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  • Springer  (42,164)
  • American Physical Society  (4,473)
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  • 2005-2009
  • 1980-1984  (46,770)
  • 1925-1929
  • 1980  (46,770)
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  • 1980-1984  (46,770)
  • 1925-1929
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  • 101
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    Springer
    Meteorology and atmospheric physics 29 (1980), S. 205-217 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Mit Hilfe approximierter ageostrophischer Windkomponenten und iterativer Integration in einem quasi Lagrangeschen System werden Trajektorien abgeleitet. Die Verifikation erfolgt an Hand der Verlagerung charakteristischer Wolkensysteme mittels Satellitenbilder.
    Notes: Summary Trajectories are computed with the help of approximated ageostrophic windcomponents and the iterative integration method in a quasi Lagrangian system. The displacement of distinctive cloud systems localized from satellite images is used for verification.
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  • 102
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    Meteorology and atmospheric physics 29 (1980), S. 219-233 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Es wird ein Parameter zur Feststellung des Minimalbereiches der übergeostrophischen Komponente der zonalen Strömung in einem westlichen Jet Stream aus der Bedingung bestimmt, daß eine geostrophische Bewegung nur in stabil geschichteten Medien möglich ist. Die Größe des übergeostrophischen Zonalwindes im Kerngebiet eines durchschnittlichen westlichen Jet Stream mittlerer Breiten wurde bei nahe von 60% der beobachteten zonalen Windgeschwindigkeit festgestellt. Die durch diese übergeostrophischen Zonalwindkomponenten verursachten nicht geostrophischen Querzirkulationen werden als thermisch indirekt und für die Entwicklung von einigen beobachteten Erscheinungen wie der Jet Stream Front, der Unterbrechung der nördlichen Tropopause quer zum Kern und der Clear air turbulence-Zonen in bestimmten Regionen eines westlichen Jet Stream als günstig erwiesen.
    Notes: Summary A parameter, for determining the minimum super-geostrophic component of zonal flow in a westerly jet stream, was identified, by invoking the condition that geostrophic motion is possible only in stably stratified media. The magnitude of super geostrophic zonal wind in the core region of an average mid-latitudinal westerly jet stream was found to be nearly 60% of the observed zonal wind speed. The non-geostrophic transverse circulations induced by this super-geostrophic zonal wind components were shown to be thermally indirect in nature and favourable for the formation of some of the observed features like jet stream front, break of the northern tropopause across the core and CAT (clear air turbulence) zones in certain regions of a westerly jet stream.
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  • 103
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    Meteorology and atmospheric physics 29 (1980), S. 249-267 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Mit Verwendung von in der zweiten Phase der Venezueler internationalen meteorologischen und hydrologischen Experimente (VIMHEX-1972) gesammelten Radar-Daten wurde eine Klassifikation von Unwettern in Böenlinien, in Gewittergruppen und in isolierten Gewittern vorgenommen. Die Verhältnisse in der nahen Umgebung während des Vorrückens dieser Typen von Unwetter werden untersucht. Die Modifikation der Umgebung wird, abgeleitet aus der trocken-statischen Energie, aus der feucht-statischen Energie, aus dem latenten Wärmegehalt und aus den relativen Winden, ebenfalls studiert und ein für die Unwetter entwickeltes Modell wird vorgelegt. Schließlich werden einige Aspekte der Bewegung der Unwettergebilde beschrieben.
    Notes: Summary A classification of storms in squall lines, thunderstorm clusters, and isolated thunderstorms was made using radar data collected during the second phase of the Venezuelan International Meteorological and Hydrological Experiments (VIMHEX-1972). The near-environmental conditions in advance of these types of storms are examined. The modification of the environment, as deduced from the dry static energy, moist static energy, latent heat content and relative winds is also studied, and a conceptual model for the storms is presented. Finally, some aspects of storm movement are described.
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  • 104
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    Meteorology and atmospheric physics 29 (1980), S. 235-247 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Die Untersuchung wurde an einem äquivalenten barotropen Modell zum Studium der Stabilität des meridionalen Windes im 200 mb-Niveau im Sommer in den Tropen durch-geführt. Das von Wiin-Nielsen für mittlere Breiten eingeführte äquivalente Modell wurde mit einigen Änderungen auch für die Tropen angenommen. Es wurde gefunden, daß der meridionale Wind einer Anzahl von überlagerten Rossby-Wellen äquivalent ist, so daß sich das Stabilitätsproblem der meridionalen Strömung auf das Stabilitätsproblem von Rossby-Wellen zurückführen läßt. In der vorliegenden Untersuchung wurde die Stabilität einer Rossby-Welle mit einer Störung, die einen zonalen Wind ergibt, geprüft. Es wurde gefunden, daß kurze Rossby-Wellen instabil sind, so daß die kurzen Rossby-Wellen ihre kinetische Energie auf den zonalen Wind übertragen. Das von Lorenz hinsichtlich der Instabilität der Rossby-Welle für mittlere Breiten gewonnene Ergebnis wurde mit dem äquivalenten barotropen Modell verbessert.
    Notes: Summary The present study is conducted in the equivalent barotropic model to study the stability of meridional wind at 200 mb level in tropics during summer. The equivalent barotropic model, which was introduced by Wiin-Nielsen [1] for midlatitude, is accepted for tropics after some possible changes. The meridional wind is found to be equivalent to a number of superposed dispersive Rossby waves, so the stability problem of meridional flow reduces to the stability problem of Rossby waves. In the present study, the stability of single Rossby wave is tested with a perturbation which gives zonal wind. It is found that the short Rossby waves are unstable, so the short Rossby waves release their kinetic energy to the zonal wind. Thus, the short waves of the spectral meridional flow release their kinetic energy to the zonal wind. For midlatitude, Lorenz's problem regarding the instability of Rossby wave is improved using the equivalent barotropic model.
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  • 105
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    Meteorology and atmospheric physics 29 (1980), S. 279-299 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Es werden die monatlichen und jahreszeitlichen Mittel, die Extreme und die Veränderlichkeit des Meereises der Süd-Hemisphäre aufgrund 5jähriger Beobachtungen untersucht. Seine Veränderlichkěit ist am größten in den geographischen Längen der Küsteneinbuchtungen der Antarktis; es wurde auch eine kleine aber allgemeine Abnahme seiner Ausdehnung in allen Jahreszeiten dieser Beobachtungsperiode festgestellt. Zum Maximum der Eisausdehnung (Juli bis November) nimmt das 5jährige Mittel der zonalen Westwinde im Norden des Eises mit zunehmender Eisausdehnung zu; in einzelnen Jahren besteht jedoch zum Maximum der Eisausdehnung keine deutliche Korrelation zwischen der zonal gemittelten Eisausdehnung und der Stärke der zonalen Westströmung im vorhergehenden oder folgenden Monat. Der Vergleich mit dem 5jährigen Mittel der Längenverteilung der atmosphärischen Druck-Maxima und Minima in der Breite des antarktischen Trogs weist allgemein auf Asymmetrien im Eisrand hin, derart, daß er in Gebieten mit häufigem Tiefdruck weiter nördlich liegt und veränderlicher ist und in Gebieten mit relativ hohem Druck weiter südlich liegt. Die Untersuchung einer spezifischen Längenzone zeigt, daß die Verteilung der Eisausdehnung deutlich regional ist und offenbar mit Änderungen in der kombinierten ozeanischen und atmosphärischen Zirkulation in den antarktischen Einbuchtungen in Beziehung steht.
    Notes: Summary The monthly and seasonal means, extremes and variability of the Southern Hemisphere sea ice are examined for a five year period. Its variability is found to be greatest in the longitudes of the Antarctic coastal embayments, and a small but general decline in extent at all seasons throughout the period is observed. At near maximum ice extent (July to November), the 5 year mean of the zonal westerlies to the north of the ice increases with increasing ice extent; however for individual years, at maximum ice extent, there is no clear correlation between zonally averaged ice extent and the strength of the zonal westerlies in the preceding or succeeding month. Comparison with the 5 year mean longitudinal pattern of atmospheric pressure maxima and minima at the latitude of the Antarctic trough points generally to asymmetries in the ice edge, such that it is further north and more variable in regions of frequent low pressure, and further south in regions of relatively high pressure. Examination of a specific longitudinal zone indicates that the pattern of ice extent is clearly regional, and apparently related to variations in the combined oceanic and atmospheric circulation particularly in the Antarctic embayments.
