Cotauberian Operators on L1(0, 1) Obtained by Lifting

ABSTRACT:We show that the set Td(L1(0, 1)) of cotauberian operators acting on L1(0, 1) is not open, and T ? Td(L1(0, 1)) does not imply T** cotauberian. As a consequence, we derive that the set T(L8(0, 1)) of tauberian operators acting on L8(0, 1) is not open, and that T ? T(L8(0,1)) does not imply T** tauberian

Higher-order reverse automatic differentiation with emphasis on the third-order

It is commonly assumed that calculating third order information is too expensive for most applications. But we show that the directional derivative of the Hessian ( D3f(x)⋅d ) can be calculated at a cost proportional to that of a state-of-the-art method for calculating the Hessian matrix. We do this by first presenting a simple procedure for designing high order reverse methods and applying it to deduce several methods including a reverse method that calculates D3f(x)⋅d . We have implemented this method taking into account symmetry and sparsity, and successfully calculated this derivative for functions with a million variables. These results indicate that the use of third order information in a general nonlinear solver, such as Halley–Chebyshev methods, could be a practical alternative to Newton’s method. Furthermore, high-order sensitivity information is used in methods for robust aerodynamic design. An efficient high-order differentiation tool could facilitate the use of similar methods in the design of other mechanical structures

Reverse accumulation and accurate rounding error estimates for taylor series coefficient

Original article can be found at: http://www.informaworld.com/smpp/title~content=t713645924~db=all Copyright Taylor and Francis/ Informa.We begin by extending the technique of reverse accumulation so as to obtain gradients of univariate Taylor series coefficients. This is done by re-interpreting the same formulae used to reverse accumulategradients in the conventional (scalar) case. Thus a carefully written implementation of conventional reverse accumulation can be extended to the Taylor series valued case by (further) overloading of the appropriate operators. Next, we show how to use this extended reverse accumulation technique so as to construct accurate (i.e. rigorous and sharp) error bounds for the numerical values of the Taylor series coefficients of the target function, again by re-interpreting the corresponding conventional (scalar) formulae. This extension can also be implemented simply by re-engineering existing code. The two techniques (reverse accumulation of gradients and accurate error estimates) each require only a small multiple of the processing time required to compute the underlying Taylor series coefficients. Space "requirements are comparable to those for conventional (scalar) reverse accumulation, and can be simply managed. We concluded with a discussion of possible implementation strategies and the implications for the re-use of code.Peer reviewe

Triple-Effekt-Maschine mit festem und fluessigem Absorber. Detaillierter Ergebnisbericht und Anhang zum Schlussbericht

This report is an appendix to the final report. It explains the theoretical fundamentals of the project and presents the results and solution strategies. It comprises four parts: (a) Thermodynamic concept: Fundamentals; introduction to the thermodynamic fundamentals of sorption refrigerators as required for understanding the report; (b) Part load behaviour of a lithium bromide double effect plant: Theoretical and experimental investigations; description of the plant; theoretical preparation and experimental investigation of steady part-load behaviour. (c) Implementation of a triple effect plant: Concept and design; characterization of the performance characteristics of the component plants; development of a concept for coupling the two component plants; setup and control of the system. (d) Operation of a triple effect plant: Experiments adn findings; survey of experiments; description, evaluation and interpretation of results.Der vorliegende detaillierte Ergebnisbericht ist als Anhang zum Schluss- und Erfolgskontrollbericht zu verstehen. Er erlaeutert die theoretischen Grundlagen fuer das Projekt und stellt die Ergebnisse und Loesungswege detailliert dar. Damit gliedert er sich in die Teile: (a) Thermodynamisches Konzept: Grundlagen Einfuehrung in die zum Verstaendnis der Arbeit erforderlichen thermodynamischen Grundlagen der Sorptionskaelteanlagen. Motivation und Herleitung des Konzeptes zur Verbesserung ihrer Primaerenergieeffizienz. (b) Teillastverhalten einer Lithiumbromid-Double-Effect-Anlage: Theorie und Experimente Vorstellung der Anlage, theoretische Vorbereitung und experimentelle Untersuchung des stationaeren Teillastverhaltens. (c) Realisierung einer Triple-Effect-Anlage: Konzept und Aufbau Charakterisierung der Betriebseigenschaften der Teilanlagen, Entwicklung eines Konzepts zur Kopplung der beiden Teilanlagen, Aufbau und Regelung des Systems. (d) Betrieb einer Triple-Effect-Anlage: Experimente und Ergebnisse Ueberblick ueber die durchgefuehrten Experimente, Darstellung, Auswertung und Interpretation der erzielten Ergebnisse. (orig.)Available from TIB Hannover: F01B1223+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEBundesministerium fuer Bildung und Forschung, Berlin (Germany)DEGerman