glass synthesis. Heat treatment leads to cluster coarsening and formation of nanoparticles.     

Topological instability along filamented invariant surfaces

In dynamical systems with a zero Lyapunov exponent, weak mixing can be governed by a specific topological structure of some surfaces that are invariant with respect to particle dynamics. In particular, when the genus of the invariant surfaces is more than one, they may have weak mixing and the corresponding fractional kinetics. This possibility is demonstrated by using a typical example from plasma physics, a three-dimensional resistive pressure-gradient-driven turbulence model. In a toroidal geometry and with a low-pressure gradient, this model shows the emergence of quasicoherent structures. In this situation, the isosurfaces of the velocity stream function have a web structure with filamentary surfaces emerging from the outer region of the torus and covering the inner region. The filamentary surfaces can result in stochastic jets of particles that cause a "topological instability." In such a situation, particle transport along the surfaces is of the anomalous superdiffusion type.     

Meet-distributive lattices and the anti-exchange closure

This paper defines the anti-exchange closure, a generalization of the order ideals of a partially ordered set. Various theorems are proved about this closure. The main theorem presented is that a latticeL is the lattice of closed sets of an anti-exchange closure if and only if it is a meet-distributive lattice. This result is used to give a combinatorial interpretation of the zetapolynomial of a meet-distributive lattice. Work done while the author was an Applied Mathematics Fellow at M.I.T. Presented by R. P. Dilworth