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  • 106
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    Meteorology and atmospheric physics 29 (1980), S. 327-332 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Die Maximalwellen energiereicher Erdbeben mit Herd in der oberen Kruste rufen im äußeren Schütterbereich häufig Resonanzeffekte hervor, die eine örtliche Steigerung der Bebenintensität zur Folge haben. Eine Bewertung solcher Intensitäten nach den gebräuchlichen makroseismischen Skalen ist derzeit nicht möglich. Geht man davon aus, daß die primären Bebenwirkungen an der Erdoberfläche eine Folge der vom Bebenherd abgestrahlten Schwingungsenergie sind und daß die makroseismische IntensitätI (oMSK oder MM) ein logarithmisches Maß für die Bebenwirkungen ist, dann gilt offenbarI=log10 E+const, wennE die örtliche Energiestromdichte (Flächendichte der seismischen Energie) ist. Während im Epizentralbereich wegen der Unregelmäßigkeit der Erdstöße ausgeprägte Resonanzeffekte fehlen, muß man in herdfernen Gebieten, wo die Sg-Maximalwellen des Bebens schon weitgehend harmonisch sind, bei schwingungsanfälligen dünnen Bodenschichten und/oder Bauwerken mit entsprechender Eigenperiode Resonanzschwingungen erwarten, die eine Anhebung der lokalen Bebenintensität um ΔI (oMSK oder MM) bewirken. Mit Hilfe von empirischen Näherungsformeln kann man zu einer Abschätzung dieser Intensitätssteigerung kommen. Sie beträgt ΔI=0,28M s+0,4, mitM s als Oberflächenwellen-Magnitude. Die von der Epizentraldistanz und Magnitude abhängigen Resonanzfrequenzen liegen in der Regel zwischen 0,5 und 2 Hz. Die denkbare Intensitätssteigerung durch Resonanz im Falle eines Bebens der Magnitude 4,0 (7,0) liegt bei 1,5° (2,4°) MSK oder MM. Daraus folgt z. B., daß viele der in Hochhäusern bemerkten und mitI=IIo bewerteten Beben eigentlich mitI=Io zu klassifizieren sind und daß das Anschlagen kleiner Glocken oder das Stehenbleiben von Pendeluhren am Rande des Schüttergebietes eines energiereichen Bebens nichtI=Vo (−VIo), sondernI=IIIo (−IVo) entspricht. Die 12teiligen makroseismischen Skalen sind daher in entsprechender Weise zu ergänzen.
    Notes: Summary In the epicentral area of an earthquake with the focus within the upper crust the rocking is irregular and therefore resonance effects are lacking, but far off the hypocentre, where theSg maximum waves are nearly sinusoidal, thin layers of soil and/or buildings with an appropriate natural period react with resonance oscillations, by which the local macroseismic intensity is increased by ΔI (oMSK or MM). The resonance frequencies — functions of magnitude and hypocentral distance — mostly range from 0.5 to 2 Hz. The increase of intensity can be assessed by the aid of the formula ΔI=0.28M s+0.4, found by the author (M s=surface wave magnitude). Hence, in case of an earthquake withM s=4.0 (7.0) the marginal increase of intensity by resonance amounts to 1.5° (2.4°) MSK or MM. This implies, e. g., that many earthquakes perceived in tall buildings and considered asI=IIo has to be classified asI=Ic correctly, and the ringing of small bells or the stopping of pendulum clocks in the outskirts of the shaken area of a strong earthquake corresponds toI=IIIo (−IVo), and not toI=Vo (−VIo). A valuation of such intensities by the aid of the usual macroseismic scales is not possible, and therefore these scales are to be supplemented in an appropriate way.
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  • 107
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    Meteorology and atmospheric physics 29 (1980), S. 67-87 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung In einem Artikel von Garrat ([5], S. 915), der sich zusammenfassend und kritisch mit der jüngsten Forschung über die aerodynamische Reibung über einer Wasseroberfläche auseinandersetzt, heißt es: “Die Auswirkungen des Fetches, der Dauer und der Unstetigkeit eines Windes sind unbekannt und verstecken sich wohl hinter der Streuung der experimentellen Resultate”. In unserem Artikel ist ein Versuch unternommen worden, vorhandene Resultate von Experimenten am Genfersee auf eine Fetchabhängigkeit zu untersuchen. Dabei wird eine funktionelle Beziehung zwischen dem lokalen Reibungs- oder Widerstandskoeffizienten,C 10, und einer Fetch-Reynoldszahl, (U 10 F)/ν, mit einer dimensionslosen Rauhigkeit,F/y 0, als Parameter vorgeschlagen. Weiter wird gezeigt, daß eine Beziehung zwischen dem Rauhigkeitsparameter und dem Seegang (ausgedrückt als signifikante Welle,H 1/3) möglich ist. Diese Studie sollte als Vorstudie angesehen werden; sie diente unter anderem als Grundlage für ein größeres aerodynamisches Projekt am Genfersee.
    Abstract: Résumé Dans un article récent sur le coefficient de frottement, Garrat ([5], p. 915) laisse supposer que «les effets du fetch, de la durée et de la variabilité du vent s'ils existent, demeurent obscurs dans la dispersion des données expérimentales». Dans cet article, on essayera d'analyser l'éventuelle dépendance du fetch sur les données obtenues au cours des campagnes de mesures sur le Léman. On admettra qu'une relation entre le coefficient de frottement local,C 10, et le nombre de Reynolds de fetch,(U 10 F)/ν, existe, avec la rugosité adimensionelle,F/y 0, comme paramètre. Puis on discutera de l'éventuelle relation entre le paramètre de rugosité et l'état de surface du lac (exprimé ici en fonction de la vague significative). Cette étude est à considérer plutôt comme un travail préliminaire à l'établissement d'un nouveau programme expérimental projeté sur le Léman.
    Notes: Summary In a recent review on the drag coefficient, Garrat ([5], p. 915) pointed to the fact that “The effect (if any) of the fetch, wind duration and unsteadyness remains obscure in this experimental data scatter”. The present paper makes an attempt to analyse, in the light of a fetch dependency, data which have been accumulated on the Lake of Geneva. Postulated is a possible functional relationship between the local drag coefficient,C 10, and a fetch Reynolds number, (U 10 F)/ν, with a dimensionless roughness,F/y 0, as parameter. Subsequently, a possible relationship between the roughness parameter and the sea state (expressed presently with the significant wave) is discussed. The present study should be considered as preliminary in as much as it served to establish another field programme on Lake Geneva.
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  • 108
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    Meteorology and atmospheric physics 29 (1980), S. 89-107 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Summary There are typical cloud configurations in satellite images which are produced and/or maintained mainly by vorticity. These are: comma, enhanced cumuli, wave in a frontalband, upper level low and the cloud spiral of a low. Looking at satellite images there can be observed sometimes an increase sometimes a decrease during the further development of the cloud systems. The type of further development is also dependent on the value of the associated vorticity. In this paper there is examined the relationship between cloud systems and vorticity and there are investigated thresholds of vorticity. Are these thresholds, which are different for the different cloud systems, exceeded, one can conclude — with a certain degree of probability — that cloud systems will increase (that means a further weather activity). Are the thresholds not exceeded one can expect a decrease of the cloud systems.
    Notes: Zusammenfassung Es gibt typische Bewölkungskonfigurationen, die überwiegend durch Vorticity produziert und/oder aufrecht erhalten werden. Dazu gehören: Komma, enhanced Cumulibewölkung, Welle im Frontalband, Höhentief und Kern eines Tiefdruckwirbels. Aus Satellitenbildern kann beobachtet werden, daß sich die Bewölkungssysteme manchmal während ihrer Entwicklung verstärken, manchmal abschwächen. Die Art der Weiterentwicklung hängt unter anderem von der Stärke der zugeordneten Vorticity ab. In dieser Arbeit werden die Zusammenhänge zur Vorticity untersucht und Schwellwerte der Vorticity aufgestellt. Werden die Schwellwerte, die für die einzelnen Systeme verschieden sind, überschritten, so kann mit einer bestimmten Wahrscheinlichkeit auf Verstärkung (weitere Wetterwirksamkeit) geschlossen werden. Werden die Schwellen unterschritten, kann Abschwächung des Systems angenommen werden.
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  • 109
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    Meteorology and atmospheric physics 29 (1980), S. 119-130 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Eine Analyse einer großen Zahl von Groß-Regenfällen in Verbindung mit tropischen Depressionen, Zyklonen und schweren Unwettern hat ergeben, daß Groß-Regenfälle im September 1880 und im Juli 1927 über die Niederung des Landes die größten Flächenniederschlagshöhen in Indien brachten. Diese Rekord-Niederschlagshöhen wurden für verschiedene Flächengrößen und Andauern bestimmt und mit ähnlichen Rekord-Flächenniederschlagshöhen über dem tropischen Gebiet der USA verglichen. Diese Untersuchung hat gezeigt, daß für Andauern von zwei und drei Tagen die Rekord-Flächenniederschlagshöhen in Indien größer waren als in den USA. Für die Andauer von einem Tag waren bis zu einer Fläche von 5180 km2 (2000 Quadratmeilen) diese Flächenniederschlagshöhen in den USA größer, für größere Flächen waren sie aber in Indien entweder größer oder nahezu gleich wie in den USA.
