Average Case Analysis in Database Problems

In a variety of applications ranging from environmental and health sciences to bioinformatics, it is essential that data collected in large databases are generated stochastically. This states qualitatively new problems both for statistics and for computer science. Namely, instead of deterministic (usually worst case) analysis, the average case analysis is needed for many standard database problems. Since both stochastic and deterministic methods and notation are used it causes additional difficulties for an investigation of such problems and for an exposition of results. We consider a general class of probabilistic models for databases and study a few problems in a probabilistic framework. In order to demonstrate the general approach, the problems for systems of database constraints (keys, functional dependencies and related) are investigated in more detail. Our approach is based on consequent using Rényi entropy as a main characteristic of uncertainty of distribution and Poisson approximation (Stein–Chen technique) of the corresponding probabilities.     

Berechnung des bezüglich dem Wärmeübergang durch Filmkondensation optimalen Wellenprofiles mit Hilfe der Variationsrechnung

Zusammenfassung Seit R. Gregorig ist bekannt, daß eine feine Wellung der Oberfläche auf deutlich verbesserte Kondensationswerte an vertikalen Wänden führt. Ungeklärt blieb aber bislang die Frage, ob es eine optimale Auslegung der Wellenformen gibt. Alle Rechenverfahren zu diesem Thema beruhen entweder auf starken Restriktionen in der Gesamtheit der Wellenprofile, welche im Lösungsweg erfaßt werden, oder sie beinhalten starke vereinfachende Annahmen über den Zusammenhang zwischen der Filmhautkontur und der Wellung der Rohrwand. Das hier angezeigte Lösungsverfahren benötigt keine derartigen einschränkenden Annahmen. Sein Ergebnis zeigt die bezüglich dem Wärmeübergang durch Filmkondensation optimale Wellenform an.

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Summary The significance of surface tension forces for film condensation on tubes with finely fluted of finned surfaces was formulated for the first time by Gregorig. Gregorig's solution and attempts to extend his solution have been limited to special shapes or involved additional simplifying assumptions.This study presents a convenient method for optimizing the design of the tube surface. The solution procedure involves all theoretical tube wall profiles and is not limited by additional simplifying assumptions. The optimization was carried out by using the Euler-Lagrange differentional equations. The optimal profile shape with respect to condensation heat transfer is about half as thick as the shapes proposed in previous publications.

     

NMR relaxation study of thermal degradation in cured PMR polyimides

We have studied cross-linking and thermal degradation of high-performance first-and second-generation PMR-15 polyimides, both thermoset and thermoplastic versions, by performing nonspectroscopic NMR solid echo T^*₂ relaxation measurements at temperatures up to 430°C using probes built for this purpose. We employ signal averaging and automated decomposition of the relaxation decays into two Gaussian components, the slower of which gradually appears above 300°C. Tracking the molecular mobility spectrum in terms of the relative intensity of the components and their relaxation times as temperature is cycled, we detect essentially no irreversible effects below the glass transition, measure permanent mobility reductions attributable to completion of cure, and find that exposure to temperatures above 380°C on the order of 1 h is required for substantial thermal degradation to occur. These results are closely supported by thermal and mechanical measurements on parallel specimens. Second-generation PMR resins appear to have higher microscopic rigidity and reduced viscous fraction at high temperatures. ©1995 John Wiley & Sons, Inc.     

Equilibrium attractivity of Krylov-W-methods for nonlinear stiff ODEs

Since implicit integration schemes for differential equations which use Krylov methods for the approximate solution of linear systems depend nonlinearly on the actual solution a classical stability analysis is difficult to perform. A different, weaker property of autonomous dissipative systemsy′=f(y) is that the norm ‖f(y(t))‖ decreases for any solutiony(t). This property can also be analysed for W-methods using a Krylov-Arnoldi approximation. We discuss different additional assumptions onf and conditions on the Arnoldi process that imply this kind of attractivity to equilibrium points for the numerical solution. One assumption is general enough to cover quasilinear parabolic problems. This work was supported by Deutsche Forschungsgemeinschaft.     

Synthesis and Crystal Structure of a new O,N Lithium Coordination Polymer

The reaction of 4‐Amino‐6‐methyl‐1, 2, 4‐triazine‐3(2H)‐thione‐5‐one (HAMTTO) with n‐butyl lithium in dimethoxyethane (DME) gives the complex [Li(DME)(AMTTO)] ( 1 ). 1 was characterized by elemental analysis, IR‐ and mass‐spectrometry and an X‐ray structure analysis [space group P2₁/n, Z = 4, lattice dimensions at —80 °C: a = 867.6(1), b = 1721.5(2), c = 931.8(1) pm, β = 112.81(1)°, R₁ = 0.0315. The complex is a coordination polymer along [001] with a zig‐zag arrangement.     

Rates of virtually self-exchange energy transfer processes of ruthenium(II) polypyridine complexes

The rate constants of electronic energy transfer from the lowest excited state of Ru(bpy)₂(L)²⁺ or Ru(bpy)(L)₂²⁺ 10 Ru(L)₃²⁺ (b     

Elastic proton-proton scattering: Excitation functions from 0.45 to 2.5 GeV

Excitation functions of the differential cross sections dσ/dgw, analyzing powers A_N and spin correlation parameters A_NN, A_SS and A_SL have been measured with internal targets at the Cooler Synchrotron COSY. Data were taken continously during the acceleration and deceleration of the internal beam for kinetic energies between 450 and 2500 MeV and scattering angles 30° σ_cm 90°. Details of the experimental method are presented. The results provide excitation functions and angular distributions of high precision and internal consistency. No evidence for narrow structures are found. Upper limits on the coupling of narrow resonances to elastic scattering in the mass range √s = 2.2…2.8 GeV are deduced. The data have significant impact on phase shift solutions.