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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Probability theory and related fields 14 (1970), S. 257-263 
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The concept of duality plays an important role in mathematical programming and has been studied extensively in a finite dimensional Eucledian space, (see e.g. [13, 4, 6, 8]). More recently various dual problems with functionals as objective functions have been studied in infinite dimensional vector spaces [5, 7, 1, 10, 12]. In this note we consider a nonlinear minimization problem in a partially ordered Banach space. It is assumed that the objective function of this problem is given by a (nonlinear) operator and that its feasible domain is defined by a system of (nonlinear) operator inequalities. In analogy to the finite dimensional case we associate with this minimization problem a dual maximization problem which is defined in the Cartesian product of certain Banach spaces. It is shown that under suitable assumptions the main results of the finite dimensional duality theory can be extended to this general case. This extension is based on optimality conditions obtained in [11].
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Computing 14 (1975), S. 79-105 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es ist bekannt, daß die Anwendung von Methoden der konjugierten Richtungen sowie von geeigneten Modifikationen der Methode der konjugierten Gradienten zur Bestimmung des Minimums einer Funktion vonn Variablen einen-Schritt quadratische Konvergenzgeschwindigkeit ergibt. Eine Menge vonn aufeinanderfolgenden Richtungsvektoren, die von einer dieser Methoden erzeugt worden sind, enthalten Information über die zu minimierende Funktion, die dazu benutzt werden kann, die Konvergenzgeschwindigkeit zu erhöhen durch Ausführung besonderer Iterationsschritte. Unter geeigneten Voraussetzungen ergibt sich für die beschleunigte Methode der konjugierten Gradienten eine (n+1)-Schritt kubische Konvergenzgeschwindigkeit. Die Konvergenzgeschwindigkeit der beschleunigten Methode der konjugierten Richtungen ist in Abhängigkeit von der Häufigkeit der besonderen Iterationsschritte entweder (n+1)-Schritt kubisch oder 2-Schritt superlinear.
    Notes: Abstract Methods of conjugate directions and reset versions of the conjugate gradient method have ann-step quadratic rate of convergence when they are applied to the unconstrained minimization of a function ofn variables. A set ofn consecutive directions of descent generated by one of these methods contains information on the function to be minimized which is used to accelerate the convergence by perorming simple special steps. Under appropriate assumptions the rate of convergence of an accelerated reset version of the conjugate gradient method is (n+1)-step cubic. Depending on the frequency of the special step the rate of convergence of the method of conjugate directions is (n+1)-step cubic or 2-step superlinear.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Mathematische Annalen 184 (1970), S. 133-154 
    ISSN: 1432-1807
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    European archives of oto-rhino-laryngology and head & neck 219 (1978), S. 309-310 
    ISSN: 1434-4726
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    European archives of oto-rhino-laryngology and head & neck 213 (1976), S. 489-489 
    ISSN: 1434-4726
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    European archives of oto-rhino-laryngology and head & neck 219 (1978), S. 115-177 
    ISSN: 1434-4726