    Notes: Summary On the basis of analysis of a large number of rainstorms associated with tropical disturbances such as depressions, cyclonic storms and severe storms, it has been found that September, 1880 and July, 1927 rainstorms over the plain areas of the country gave the highest areal rain depths in India. These rain depths have been worked out for different areas and durations and have been compared with the similar areal rain depths over the tropical region of USA. This study has shown that for durations of 2 and 3 days, Indian areal rain depths have been higher in magnitude when compared to USA rain depths. For one-day duration, upto 5180 sq.km (2000 sq.miles) area, USA areal rain depths are greater, while for larger areas Indian rain depths are either higher or almost equal with that of USA.
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    Meteorology and atmospheric physics 29 (1980), S. 131-141 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Während der Monsun-, Premonsun- und Postmonsunzeiten über der tropischen Station Calcutta bei Gewittern auftretende Atmospherics zeigen einige typische Charakteristiken. In allen Fällen ist ein stufenweises Ansteigen (GRA) und ein gleichmäßiges Abklinge (SRA) der Atmospherics festgestellt worden. Zwischen diesen zwei Änderungen tritt eine plötzliche Steigerung der Atmospherics (SEA) auf, die manchmal aus zwei Komponenten SEA1 und SEA2 zusammengesetzt ist. Diese bei 10 und 20 kHz beobachteten Tatbstände der integrierten Feldintensität der Atmospherics (IFIA) wurden in ihrer Beziehung zu Monsun-, premonsunalen und postmonsunalen Gewittern kritisch untersucht. Die Ergebnisse zeigen, daß der Niederschlag während der Monsun- und postmonsunalen Gewitter mit dem gleichmäßigen Rückgang der IFIA verbunden ist, während er bei den premonsunalen Gewittern mit der zweiten plötzlichen Steigerung der Atmospherics in Verbindung steht. Diese Anomalien wurden mit Ladungstrennungen in Gewittern in Zusammenhang gebracht. Ferner wurden auch die Unterschiede der entsprechenden Amplituden bei 10 und 20 kHz bei den verschiedenen Variationen der IFIA kritisch untersucht.
    Notes: Summary Thunderstorm associated atmospherics during the monsoon, premonsoon and postmonsoon seasons over the tropical station Calcutta show some typical characteristics. In all the cases gradual rise of atmospherics (GRA) and steady recovery of atmospherics (SRA) have been found. In between the above two changes, there is the sudden enhancement of atmospherics (SEA) which is some times composed of two components SEA1 and SEA2. All the above facts of the integrated field intensity of atmospherics (IFIA) observed at 10 and 20 kHz have been critically examined here in relation to monsoon, premonsoon and postmonsoon thunderstorms. The results exhibit that the precipitation is associated with the steady recovery of IFIA during the monsoon and postmonsoon thunderstorms while that during premonsoon thunderstorms is associated with the second sudden enhancement. These anomalies have been interpreted in terms of charge separation within thunderclouds. Moreover, the difference of the respective amplitudes at 10 and 20 kHz of the different variations of IFIA have also been critically focussed.
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    Meteorology and atmospheric physics 29 (1980), S. 157-165 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Eine mit der H-N-Methode durchgeführte numerische Berechnung hat die Existenz einer zyklonalen elliptischen Zelle im inneren Teil des Liguirischen Meeres ergeben. Dieses Resultat ist in Übereinstimmung mit dem auf einer Kreuzfahrt im März 1952 im selben Gebiet experimentell entdeckten Wirbel. Es wurde der Einfluß der seitlichen Küstenbergrenzungen am nordöstlichen Zugang zum Becken des Tyrrhenischen Meeres in Rechnung gezogen und die Annahme südlicher Winde als treibenden Mechanismus für diesen Wirbel besprochen.
    Notes: Summary A numerical calculation computed by the H-N method has shown the existence of a cyclonic elliptic cell in the inner part of the Ligurian Sea. This result agrees with an experimental vortex discovered in the same area during a cruise in March 1952. The influence of the lateral coastal boundaries at the north-eastern entrance of the basin into the Tyrrheinian Sea has been taken into account and the hypothesis of southerly winds as the forcing mechanism of this vortex has been discussed.
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    Meteorology and atmospheric physics 29 (1980), S. 167-178 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Summary Seismic and gravimetric measurements as well as investigations of the orientation of joints were made in the basin of Horn in Lower Austria. In this region, Tertiary sediments overlie mica-schists and phyllites of the Bohemian Massif. The investigations show that the top of the basement can be found with great accuracy by the geophysical methods employed. It is also seen that the joint orientations in the Bohemian Massif correspond to those expectable from the action of the regional “European” neotectonic stress system.
    Notes: Zusammenfassung Im Horner Becken (Niederösterreich) wurden Kluftmessungen, gravimetrische Aufnahmen und seismische Messungen durchgeführt. In dieser Gegend liegen tertiäre Ablagerungen auf Glimmerschiefern und Phylliten der Böhmischen Masse. Die Arbeit zeigt, daß die Anwendung geophysikalischer Methoden die Grenze und den Verlauf des Grundgebirges mit hoher Genauigkeit feststellen läßt. Weiters ist ersichtlich, daß auch in der Böhmischen Masse die Kluftstellungen dem großräumigen neotektonischen Spannungsfeld entsprechen.
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    Meteorology and atmospheric physics 29 (1980), S. 179-191 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Summary A new method is described in determining the anisotropic character of rocks concerning its fabric and its electrical properties. Low frequency capacities and high frequency conductivities of brine-saturated rocks and pure electrolytes are used to measure the electrical and fabric characteristics of anisotropic rocks.
    Notes: Zusammenfassung Gefügeelektrische Parameter von Gesteinen werden unter Verwendung von Kapazitätsbestimmungen bei Niederfrequenz und durch Leitfähigkeitsmessungen bei hohen Frequenzen ermittelt. Diese Untersuchungen werden einerseits an Gesteinsproben, andererseits an reinen Elektrolytlösungen, die zum Sättigen von Gesteinsproben dienen, vorgenommen. Dabei konnten Anisotropieerscheinungen beobachtet werden.
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    Meteorology and atmospheric physics 29 (1980), S. 143-155 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Summary The device consists of a narrow-band active receiving antenna with two separate antenna bodies for the frequencies of 10 and 27 kHz, respectively. Each body contains a block of ferrite rods with a wire coil and condensers, a fully integrated signal amplifier, an impedance transformer and an electronic thermostat. The received atmospherics impulses are conducted to a signal processor. Here they are transformed to pulses of constant amplitude which are summed up and stored in a sample-and-hold-circuit. After every ten pulses the storage circuit is automatically discharged. The device can separate strong periodical interference pulses from the statistically occurring natural atmospherics and eliminate them. It can also indicate signals originating from blizzards as high narrow peaks. Some examples of registered patterns of atmospherics in different weather situations are shown.
    Notes: Zusammenfassung Die Anlage besteht aus einer schmalbandigen aktiven Empfangsantenne mit zwei getrennten Antennenkörpern für die Empfangsfrequenzen 10 und 27 kHz. Jeder Antennenkörper enthält einen Block von Ferritstäben mit Drahtwicklung und Kondensatoren, einen vollintegrierten Signalverstärker, einen Impedanzwandler sowie einen elektronischen Thermostaten. Die empfangenen Atmospherics-Impulse werden in einer Signalverarbeitungsanlage zu Impulsen konstanter Amplitude verformt und in einer Speicherschaltung (Sample-and-Hold-Schaltung) aufsummiert. Nach Eingang von jeweils 10 Impulsen wird der Speicher automatisch entladen. Die Anordnung hat ferner die Eigenschaft, starke periodische Störimpulse von den stochastischen Atmospherics-Signalen der Natur zu trennen und zu unterdrücken sowie Blitzsignale als hohe Spitzen erkennbar werden zu lassen. Einige Registrierbeispiele zeigen die bei verschiedenen Wetterlagen auftretenden Impulsmuster.
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    Meteorology and atmospheric physics 29 (1980), S. 193-196 
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    European journal of nutrition 19 (1980), S. 66-68 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
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    European journal of nutrition 19 (1980), S. 69-69 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
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    European journal of nutrition 19 (1980), S. 95-102 
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    European journal of nutrition 19 (1980), S. 145-145 
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    European journal of nutrition 19 (1980), S. 154-158 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Notes: Summary The role of pH on tissue alkaline phosphatases have been investigated in different human tissues. Different isoenzymes have been observed in different organs. Bone and liver were similar in having the isoenzymes optimally active at 9.4 and pH 9.9. The kidney has a single alkaline phosphatase optimally active at pH 9.2, while the adrenal gland has two isoenzymes of optimum pH 9.2 and 10.1. Intestinal alkaline phosphatase was optimally active at pH 9.7.
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    European journal of nutrition 19 (1980), S. 159-162 
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    Notes: Summary Boulti fish (Tilapia nilotica Linn.) from Naser's lake in Aswan was converted to a ready marketable product (paste) in aluminium tubes. The quality of the product was ascertained by chemical indices. The product has a good flavour and can be kept for 5 weeks without undesirable changes. It is concluded that the production of fish paste in aluminium tubes is one of the possibilities of converting fish to precooked product.
