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  • Drosophila  (116)
  • CR: 5.17  (98)
  • Calcium  (98)
  • Springer  (312)
  • Annual Reviews
  • 1980-1984  (312)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Planta 152 (1981), S. 450-456 
    ISSN: 1432-2048
    Keywords: Calcium ; Cell elongation ; Gibberellin ; Lactuca ; pH and growth
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The relationship between calcium ions and gibberellic acid (GA3)-induced growth in the excised hypocotyl of lettuce (Lactuca sativa L.) was investigated. The short-term kinetics of growth responses were measured using a linear displacement transducer. Test solutions were added either as drops to the filter paper on which the hypocotyl stood (“non-flow-past”) or by switching solution flowing past the base of hypocotyl (“flow-past”), resulting in differences in growth behavior. Drops of CaCl2 added at a high concentration (10 mM) inhibited growth within a few minutes. This inhibition was reversed by ethylenediaminetetraacetic acid (EDTA). Drops of EDTA or ethyleneglycol-bis(2-aminoethylether)-tetraacetic acid caused a rapid increase in growth rate. Growth induced by EDTA was not further promoted by GA3. A continuous H2O flow resulted in growth rates comparable to those in response to GA3. Addition of CaCl2 to the flow-past medium inhibited growth and this inhibition was reversed by a decrease in CaCl2 concentration. The growth rate was found to be a function of CaCl2 concentration. When a constant CaCl2 concentration was maintained by the flow-past medium, a shift in pH from 5.5 to 4.25 had no obvious effect on hypocotyl elongation. Gibberellic acid was found to reverse the inhibitory effect of CaCl2, causing an increase in growth rate similar to that found previously when GA3 was added to hypocotyls grown in H2O under non-flow-past conditions. We propose that gibberellin controls extension growth in lettuce hypocotyl sections by regulating the uptake of Ca2+ by the hypocotyl cells.
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  • 2
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    Planta 158 (1983), S. 320-328 
    ISSN: 1432-2048
    Keywords: Calcium ; Egeria ; Fluorescent probe ; Ions, group II ; Symplast
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The hydrophyllic dyes fluorescein glutamic acid, fluorescein glutamylglutamic acid (F(Glu)2), fluorescein hexaglycine, fluorescein leucyldiglutamyl-leucine and 6-carboxyfluorescein are unable to pass the plasmalemma in leaves of E. densa. However, when injected into single cells the dye conjugates of molecular weight 665 dalton or less move freely from cell-to-cell. This intercellular movement presumably occurs via the plant symplast. Movement of F(Glu)2 from the injected cell occurs with greatly reduced frequency when Ca2+, Mg2+ or Sr2+ are injected into the cell immediately prior to the dye. The fraction of dye injections leading to movement declines with increasing group II ion concentration in the electrode tip, up to 10 mM. Sodium and K ions do not affect dye movement. When dye injection is delayed 30 min after Ca2+ injection, dye movement is no longer inhibited. Thus the cells recover from the Ca2+ injection, indicating that the ion does not cause major cell damage. Recovery from Mg2+ injection is not complete within 60 min. Treatment of leaves with chemicals expected to raise the concentration of free intracellular group II ions, notably the mitochondrial uncoupler carbonyl cyanide p-trifluoromethoxyphenyl hydrazone, the inhibitor of mitochondrial Ca2+ uptake trifluralin, or the ionophore A23187 also inhibits dye movement, while the calmodulin inhibitor trifluoperazine does not. Cytoplasmic streaming is inhibited by Ca2+ or Mg2+ injection and by the metabolic inhibitors. However when streaming is stopped by cytochalasin B, dye movement is not inhibited. Hence steaming is not necessary for dye movement. Thus the cytoplasmic concentration of free group II ions may directly regulate the permeability of the plant symplast.
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  • 3
    ISSN: 1432-2048
    Keywords: Calcium ; Cation exchange ; Lycopersicon esculentum ; Rhythm ; diurnal Transport (calcium) ; Zea mays
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Tomato (Lycopersicon esculentum Mill. cv. Moneymaker) and maize (Zea mays L. cv. spec.) plants were supplied with 45Ca-labeled nutrient solutions for a period of 8 or 16 h in the dark, in the light, or in a light-dark régime. Plant parts were analyzed for 45Ca content. The partitioning of 45Ca between mature leaves and meristems was shown to be affected by the presence of light. The transport of 45Ca to meristems was higher in a dark period than in a comparable light period. Experiments with excised tomato shoots yielded similar distribution patterns of 45Ca over leaves and meristems, thus excluding root pressure as the main driving force for the enhanced import of 45Ca into the meristems in the dark. Results are discussed in terms of cation-exchange transport and competition between the various calcium sinks.