    Keywords: Inner ear vessels ; Anatomy ; Morphology ; Angioarchitecture and vasomotion ; InnenohrgefÄ\e ; Anatomie ; Morphologie ; Angioarchitektur und Vasomotion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Description / Table of Contents: Zusammenfassung Die Durchblutung eines Organs hÄngt neben zahlreichen anderen Faktoren auch entscheidend von der Vaskularisation ab. über die Äu\erst interessante GefÄ\strombahn des Innenohrs liegen zahlreiche Untersuchungen vor, dennoch sind die Aussagen zu deren Topographie, Morphologie und Funktion unvollstÄndig. In der vorliegenden Arbeit wird zu diesen Fragen anhand von 1. GefÄ\injektionen mit Berlinerblau und Silbernitrat, 2. histologischen Untersuchungen, 3. rasterelektronenmikroskopischen Studien, 4. vitalmikroskopischen Beobachtungen und 5. histometrischen Untersuchungen von GefÄ\weiten ohne und nach Gaben vasoaktiver Pharmaka ein tierexperimenteller Beitrag geleistet. Mit Hilfe der GefÄ\injektionstechniken gelingt eine lückenlose Darstellung der topographischen VerlÄufe der cochleÄren GefÄ\e und mit der Silbernitratperfusion darüber hinaus eine Aussage zur Angioarchitektonik, da dabei ein kontinuierliches und konturenscharfes endotheliales und — wenn vorhanden — auch muskulÄres Zellgrenzlinienmuster entsteht. Das Aufbauprinzip der cochleÄren GefÄ\e ist Äu\erst klar gegliedert. Diese weisen in dem dreidimensionalen Raum der Schnecke eine scharfe Trennung arterieller Zu- und venöser Abflüsse auf. Die zwei vorhandenen terminalen Strombahngebiete sind analog gegliedert und bestehen aus einzelnen Strombahneinheiten, an deren Anfang muskelhaltige arteriolÄre GefÄ\konvolute liegen. Die GefÄ\e der Cochlea sind insgesamt muskelschwach. Die Arteriolen werden von breiten perivasculÄren RÄumen begleitet, welche sich insbesondere rasterelektronenmikroskopisch gut darstellen. Sphinktersysteme lassen sich in der terminalen GefÄ\strombahn der Cochlea nicht nachweisen. Die Kapillarregionen sind sehr gefÄ\reich, sie enthalten in der lateralen Cochleawand in jeder Strombahneinheit arteriolo-venulöse Anastomosen. Die Terminologie der cochleÄren-GefÄ\e wird nach GefÄ\art, Verlaufsrichtung und topographischer Lage vereinheitlicht und systematisiert. Die GefÄ\e werden neben anderen Untersuchungen vorwiegend anhand ihres Endothelzellgrenzlinienmusters klassifiziert. Die Endothelzellen der Arterien und Arteriolen sind langgestreckt, lanzett- und spindelförmig, die der drainierenden Venulen weisen breite, polygonale Zellformen mit welligen und sogar gezackten Grenzlinien auf, und dazwischen lassen sich von der arteriellen zur venösen Seite zunehmend ovalÄre, dreieckige, rhombenförmige oder unregelmÄ\ig geformte Zellen nachweisen. Biomikroskopisch lÄ\t sich bei Änderungen der HÄmodynamik des Gesamtkreislaufs durch HÄmorrhagie bzw. Hypothermie zeigen, da\ die CochleagefÄ\e den zentral regulierten GefÄ\strombahnen zuzurechnen sind. In den prÄkapillÄren Arteriolen, Kapillaren, arteriolo-venulösen Anastomosen und postkapillÄren Venulen lÄ\t sich keine Vasomotion feststellen. Die GefÄ\weitenmessungen ohne Pharmaka, nach Gaben von Vasopressin und von Papaverin, die im Blindversuch durchgeführt wurden, beweisen bei der statistischen Auswertung durch Varianzanalysen signifikante vasomotorische Effekte nur an muskelhaltigen GefÄ\en, vorwiegend im Bereich der Konvolutbildungen der Arteriolen zu Beginn jeder GefÄ\strombahneinheit. Diesen SchlingengefÄ\en wird neben der DÄmpfung der arteriellen Pulswelle daher eine wesentliche Rolle bei der Blutstromregulierung zugeschrieben. Nach Vasopressingaben lassen sich an den zur Schnecke führenden Arterien spastische peristaltikartige Kontraktionen nachweisen, die die Ursache „vaskulÄrer UnfÄlle“ des Innenohrs darstellen könnten.