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    Notes: Summary R.B.C.'s amino acid pattern was investigated in control and PEM subjects. The effect of oral dosing with cysteine, tryptophan and lysine on total amino acid nitrogen level of R.B.C.s was also studied. Results revealed that in moderate and severe kwashiorkor the total essential and non-essential R.B.C.'s amino acids were decreased. In 2nd grade marasmus the total R.B.C.'s amino acids in general showed lower values than normal. After oral administration of the tested amino acids, the transport index calculated as the level of maximum value of the total R.B.C.'s amino acids reached to the fasting level was lower in malnourished cases relative to controls except in 2nd grade marasmic cases given tryptophan or lysine. This criteria was considered to indicate lower rate of amino acid transport to R.B.C.s due to lower concentration in plasma or shift of transport mechanism from active transport to exchange diffusion.
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    OR spectrum 1 (1980), S. 143-168 
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    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Die Elemente der Modellierungskonzeption System Dynamics werden beschrieben und anhand von zwei einfachen Lager- und Produktionsplanungsmodellen demonstriert. Nach der Darstellung des Aufbaus eines implementierten System Dynamics Modells wird die Anwendbarkeit dieses Modellierungskonzeptes kritisch analysiert.
    Notes: Summary The fundamentals of the modelling approach System Dynamics are described and illustrated by two simple inventory and production planning models. After discussing the structure of an implemented System Dynamics model the applicability of this modelling approach is critically analysed.
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    OR spectrum 1 (1980), S. 169-181 
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    Description / Table of Contents: Summary This paper discusses a heuristic algorithm for solving a special scheduling problem: the assignment of a set of ships to a set of routes under specific complex restrictions. The usefulness of the resulting schedule is demonstrated by comparisation with a given schedule for container ships in the Europe — Australia — NewZealand service.
    Notes: Zusammenfassung In der vorliegenden Arbeit wird ein heuristisches Verfahren zur Lösung eines besonderen Reihenfolgeproblems behandelt: die Zuordnung einer Menge von Schiffen zu einer Menge von Routen unter besonderen, komplexen Bedingungen. Die Brauchbarbeit des sich ergebenden Fahrplans wird durch Vergleich mit einem gegebenen Fahrplan für Container-Schiffe im Liniendienst zwischen Europa und Australien/Neuseeland veranschaulicht.
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    OR spectrum 1 (1980), S. 183-198 
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    Description / Table of Contents: Summary Personnel expense planning is of great importance within big enterprise corporate planning. Orientation points are given from total economic development and from the market. The task is to find out personnel expense depending on personnel figures, work time requirement, etc. by implementation of a general matrix model. Non linear components are includet. The model runs in routine.
    Notes: Zusammenfassung Die Personalaufwandsplanung hat für die Unternehmensplanung eines Großunternehmens besondere Bedeutung. Orientierungspunkte dabei sind die gesamtwirtschaftliche Entwicklung und die Absatzmarktlage. Aufgabe ist die Ermittlung des Personalaufwands in Abhängigkeit von Belegschaftszahlen, Arbeitszeitbedarf usw. mit Hilfe eines allgemeinen Matrizenmodells, das auch nichtlineare Komponenten enthält. Das Modell ist routinemäßig im Einsatz.
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    OR spectrum 1 (1980), S. 209-209 
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    OR spectrum 1 (1980), S. 207-209 
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    OR spectrum 1 (1980), S. 210-210 
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    Description / Table of Contents: Zusammenfassung Diese Arbeit untersucht die Parameter-Abhängigkeit von Ergebnissen kriegerischer Auseinandersetzungen zweier homogener Gegner (insbesondere Vernichtung eingesetzter Kräfte), die mit Gleichungen der Lanchester-Theorie mit zeitabhängigen Verlustraten modelliert werden. Es wurde gezeigt, daß die Vorhersage der Vernichtung von Kräften von sogenannten Paritätsbedingungen nur von Verlustraten abhängen. Neue wichtige Ergebnisse geben Auskunft, wie diese Paritätsbedingungen von der Kampfintensität und der relativen Feuereffektivität der Gegner abhängen. Bisherige analytische Ergebnisse des Autors können Anwendung in einer viel umfangreicheren Art von Verlustraten finden. Diese neuen Ergebnisse erlauben es, daß eine umfangreiche Art von Gleichungen der LanchesterTheorie moderner Kriegsführung mit zeitlicher Feuereffektivitätsveränderung beinahe so leicht untersucht werden können, wie das klassische Modell von Lanchester mit konstanter Verlustrate.
    Notes: Summary This paper studies the parametric dependence of battle outcome (in particular, force annihilation) for combat between two homogeneous forces modelled by Lanchester-type equations of modern warfare with time-dependent attrition-rate coefficients. Force-annihilation prediction has been shown to depend on a so-called parity-condition parameter, which depends on only the attrition-rate coefficients. New important results are given on how the parity-condition parameter depends on the intensity of combat and the relative fire effectiveness of the combatants. Previous analytical results of the author are shown to apply to a much wider class of attrition-rate coefficients. These new results allow a wide class of Lanchester-type equations of modern warfare with temporal variations in fire effectiveness to be studied almost as easily as Lanchester's classic constant-coefficient model.
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    OR spectrum 1 (1980), S. 211-232 
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    Description / Table of Contents: Summary This article gives an overview on the mathematical methods of cluster analysis. It describes algorithms for constructing homogeneous classes of objects, several criteria for the evaluation of classifications, and some examples of application.
    Notes: Zusammenfassung Dieser Artikel gibt einen Überblick über die mathematischen Methoden der Clusteranalyse. Er berichtet über Algorithmen zur Konstruktion von homogenen Objektklassen, über Verfahren zur Bewertung von Klassifikationen sowie über praktische Anwendungsfälle.
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    OR spectrum 1 (1980), S. 243-249 
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    Description / Table of Contents: Summary Selected real-world nonlinear programming applications are presented that have arisen in different industries, namely food, electric utility, insurance and engineering. The models belong to the class of all-quadratic programs, that is, a quadratic function is to be minimized subject to quadratic constraints. The problems are solved by means of computer software for the Sequential Unconstrained Minimization Technique (SUMT) and for Geometric Programming.
    Notes: Zusammenfassung Es wird über einige ausgewählte Anwendungen der nichtlinearen Programmierung berichtet, die in unterschiedlichen Wirtschaftszweigen aufgetreten sind, nämlich in der Nahrungsmittelindustrie, in der Energieversorgungswirtschaft, in der Versicherungswirtschaft und im Maschinenbau. Die Modelle gehören der Klasse der ganz-quadratischen Programme an, d.h. eine quadratische Zielfunktion ist zu minimieren unter quadratischen Nebenbedingungen. Die Optimierungsprobleme werden mit Hilfe von Computersoftware für die Sequential Unconstrained Minimization Technique (SUMT) und für die Geometrische Programmierung gelöst.
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    OR spectrum 1 (1980), S. 233-242 
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    Description / Table of Contents: Zusammenfassung Wir betrachten Markoffsche Entscheidungsprozesse mit endlichem Zustands- und Aktionenräumen für das Kriterium des Durchschnittsertrags. Wir untersuchen die Methode der wertorientierten sukzessiven Approximation, die für das Kriterium des Gesamtertrags von Van Nunen ausführlich untersucht wurde. Unter einer starken Aperiodizitätsbedingung und verschiedenen Voraussetzungen, die eine Unabhängigkeit des optimalen Durchschnittsertrages vom Anfangszustand garantieren, beweisen wir die Konvergenz der Methode.
    Notes: Summary We consider the Markov decision process with finite state and action spaces at the criterion of average reward per unit time. We study the method of value oriented successive approximations, extensively treated by Van Nunen for the total reward case. Under a strong aperiodicity assumption and various conditions which guarantee that the gain of the process is independent of the starting state we show that the method converges and produces nearly optimal policies.
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    OR spectrum 1 (1980), S. 261-264 
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    Description / Table of Contents: Summary In network applications the problem of sensitivity often is of great practical interest. The aim of this paper is to provide indices of sensitivity for the arcs and vertices of a network, depending on the number of paths running through. In connection with a powerful algorithm for computing these numbers, the indices will be useful for considerations of sensitivity.
    Notes: Zusammenfassung Sensitivitätsbetrachtungen in Netzen sind in vielen praktischen Anwendungsfällen von großem Interesse. In dieser Arbeit werden für die Knoten und Kanten eines Netzes Sensitivitätsindices angegeben, die auf der Anzahl der durch sie verlaufenden Wege des Netzes basieren. Zusammen mit einem leistungsfähigen Algorithmus zur Berechnung dieser Anzahlen stellen diese Indices ein brauchbares Mittel für Sensitivitätsbetrachtungen in Netzen dar.
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    Description / Table of Contents: Summary This contribution describes the solution of an one-dimensional cutting problem in the context of a production control system. The solution of the cutting problem is demonstrated at the example of the production of central heating radiator units. The procedure is subdivided in an initial heuristic phase in order to concentrate the problem description. Afterwards an optimization phase is added to find the best solution of the reduced problem by using Linear Programming. Test results of field experiences are given. The last part of the contribution shows the integration of this solution in the global material and machine planning and control moduls. This is done by the determination of the interfaces of the batch oriented production control system and the process control of an NC saw machine.
