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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Potential analysis 1 (1992), S. 1-35 
    ISSN: 1572-929X
    Keywords: 47A75 ; 31C25 ; Sierpinski gasket ; Laplacian ; Dirichlet form ; eigenvalue ; spectral dimension ; integrated density of states ; decimation method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A complete description of the eigenvalues of the Laplacian on the finite Sierpinski gasket is presented. We then demonstrate highly oscillatory behaviours of the distribution function of the eigenvalues, the integrated density of states (for the infinite gasket) and the spectrum of the Laplacian on the infinite gasket. The method has two ingredients: the decimation method in calculating eigenvalues due to Rammal and Toulouse and a simple description of the Dirichlet form associated with the Laplacian.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematische Annalen 293 (1992), S. 343-348 
    ISSN: 1432-1807
    Keywords: 60J45 ; 31C15 ; 35S99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1432-1335
    Keywords: Human ovarian cancer cells ; Antineoplastic prostaglandins ; Cisplatin ; Adjuvant effects ; Nude mice
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary Effects of antineoplastic prostaglandins (PG) on human ovarian cancer cell growth were examined by using HR cells derived from ascites of a patient with serous cystadenocarcinoma of the ovary. With regard to inhibition of cancer cell proliferation in vitro, the effects of Δ7-PGA was most marked, followed by that of Δ12-PGJ2, PGJ2 and PGD2. When antineoplastic prostaglandins were administered to nude mice bearing HR cells, tumor growth in groups treated with PGJ2 and Δ12-PGJ2 alone was significantly inhibited 63 days after tumor inoculation, compared to that in an untreated group. Consequently, a significant prolongation of median survival was obtained with Δ12-PGJ2, compared to that in untreated groups and in groups with cisplatin alone. In addition, when prostaglandins were administered together with cisplatin, adjuvant inhibitory effects on the tumor growth were obtained 35, 56 and 63 days after tumor inoculation. Subsequently a significant prolongation of median survival was observed when cisplatin was combined with PGD2 or Δ7-PGJ1, compared to the results in groups treated with PGD2 alone, Δ7-PGJ1 alone or cisplatin alone. Combination of PGJ2 or Δ12-PGJ2 and cisplatin resulted in a significant decrease of hematocrit and body weight 63 days after tumor inoculation, suggesting a deterioration of the median survival. These results suggest that combination of PGD2 or Δ7-PGJ1 with cisplatin may be of clinical use for ovarian cancer resistant to cisplatin.
    Type of Medium: Electronic Resource
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