    Notes: Summary The inner ear as an example of a highly specialized sensory organ also possesses a highly specialized vascularisation. This represents an impressive example for a reasonable adaption of the terminal blood vessels to a specific function of the organ fulfilling more than only the nutrition. In this paper the microvascular bed of the cochlea is examined using both the injection method of the vessels and the biomicroscopic observation in vivo. The combination of these technics supported by histologic and stereoscan microscopic examinations has made it possible to give an account of the functional morphology of the inner ear vessels. As a detailed structural analysis of the vessels morphology with the help of dyes that fill the whole of the vessels space (i.e. Berlin blue) is not possible, perfusion experiments with silver nitrate were performed on the inner ear. After the perfusion the vessels are cleaned again, the silver however imbibes the intercellular reticular substances and after exposure produces a continous and sharp framework of the endothelium and — when present — muscular cells, thus showing the angioarchitectural contours. There is a very clear division of the cochlear vessels in a three dimensional space: The arterial and venous vessels are vividly separated from one another, forming two systems of microvascular units in the lateral wall and the spiral lamina. Each unit begins with special blood vessel convoluts in the modiolus, consisting of loops of arterioles. They are weakly muscularized whereas no muscle structures are seen elsewhere in the other parts of the inner ear vessels. There are no a.-v. anastomoses or sphinkters at all. The function of the vessel loops in the modiolus is to flatten the pulse wave as well as to regulate the blood flow in the microvascular bed by vasomotion. This was prooved by statistical examinations of 1200 measurements of the widths of the vessels at several points of the cochlea in a blind study with and without vasoactive drugs. The terminology of the vessels is not standardized. The nomenclature in this paper has regard to the classification of the vessels, the course and the topographic localisation. Silver staining reveals changes in the form of the endothelium cells from the arterial towards the venous end. While the arteries show a long stretched spinle or lancet like form they change over blunt, oval, triangular or rhomboid forms into polygonal cells with spiked border lines at the venules. All experiments together give an account that the blood supply of the inner ear is in close correlation with the blood supply of the brain and too possesses autoregulative mechanisms, which must be localized in the convoluts at the beginning of every microvascular unit of the cochlear vessels.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 13 (1974), S. 497-518 
    ISSN: 1573-2878
    Keywords: Conjugate-gradient method ; unconstrained minimization ; superlinearly convergent algorithms ; mathematical programming ; quadratically convergent algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For the problem of minimizing an unconstrained function, the conjugate-gradient method is shown to be convergent. If the function is uniformly strictly convex, the ultimate rate of convergence is shown to ben-step superlinear. If the Hessian matrix is Lipschitz continuous, the rate of convergence is shown to ben-step quadratic. All results are obtained for the reset version of the method and with a relaxed requirement on the solution of the stepsize problem. In addition to obtaining sharper results, the paper differs from previously published ones in the mode of proof which contains as a corollary the proof of finiteness of the conjugate-gradient method when applied to a quadratic problem rather than assuming that result.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 10 (1972), S. 57-66 
    ISSN: 1573-2878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A method of conjugate directions, the projection method, for solving unconstrained minimization problems is presented. Under the assumption of uniform strict convexity, the method is shown to converge to the global minimizer of the unconstrained problem and to have an (n − 1)-step superlinear rate of convergence. With a Lipschitz condition on the second derivatives, the rate of convergence is shown to be a modifiedn-step quadratic one.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    European archives of oto-rhino-laryngology and head & neck 207 (1974), S. 505-505 
    ISSN: 1434-4726
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary The film shows a woman with a hemangioma of the whole tongue and parts of the cheek. When bending the head the patient could not keep her tongue in the mouth, as she became very heavy by the overflow with blood. Caused by the macroglossia the articulation was disturbed. We were successful in reducing the size of the tongue by multiple electrocoagulations.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    European archives of oto-rhino-laryngology and head & neck 210 (1975), S. 266-266 
    ISSN: 1434-4726
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary Making use of a complicated injection method, whereby the upper enblooded part of the body is irrigated by Berliner Blau or silver nitrate, not only the topographic course but also the angioarchitectural framework of the endothelian and muscular cells of the inner ear vessels of the guinea pig are outlined. Staining with silver reveals a characteristic form of the endothelium cells from the arterial towards the venous end of the terminal vessels of the cochlea. By means of this method on one side a morphologic classification of the vessels on the other side a clear nomenclature are possible.
    Type of Medium: Electronic Resource
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