    Notes: Zusammenfassung In diesem Beitrag wird am Beispiel der Produktion von Radiator-Heizungskörpern die Lösung des Zuschnittproblems der Vor- und Rücklaufrohre mit einem heuristisch-optimierenden Verfahren dargestellt. Die heuristische Vorschaltphase des Verfahrens ermöglicht bei geschickter Wahl der Kriterien eine Reduktion der Dimension des Verschnittproblems, ohne die Lösungsgüte unzulässig einzuschränken. Im Rahmen der reduzierten Problembeschreibung folgt anschließend die Optimierungsphase durch Anwendung der Linearen Programmierung. Es werden Testergebnisse im praktischen Einsatz des Verfahrens beschrieben. Weiterhin wird die Betrachtung der Integration des Verfahrens in ein globales EDV-gestütztes Produktionsplanungs- und -steuerungssystem behandelt, indem die Schnittstellen in der Material- und Terminbewirtschaftung zwischen dem stapelorientierten Planungskonzept und der Prozeßkontrolle einer NC-Sägeanlage definiert werden.
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    OR spectrum 1 (1980), S. 265-265 
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    OR spectrum 1 (1980), S. 270-270 
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    OR spectrum 1 (1980), S. 271-272 
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    OR spectrum 1 (1980), S. 272-272 
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    OR spectrum 2 (1980), S. 79-89 
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    Description / Table of Contents: Zusammenfassung In einer Simulationsstudie werden mehrere hierarchische Methoden zur Produktionsplanung und Lagerhaltung untersucht, die zusammen mit der Materialbedarfsplanung eingesetzt werden können. Die verwendeten Daten stammen aus einem Unternehmen, dessen Endprodukt eine komplexe Struktur besitzt. In dem zunächst gebildeten aggregierten Modell werden alle Teilprodukte zu einer Produktgruppe und alle Maschinen zu einer Maschinengruppe zusammengefaßt. Mit Hilfe verschiedener Lösungsmethoden wurde dieses aggregierte Planungsproblem gelöst. Ausgehend von der Optimallösung des aggregierten Modells wird der detaillierte Produktionsplan in der Weise ermittelt, daß durch Variation der Freigabezeiten und durch Variation der Auftragsgrößen dieser an die Optimallösung möglichst gut angepaßt wird. Unsere Ergebnisse zeigen, daß sehr einfache hierarchische Planungsmethoden signifikante Kostenminderungen verglichen mit einer Materialbedarfsplanung auf der Basis prognostizierter Nachfragen ergeben können.
    Notes: Summary Hierarchical planning methods which can be utilized in connection with material requirements planning have been evaluated in a simulation study. Data have been obtained from a company producing one final product having a complex structure. In the aggregate model all items are aggregated into one product group and all machines into one machine group. Different solution methods have been used for solving the aggregate planning problem. The aggregate plan is disaggregated by adjusting the detailed production plans using two methods involving changes of order release times and changes of order quantities. Our results indicate that also very simple hierarchical planning processes can give significant cost reductions compared to using material requirements planning based on predicted demand.
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    Monatshefte für Mathematik 89 (1980), S. 1-8 
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    Monatshefte für Mathematik 89 (1980), S. 19-44 
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    Notes: Abstract A new proof of a theorem of W. Neiss is given that the rays of the Quadratwurzelschnecke are uniformly distributed mod 2 π. The exact order of the discrepancy of the sequence is determined. Multidimensional generalizations of this sequence are also considered. It is shown that the Quadratwurzelschnecke is something like a roulette.
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    Monatshefte für Mathematik 89 (1980), S. 45-56 
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    Notes: Abstract We continue our investigations started in a paper with the same title. The γ-length of a curve defined in this paper can be written as an integral along the curve. Furthermore, we determine necessary and sufficient conditions for the existence of a measure of orientated lines which generates a given non-symmetric pseudo-metric.
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    Monatshefte für Mathematik 89 (1980), S. 9-17 
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    Notes: Abstract The spaceG B of $$\bar B$$ -orbits of an [FIA] B − groupG is a commutative hypergroup (=commutative convo in Jewett's terminology). Its space of “hypergroup characters” is a hypergroup itself (see [3]) which can be identified withE (G, B) (the extreme points ofB-invariant positive definite continuous functionsp:G→ℂ withp (e)=1), endowed with the topology of compact convergence. We determine the structure space ofL 1 (E(G, B), μ PL ) whereμ PL is the Plancherel measure (which is the “Haar measure” ofE(G, B)) and characterize the convolution algebrasM (E(G, B)) andL 1 (E(G, B)) via the inverse Fourier-Stieltjes transformation.
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    Monatshefte für Mathematik 89 (1980), S. 57-67 
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    Notes: Abstract We prove that there exist in the Hilbert spacel 2 a lower semicontinuous convex function ϕ andu o such that the bounded and strong solutionu of the equation (d 2 u/dt 2) (t)∈∂ϕ (u(t)),t〉0,u(0)=u o is weakly but not strongly convergent inl 2 ast→+∞.
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    Monatshefte für Mathematik 89 (1980), S. 69-76 
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    Notes: Abstract Let Λ be a lattice inR n . Consider the systemS of unit spheres centered at the lattice points of Λ.S is called ak-fold lattice packing (covering) if each point inR n lies in at most (least)k of the open (closed) spheres ofS. Letd k n (D k n ) be the density of the closest (thinnest)k-fold lattice packing (covering) ofR n . After dealing several cases left by G. Fejes Tóth and A. Florian, we have concluded thatd k n 〉kd 1 n for all (n, k) (n≥2,k≥2) except (2, 2), (2, 3), (2, 4); andD k 3 〈k D 1 3 for allk≥2.
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    Monatshefte für Mathematik 89 (1980), S. 95-100 
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    Notes: Abstract The continued fraction expansions of a certain class of numbers of the form. $$u^{ - k_0 } \pm u^{ - k_1 } \pm u^{ - k_2 } \pm ...$$ have a definite pattern.
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    Monatshefte für Mathematik 89 (1980), S. 87-93 
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    Notes: Abstract All Convex Polytopes in ℝ 4 the Facets of Which Are Regular Tetrahedra. Continuing in ℝ n (n≥4) the study of convex polytopes the facets of which are regular, it is proved: Regular polytopes and the two bipyramids over the tetrahedron and the icosahedron are the only convex polytopes in ℝ4 the facets of which are regular tetrahedra.
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    Monatshefte für Mathematik 89 (1980), S. 101-109 
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    Notes: Abstract In this paper we consider special subdivisions ofK 4 in which some of the edges are left undivided. A best possible extremal-result for the case where the edges of a Hamiltonian path are left undivided is obtained. Moreover special subdivisions as subgraphs of 4-chromatic graphs are studied. Our main-result on 4-chromatic graphs says that any 4-critical graphG contains an odd cycleC without diagonals such thatG-V (C) is connected.
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    Monatshefte für Mathematik 89 (1980), S. 131-140 
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    Notes: Abstract In the main part of the paper thep-discrepancy of chains is studied. The paper is a continuation of [4].
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    Monatshefte für Mathematik 89 (1980), S. 121-129 
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    Notes: Abstract We prove that the periodic point measures are dense in the space or invariant measures for ergodic toral automorphisms.
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    Monatshefte für Mathematik 89 (1980), S. 111-120 
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    Notes: Abstract To measure the uniformity of such a distribution, a new notion of discrepancy (D LV) is studied, which combines two interesting features: 1) The infinite sequences, which are uniformly distributed (in the usual sense), are characterized byD LV→0 under rather general conditions on the space. 2) Forn points on the sphere,n∈{4, 6, 12},D LV attains its minimum for the vertices of a regular polyhedron.
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    Monatshefte für Mathematik 89 (1980), S. 141-162 
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    Notes: Abstract LetG be a locally compact group acting on a topological space. Here we define some boundedness conditions for the action. For a nondiscrete locally compact vector spaceV andg∈G L (V), layering structures forV and the projective spaceP (V) ofV are obtained. From the layering structures, we derive then density properties of subgroups ofG with boundedness conditions. We generalize the Borel density theorem and Prasad's theorem on automorphisms of algebraic semi-simple groups. Some new results onp-adic groups are added.
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    Monatshefte für Mathematik 89 (1980), S. 175-183 
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    Notes: Abstract The finite projective designs with rank 3 collineation groupsG such thatG p =G l for some point-block pair (P, l) are divided into 4 classes. 2 of these classes are formed by the Paley designs and the designs complementary to the Paley designs. For the other 2 classes restrictions on the parameters are obtained. In particular it is shown that the only such design having λ=1 is the projective plane of order 2.
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    Monatshefte für Mathematik 89 (1980), S. 185-204 
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    Notes: Abstract We study the problem under what conditions a cylindrical measure on a locally convex vector lattice is a Radon measure on the positive cone of the vector lattice. For some special vector lattices necessary and sufficient conditions are given. These results are applied to the construction of random measures on not necessarily locally compact state spaces.