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  • 4
    ISSN: 1432-2048
    Keywords: Bryophyta ; Bud formation (moss) ; Calcium ; Chlorotetracycline ; Cytokinin ; Funaria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract We have investigated the changes in membrane-associated calcium that occur during cytokinin induced bud formation in Funaria hygrometrica Hedw. using the fluorescent Ca2+-chelate probe chlorotetracycline (CTC). In the target caulonema cells a localization of CTC fluorescent material becomes evident at the presumptive bud site 12 h after cytokinin treatment. By the time of the initial asymmetric division this region is four times as fluorescent as the entire caulonema cell. Bright CTC fluorescence remains localized in the dividing cells of the bud. To relate the changes in CTC fluorescence to changes in Ca2+ as opposed to membrane-density changes we employed the general membrane marker N-phenyl-1-naphthylamine (NPN). NPN fluorescence increases only 1.5 times in the initial bud cell. We conclude that the relative amount of Ca2+ per quantity of membrane increases in this localized area and is maintained throughout bud formation. We suggest that these increases in membrane-associated Ca2+ indicate a localized rise in intracellular free Ca2+ concentration brought about by cytokinin action.
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  • 5
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    Planta 160 (1984), S. 12-20 
    ISSN: 1432-2048
    Keywords: Calcium ; Calmodulin ; Germination (spore) ; Onoclea ; Phytochrome and Ca2+ ; Pteridophyta
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Phytochrome is confirmed to be the photoreceptor pigment in the germination response of Onoclea sensibilis L. by demonstrating red-far-red (R-FR) photoreversibility. External Ca2+ is required for this response with a threshold at a submicromolar concentration. Ethylene glycol-bis(β-amino-ethyl ether)-N,N,N′,N′-tetraacetic acid, La3+ and Co2+ reversibly inhibit germination. Lanthanum only inhibits germination when applied before or during irradiation, indicating that the external Ca2+ requirement is transient, although in the absence of Ca2+ the R-stimulated system remains maximally poised to accept the ion for over 4 h after irradiation. The ability to respond to Ca2+ 4.1 h after R-irradiation is not reversed by FR-irradiation, indicating that Ca2+ transport has been uncoupled from phytochrome. Barium and Sr2+, but not Mg2+ can substitute for Ca2+. Artificially increasing the concentration of intracellular free Ca2+ with the ionophore A 23187 stimulates germination in the dark. The Ca2+-calmodulin antagonists, trifluoperizine and chlorpromazine, reversibly inhibit germination. Calcium is required in phytochrome-mediated fern spore germination; it may be acting as a second messenger.
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  • 6
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    Journal of molecular evolution 18 (1982), S. 310-314 
    ISSN: 1432-1432
    Keywords: Neutral mutation theory ; Natural selection ; Protein evolution ; Levene model ; Environmental variability ; Genetic variability ; Drosophila
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary If a phenotypic character is under stabilizing selection, the selective disadvantage of a nonoptimal genotype will decrease exponentially to zero as the proportion of phenotypic variation that is environmental in origin -V e /V p - increases. Under the modified mutation-drift hypothesis of genetic polymorphism, the proportion of mutations that are effectively neutral and average heterozygosity should increase with this ratio. Invertebrates, because of their small size, fast development, and low degree of homeostasis (relative to vertebrates), are expected to show a larger environmental component of phenotypic variation than vertebrates. This may help explain why invertebrates are in general more genetically variable than vertebrates and why, when laboratory populations ofDrosophila are maintained in heterogeneous environments, genetic variability is lost less rapidly than when they are kept in constant conditions.
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  • 7
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    Journal of molecular evolution 16 (1980), S. 37-46 
    ISSN: 1432-1432
    Keywords: Evolution ; Drosophila ; Temperature ; Mitochondrial enzymes ; Kinetic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary The evolutionary behavior of two mitochondrial enzymes (L-glycerol 3-phosphate:cytochrome c oxidoreductase E.C.1.1.1.95,αGPO, and L-malate: NAD+ oxidoreductase, E.C.1.1.1.37, m-MDH) obtained from several temperate and tropicalDrosophila species was examined by comparing their catalytic properties, which related to temperature (Km-Ea-Q10-Thermostability). MitochondrialαGPO or m-MDH obtained either from temperate or from tropical species was found to exhibit similar catalytic properties while for both cytosolic enzymes, theαGPDH and s-MDH, Km patterns were similar among species from the same thermal habitat and different between thermal habitats. In combination with other observations reported in the literature these facts support the view that the function, and probably the structure, of mitochondrial enzymes are better conserved in evolution than those of the corresponding enzymes found in the cytosol. It is proposed that the relative invariance of the mitochondrial enzymes structure is probably linked to a necessary relative invariance of molecular interactions inside the mitochondrion.
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  • 8
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    Journal of molecular evolution 20 (1984), S. 251-264 
    ISSN: 1432-1432
    Keywords: Drosophila ; Genome evolution ; 68C Glue gene cluster ; Drosophila melanogaster species subgroup
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary The 68C puff is a highly transcribed region of theDrosophila melanogaster salivary gland polytene chromosomes. Three different classes of messenger RNA originate in a 5000-bp region in the puff; each class is translated to one of the salivary gland glue proteins sgs-3, sgs-7, or sgs-8. These messenger RNA classes are coordinately controlled, with each RNA appearing in the third larval instar and disappearing at the time of puparium formation. Their disappearance is initiated by the action of the steroid hormone ecdysterone. In the work reported here, we studied evolution of this hormone-regulated gene cluster in themelanogaster species subgroup ofDrosophila. Genome blot hybridization experiments showed that five other species of this subgroup have DNA sequences that hybridize toD. melanogaster 68C sequences, and that these sequences are divided into a highly conserved region, which does not contain the glue genes, and an extraordinarily diverged region, which does. Molecular cloning of this DNA fromD. simulans, D. erecta, D. yakuba, andD. teissieri confirmed the division of the region into a slowly and a rapidly evolving protion, and also showed that the rapidly evolving region of each species codes for third instar larval salivary gland RNAs homologous to theD. melanogaster glue mRNAs. The highly conserved region is at least 13,000 bp long, and is not known to code for any RNAs.
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  • 9
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    Monatshefte für Chemie 112 (1981), S. 149-156 
    ISSN: 1434-4475
    Keywords: Calcium ; Gallium ; Oxygen ; Single Crystal ; X-Ray
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The hitherto unknown compound Ca3Ga4O9 was prepared and investigated by X-ray single crystal methods. Ca3Ga4O9 has orthorhombic symmetry:a=1435.8;b=1682.5;c=532.1 pm; space group C 2v 11 −Cmm2,Z=6. The tetrahedra network (circles of 4 and 5 GaO4-tetrahedra) and the surrounding of Ca2+ are described and discussed with respect to other oxogallates.
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  • 10
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    Calcified tissue international 33 (1981), S. 365-368 
    ISSN: 1432-0827
    Keywords: Absorptiometry ; Osteoporosis ; Spinal bone ; Bone mineral content ; Neutron activation ; Calcium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary Dual-photon absorptiometry using153Gd (44 and 100 keV) was used to measure the bone mineral content (BMC) of the trunk and of the total body (TBBM) in 7 volunteers with no overt bone disease. These values were compared to those obtained with partial-body neutron activation of calcium (trunk Ca). The trunk Ca seemed to represent best a 60 × 30 cm area; the correlation coefficient with the corresponding BMC in that area was 0.97 (SEE ⋍ 7%). Trunk Ca was also highly correlated with TBBM (r=0.96; SEE=8%) and with radius BMC (r=0.92; SEE=11%), but the correlations with the BMC of smaller subareas of the trunk were lower (r⋍0.9; SEE ∼ 12%). The BMC of the lumbar spine was only moderately correlated with trunk Ca, radius BMC and TBBM (r ∼ 0.82; SEE ∼ 18%), and only slightly more associated with trunk BMC (r ∼ 0.88; SEE ∼ 14%). The BMC of the combined lumbar-thoracic spine showed higher correlations with trunk Ca, radius BMC and TBBM (r ∼ 0.87; SEE ∼ 13%), and trunk BMC (r=0.93; SEE ∼ 10%). An accurate and sensitive measure of spinal status requires a direct measurement of that area.
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  • 11
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    Calcified tissue international 30 (1980), S. 209-216 
    ISSN: 1432-0827
    Keywords: Calvarium ; cAMP ; Vitamin D3 metabolites ; Calcium ; Parathyroid hormone
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary