The spontaneous formation of inhomogeneity in a classical one-particle “gas”: An example in silico

A single classical isoergic particle was placed in a cube and allowed to propagate for 100 ns to 10 ms. The interaction of the particle with the inner wall of the cube was modeled as a linear combination of specular and random reflection, the extent of the combination being governed by a user-defined “roughness” parameter α. As a function of α, the particle’s relative pressure and density spontaneously took on an inhomogenous distribution.     

Mixing Multilinear Operators with or Without a Linear Analogue

As a natural extension of mixing linear operators we introduce new notions of mixing multilinear operators with or without a linear analogue. We prove Pietsch’s composition theorems in this new context extending recent results from the case of dominated operators.     

Block-Projections Algorithms with Blocks Containing Mutually Orthogonal Rows and Columns

In this paper we present an algorithm which, for a given (sparse) matrix, constructs a partition of its set of row-indices, such that each subset of this partition (except the last one obtained) contains indices which correspond to mutually orthogonal rows. We then use such decompositions in some classes of block-projections methods, previously extended by the author to general inconsistent linear least-squares problems. Numerical experiments on an inconsistent and rank-deficient least-squares model problem are described in the last section of the paper.     

Exact controllability for the magnetohydrodynamic equations

We study the local exact controllability of the steady state solutions of the magnetohydrodynamic equations. The main result of the paper asserts that the steady state solutions of these equations are locally controllable if they are smooth enough. We reduce the local exact controllability of the steady state solutions of the magnetohydrodynamic equations to the global exact controllability of the null solution of the linearized magnetohydrodynamic system via a fixed‐point argument. The treatment of the reduced problem relies on two Carleman‐type inequalities for the backward adjoint system. © 2003 Wiley Periodicals, Inc.     

Establishing norms for age-related changes in proton T1 of human brain tissue in vivo

The goal of this study was to determine the expected normal range of variation in spin-lattice relaxation time (T₁) of brain tissue in vivo, as a function of age. A previously validated precise and accurate inversion recovery method was used to map T₁ transversely, at the level of the basal ganglia, in a study population of 115 healthy subjects (ages 4 to 72; 57 male and 58 female). Least-squares regression analysis shows that T₁ varied as a function of age in pulvinar nucleus (R² = 56%), anterior thalamus (R² = 51%), caudate (R² = 50%), frontal white matter (R² = 47%), optic radiation (R² = 39%), putamen (R² = 36%), genu (R² = 22%), occipital white matter (R² = 20%) (all p < 0.0001), and cortical gray matter (R² = 53%) (p < 0.001). There were no significant differences in T₁ between men and women. T₁ declines throughout adolescence and early adulthood, to achieve a minimum value in the fourth to sixth decade of life, then T₁ begins to increase. Quantitative magnetic resonance imaging provides evidence that brain tissue continues to change throughout the lifespan among healthy subjects with no neurologic deficits. Age-related changes follow a strikingly different schedule in different brain tissues; white matter tracts tend to reach a minimum T₁ value, and to increase again, sooner than do gray matter tracts. Such normative data may prove useful for the early detection of brain pathology in patients.     

Book reviews

Unsigned book reviews are by the Book Review Editor.     

The Hyers-Ulam stability of nonlinear recurrences

We show some Hyers-Ulam type stability results for some nonlinear recurrences in metric spaces.     

Structure of Pareto optima in an infinite-horizon economy where agents have recursive preferences

This article generalizes the one-agent growth theory with discounting to the case of several agents with recursive preferences. In a multi-consumption goods world, we show that, under some regularity conditions, any Pareto optimum can be viewed as a function of a trajectory of a dynamical system. The state space can be chosen to be the product of the space of capitals and the unit simplex. We define and study the properties of generalized value functions.