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    Monatshefte für Mathematik 89 (1980), S. 171-174 
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    Monatshefte für Mathematik 89 (1980), S. 163-170 
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    Notes: Abstract The question whether there exist closed orthogonal polygons formed by generators of a given hyperboloid is a poristic problem: For a prescribed number 2n of sides there exists either no polygon of the required kind or an infinite continuous set of such polygons. After having led back the solution to the classic theorem of Poncelet, closure conditions are developed for the casesn=2, 3, 4, 5 and 6.
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    Monatshefte für Mathematik 89 (1980), S. 205-218 
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    Notes: Abstract We continue the investigation of [2]–[5]. It is shown that potentials of convolution semigroups are local pseudomeasures. We study positive and almost positive local pseudomeasures and give some examples and applications.
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    Monatshefte für Mathematik 89 (1980), S. 219-222 
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    Notes: Abstract Let $$R \subseteq \left\{ {1,2,...,m} \right\}$$ . LetG m (R) be the graph whose vertices are the numbers 1, 2, ...,m and whose edges are all pairs {a, b} such thata+b≡r (modm) for somer∈R. LetC m (R) be the number of connected components ofG m (R). Letd be the greatest common divisor ofm and the differencesr j −r j or allr i ,r j ∈R. ThenC m (R) is equal to (i) (d+1)/2 ifd is odd, (ii)d/2 ifd is even andr is odd for allr∈R, or (iii) (d/2)+1 ifd is even andr is even for allr∈R.
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    Monatshefte für Mathematik 89 (1980), S. 223-233 
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    Notes: Abstract This paper deals with estimates for the number of lattice points (i. e. points of the plane with integer coordinates) in the domains indicated above. For a wide class of real exponentsn andm the exact order of magnitude of the error term is determined and its behaviour for growingR is discussed.
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    Monatshefte für Mathematik 89 (1980), S. ii 
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    Monatshefte für Mathematik 89 (1980), S. 235-242 
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    Notes: Abstract A description is given of the lattice of all two-sided ideals of the fixed-point algebra of a product type action of a finite group on a UHF-algebra.
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    Monatshefte für Mathematik 89 (1980), S. 315-322 
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    Notes: Abstract It is proved that iff∈L 1(ℝ),f'∈L 1(ℝ) and ∫∣x∣ i ∣f(x)∣dx〈∞ fori=1, ...,k−1 and ifA=(a ij ) is a (k×k)-matrix with non-vanishing determinant, for $$\tilde f_A (\zeta ): = \smallint \exp (i\zeta _1 \sum\limits_{j = 1}^k {a_{1j} x^j } + ... + i\zeta _k \sum\limits_{j = 1}^k {a_{kj} x^j } )f(x)dx$$ the following relation holds: $$\tilde f_A (\zeta ) = O(\left\| \zeta \right\|)^{ - b_k } with b_k : = (\sum\limits_{j = 1}^k {j!)^{ - 1} } for k \in \mathbb{N}$$ .
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    Monatshefte für Mathematik 90 (1980), S. 91-100 
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    Notes: Abstract D. Shanks [11] has given a heuristical argument for the fact that there are “more” primes in the non-quadratic residue classes modq than in the quadratic ones. In this paper we confirmShanks' conjecture in all casesq〈25 in the following sense. Ifl 1 is a quadratic residue,l 2 a non-residue modq, ε(n, q, l 1,l 2) takes the values +1 or −1 according ton≢l 1 orl 2 modq, then $$\mathop {\lim }\limits_{x \to \infty } \sum\limits_p {\varepsilon (p,q,l_1 ,l_2 )} \log pp^{ - \alpha } \exp ( - (\log p)^2 /x) = - \infty$$ for 0≤α〈1/2. In the general case the same holds, if all zeros ϱ=β+yγ of allL(s, χ modq),q fix, satisfy the inequality β2−γ2〈1/4.
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    Monatshefte für Mathematik 90 (1980), S. 101-115 
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    Notes: Abstract In [9]H. Reiter introduced functions of translation type on a locally compact group to show some functorial properties of the spaceS (G) of Schwartz-Bruhat functions. We shall investigate functorial properties of the Segal algebraP 1 (G) which is defined by means of a more general version of functions of translation type without using a norm. Furthermore we shall introduce a new Segal algebraE 1 (G) that is closely related to these functorial properties.
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    Monatshefte für Mathematik 90 (1980), S. 185-194 
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    Notes: Abstract A surfaceM in a Riemannian manifold is said to have parallel normalized mean curvature vector if the mean curvature vector is nonzero and the unit vector in the direction of the mean curvature vector is parallel in the normal bundle. In this paper, it is proved that every analytic surface in a euclideanm-spaceE m with parallel normalized mean curvature vector must either lies in aE 4 or lies in a hypersphere ofE m as a minimal surface. Moreover, it is proved that if a Riemann sphere inE m has parallel normalized mean curvature vector, then it lies either in aE 3 or in a hypersphere ofE m as a minimal surfaces. Applications to the classification of surfaces with constant Gauss curvature and with parallel normalized mean curvature vector are also given.
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    Monatshefte für Mathematik 90 (1980), S. 207-218 
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    Notes: Abstract This paper is part of a program aiming at the classification of all higher-dimensional locally compact translation planes whose collineation groups have large dimension. In the present paper we determine all eight-dimensional locally compact translation planes which admit acompact collineation group Σ of dimension at least 5 acting almost effectively on the translation axis. In fact, Σ is isomorphic either to Spin4ℝ or toSO 4(ℝ). The case∑ ≅ Spin4(ℝ) has already been treated elsewhere ([6]). Here, the planes with∑ ≅SO 4(ℝ) are explicitly determined and studied in detail.
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    Monatshefte für Mathematik 90 (1980), S. 229-232 
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    Notes: Abstract Though we cannot improve on the upper bound in Dirichlet's approximation theorem,Kaindl has shown that the upper bound can be lowered fromt n tot n −t n−1−t n−2−...−t−1, if we admit equality. We show thatKaindl's upper bound is lowest possible in this case. The result is then generalized to linear forms.
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    Monatshefte für Mathematik 90 (1980), S. 219-228 
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    Notes: Abstract Motivated by an investigation ofKuz'min [2], in this note we introduce a topology on the set $$\mathfrak{A}_\gamma (F)$$ of nonassociative algebras of a fixed dimensionr〈∞ over a local fieldF. We obtain a space, which is notT 1. If the trivial algebra $$\mathfrak{A}_0^\gamma $$ is removed, the remaining subspace is quasicompact. The space is homeomoprhic to the group of square classes ofF *; forr≥3 the space is notT 1. The set of division algebras is open in .
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    Monatshefte für Mathematik 90 (1980), S. 233-235 
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    Notes: Abstract It is shown that certain invariant means are unique.
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    Monatshefte für Mathematik 90 (1980), S. 237-248 
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    Notes: Abstract Simultaneous interval elimination is considered in order to shorten the length of the interval containing the location of the maximum value of a strictly unimodal function on the unit interval. As well known, the optimal choice of the points of evaluation is not unique, if the maximum value of spacings is used as an objective function. It is shown in this note that the mean value gives unique optimal solutions.
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    Monatshefte für Mathematik 90 (1980), S. 267-289 
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    Notes: Abstract This paper deals with conditions under which a meromorphic function cannot satisfy any algebraic differential equation having coefficients in a given field of meromorphic functions. The conditions given involve the growth of the function, a representation for the function, or the sequence of zeros and poles of the function.
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    Monatshefte für Mathematik 90 (1980), S. 259-266 
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    Notes: Abstract For a latticeL, a∈L is a fixed point ofL if and only iff(a)=a for every automorphismf ofL. Let Aut (L) andS (L) denote the group of automorphisms ofL and the sublattice of fixed points ofL, respectively. It is shown that ifG is a finite group other thanZ 2 2 ,Z 2 3 ,Z 2 4 ,Z 3 2 or the quaternion group of order 8 andL is a finite automorphism free distributive lattice that is not near Boolean then there is a finite distributive latticeL′ such that Aut (L′)≇G andS(L′)≇L.
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    Monatshefte für Mathematik 90 (1980), S. 297-301 
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    Notes: Abstract An asymptotic expression for the difference between the extreme discrepancy and theL p -discrepancy of a sequence of points in thes-dimensional unit cube (0, 1] s ,s≥1, is given.
