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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 25 (1975), S. 103-107 
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The application of spatial discretization (discrete ordinate method) to a class of integro-differential equations is discussed. It is shown that consistency in the approximation of the operators implies convergence of the approximate solution to the true solution.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-0843
    Keywords: Cyclopentenyl cytosine ; Phase I trials ; CTP synthase ; Pharmacokinetics ; Hypotension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Cyclopentenyl cytosine (CPE-C) is an investigational drug that is active against human solid tumor xenografts. The 5′-triphosphate of CPE-C inhibits CTP synthase, and depletes CTP and dCTP pools. We conducted a phase I clinical trial of CPE-C given as a 24-h continuous i. v. infusion every 3 weeks in 26 adults with solid tumors. The starting dose rate, 1 mg/m2 per h, was selected on the basis of both preclinical studies and pharmacokinetic data from two patients obtained after a test dose of 24 mg/m2 CPE-C as an i. v. bolus. Dose escalation was guided by clinical toxicity. A total of 87 cycles were given, and ten patients received four or more cycles. The mean CPE-C steady-state plasma levels (Cpss) increased linearly from 0.4 μM to 3.1 μM at dose levels ranging from 1 to 5.9 mg/m2 per h (actual body weight); the mean total body clearance was 146±38 ml/min per m2. CPE-C was eliminated by both renal excretion of intact drug and deamination to cyclopentenyl uracil in an apparent 2∶1 ratio. CTP synthase activity in intact bone marrow mononuclear cells was inhibited by 58% to 100% at 22 h compared to matched pretreatment samples at all CPE-C dose levels. When all data were combined, flux through CTP synthase was decreased by 89.6%±3.1% at 22h (mean ± SE,n=16), and remained inhibited by 67.6%±7.7% (n=10) for at least 24 h post-CPE-C infusion. Granulocyte and platelet toxicities were dose-dependent, and dose-limiting myelosuppression occurred during the initial cycle in two of three patients treated with 5.9 mg/m2 per h. Four of 11 patients (4 of 20 cycles) who received 4.7 mg/m2 per h CPE-C experienced hypotension 24–48 h after completion of the CPE-C infusion during their first (n=2), third (n=1) and sixth cycles (n=1), respectively. Two of these patients died with refractory hypotension despite aggressive hydration and cardiopulmonary resuscitation. One of 12 patients (28 total cycles) treated with 3.5 mg/m2 per h CPE-C experienced orthostatic hypotension during cycle 1, and this patient had a second episode of orthostatic hypotension at a lower dose (3.0 mg/m2per h). Hypotension was not seen in patients receiving ≤2.5 mg/m2 per h CPE-C. The occurrence of hypotension did not directly correlate with either CPE-C Cpss, CPE-U plasma levels, pretreatment cytidine plasma levels, baseline CTP synthase activity, or with the degree of enzyme inhibition during treatment. While the hypotension appeared to be dose-related, its unpredictable occurrence and the uncertainty concerning the mechanism preclude a recommendation of a tolerable dose for future studies.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1432-0843
    Keywords: Key words Cyclopentenyl cytosine ; Phase I trials ; CTP synthase ; Pharmacokinetics ; Hypotension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract  Cyclopentenyl cytosine (CPE-C) is an investigational drug that is active against human solid tumor xenografts. The 5′-triphosphate of CPE-C inhibits CTP synthase, and depletes CTP and dCTP pools. We conducted a phase I clinical trial of CPE-C given as a 24-h continuous i.v. infusion every 3 weeks in 26 adults with solid tumors. The starting dose rate, 1 mg/m2 per h, was selected on the basis of both preclinical studies and pharmacokinetic data from two patients obtained after a test dose of 24 mg/m2 CPE-C as an i.v. bolus. Dose escalation was guided by clinical toxicity. A total of 87 cycles were given, and ten patients received four or more cycles. The mean CPE-C steady-state plasma levels (Cpss) increased linearly from 0.4 μM to 3.1 μM at dose levels ranging from 1 to 5.9 mg/m2 per h (actual body weight); the mean total body clearance was 146±38 ml/min per m2. CPE-C was eliminated by both renal excretion of intact drug and deamination to cyclopentenyl uracil in an apparent 2:1 ratio. CTP synthase activity in intact bone marrow mononuclear cells was inhibited by 58% to 100% at 22 h compared to matched pretreatment samples at all CPE-C dose levels. When all data were combined, flux through CTP synthase was