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  • 1
    Online Resource
    Online Resource
    Comparison and oscillation theory of linear differential equations (1968)
    Amsterdam : Elsevier Science
    Details Availability
    Keywords: Differential equations, Linear ; Differential equations, Linear ; Differential equations, Linear ; Electronic books ; Electronic books
    Description / Table of Contents: Sturm-type theorems for second order ordinary equations -- Oscillation and nonoscillation theorems for second order ordinary equarions -- Fourth order ordinary equations -- Third order ordinary equations, nth order ordinary equations and systems -- Partial differential equations
    Type of Medium: Online Resource
    Pages: Online Ressource (vi, 227 pages)
    Edition: Online-Ausg.
    ISBN: 0126789509 , 9780126789508
    Series Statement: Mathematics in Science and Engineering v. 48
    URL: http://www.sciencedirect.com/science/book/9780126789508
    URL: http://www.sciencedirect.com/science/bookseries/00765392/48
    URL: https://www.sciencedirect.com/science/bookseries/00765392/48
    DDC: 515.354
    Language: English
    Note: Includes bibliographical references and indexes. - Print version record , Sturm-type theorems for second order ordinary equations -- Oscillation and nonoscillation theorems for second order ordinary equarions -- Fourth order ordinary equations -- Third order ordinary equations, nth order ordinary equations and systems -- Partial differential equations.
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  • 2
    Electronic Resource
    Electronic Resource
    Comparison theorems for eigenvalues (1974)
    Springer
    Annali di matematica pura ed applicata 99 (1974), S. 81-107 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Comparison theorems are proved relating the smallest positive eigenvalues λ and λ* of two operator equations of type Au=λBu and A*v=λ*B*v, respectively. Sufficient conditions on the operators are given which guarantee that λ⩽λ*, with special reference to the case that A and A* are elliptic differential operators. One novelty of the theory is that B is not required to be positive. Two general techniques are described: 1) A generalization of the classical minimum principle for eigenvalues, which is appropriate for selfadjoint elliptic operators A of arbitrary even order; and 2) A differential identity related to Picone's identity, appropriate for nonselfadjoint second order elliptic operators and strongly elliptic quasilinear systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02413720
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Oscillation of nonlinear vector differential equations (1976)
    Springer
    Annali di matematica pura ed applicata 109 (1976), S. 305-315 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Oscillation criteria are obtained for vector partial differential equations of the type Δv+b(x, v)v=0, x∈G, v∈Em, where G is an exterior domain in En, and b is a continuous nonnegative valued function in G × Em. A solution v: G→Em is called h-oscillatory in G whenever the scalar product [v(x), h] (|h|=1) has zeros x in G with |x| arbitrarily large. It is shown that the spherical mean of [v(x), h] over a hypersphere of radius r in En satisfies a nonlinear ordinary differential inequality. As a consequence, the main theorems give sufficient conditions on b(x, t), depending upon the dimension n, for all solutions v to be h-oscillatory in G.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02416966
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  • 4
    Electronic Resource
    Electronic Resource
    Dietary relationships with early onset (under age 45) breast cancer in a case-control study in the United States: influence of chemotherapy treatment (1997)
    Springer
    Cancer causes & control 8 (1997), S. 713-721 
    Details
    ISSN: 1573-7225
    Keywords: Breast cancer ; chemotherapy ; diet ; United States ; women
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Methodologic investigations have addressed selection and recall biasin case-control studies of diet and breast cancer, whereas the effect ofdisease progression and medical treatment on estimates of dietary intake hasbeen largely overlooked. In a multicenter, population-based case-controlstudy of breast cancer in the United States, 1,588 newly diagnosed cases and1,451 controls completed a self-administered food-frequency questionnaire.Initial evaluation suggested increased risk related to high intakes ofcalories, carbohydrates, fat, and protein. All nutrient associations werediminished after adjustment for calories. Evaluation by stage of diseaserevealed no relation of calories to risk among women with in situ disease,but elevated risks among women with localized (odds ratio [OR] = 1.33, 95percent confidence interval [CI] = 1.0-1.7 highest cf lowest quartile) orregional and distant disease (OR = 1.79, CI = 1.3-2.4). Further evaluationshowed that the increased risk a ssociated with calories was restricted tocases who reported having been treated with chemotherapy (OR = 1.66, CI =1.3-2.1). A gradient of increasing risk with time interval from diagnosis tointerview suggested the chemotherapy regimen itself and not necessarilycharacteristics of tumors requiring this treatment was responsible for theobserved increased risk. These results indicate that epidemiologic studies ofdiet and breast cancer, particularly among young women, should evaluatepossible bias related to post-diagnosis influences.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018475203820
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  • 5
    Electronic Resource
    Electronic Resource
    A domain perturbation problem for elliptic operators (1977)
    Springer
    Annali di matematica pura ed applicata 114 (1977), S. 229-240 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Eigenvalue problems with null boundary data are considered for second order symmetric linear elliptic operators in bounded domains of Euclidean n-space. The main theorems give estimates for the perturbation of the eigenvalues and eigenfunctions under the deformation of attaching an ɛ-handle to the domain. In particular it is proved that the variation of every eigenvalue under such a deformation is of order ϕ(ɛ), where ϕ denotes the reciprocal of the parametrix.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02413788
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  • 6
    Electronic Resource
    Electronic Resource
    A study of several factors affecting the distribution of phosphorus-32 from the leaves ofPisum sativum (1960)
    Springer
    Plant and soil 12 (1960), S. 57-68 
    Details
    ISSN: 1573-5036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary 1. Distribution patterns for the movement of solutes in the phloem from leaves of pea plants were found to be relatively specific. Phosphorus-32 applied to the leaf at the first bloom node moved predominantly (to the extent of 50 to 90 per cent) to the pod at that node. Distribution of the translocate from this leaf to pods at higher nodes was negligible. 2. Translocation in the phloem of phosphorus-32 from lower leaf nodes (i.e. 5th or 7th) was predominately downward with little or no accumulation in the pods. 3. The stage of development of the flower markedly affected the distribution pattern of phosphorus-32 supplied to the leaf at the same node. Essentially no activity moved into either the flower or the vegetative portions of the plant before anthesis and fertilization had occurred in that flower, as compared to the same plant parts in plants 4 to 6 days past anthesis. The young developing embryos of the pod appear to “control” the movement of phosphorus-32 from the adjacent leaf. 4. When the metabolic activity of the pod on plants bearing one pod only was lowered by cooling (to 7°C), the movement of phosphorus-32 to this pod as well as to all other parts of the plant was markedly diminished. This inhibitory effect of the low pod temperature on translocation to the uncooled parts of the plant was negated by the presence of a second pod (uncooled) on the plant. Lowering the temperature of the first pod resulted in a substantial increase in the proportion of the P32-labelled translocate moving to the second pod.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01377761
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