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  • 1970-1974  (40)
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  • 1
    Electronic Resource
    Electronic Resource
    Zeros of accretive operators (1974)
    Springer
    Manuscripta mathematica 13 (1974), S. 365-374 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In the investigation of accretive operators in Banach spaces X, the existence of zeros plays an important role, since it yields surjectivity results as well as fixed point theorems for operators S such that I-S is accretive. Let D⊂X and T: D→X an operator such that the initial value problems (1) u′(t)=-Tu(t), u(0)=x εD are solvable. Then T has a zero iff (1) has a constant solution for some xεD. Under certain assumptions on D and T it is possible to show that (1) has a unique solution u(t,x) on [0,∞), for every xεD. In this case, define U(t): D→D by U(t)x=u(t,x). If T is accretive it turns out that U(t) is nonexpansive for every t≥0. This fact constitutes the basis for several authors concerned with this subject. They proceed with assumptions on D and X ensuring either that the U(t) must have a common fixed point xo or that U(p) has a fixed point xp for every p≥0. In the first case, U(t)xo is a constant solution of (1), whence Txo=0. In the second case, U(t)xp is a p-periodic solution of (1). Hence, one has to impose additional conditions on T which imply that a p-periodic solution must be constant, for some p〉0. The main purpose of the present paper is to show that, in certain situations, either the operators U(t) are actually strict contractions or T may be approximated by operators Tn such that the corresponding Un(t) are strict contractions. Thus, we obtain several results in general Banach spaces and a unification of some results in special spaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01171148
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  • 2
    Electronic Resource
    Electronic Resource
    Eigenschaften der Lösungsmenge eines Systems von Volterra-Integralgleichungen (1971)
    Springer
    Manuscripta mathematica 4 (1971), S. 201-212 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract By a well known theorem of H. Kneser [4] the set U of all solutions of the initial value problem $$u' = f(x,u)forx\varepsilon [0,a],u(0) = u_o $$ has the following property: If f is continuous and bounded then U(x0)={u(x0): u∈U} is a continuum (i.e. a compact and connected subset) for every x0∈[0,a]. In the present paper we claim to extend this theorem to a system of Volterra integral equations in several variables of the form x∈B∞Rm, ν=1,...,n that had been investigated in [8]. In fact we shall prove that U is a continuum of the Banach space Cn(B) of all ‘vector functions’ u(x)=(u1(x),...,un(x)), continuous on B. It is an immediate consequence from this that U(x0) is a continuum of Rn. These results will be established by the help of a suitable modification of a method used by M. Müller [5] to prove Kneser's theorem. Especially, we obtain new theorems for some initial value problems for hyperbolic equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01190276
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  • 3
    Electronic Resource
    Electronic Resource
    Remarks onP γ-compact operators (1970)
    Springer
    Mathematische Annalen 189 (1970), S. 185-190 
    Details
    ISSN: 1432-1807
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01352444
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  • 4
    Electronic Resource
    Electronic Resource
    On approximate solutions of differential equations in Banach spaces (1974)
    Springer
    Mathematische Annalen 212 (1974), S. 79-88 
    Details
    ISSN: 1432-1807
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01343982
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  • 5
    Electronic Resource
    Electronic Resource
    Das Goursat-Problem füru xy =f(x, y, u) (1971)
    Springer
    Aequationes mathematicae 6 (1971), S. 117-118 
    Details
    ISSN: 1420-8903
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01833247
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  • 6
    Electronic Resource
    Electronic Resource
    Das goursat-problem füru xy =f (x, y, u) (1971)
    Springer
    Aequationes mathematicae 6 (1971), S. 206-214 
    Details
    ISSN: 1420-8903
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01819753
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  • 7
    Electronic Resource
    Electronic Resource
    Das charakteristische Anfangswertproblem für $$u_{x_1 x_2 x_3 } = f$$ unter Carathéodory-Voraussetzungen (1971)
    Springer
    Archiv der Mathematik 22 (1971), S. 514-522 
    Details
    ISSN: 1420-8938
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01222611
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  • 8
    Electronic Resource
    Electronic Resource
    Esterase. VIII. Histochemische, elektrophoretische und quantitative Untersuchungen zum Einfluß von Phenobarbital auf die Leberesterase der Maus (1973)
    Springer
    Histochemistry and cell biology 34 (1973), S. 107-116 
    Details
    ISSN: 1432-119X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Description / Table of Contents: Zusammenfassung Bei 48 Mäusen (NMRI) beiderlei Geschlechts wurde der Einfluß von Phenobarbital auf die Leberesterase histochemisch, quantitativ und disk-elektrophoretisch untersucht. 1. Die Leberesterase zeigt primäre histochemische, quantitative und elektrophoretische Geschlechtsunterschiede. 2. Phenobarbital führt bei beiden Geschlechtern zu einer Erhöhung der Esteraseaktivität. Der Effekt ist bei männlichen Tieren etwas größer als bei weiblichen Tieren. Bei männlichen Tieren wird der Typ des Bandenmusters demjenigen weiblicher Tiere angeglichen. 3. Es besteht der Verdacht, daß der Geschlechtseffekt durch den gleichen Wirkungsmechanismus erzeugt wird wie der Phenobarbitaleffekt.
