On the analysis of stochastic divide and conquer algorithms

This paper develops general tools for the analysis of stochastic divide and conquer algorithms. We concentrate on the average performance and the distribution of the running time of the algorithm. As a special example we analyse the average performance and the running time distribution of the (2k + 1)-median version of Quicksort. Online publication October 13, 2000.     

Early Post Mortem pH decrease in porcine M. longissimus dorsi of PSE, Normal and DFD quality

The purpose of this investigation was to compare the muscle pH at exsanguination and the rate of pH changes in porcine M. longissimus dorsi (LD) of normal, DFD (Dark, Firm, Dry) and PSE (Pale, Soft, Exudative) quality. The pH was continuously measured in the LD in 116 carcasses during the first 50 min post mortem. Calculations were made both on measured pH-values and on pH-values transformed to hydrogen ion concentrations. A regression of pH or hydrogen ion concentration on time was made for each animal. These individual regressions were then combined, using a multivariate analysis to estimate regression curves for each meat quality class. The two methods for expressing pH gave somewhat different results. The relationship between the hydrogen ion concentration and time was found to be linear for normal and DFD muscles and quadratic for PSE muscles. As a consequence of the mathematical properties of pH, the relationship between pH and time was found to be quadratic for the normal and DFD qualities, and linear for the PSE quality. For both methods of calculations the slopes for the regression curves were significantly different between PSE and the other two quality classes with both calculating methods, while the slopes did not differ between normal and DFD muscle qualities. The intercepts of the regression curves differed significantly between PSE and the other two quality classes only when the calculations were made on measured pH-values without transformation. A temporary increase in pH was seen in some normal and PSE carcasses during the measured time period. Development of muscles with PSE characteristics thus seems to be initiated by a combination of a lower muscle-pH already at exsanguination and a faster pH decrease. It is also of importance to consider the special mathematical properties of the pH-value.     

Nonsingular BEM formulations for thin-walled structures and elastostatic crack problems

Summary This paper presents a unique approach, named mathematical regularization, to remove the nearly-singular and singular integrals occurring in the boundary integral formulations for the solution of the boundary value problems with a pathologica integration boundary due to the very near or coinciding parts of the total boundary. Nonsingular boundary integral equations are derived for thin-walled structure problems. In the case of crack-like problems, we present two kinds of the nonsingular integral representations of the secondary fields and the derivative boundary integral equations.     

Integration of medical responsibility

The article describes responsibility as a term with six relations and four different levels. It analyses the conflicts between different addresses, levels and values and emphasizes the need to integrate the responsibilities of the physician. The term "responsibility" provides a more differentiating analytical tool for conflicts in medical acting than the so-called "principles of biomedical ethics".     

Contribution to the history of gerontology in Germany in the 2nd half of our century

In this paper some trends of gerontology during the last 45 years in Germany are described. A survey of the development of gerontology in the former GDR is followed by an analysis of the "Zeitschrift für Alternsforschung" from 1980-1990. The main result is the predominance of publications on the care system since the middle of the 1980s. With regard to the development of gerontology in the western part of Germany, an analysis of publications in the "Zeitsschrift für Gerontologie" from 1968-1991 shows changes in the main topics during this period. Until the middle of the 1970s there was a predominance of publications in the field of: intelligence, learning, memory and perception. The emphasis of publications from 1977-1985 was on stress and coping. In the middle of the 1980s there was an increasing interest in the analysis of social network and competence in the elderly. The paper discusses these trends of gerontological research in the eastern and western parts of Germany.     

A trial with diclofenac HEP plaster as topical treatment in minor sport injuries

Diclofenac HEP plaster was tested in an open study in the treatment of different traumatic sport and overload injuries, to confirm the results of efficacy and tolerability already shown in other clinical studies. A total of 101 patients were assigned to treatment and were eligible for the evaluation of results at the end of a 14-day treatment period. The average score of spontaneous pain, assessed by means of a verbal scale and a visual analogical scale, showed a clear difference in pain rating between the beginning and end of treatment. In general 60% pain reduction was observed. The difference in analgesic activity was already apparent on the 7th day of treatment (-28%). The reduction of pain was confirmed by changes in another subjective sign related to the injury: provoked pain. This symptom decreased in a manner comparable to spontaneous pain: 61% pain reduction after 2 weeks of treatment. Global assessment of efficacy, performed by the investigator at the end of treatment, showed the clear therapeutic activity of local treatment with diclofenac HEP plaster. Satisfactory results were obtained and only 18% of the patients (most of them with chronic and persistent pain) experienced ineffective pain relief at the end of the 2-week treatment. The beneficial effects of diclofenac HEP plaster on pain are confirmed by the patients' assessment, since almost identical scores were obtained. It is striking that the overall tolerance of diclofenac HEP plaster, applied topically twice a day for 2 weeks, was "good" or "excellent" in the 101 patients treated. Any side effect was reported on the patient's card and all the patients completed the study.     