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    Monatshefte für Mathematik 90 (1980), S. 291-295 
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    Notes: Abstract Ifp≥2 is an integer, then every nonnegative integerk is represented by an expression of the form $$k = \sum\nolimits_{i = 0}^s {a_i (k)p^i } $$ with integersa i (k), 0≤a i (k)≤p−1,i=0.1,...,s. The “radical-inverse function” to the basep,Φ p (k), is defined by $$\Phi _p (k) = \sum\nolimits_{i = 0}^s {a_i (k)p^{ - i - 1} } $$ . The sequence $$\omega = (\Phi _p (k))_{k = 0}^\infty $$ is uniformly distributed modulo 1 (it may be called a one-dimensional Halton sequence). In the casep=2 it is the van der Corput sequence. The set of all numbers β∈(0, 1] such that the “local” discrepancy $$\sum\nolimits_{k = 0\chi _{\left[ {0\beta } \right)} }^{n - 1} {\left( {\Phi _p (k)} \right) - } n\beta $$ is bounded inn is determined.
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    Monatshefte für Mathematik 90 (1980), S. 311-313 
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    Notes: Abstract Generalizing results in [1], [3], [5], and [7] it is shown that the algebra generated by the quasi-regular representation λ of a discrete groupG onl 2 (G/H) satisfies a standard polynomial identity if and only if λ (G) contains an abelian normal subgroup of finite index. An analogon for topological groups is also proved.
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    Monatshefte für Mathematik 90 (1980), S. 303-309 
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    Notes: Abstract For a great class of Euler product functions (e. g. the Riemann ζ-function or the Ramanujan-functionL τ) it is shown by methods of uniform distribution that the equality $$(\mu ^{(n)} (U)^{l/n} )$$ holds for almost all Δ〉0. For countably many exceptional values of Δ there is a somewhat modified relation. This leads for all Δ〉0 to new results about the asymptotic behaviour of such a function on discrete sets.
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    Monatshefte für Mathematik 90 (1980), S. 331-337 
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    Notes: Abstract The paper gives a criterion for Buchsbaum modules over a local ringR which depends only on a finite system of elements ofR.
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    Monatshefte für Mathematik 90 (1980), S. 347-348 
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    Monatshefte für Mathematik 90 (1980), S. 315-329 
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    Notes: Abstract LetD n (x) be the discrepancy function of a sequence in [0,1) as defined in the first lines of the introduction. A well known result ofW. M. Schmidt states that limsup n→∞ sup x |D n (x)|/logn≥1/100 for every sequence. In this paper it is proved that for every sequence sup x |D n (x)|/logn≥1/100 for almost all values ofn. A more refined assertion is given in Theorem 1, a more general one in Theorem 2, while it is proved in Theorem 3 that these results are essentially the best possible. Another result ofSchmidt is that for every sequence limsup n→∞|D n (x)|/loglogn≥1/2000 for almost allx in [0, 1). In this paper it is shown that for every sequence limsup n→∞|D n (x)|/logn≥1/400 for almost allx in [0, 1). Theorem 4 contains a more refined and Theorem 5 a more general statement. Finally Theorem 6 implies that also these results are essentially the best possible.
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    Monatshefte für Mathematik 90 (1980), S. 339-345 
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    Notes: Abstract Several conditions are shown to be equivalent to the aperiodicity of a regular probability measure μ on a locally compact, separated topological GroupG. In particular, μ is aperiodic if and only if the sequence ( $$\mathop {\lim }\limits_{N \to \infty } N^{ - 1} \sum\limits_{n = 1}^N {|f(\sigma + i\Delta n)|^2 \mathop {\lim }\limits_{T \to \infty } T^{ - 1} \int\limits_0^T {|f(\sigma + it)|^2 } dt} $$ (μ (n) denoting then-th convolution power of μ) is convergent for any nonvoid open subsetU ofG with compact closure. It is always assumed that the support of μ generatesG as a closed semigroup.
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    European journal of nutrition 19 (1980), S. 47-49 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Zusammenfassung Nicht extrahierte und extrahierte Rosellesamen (Hibiscus sabdariffa L.) wurden zur Ermittlung von Feuchtigkeit, Rohprotein, ätherextrakt, stickstofffreiem Extrakt, Rohfasern, Asche, Calcium, Phosphor und Schwefel analysiert. Verdauungsversuche mit Hähnchen haben gezeigt: Verdaubares Rohprotein, gesamte verdaubare Nährstoffe, Stärkewert und kalkulierte Werte für metabolisierbare Energie für die nicht extrahierten Rosellesamen waren: 15,36%, 75,81%, 84,06% und 3184 kcal/kg entsprechend. Die entsprechenden Werte für die extrahierten Samen waren: 27,50%, 68,83%, 64,23% und 2891 kcal/kg. Iodnummer, Verseifungsnummer, Reichert-Meissel- und Polenske-Werte für Rosellesamen-öl waren: 15,63%, 258, 1,75 und 1,14 entsprechend.
    Notes: Summary Unextracted and extracted roselle seeds (Hibiscus sabdariffa L.) were analysed for determining moisture, crude protein, ether extract, nitrogen-free extract, crude fiber, ash, calcium, phosphorus and sulfur. Digestibility trials with cocks showed that the digestible crude protein, total digestible nutrients, starch value and calculated metabolizable energy for the unextracted roselle seeds were 15.36%, 75.81%, 84.06% and 3184 kcal/kg respectively, the corresponding values for the extracted seeds were 27.50%, 68.83%, 64.23% and 2891 kcal/kg. Iodine number, saponification number, Reichert-Meissel and Polenske values for the roselle seed oil were 15.63, 258, 1.75 and 1.14 respectively.
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    Notes: Summary In a group of Egyptian lead tank welders who were exposed to lead fumes for periods to 22 years the changes in serum lipids and some of the liver function tests which may elucidate the effect of lead on the liver were investigated. The results revealed increased blood lead level associated with decreased blood haemoglobin and increased urinary excretion of delta amino levulinic acid. However, no clinical abnormalities were recorded in the exposed group of the present work. Thus the increase in serum triglycerides and B-lipoprotein together with the lowering of the phospholipid/cholesterol ratio which were found may indicate premature development of atherosclerosis. Indirect evidence of the beginning of liver fattening was also provided by the increase in serum GOT, GPT, LDH enzymes and decreased albumin/globulin ratio besides the changes in serum lipid values. It is concluded therefore that lead poisoning may have a vascular as well as hepato-toxic action.
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    European journal of nutrition 19 (1980), S. 166-172 
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    Notes: Summary The changes induced by the deficiency of calories or nitrogen on the protein metabolism in rats were investigated. Animals were fed either a restricted normal diet, a protein-deficient diet or control dietad libitum. Rats receiving protein-free diet failed to grow, while the growth of animals given restricted diet was less than those fedad libitum. Despite that, the dietary deficiency of either calories or proteins caused the loss of protein and increased the incorporation of 1−C14 glycine into liver proteins. The contents of liver-free amino acids and urea were significantly increased only in the protein-deficient rats.
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    European journal of nutrition 19 (1980), S. 173-178 
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    Notes: Summary The effect of vitamin B12 on the metabolic alterations due to tetracycline toxicity was studied experimentally on laboratory animals. Treatment of Sprague-Dawley rats with 120 or 250 mg tetracycline (i.p.) per kg per day for two or three days caused an accumulation of lipids, mainly triglycerides in the liver of 75% of animals studied, while phospholipid level tend to decrease. These doses are approximately twice and four times the recommended maximum dose for man. In the present work no direct relationship was observed between dose of tetracycline and hepatic accumulation of triglyceride, although livers of rats treated with 250 mg tetracycline/kg appeared uniformly pale yellow. Elevated serum triglyceride was found predominantly in rats treated with 120 mg/kg, while there was no obvious difference between serum triglyceride of rats treated with 250 mg tetracycline and control rats, indicating a block in the release of hepatic triglycerides. Where protection by vitamin B12 was studied, the vitamin was given i.m. (50 μg/ animal) 3 hours before the injection of 120 mg tetracycline per kg. There was a good evidence that lipid abnormalities caused by tetracycline improved by vitamin B12. Thus both hepatic and serum total lipid and triglycerides were significantly lower than those of rats treated with tetracycline, although hepatic total cholesterol was significantly increased as in case of tetracycline only.
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    European journal of nutrition 19 (1980), S. 191-202 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Notes: Summary Defatted sunflower-seed meal, sunflower-seed protein concentrate and protein isolate were fed to protein-depleted chicks. The effect of the enrichment of meal and of protein isolate with lysine, methionine, or a mixture of both on the nutritional value was investigated. Sunflower-seed protein products are primarily limited in lysine. Food consumption, weight gain and protein/efficiency ratio reveal superior performance of lysine- or lysine- and methionine-enriched meal or protein isolate, as compared to the correponding non-enriched products. Methionine enrichment does not improve the nutritional quality and even result in inferior performance. Non-enriched protein isolate supports better growth than non-enriched meal specially at later stages of chick growth.
