Two models for josephson oscillators

Two exactly soluble quantum mechanical models for tunneling oscillators are discussed. The first one is a closed weak coupling system, in which the current is nondissipative. In the second, open strong coupling system the oscillation occurs as a reservoir driven phase transition of the first kind far from thermal equilibrium.     

Collective excitations in superconductors

The excitations connected with quantum condensation of a fermion gas are calculated quantitatively along the lines of a previous paper. We find exact agreement with earlier results: excitations of the phonon type in the absence of Coulomb interaction, strong indications for their nonexistence in the presence of this interaction.     

Almost block independence and bernoullicity of ℤ d -actions by automorphisms of compact abelian groups

Summary We prove that a ^d -action by automorphisms of a compact, abelian group is Bernoulli if and only if it has completely positive entropy. The key ingredients of the proof are the extension of certain notions of asymptotic block independence from -actions to ^d -action and their equivalence with Bernoullicity, and a surprisingly close link between one of these asymptotic block independence properties for ^d -actions by automorphisms of compact, abelian groups and the product formula for valuations on global fields.Oblatum 20-X-1994     

Heat Content Asymptotics for Oblique Boundary Conditions

We consider the short-time heat content asymptotics for oblique boundary conditions. The first few coefficients in the asymptotic expansion are calculated.     

Enriques surfaces and Jacobian elliptic K3 surfaces

This paper proposes a new geometric construction of Enriques surfaces. Its starting point are K3 surfaces with Jacobian elliptic fibration which arise from rational elliptic surfaces by a quadratic base change. The Enriques surfaces obtained in this way are characterised by elliptic fibrations with a rational curve as bisection which splits into two sections on the covering K3 surface. The construction has applications to the study of Enriques surfaces with specific automorphisms. It also allows us to answer a question of Beauville about Enriques surfaces whose Brauer groups show an exceptional behaviour. In a forthcoming paper, we will study arithmetic consequences of our construction.     

NonstableK-Theory for operator algebras

We show that the homotopy groups of the group of quasi-unitaries inC ^*-algebras form a homology theory on the category of allC ^*-algebras which becomes topologicalK-theory when stabilized. We then show how this functorial setting, in particular the half-exactness of the involved functors, helps to calculate the homotopy groups of the group of unitaries in a series ofC ^*-algebras. The calculations include the case of all AbelianC ^*-algebras and allC ^*-algebras of the formAB, whereA is one of the Cuntz algebras O_n n=2, 3, ..., an infinite dimensional simpleAF-algebra, the stable multiplier or corona algebra of a-unitalC ^*-algebra, a properly infinite von Neumann algebra, or one of the projectionless simpleC ^*-algebras constructed by Blackadar.     

Order and chaos in Hofstadter's Q(n) sequence

A number of observations are made on Hofstadter's integer sequence defined by Q(n) = Q(n − Q(n − 1)) + Q(n − Q(n − 2)), for n > 2, and Q(1) = Q(2) = 1. On short scales, the sequence looks chaotic. It turns out, however, that the Q(n) can be grouped into a sequence of generations. The k‐th generation has 2^k members that have “parents” mostly in generation k − 1 and a few from generation k − 2. In this sense, the sequence becomes Fibonacci type on a logarithmic scale. The variance of S(n) = Q(n) − n/2, averaged over generations, is ≅2^αk, with exponent α = 0.88(1). The probability distribution p*(x) of x = R(n) = S(n)/n^α, n ≫ 1, is well defined and strongly non‐Gaussian, with tails well described by the error function erfc. The probability distribution of x_m = R(n) − R(n − m) is given by p_m(x_m) = λ_m p*(x_m/λ_m), with λ_m → √2 for large m. © 1999 John Wiley & Sons, Inc.     

Gradient-echo imaging of hemorrhage at 1.5 Tesla

We report in vitro and in vivo MR studies of hemorrhage using the gradient-echo pulse sequence, FISP (steady state free precession) and FLASH (spoiling of transverse magnetization) at 1.5 Tesla. Phantoms containing methemoglobin, ferromagnetic particles, human serum and blood clot were scanned using both spin-echo and gradient-echo techniques. FLASH signal intensities were more sensitive to methemoglobin concentration than high T1-weighted spin-echo images. FISP showed little change in signal intensity with varying concentrations of methemoglobin and a contrast relationship similar to T2-weighted spin-echo techniques. FISP and FLASH showed intensity changes at lower concentrations of ferromagnetic material than T2-weighted spin-echo sequences. In vitro blood clot was less intense when observed by FISP and FLASH sequences than on the T2-weighted spin-echo sequences. Maximum contrast between clot and other blood components occurred at a flip angle of 45 degrees for FLASH and 60 degrees for FISP. FISP and FLASH scans of patients with hemorrhage demonstrated a marked decrease in signal intensity in the region of blood clot. This decrease was more pronounced with the gradient-echo sequences than with T2-weighted spin-echo images. We conclude that FLASH is useful for detecting methemoglobin and that both FISP and FLASH are useful for evaluating hemorrhage because of their sensitivity to methemoglobin.     

A local–global principle for algebras with involution and hermitian forms

 Weakly hyperbolic involutions are introduced and a proof is given of the following local–global principle: a central simple algebra with involution of any kind is weakly hyperbolic if and only if its signature is zero for all orderings of the ground field. Also, the order of a weakly hyperbolic algebra with involution is a power of two, this being a direct consequence of a result of Scharlau. As a corollary an analogue of Pfister's local–global principle is obtained for the Witt group of hermitian forms over an algebra with involution. Received: 29 October 2001; in final form: 9 August 2002 / Published online: 16 May 2003 Mathematics Subject Classification (2000): 16K20, 11E39