decreased by 89.6%±3.1% at 22 h (mean±SE, n=16), and remained inhibited by 67.6%±7.7% (n=10) for at least 24 h post-CPE-C infusion. Granulocyte and platelet toxicities were dose-dependent, and dose-limiting myelosuppression occurred during the initial cycle in two of three patients treated with 5.9 mg/m2 per h. Four of 11 patients (4 of 20 cycles) who received 4.7 mg/m2 per h CPE-C experienced hypotension 24–48 h after completion of the CPE-C infusion during their first (n=2), third (n=1) and sixth cycles (n=1), respectively. Two of these patients died with refractory hypotension despite aggressive hydration and cardiopulmonary resuscitation. One of 12 patients (28 total cycles) treated with 3.5 mg/m2 per h CPE-C experienced orthostatic hypotension during cycle 1, and this patient had a second episode of orthostatic hypotension at a lower dose (3.0 mg/m2per h). Hypotension was not seen in patients receiving ≤2.5 mg/m2 per h CPE-C. The occurrence of hypotension did not directly correlate with either CPE-C Cpss, CPE-U plasma levels, pretreatment cytidine plasma levels, baseline CTP synthase activity, or with the degree of enzyme inhibition during treatment. While the hypotension appeared to be dose-related, its unpredictable occurrence and the uncertainty concerning the mechanism preclude a recommendation of a tolerable dose for future studies.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    BIT 24 (1984), S. 92-101 
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we introduce and explore the concept of uncertainty of an approximate solution of a linear operator equation. This uncertainty is a measure of the difference between a computed solution and other plausible answers. When the operator equation is wellposed, the uncertainty is closely related to the more traditional notion of the accuracy of an approximate solution. However, for illposed equations, the uncertainty concept gives a new way of looking at such problems and helps in assessing the meaning of the computed results.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    BIT 17 (1977), S. 329-337 
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We establish convergence rates for a method of approximate solution of certain singular integral equations. The method considered involves an expansion of the kernel of the equation in terms of Chebyshev polynomials.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    BIT 11 (1971), S. 413-421 
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The numerical solution of Volterra integral equations of the first kind can be accomplished if the integral is replaced by certain simple quadrature rules, such as the midpoint or the trapezoidal methods. When the kernel of the integral equation oscillates more rapidly than the solution one can use product integration techniques to increase the accuracy. Such an approach is investigated in this paper.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    BIT 12 (1972), S. 528-533 
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A convergence theorem is given for the numerical computation of eigenvalues of self-adjoint operators. The computed eigenvectors are used to construct trial solutions which can be used to obtain easily computable and accurate error estimates.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Journal of engineering mathematics 3 (1969), S. 245-249 
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Summary Dual integral equations with Hankel kernels are reduced to simple integral equations whose unknowns are physically meaningful quantities. Numerical methods for solving these integral equations are established and applied to a problem in electrostatics.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 991-1000 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The solution of the quantum-mechanical one-particle problem involving a Coulomb potential with a cut-off contains Whittaker functions, difficult to evaluate individually. However, the energy expression involves a ratio of two contiguous Whittaker functions, and the entire ratio is easily expressed as a convergent continued fraction. Representative energy eigenvalues are calculated, correcting the errors due to an earlier Bessel function approximation by Wannier.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Book
    Book
    Philadelphia, PA :SIAM,
    Title: Analytical and numerical methods for Volterra equations; 7
    Author: Linz, Peter
    Publisher: Philadelphia, PA :SIAM,
    Year of publication: 1985
    Pages: 227 S.
    Series Statement: SIAM studies in applied mathematics 7
    Type of Medium: Book
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