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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
    Periodic solutions of differential equations in Banach spaces (1978)
    Springer
    Manuscripta mathematica 24 (1978), S. 31-44 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let X be a Banach space, D⊂X, f: [0,∞)xD→X continuous and ω-periodic. In this paper we consider various conditions on D and f sufficient for existence of an ω-periodic solution of the differential equation u′=f(t,u). In the main, we shall assume that D is closed bounded and convex and f satisfies a boundary condition at δD such that D is flow invariant for u′=f(t,u). The map f is assumed to be either compact or dissipative or a certain perturbation of such maps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01168561
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  • 3
    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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  • 4
    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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  • 5
    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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  • 6
    Electronic Resource
    Electronic Resource
    Biochemical markers in inbred strains of the rat (Rattus norvegicus) (1984)
    Springer
    Immunogenetics 19 (1984), S. 257-266 
    Details
    ISSN: 1432-1211
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00364769
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  • 7
    Electronic Resource
    Electronic Resource
    Integrating Physical and Chemical Characteristics of Lakes into the Glacially Influenced Landscape of the Northern Cascade Mountains, Washington State, USA (1999)
    Springer
    Environmental management 24 (1999), S. 219-228 
    Details
    ISSN: 1432-1009
    Keywords: KEY WORDS: Limnology; Mountain lakes; Water quality; North Cascades National Park Service Complex; National Park Service
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002679900228
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  • 8
    Electronic Resource
    Electronic Resource
    Vakuum-Wärmedämmung bei Stahlmantel-Fernheizrohren (1984)
    Springer
    Heat and mass transfer 18 (1984), S. 129-140 
    Details
    ISSN: 1432-1181
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Zusammenfassung Zur Zeit gewinnen neue Entwicklungen von Fernheizrohr-Verlegungssystemen an Bedeutung, mit denen die Investitions- und Betriebskosten herabgesetzt und die Lebensdauer und Betriebssicherheit heraufgesetzt werden können. In diesem Zusammenhang steht diese Untersuchung zur Wärmedämmung eines Vakuum-Stahlmantelrohres, bei dem sich durch Druckabsenkung im Ringraum die effektive Wärmeleitfähigkeit der faser- oder pulverartigen Isoliermaterialien herabsetzen läßt (Smoluchowski-Effekt). Die Ergebnisse zur effektiven Wärmeleitfähigkeit der Isolierungen zeigen, daß die Werte bei 1 mbar etwa 30 bis 60% und bei 0,1 mbar noch etwa 15 bis 25% der Werte bei Atmosphärendruck betragen.
    Notes: Abstract New developments in district heating supply, which lower the investment and operation costs and increase the service life and operational safety are gaining greater significance. In this connection stands this investigation of the heat insulation in vacuum steel-jacket pipe systems, in which the pressure reduction in the closed ring cavity lower the effective conductivity of the fibrous or porous insulating materials (Smoluchowski effect). The results for the values of the effective thermal conductivity of the insulations are at 1 mbar only 30 to 60% and at 0.1 mbar approximately 15 to 25% of the values at atmospheric pressure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01466344
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  • 9
    Electronic Resource
    Electronic Resource
    Histochemische und quantitative Untersuchungen zur Verteilung der sauren Phosphatase in der Rattenniere (1967)
    Springer
    Histochemistry and cell biology 10 (1967), S. 193-200 
    Details
    ISSN: 1432-119X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Description / Table of Contents: Zusammenfassung Die saure Phosphatase von Rattennieren wurde histochemisch dargestellt und die spezifische Aktivität in Rinde und Markaußenstreifen bestimmt. Folgende Befunde wurden erhoben: 1. Bei männlichen Tieren beträgt die spezifische Aktivität in der Rinde 3,05 MKH, im Außenstreifen 2,16 MKH. Im Einklang damit zeigt im histochemischen Präparat die Rinde bei 83% aller Tiere eine stärkere Reaktion als der Außenstreifen. 2. Bei weiblichen Tieren beträgt die spezifische Aktivität in der Rinde 2,91 MKH (Östrus) bzw. 3,3 MKH (Diöstrus) und im Außenstreifen 2,3 MKH (Östrus) bzw. 2,5 MKH (Diöstrus). Nur der Unterschied zwischen Rindenwerten ist signifikant. Im Gegensatz zum quantitativen Ergebnis zeigt bei etwa 50% aller Tiere der Außenstreifen im histochemischen Präparat eine stärkere Reaktion als die Rinde. Unter 51 Weibchen wurde nur eines angetroffen, bei welchem im histochemischen Bild die Rinde eine stärkere Reaktion hat. 3. Als Ursache der Diskrepanz der Ergebnisse wird eine geschlechts- und ortsspezifische Anordnung der Isoenzyme vermutet, die eine unterschiedliche Empfindlichkeit gegenüber verschiedenen Inkubationsmedien haben.
    Notes: Summary The acid phosphatase of rat kidneys was demonstrated histochemically and the specific activities in the cortex and the outer stripe of the medulla were determined. The results are as follows: 1. In males the specific activity in the cortex is 3,05 MKH, in the outer stripe 2,16 MKH. According to our findings the cortex shows in the histochemical section in 83% of all animals an effect more marked than in the outer stripe. 2. In females the specific activity in the cortex is 2,91 MKH (oestrus) respectively 3,3 MKH (dioestrus) and in the outer stripe 2,3 MKH (oestrus) respectively 2.5 MKH (dioestrus). Only the difference between the quantities of the cortex is significant. In contrast to the quantitative result the outer stripe in about 50% of all animals shows an effect which is more marked than in the cortex. Among 51 female animals we have only found one where the cortex shows a marked reaction in the histochemical section. 3. The discrepancy of the results may be explained by the specific localization of the isoenzymes according to structure and sex which show a different sensibility in regard to various media of incubation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00311406
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  • 10
    Electronic Resource
    Electronic Resource
    Nonspecific esterases of mammalian testis (1985)
    Springer
    Histochemistry and cell biology 82 (1985), S. 547-555 
    Details
    ISSN: 1432-119X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Notes: Summary Ten different nonspecific esterases in both mouse (Mus musculus) and rat (Rattus norvegicus) testis were identified following the analysis of electrophoretic patterns using genetic, developmental, and biochemical criteria. None of the enzymes were unique to testis, although the pattern of activity was testis specific. The enzymes comprised, in each species, six carboxylesterases (EC 3.1.1.1), one arylesterase (EC 3.1.1.2), one acetylesterase (EC 3.1.1.6), and two butyrylesterases (tentative designation). Cholinesterase (EC 3.1.1.8) was not detected. Individual homology relationships were recognized between the two species for all of these activities, except three of the carboxylesterases; however, these were coded for by homologous gene clusters. Similarities between the two species extended to the developmental course of expression and the modulation of the pattern of activity by the testicular feminization (Tfm) mutation. We describe the effects of the sex reversal (Sxr) mutation in the mouse, as well as the distribution of individual activities between Leydig cells and seminiferous tubules. The results of earlier histochemical studies are interpreted in the light of the present investigation. The correspondence between mouse- and rat-testis esterases suggests that the results could serve as a basis for mammalian testis esterase systems in general.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00489976
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