Lagegeregelte servoantriebe ohne mechanische sensoren

Mechanische Sensoren zur Drehzahl- und Lageerfassung bei elektrischen Antrieben verursachen Kosten, vergrößern das Bauvolumen des Antriebs, bedingen die Datenübertragung zwischen Regler und Sensor und schränken das Einsatzgebiet des Antriebs ein. Daher wurden verschiedene Konzepte zum Ersatz dieser mechanischen Sensoren entwickelt. Sie unterscheiden sich durch den Aufwand, die benötigte Genauigkeit (Pumpenantrieb Servoantrieb) und dem gewünschten Betriebsbereich.In diesem Beitrag wird die Realisierung des sensorlosen Betriebs einer permanenterregten Synchronmaschine durch ein Kalman-Filter beschrieben. Durch Simulation und durch praktische Untersuchungen konnte gezeigt werden, daß die Schätzung von Lage und Drehzahl die Genauigkeitsanforderungen für eine indirekte Lageregelung erfüllt. Eine solche Lageregelung besitzt keinen mechanischen Sensor mehr.     

Integral-equation representations of flow elastoplasticity derived from rate-equation models

Summary Two integral-equation representations are presented in this paper, based on the exact integrations of the conventional rate-equation model of associativeJ ₂ flow elastoplasticity with combined-isotropic-kinematic hardening-softening. Among them the strain-controlled integral-equation representation has two new naturally defined material functionsY(Z) andU(Z) of the normalized active workZ, which plays the role of intrinsic time. One of the immediate benefits derivable from the new representations is, owing to the explicit unfolding of the highly nonlinear path-dependence between stress and strain without a detour to the evolutions of internal state variables, their adaptability for direct calculations without any iteration. Indeed, it is itself a constructive algorithm. It is shown that at a realistic level of precision, the strain-controlled integral-equation representation saves 99% or more of the CPU time compared with the widely used elastic predictor-radial return algorithm of the rate-equation representation.List of symbols e _ij ,e _ij ^e ,e _ij ^p strain deviator, elastic strain deviator, plastic strain deviator - effective strain - ^p effective plastic strain - e ₁,e ₂,e ₃ principal strain deviator,e ₃=–e ₁–e ₂ - e _tan,e _rad tangential strain increment, radial strain increment - E Young's modulus, assumed to be constant - f yield function in stress space - F yield function in strain space - G shear modulus, assumed to be constant - G(Z ₁,Z ₂) shear relaxation function of elastoplasticity - h( ^p ),k( ^p ) material functions of plasticity for the stress-space rate-equation representation - material functions of plasticity for the strain-space rate-equation representation - I ₂ second invariant of the deviatoric strain tensor - J ₂ second invariant of the deviatoric stress tensor - J(z ₁,z ₂) shear creep function of elastoplasticity - K bulk modulus, assumed to be constant - p dummy variable of integration in place of the effective plastic strain - r _ij active stress - R _ij active strain - effective active-stress, i.e. times Euclidean length of active stress - effective active-strain, i.e. times Euclidean length of active strain - S _ij ,S _ij ^e ,S _ij ^r stress deviator, elastic stress deviator, stress relaxation - effective stress - effective stress relaxation - S ₁,S ₂,S ₃ principal stress deviator,S ₃=–S ₁–S ₂ - t, , , time - t ₀ zero-value time - t _u latest unloading time - y(z), u(z) material functions of plasticity for the stress-controlled integral-equation representation - Y(Z), U(Z) material functions of plasticity for the strain-controlled integral-equation representation - z normalized active complementary-work - material functions defined for use in convertingh( ^p ) andk( ^p ) toy(z) andu(z) - Z normalized active work - material functions defined for use in convertingh( ^p ) andk( ^p ) toY(Z) andU(Z) - _ij back stress - A _ij back strain - _ij , _ij ^e , _ij ^p strain, elastic strain, plastic strain - _y (initial) yield strain, _y =h(0)/2G - Poisson's ratio assumed to be constant - _ij , _ij ^e , _ij ^r stress, elastic stress, stress relaxation - _y (initial) yield stress, yield strength, _y =h(0)