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  • 191
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    European journal of nutrition 19 (1980), S. 272-275 
    ISSN: 1436-6215
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Zusammenfassung Es wurde die Bestimmung von fünf Mineralien in den häufigsten ägyptischen Futtermitteln durchgeführt. Knochenmehl und Fischmehl haben den höchsten Calciumgehalt mit 33,43 % bzw. 9,25 %, während Weizen und andere Getreidearten die niedrigsten Werte besitzen: 0,04 % bzw. 0,02 %. Knochenmehl und Fleischmehl haben den höchsten Phosphorgehalt: 12,31 % bzw. 5,06 %, während Getreide und Weizenstroh die niedrigsten Werte haben: 0,26% und 0,23%. Fleisch- und Fischmehl haben den höchsten Schwefelgehalt, nämlich 0,89 % und 0,68 %, während Weizenstroh und Knochenmehl die niedrigsten Werte besitzen: 0,20% bzw. 0,18 %. Reis und Weizenkleie haben die höchsten Magnesiumwerte: 395,3 und 99,8 mg/kg. Den niedrigsten Gehalt zeigen Getreidekörner und Magermilchpulver, nämlich 7,2 und 3,1 mg/kg. Knochen- und Fleischmehl haben den höchsten Eisengehalt: 0,127 % bzw. 0,084 %, während Gerste und Magermilchpulver den niedrigsten Eisengehalt von allen Futtermitteln haben: 0,004 %.
    Notes: Summary Determination of five minerals for the more common Egyptian feedstuffs was conducted. Bone and fish meals contained the highest amounts of calcium, 33.43 and 9.25 %, while wheat and corn grains contained the lowest amounts, 0.04 and 0.02 %, respectively. Bone and meat meals contained the highest amounts of phosphorus, 12.31 and 5.06 %, while corn grains and wheat straw contained the lowest amounts, 0.26 and 0.23 %, respectively. Meat and fish meals contained the highest amounts of sulfur, 0.89 and 0.68 %, while wheat straw and bone meal contained the amounts of sulfur, 0.89 and 0.68 %, while wheat straw and bone meal contained the lowest amounts, 0.20 and 0.18%, respectively. Rice and wheat brans contained the highest amounts of manganese, 395.3 and 99.8 mg/kg, while corn grains and dried skim milk contained the lowest amounts, 7.2 and 3.1 mg/kg. Bone and meat meals contained the highest amounts of iron, 0.127 and 0.084 %, while barley and dried skim milk contained the lowest amounts, 0.004 for each feed material, respectively.
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  • 192
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    European journal of nutrition 19 (1980), S. 276-279 
    ISSN: 1436-6215
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary The activity of alkaline phosphatase in small intestine mucosa was increased by about 40% in rats adapted to a high fat diet in comparison to high-carbohydrate-adapted animals. As high fat-feeding leads to an increase in the intestine's capacity to absorb fat, this finding is consistent with the hypothesis that alkaline phosphatase in the small intestine epithelium plays a role in fat absorption.
    Notes: Zusammenfassung Bei fettreich gegenüber kohlenhydratreich ernährten Ratten wurden für die Aktivität der alkalischen Phosphatase der Dünndarmmucosa um ca. 40% höhere Werte gefunden. Dieser Befund steht mit der Hypothese im Einklang, da\ die alkalische Phosphatase des Dünndarmepithels bei der Fettresorption eine Rolle spielt, da fettreiche Ernährung auch zu einer Steigerung der Fettresorptionskapazität führt.
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  • 193
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    European journal of nutrition 19 (1980), S. 280-289 
    ISSN: 1436-6215
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary The influence of vitamin E (9, 90, 450 mg dl-α-tocopherol acetate/100 g diet), protein quality and temperature (70
    Notes: Zusammenfassung In Experimenten an Ratten wurde der Einflu\ der Verfütterung von unterschiedlichen Mengen roher bzw. hitzebehandelter (70
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  • 194
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    European journal of nutrition 19 (1980), S. 290-295 
    ISSN: 1436-6215
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary Caffeine is ingested not only with beverages as coffee, tea, coca-cola but also in form of many analgetic drugs. Therefore interactions of this substance with other biologically active substances and drugs should be expected, and the knowledge of these would be of practical importance. The interactions between caffeine and alcohol, smoking, salicylic acid, phenacetin, barbiturates, and theobromin are described.
    Notes: Zusammenfassung Coffein wird nicht nur in Getränken wie Kaffee, Tee, Coca-Cola, sondern auch in zahlreichen analgetisch wirkenden Mischpräparaten häufig aufgenommen. Aus diesem Grunde sind Wechselwirkungen dieser Verbindung mit anderen Wirkstoffen und Arzneimitteln zu erwarten und deren Kenntnis auch von praktischer Bedeutung. Es wird auf Wechselwirkungen zwischen Coffein und Alkohol, Rauchen, Salizylsäure, Phenacetin, Barbituraten, Nikotinsäure und Theobromin verwiesen.
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  • 195
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    European journal of nutrition 19 (1980), S. 296-301 
    ISSN: 1436-6215
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Notes: Summary Supramine, a food mixture produced in Egypt by El-Nil Pharmaceutical Company supported by UNICEF. The product suffers from two problems: It is not well liked by the children, and its shelf life is relatively short. Studies were made to overcome these problems. Pretreatment of the ingredients such as cooking, autoclaving or roasting markedly improved palatability of the product. Adjustment of the conditions of the enzyme action increased hydrolysis of the starchy material making the product more soft and digestable. Formulation of new mixtures gave the chance to the product to satisfy the wish of a wide sector of the consumers. The heat treatment made to the ingredients minimized contamination and prolonged shelf life of the product.
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  • 196
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    OR spectrum 2 (1980), S. 99-109 
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Summary Since 1977 it is legal in Germany to use sampling methods when taking the yearly inventory. This can lead to very substancial savings. Publications so far concentrate on the application of these methods to ending inventory. We, therefore, focus our considerations on applicability and procedural questions with respect to perpetual inventory taking.
    Notes: Zusammenfassung Seit 1977 ist die Verwendung mathematisch-statistischer Verfahren zur Durchführung der Inventur in Deutschland gesetzlich zugelassen. Die hierdurch möglichen Rationalisierungseffekte können sehr erheblich sein. Über die Anwendung dieser Verfahren bei der Stichtagsinventur liegen bereits eine Anzahl von Veröffentlichungen vor. Daher werden hier hauptsächlich Möglichkeiten und Probleme der Anwendung von Stichprobenverfahren bei der permanenten Inventur behandelt.
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  • 197
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    OR spectrum 2 (1980), S. 118-119 
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
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  • 198
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    OR spectrum 2 (1980), S. 111-117 
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Summary The subject of this essay is the estimation of the effect of reducing the maximum permissable levels of petrol in petrol station tanks on forwarding. Optimum maximum permissable storage levels, dependant on sales, are determined from the minimum of the objective function. This is calculated from the difference between a) interest savings, due to reduced storage and b) increased cost of forwarding. The calculation of interest savings is elementary; the increase in expense is worked out by setting various maximum levels, based on average sales and the distance to the delivery point. For several assumed stochastic runs of daily sales, the forwarding of trucks is simulated for a fixed period under reduced maximum permissable storage levels. The results of the simulations are used to estimate the increase of expense of forwarding.
    Notes: Zusammenfassung In diesem Aufsatz wird versucht, die Auswirkungen verringerter Agenturbestände (das sind die Obergrenzen für die Lagerung von Kraftstoffen in Tankstellen) auf die Spedition zu bewerten. Das Minimum der Zielfunktion, gebildet aus der Differenz zwischen Zinseinsparungen aus der Bestandsreduzierung einerseits und den Mehrkosten aus der Spedition andererseits, wird zur Bestimmung von absatzabhängigen optimalen Agenturbeständen benutzt. Die Zinseinsparungen sind elementar berechenbar; zur Berechnung der Mehrkosten werden verschiedene, vom Durchschnittsabsatz und von der Entfernung zur Lieferstelle abhängige Höchstgrenzen an Agenturbeständen festgelegt. Für mehrere angenommene stochastische Absatzverläufe wird dann die Tankwagendisposition bei reduzierten Agenturbeständen über einen festen Zeitraum simuliert. Aus den auf ein Jahr hochgerechneten Simulationsergebnissen werden die Mehrkosten der Spedition bestimmt.
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  • 199
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    OR spectrum 2 (1980), S. 47-58 
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Summary For the long-term planning of a telecommunication network, a computer-assisted procedure was developed by the Research Institute of the Deutsche Bundespost. This procedure as well as the experience gained with its application are described. Even with varying input parameters, the calculated network structure should remain stable. Investigations to this effect were carried out, the results of which are described and analyzed.
    Notes: Zusammenfassung Für die langfristige Planung eines Fernmeldenetzes wurde im Forschungsinstitut der Deutschen Bundespost ein EDV-gestütztes Verfahren entwikkelt. Die dabei verwendete Methode wird zunächst dargestellt, danach wird über die Erfahrungen, die bei ihrer Anwendung gewonnen wurden, berichtet. Da die berechnete Netzstruktur sich nur wenig ändern darf, wenn die Eingangsparameter (Kostenanteile, Bedarf an Kanalkapazität) variieren, wurden Stabilitätsuntersuchungen durchgeführt. Die Ergebnisse dieser Untersuchungen werden dargestellt und analysiert.
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  • 200
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    OR spectrum 2 (1980), S. 64-64 
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
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