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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    BIT 27 (1987), S. 374-388 
    ISSN: 1572-9125
    Keywords: 65D07 ; 65L05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper the general classV of spline-collocation methods for first order systems of ordinary differential equations is investigated. The methods can in part be regarded as so-called multivalue methods. This type contains the generalized singly-implicit methods treated by Butcher. It is shown here, how any multivalue type representative ofV yields a matrix valued functionψ, for the characterization of stability at infinity. It is shown in particular, that the structure ofψ allows us to construct infinity-stable methods by an appropriate choice of the collocation points.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    BIT 29 (1989), S. 295-310 
    ISSN: 1572-9125
    Keywords: 65L05 ; 65L20 ; 65D07 ; Ordinary differential equations ; collocation methods ; A-stability ; confluence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper the general classV of spline-collocation methods presented by Mülthei is investigated. The methods ofV approximate solutions of first order initial value problems. ClassV contains as subclass the methods of so-called multivalue type, and in particular contains the generalized singly-implicit methods treated by Butcher. Any multivalue type representativeU εV yields a matrix valued function Ω corresponding toU, which characterizes the region of absolute stability ofU. If a sequence (U(δ)) of multivalue type representatives ofV tending to some singlevalue type representative $$\tilde U$$ εV is considered, it can easily be seen by the structure of Ω, that the sequence of the greatest eigenvalues of the Ω(.,δ) tends to the stability function $$\tilde R$$ corresponding to $$\tilde U$$ . This fact allows one to construct one-parameter families of A-stable methods of multivalue type.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    European journal of clinical pharmacology 14 (1978), S. 405-412 
    ISSN: 1432-1041
    Keywords: Colloidal plasma substitutes ; cross-linked polypeptides ; Haemaccel® ; pharmacokinetics ; renal failure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Medicine
    Notes: Summary Infusions of 3.5% isocyanate cross-linked polypeptide solution 500 ml were given to 52 patients with normal or impaired renal function: glomerular filtration rate (GFR)=0–133 ml/min. The serum concentration and urinary excretion of hydroxyproline were measured and the equivalent polypeptide concentrations were calculated from the results. In patients with normal renal function (GFR〉90 ml/min) the proportion of polypeptide excreted in the urine up to 12 h was 45.4±2.6% ( $$\bar X$$ ±SEM), up to 24 h 47.7±2.9% and up to 48 h 49.3±3.4%. In patients with moderate renal insufficiency (GFR=30–90 ml/min) there was no decrease in polypeptide excretion and even in patients with more serious impairment of GFR (11–30 ml/min) 48-h urinary polypeptide excretion was still 40.6±5.9%. In patients with GFR of 2–10 ml/min polypeptide excretion fell to 10.7±3.2% during the first 12 h, although there was an increase in later collection periods as compared to patients with normal renal function −19.9±3.9% in 24 h and 27.0±3.5% in 48 h. The elimination half-life (t1/2) calculated from serum concentrations was 505±30 min ( $$\bar X$$ ±SEM) in patients with normal renal function (GFR〉90 ml/min). Only when the GFR fell below 30 ml/min did it slowly begin to increase. In patients with minimal residual renal function (GFR=0–0.5 ml/min), who were on haemodialysis, the elimination half-life was 985±49 min, i.e. approximately twice the normal. Twice weekly infusion of 3.5% polypeptide solution 500 ml over a period of 6 weeks did not produce any significant cumulation in haemodialysis patients (GFR=0–0.5 ml/min). A weekly dose of polypeptide 35 g appeared to be quite safe when given for several weeks, even to anuric patients. As no significant amount of polypeptide was lost during haemodialysis, the dose can be chosen without taking into account any effect of intermittent haemodialysis.
    Type of Medium: Electronic Resource
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