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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Mathematische Zeitschrift 188 (1985), S. 283-286 
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematische Zeitschrift 199 (1988), S. 115-117 
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 90 (1980), S. 153-161 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We generalize the Jörgens-Vidav semigroup perturbation theorem: If (U (t)), (V (t)) are s. c. semigroups, the generator of (V (t)) a bounded perturbation of the generator of (U (t)), and some remainder in the iteration series ofV (t) is strictly power compact, then the spectrum ofV (t) outside the spectral disc ofU (t) consists of eigenvalues of finite algebraic multiplicity. As a prerequisite, we show the invariance of components of the essential resolvent set of an operator under relatively power compact pertubations.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 9 (1985), S. 227-230 
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A nonnegative potential V: ℝv→ℝ is constructed for which V ∉ L q (G) for any nonempty open G⊂→v, q〉0, and for which nevertheless W inf2 sup1 ∩ Q(V) is dense in W inf2 sup1 , i.e., is a form core for −1/2Δ in L 2.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Archiv der Mathematik 39 (1982), S. 455-462 
    ISSN: 1420-8938
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 104 (1986), S. 243-250 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract LetH p =−1/2Δ+V denote a Schrödinger operator, acting inL p ℝ v , 1≦p≦∞. We show that σ(H p )=σ(H 2) for allp∈[1, ∞], for rather general potentialsV.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1432-2048
    Keywords: Cell cycle ; Chlamydomonas ; Cell wall ; Autolysin
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract In light-dark-synchronized cultures of the unicellular green algaChlamydomonas reinhardtii, release of zoospores from the wall of the mother cell normally takes place during the second half of the dark period. The recently isolated mutant ‘ls’, however, needs light for the liberation of zoospores when grown photoautotrophically under a 12 h light-12 h dark regime. The light-induced release of zoospores was found to be prevented by addition of the photosystem-II inhibitor 3-(3′,4′-dichlorophenyl)-1,1-dimethylurea. Furthermore, light dependence of this process was shown to be abolished when the mutant ‘ls’ was grown either photoautotrophically under a 14 h light-10 h dark regime or in the presence of acetate. Our findings indicate that the light-dependency of zoospore liberation observed in cultures of this particular mutant during photoautotrophic growth under a 12 h light-12 h dark regime might be attributed to an altered energy metabolism. The light-induced release of zoospores was found to be prevented by addition of cycloheximide or chloramphenicol, antibiotics which inhibit protein biosynthesis by cytoplasmic and organellar ribosomes, respectively. Actinomycin D, an inhibitor of RNA synthesis, however, did not affect the light-induced liberation of zoospores. Sporangia accumulate in stationary cultures of the mutant ‘ls’. Release of zoospores was observed when these sporangia were collected by centrifugation and incubated in the light after resuspension in fresh culture medium. Since liberation of zoospores was not observed after dilution of the stationary cultures with fresh culture medium, we suppose that components which interfere with the action of the sporangial autolysin are accumulated in the culture medium of the mutant ‘ls’.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 81 (1981), S. 31-38 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract For a stochastic operatorU on andL 1-space, i.eU is linear, positive, and norm preserving on the positive cone ofL 1, it is shown thatU decreases relative information between two nonnegativeL 1-functions. Furthermore it is shown that the following properties ofU are closely related:U is energy decreasing (energy preserving),U isH-decreasing, whereH is Boltzmann'sH-functional, and the Maxwell distributions are fixed points ofU.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Mathematische Annalen 253 (1980), S. 63-87 
    ISSN: 1432-1807
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Acta applicandae mathematicae 2 (1984), S. 311-331 
    ISSN: 1572-9036
    Keywords: 47D05 ; 82A70 ; 47B55 ; 47G05 ; 35K22 ; 35F15 ; 35C15 ; linear transport theory ; neutron transport equation ; Boltzmann equation ; semigroups ; perturbations ; irreducibility ; collision ; absorption ; scattering ; spectrum ; Dyson-Phillips expansion ; flows
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present methods using positive semigroups and perturbation theory in the application to the linear Boltzmann equation. Besides being a review, this paper also presents generalizations of known results and develops known methods in a more abstract setting. In Section 1 we present spectral properties of the semigroup operatorsW a(t) of the absorption semigroup and its generatorT a. In Section 2 we treat the full semigroup (W(t);t≧0) as a perturbation of the absorption semigroup. We discuss part of the problems (perturbation arguments and existence of eigenvalues) which have to be solved in order to obtain statements about the large time behaviour ofW(·). In Section 3 we discuss irreducibility ofW(·). In four appendices we present abstract methods used in Sections 1, 2 and 3.
    Type of Medium: Electronic Resource
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