Fast method to compute the scalar product of gradient and given vector

The paper deals with a special problem in Automatic Differentiation. Letf be a rational function ofn variables, let #(f) denote the number of operations to evaluatef(x), letg denote the gradient off. Many algorithms for minimizingf(x) require the scalar productg(u) ^tv. In the standard method for computingg(u) ^tv the amount of work grows withn·#(f). In this note a new method for computingg(u) ^tv is presented. The new method is considerably faster, its amount of work only grows with #(f).     

The possibility of evolving a theory for predicting the service life of reinforced concrete structures

The development in recent years with increasing air pollution, increasing need of energy saving and last not least the growing number of damage in old structures leads to a raising demand to calculate the durability of structures, too. The paper has been prepared by request of the RILEM Technical Committee 45-LTO to show that, in principle, it is possible to evolve a theory for predicting the service life of r.c. structures and to sketch a way how that could be achieved. A lot of necessary basic data can be found scattered in the literature. To collect these data will be the first step to take.     

Head-to-head polymers: 33. Bromination of cis-1,4-polybutadiene to head-to-head poly(vinyl bromide)

Cis-1,4-polybutadiene (PB) in a 0.5% solution of a solvent mixture of dichloromethane and 1,2-dibromoethane or tetrahydrofuran was quantitatively brominated with elemental bromine at 0°C under careful exclusion of oxygen to head-to-head poly(vinyl bromide). Partially brominated PB has a structure of random or block sequences of butadiene units in the polymer depending on the bromination solvent but shows no stereospecificity in the CHBrCHBr-dyads. Partially brominated PB with block structure showed a microphase-separated morphology over a wide range of composition. Microphase separation is less pronounced for the more random structure of butadiene units. I.r and ¹³C n.m.r. spectroscopy of the partially brominated PB was used to follow the progress of the bromination.     

Datenschutz nach BSI-Grundschutz?

Datenschutzmanagement ist eine gesetzlich verankerte Aufgabe, muss sich aber unter Wirtschaftlichkeitsgesichtspunkten in der betrieblichen und zunehmend auch der behördlichen Praxis in andere, bereits etablierte Prozessmanagementstrukturen wie ITIL oder Informationssicherheits-management Systeme (ISMS) einordnen. In diesem Beitrag werden die Möglichkeiten untersucht, die IT-Grundschutz als ein zukünftiges, ISO 27001-kompatibles ISMS bietet. Unter dem Gesichtspunkt der Normierung scheint eine Aktualisierung des Bausteins 3.5 “Datenschutz” dringend.     

Successive overrelaxation method with projection for finite element solutions of nonlinear radiation cooling problems

In this paper, we consider the successive overrelaxation method with projection for obtaining the finite element solutions under the nonlinear radiation boundary conditions. In particular we establish the convergence of the successive overrelaxation method with projection. Some numerical results are also given to illustrate the usefulness.     

Embedding universal computer arithmetic in higher programming languages

In numerical computations mainly real and complex numbers, intervals as well as matrices and vectors with such components occur. It is well known that the arithmetic operations with real numbers, complex numbers etc. can be carried over to real floating-point numbers, complex floating-point numbers etc. using roundings. This proceeding results in agreeable arithmetic-, order- and compatibility-properties for an abundance of numerical data types and the accompanying arithmetic operations. Most programming languages however only provide real floating-point numbers; all the other data types and operations have to be simulated, e. g. in the form of arrays and procedure calls, which often causes loss of accuracy and arithmetic properties. Furthermore the complicate notation makes programs difficult to read. Therefore in this article an extension of PASCAL is presented which serves as an example for the way these numerical data types can be embedded into the syntax of a programming language.     

How to avoid logarithms in comparisons with uniform random variables

In many algorithms for sampling from non-uniform distributions the logarithm of a uniform deviate must be compared with some test quantity. It is shown that all these comparisons can be done efficiently without calling a logarithm subprogram: two procedures for this task are presented and compared.     

The “burning ship” and its quasi-Julia sets

By manipulating the imaginary part of the complex-analytic quadratic equation, we obtain, by iteration, a set that we call the “burning ship” because of its appearance. It is an analogue to the Mandelbrot set (M-set). Its nonanalytic “quasi”-Julia sets yield surprizing graphical shapes.