Rigid sets and nonexpansive mappings

We introduce a new class of normed spaces (not necessarily finite dimensional), which contains the finite dimensional normed spaces with polyhedral norm. We study the properties of rigid sets of the spaces of this class and we apply the results to limit sets of the sequences of iterates of nonexpansive maps.

     

Fermi gas on a lattice in the van Hove limit

We study a Fermi gas with general translation-invariant many-body interactions on a (v3)-dimensional lattice. A complete analysis is given of the perturbative terms up to second order and the program put forward by N. M. Hugenholtz for the derivative of the Boltzmann equation is verified to second order.     

The Constants in the Central Limit Theorem for the One-Dimensional Edwards Model

The Edwards model in one dimension is a transformed path measure for one-dimensional Brownian motion discouraging self-intersections. We study the constants appearing in the central limit theorem (CLT) for the endpoint of the path (which represent the mean and the variance) and the exponential rate of the normalizing constant. The same constants appear in the weak-interaction limit of the one-dimensional Domb–Joyce model. The Domb–Joyce model is the discrete analogue of the Edwards model based on simple random walk, where each self-intersection of the random walk path recieves a penalty e ^–2. We prove that the variance is strictly smaller than 1, which shows that the weak interaction limits of the variances in both CLTs are singular. The proofs are based on bounds for the eigenvalues of a certain one-parameter family of Sturm–Liouville differential operators, obtained by using monotonicity of the zeros of the eigen-functions in combination with computer plots.     

Limites dégénérées de séries discrètes, formes automorphes et variétés de Griffiths–Schmid: le cas du groupe U (2, 1)

Let G be an inner anisotropic form of an unitary group of 3 variables over Q, such that G_RU(2,1), and be an automorphic representation of G(A) whose archimedean component is a degenerate limit of discrete series; such a never occurs in the cohomology (coherent or étale) of a Shimura variety. We show that however it does appear in the coherent cohomology of some line bundle over an associated Griffiths-Schmid variety. Moreover we study cup products between such cohomology classes and some other automorphic cohomology classes and we prove some non-vanishing results.     

Discrete universality of the <Emphasis Type="Italic">L</Emphasis>-functions of elliptic curves

A discrete universality theorem is obtained in the Voronin sense for the L-functions of elliptic curves. We use the difference of an arithmetical progression h > 0 such that \(\exp \left\{ {\frac{{2\pi k}}{h}} \right\}\) is rational for some k ≠ 0. A limit theorem in the space of analytic functions plays a crucial role in the proof.     

Large Deviations of Queues Sharing a Randomly Time-Varying Server

We consider a discrete-time model where multiple queues, each with its own exogenous arrival process, are served by a server whose capacity varies randomly and asynchronously with respect to different queues. This model is primarily motivated by the problem of efficient scheduling of transmissions of multiple data flows sharing a wireless channel. We address the following problem of controlling large deviations of the queues: find a scheduling rule, which is optimal in the sense of maximizing

Limits of detection and decision. Part 3

It has been shown that the MARLAP (Multi-Agency Radiological Laboratory Analytical Protocols) for estimating the Currie detection limit, which is based on ‘critical values of the non-centrality parameter of the non-central t distribution’, is intrinsically biased, even if no calibration curve or regression is used. This completed the refutation of the method, begun in Part 2. With the field cleared of obstructions, the true theory underlying Currie's limits of decision, detection and quantification, as they apply in a simple linear chemical measurement system (CMS) having heteroscedastic, Gaussian measurement noise and using weighted least squares (WLS) processing, was then derived. Extensive Monte Carlo simulations were performed, on 900 million independent calibration curves, for linear, “hockey stick” and quadratic noise precision models (NPMs). With errorless NPM parameters, all the simulation results were found to be in excellent agreement with the derived theoretical expressions. Even with as much as 30% noise on all of the relevant NPM parameters, the worst absolute errors in rates of false positives and false negatives, was only 0.3%.     

Pure inductive limit state and Kolmogorov's property

Let be a C^*-dynamical system where be a semigroup of injective endomorphism and ψ be an (λ_t) invariant state on the C^* subalgebra and is either non-negative integers or real numbers. The central aim of this exposition is to find a useful criteria for the inductive limit state canonically associated with ψ to be pure. We achieve this by exploring the minimal weak forward and backward Markov processes associated with the Markov semigroup on the corner von-Neumann algebra of the support projection of the state ψ to prove that Kolmogorov's property [A. Mohari, Markov shift in non-commutative probability, J. Funct. Anal. 199 (2003) 189–209] of the Markov semigroup is a sufficient condition for the inductive state to be pure. As an application of this criteria we find a sufficient condition for a translation invariant factor state on a one-dimensional quantum spin chain to be pure. This criteria in a sense complements criteria obtained in [O. Bratteli, P.E.T. Jorgensen, A. Kishimoto, R.F. Werner, Pure states on , J. Operator Theory 43 (1) (2000) 97–143; A. Mohari, Markov shift in non-commutative probability, J. Funct. Anal. 199 (2003) 189–209] as we could go beyond lattice symmetric states.     

Direct limits of infinite-dimensional Lie groups compared to direct limits in related categories

Let G be a Lie group which is the union of an ascending sequence G₁⊆G₂⊆? of Lie groups (all of which may be infinite-dimensional). We study the question when in the category of Lie groups, topological groups, smooth manifolds, respectively, topological spaces. Full answers are obtained for G the group Diffc(M) of compactly supported C^∞-diffeomorphisms of a σ-compact smooth manifold M; and for test function groups of compactly supported smooth maps with values in a finite-dimensional Lie group H. We also discuss the cases where G is a direct limit of unit groups of Banach algebras, a Lie group of germs of Lie group-valued analytic maps, or a weak direct product of Lie groups.