A classification of orbits admitting a unique invariant measure

We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability measures on this space that are $S_{\infty }$-invariant and concentrated on a single isomorphism class must be zero, or one, or continuum. Further, such an isomorphism class admits a unique $S_{\infty }$-invariant probability measure precisely when the structure is highly homogeneous; by a result of Peter J. Cameron, these are the structures that are interdefinable with one of the five reducts of the rational linear order $(\mathbb{Q},<)$.     

Decay estimates of functions through singular extensions of vector-valued Laplace transforms

Let X be a Banach space and let f∈L^∞(R⁺;X) whose Laplace transform extends analytically to some region containing iR?{0}, possibly having a pole at the origin. In this paper, we give estimates of the decay of certain slight suitable modification of f in terms of the growth of its Laplace transform along the imaginary axis. This technique is applied to obtain decay estimates of smooth orbits of bounded C₀-semigroups whose infinitesimal generators have an arbitrary finite boundary spectrum. These results are close to those given recently by C.J.K. Batty and T. Duyckaerts.     

Observer synthesis method for Lipschitz nonlinear discrete-time systems with time-delay: An LMI approach

In this paper, we address the problem of observer design for a class of Lipschitz nonlinear discrete-time systems with time-delay. The main contribution lies in the use of a new structure of the proposed observer with a novel Lyapunov-Krasovskii functional. Thanks to these designs, new nonrestrictive synthesis conditions, expressed in terms of linear matrix inequalities (LMIs), are obtained. Indeed, the obtained LMIs contain more degree of freedom than those established by the approaches available in the literature which consider a simple Luenberger observer with a simple Lyapunov function for the stability analysis. An extension of the presented result to H_∞ performance analysis is given in order to take into account the noise (if it exists) affecting the considered system.     

Logarithmic residues, generalized idempotents, and sums of idempotents in Banach algebras

In a commutative Banach algebraB the set of logarithmic residues (i.e., the elements that can be written as a contour integral of the logarithmic derivative of an analyticB-valued function), the set of generalized idempotents (i.e., the elements that are annihilated by a polynomial with non-negative integer simple zeros), and the set of sums of idempotents are all the same. Also, these (coinciding) sets consist of isolated points only and are closed under the operations of addition and multiplication. Counterexamples show that the commutativity condition onB is essential. The results extend to logarithmic residues of meromorphicB-valued functions.     

Der Verband der zusammenhängenden Untergruppen einer kommutativen algebraischen Gruppe

We classify the connected commutative algebraic groups having as lattice of connected closed subgroups a projective space and determine the coordinate fields of these projective spaces. Furthermore we determine the not necessarily commutative connected algebraic groups with a distributive or boolean lattice of connected closed subgroups.

Received: 3 December 2004     

~（95）Mo NMR谱及其在钼化学研究中的应用

对~（９５）ＭｏＮＭＲ的特点、提供的信息、发展历史以及研究现状作了较为全面的介绍。结合本实验室研究工作和部分文献报道对其在钼化学研究中的应用进行了较为详细的论述，同时还指出影响~（９５）ＭｏＮＭＲ的因素并进行了简单分类和讨论。     

Recent developments in the line-by-line modeling of outgoing longwave radiation

High frequency resolution radiative transfer model calculations with the Atmospheric Radiative Transfer Simulator (ARTS) were used to simulate the clear-sky outgoing longwave radiative flux (OLR) at the top of the atmosphere. Compared to earlier calculations by Clough and coworkers the model used a spherical atmosphere instead of a plane parallel atmosphere, updated spectroscopic parameters from HITRAN, and updated continuum parameterizations from Mlawer and coworkers. These modifications lead to a reduction in simulated OLR by approximately 4.1%, the largest part, approximately 2.5%, being due to the absence of the plane parallel approximation. As a simple application of the new model, the sensitivity of OLR to changes in humidity, carbon dioxide concentration, and temperature were investigated for different cloud-free atmospheric scenarios. It was found that for the tropical scenario a 20% change in humidity has a larger impact than a doubling of the carbon dioxide concentration. The sensitive altitude region for temperature and humidity changes is the entire free troposphere, including the upper troposphere where humidity data quality is poor.     

Fourier multipliers and periodic solutions of delay equations in Banach spaces

In this paper we characterize the existence and uniqueness of periodic solutions of inhomogeneous abstract delay equations and establish maximal regularity results for strong solutions. The conditions are obtained in terms of R-boundedness of linear operators determined by the equations and Lp- Fourier multipliers. Periodic mild solutions are also studied and characterized.     

Symplectic tori in rational elliptic surfaces

Let E(1)_p denote the rational elliptic surface with a single multiple fiber f_p of multiplicity p. We construct an infinite family of homologous non-isotopic symplectic tori representing the primitive 2-dimensional homology class [f_p] in E(1)_p when p>1. As a consequence, we get infinitely many non-isotopic symplectic tori in the fiber class of the rational elliptic surface . We also show how these tori can be non-isotopically embedded as homologous symplectic submanifolds in other symplectic 4-manifolds.     

Complexity results on restricted instances of a paint shop problem for words

We study the following problem: an instance is a word with every letter occurring twice. A solution is a 2-coloring of its letters such that the two occurrences of every letter are colored with different colors. The goal is to minimize the number of color changes between adjacent letters.This is a special case of the paint shop problem for words, which was previously shown to be NP-complete. We show that this special case is also NP-complete and even APX-hard. Furthermore, derive lower bounds for this problem and discuss a transformation into matroid theory enabling us to solve some specific instances within polynomial time.