    Notes: Summary The influence of phenobarbital upon the esterase activity of liver was studied in 48 mice of either sex by quantitative, electrophoretic and histochemical methods. 1. The esterase of mouse liver shows primary histochemical, quantitative and electrophoretic differences related to sex. 2. A higher activity of esterase has been observed in both sexes under the influence of phenobarbital. Males show a slightly higher phenobarbital effect than females. The male type of banding pattern shifts towards the female type. 3. It seems possible that the sex-depending and the phenobarbital effect are caused by the same mechanism.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00303983
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  • 9
    Electronic Resource
    Electronic Resource
    Hormonabhängige Enzymverteilung in Geweben (1971)
    Springer
    Histochemistry and cell biology 28 (1971), S. 145-159 
    Details
    ISSN: 1432-119X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Description / Table of Contents: Zusammenfassung Die Nieren von insgesamt 34 männlichen und weiblichen Mäusen (NMRI, C57BL und hr/hr Oslo) wurden auf ihr Verhalten gegenüber verschiedenen Aminosäurearylamiden histochemisch und — davon unabhängig — quantitativ untersucht. Die quantitativen Messungen wurden z. T. an isolierten Nierenzonen (Rinde, Außenstreifen, Innenzone) vorgenommen. 1. Es ist wahrscheinlich, daß die Spaltwirkung auf die Substrate zum größten Teil der Wirkung einer Aminosäure-Arylamidase zuzuschreiben ist, nicht aber der klassischen Leucinaminopeptidase. 2. Bei allen untersuchten Tierstämmen ist sowohl die histochemisch darstellbare wie die quantitativ meßbare Enzymaktivität bei den weiblichen Tieren größer. Dieser Geschlechtsunterschied findet sich bei sämtlichen verwendeten Substraten. Die Geschlechtsunterschiede sind zumindest vorwiegend auf die Hauptstücke beschränkt. 3. Es werden Stammesunterschiede hinsichtlich der Gesamtaktivität, der Enzymverteilung und der Geschlechtsunterschiede festgestellt.
    Notes: Summary The hydrolysis of four amino acid arylamides by the kidneys of 34 male and female mice was investigated by histochemical and — undependently — chemically quantitative methods. The quantitative measurements were undertaken on the isolated zones of the kidney (Cortex, outer stripe of the medulla, inner zone). 1. It was shown that the splitting of the substrates, probably, is mainly due to the action of a amino acid aryl amidase but not due to the classical leucine aminopeptidase. 2. In all strains, the histochemical activity and the quantitatively measurable enzyme activity is greater in the females than in the males. This sex difference was found with all substrates. The sex differences are mainly, if not at all, limited to the proximal tubules. 3. Strain differences of total enzyme activity, of enzyme distribution, and of sex differences were established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00279859
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  • 10
    Electronic Resource
    Electronic Resource
    Esterase (1974)
    Springer
    Histochemistry and cell biology 39 (1974), S. 361-370 
    Details
    ISSN: 1432-119X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Description / Table of Contents: Zusammenfassung Mittels der Acrylamid-Diskelektrophorese wurde der Einfluß von Testosteronpropionat auf das Bandenmuster der Nierenesterase in adulten und juvenilen weiblichen NMRI-Mäusen untersucht. Ergänzende Befunde wurden an kastrierten und adrenalektomierten Männchen erhoben. Sechs elektrophoretisch gut definierte Esterasebanden können in adulten Weibchen durch Testosteron verstärkt werden. Es handelt sich um genau die Banden, welche die Geschlechtsunterschiede der Nierenesterase kennzeichnen. Eine Bande wird durch Testosteron reduziert, eine weitere Gruppe verhält sich indifferent. Bei Abwesenheit des Hormons (Kastration, Adrenalektomie) stellt sich die Stärke der sechs Banden auf einen konstitutiven Wert ein, welcher den Verhältnissen normaler Weibchen entspricht. Damit steht fest, daß die Abhängigkeit der sechs Banden von Testosteron unvollständig ist. Die möglichen Ursachen werden diskutiert. Die Verteilung der Esterase während der postnatalen Entwicklung läßt einen gestuften Ablauf der Genaktivierung erkennen. Mit Testosteron kann man in diesen Ablauf eingreifen, indem einzelne Komponenten vorzeitig exprimiert werden können.
    Notes: Summary The influence of testosterone propionate on the banding pattern of nonspecific esterase in adult and juvenile mice was investigated by analytic disc electrophoresis. Supplementary findings were obtained from castrated and adrenal-ectomized male animals. Six well defined electrophoretic esterase bands can be increased in adult females by testosterone. They are indentical with the six bands being responsible for the sex difference of the kidney esterase. One band is reduced by testosterone, another group is indifferent. If the hormone is absent (castration, adrenalectomy) the intensity of the six bands is adjusted to a constitutive value corresponding to the conditions in normal females. Thereby it is well established that these six bands don't absolutely depend on testosterone. The possible reasons are discussed. The distribution pattern of the esterase during the postnatal development of the kidney points to a steplike course of gene activation. Exogenous testosterone interferes with this course certain esterase components being prematurely expressed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00495687
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