Morphisms and currents in infinite nonlinear resistive networks

In this paper we develop a theory of nonlinear resistive infinite electrical networks in the framework of modular sequence spaces. After introducing the notion of network morphism, we show that currents in infinite networks can be approximated by currents in suitable finite networks. Rayleigh monotonicity law for nonlinear networks is studied in detail. Parabolic and hyperbolic networks are introduced and characterized in analogy to the linear case.     

Reflecting Brownian motions: Quasimartingales and strong Caccioppoli sets

A notion ofstrong Caccioppoli set is defined for bounded Euclidean domains. It is shown that stationary (normally) reflecting Brownian motion on the closure of a bounded Euclidean domain is a quasimartingale on each compact time interval if and only if the domain is a strong Caccioppoli set. A similar result is shown to hold for symmetric reflecting diffusion processes.Research supported in part by NSF Grant DMS 91-01675.Research supported in part by NSF Grants DMS 86-57483 and 90-23335.     

Application du prolongement analytique au problème inverse du potentiel

Sommaire Le but de cet article est établir quelques résultats nouveaux sur le problème inverse du potentiel newtonien. Nous démontrons deux théorèmes d'unicité: pour les polyédres convexes dansR ⁿ et pour les lemniscates dansR ². L'instrument principal est un lemme basé sur une idée de V. Kondrachkov rarement utilisé malgré sa puissance. Nous montrons son efficacité en liaison avec la méthode du prolongement analytique des potentiels.

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The goal of this paper is to establish some new results in the inverse Newtonian potential problem. We prove two uniqueness theorems: for convex polyhedra inR ⁿ and for lemniscates inR ². The main tool is a lemma based upon an idea of V. Kondrashkov which, though powerful, is rarely used. We show its efficiency applied together with the method of analytic continuation of potentials.

     

Potential Theoretic Approach to Rendezvous Numbers

We analyze relations between various forms of energies (reciprocal capacities), the transfinite diameter, various Chebyshev constants and the so-called rendezvous or average number. The latter is originally defined for compact connected metric spaces (X,d) as the (in this case unique) nonnegative real number r with the property that for arbitrary finite point systems {x ₁, …, x _n } ⊂ X, there exists some point x ∈ X with the average of the distances d(x,x _j ) being exactly r. Existence of such a miraculous number has fascinated many people; its normalized version was even named “the magic number” of the metric space. Exploring related notions of general potential theory, as set up, e.g., in the fundamental works of Fuglede and Ohtsuka, we present an alternative, potential theoretic approach to rendezvous numbers.     

噻胺酮麻醉剂对鼠S180肿瘤31P MRS的影响

对实验动物肿瘤进行活体³¹P MRS研究首要的是有效地固定动物.本文初步研究了用噻胺酮麻醉后的小鼠S180肿瘤在麻醉过程中³¹P MRS随时间的变异性.研究发现噻胺酮是一个安全系数高、起效快、麻醉过程适宜且对肿瘤的³¹P MRS无显著影响的麻醉药.因而噻胺酮适用于连续测定³¹P MRS的需要.     

31P CP/MAS NMR of polycrystalline and immobilized phosphines and catalysts with fast sample spinning

Cross‐polarization (CP) at fast magic angle spinning (MAS) frequencies leads to a splitting of the Hartmann–Hahn (HH) matching profile into a centerband and additional bands of higher orders. The matching profiles differ with the substance categories. Therefore, signal intensity is usually lost, when e.g. the routine standard NH₄H₂PO₄ is used for optimizing the ¹H–³¹P HH match prior to measuring phosphines and their metal complexes in polycrystalline or immobilized form. Here, a variety of model compounds, such as Ph₂PCH₂CH₂PPh₂ and (CO)₂Ni(PPh₃)₂, which can be used as ³¹P CP standards for analogous substances or materials are presented. Investigating the influences of MAS frequency, contact time, ¹H pulse power and sample volume on the matching profiles of the model compounds leads to general trends. Thereby, a new strategy for measuring difficult samples with CP at high MAS rates has been developed: their optimum CP parameters are derived from the most intense maxima in the HH matching profiles of the corresponding model compounds. This new strategy is compared with variations of a conventional ramp sequence. Although the latter generally provide smaller signal half‐widths, the new strategy leads to higher signal intensities. The new method was successfully applied to polycrystalline and immobilized phosphines and catalysts. Copyright © 2003 John Wiley & Sons, Ltd.     

Infinite-dimensional Dirichlet operators I: Essential selfadjointness and associated elliptic equations

We give sufficient conditions for essential selfadjointness of operators associated with classical Dirichlet forms on Hilbert spaces and of potential perturbations of Dirichlet operators. We also study the smoothness of generalized solutions of elliptic equations corresponding to the Dirichlet operators.Supported by the Alexander von Humboldt Foundation.     

Langendorff灌流心脏的31P NMR谱测定

测定了Langendorff灌流大鼠和兔心脏的³¹P NMR谱.观测到PCr、ATP、SP、P_i以及PME和GPC等含磷代谢物的共振峰,各谱峰之间实现了很好的分辨.在3~5min的累加时间内测得的图谱具有较好的S/N,可用于以上含磷代谢物的定量测定,以高能含磷化合物ATP和PCr相对峰强度以及冠脉流量的变化对灌流大鼠心脏代谢的稳定性进行了考察,结果表明,在本实验条件下大鼠心脏的能量储存至少可稳定2h,用所建方法以3min的时间间隔对同一大鼠心脏缺血21min及再灌注12min过程中心脏的³¹P NMR谱进行了连续跟踪测定,并初步观测了缺血及再灌注过程中心肌细胞内ATP、PCr与P_i之间的消长关系.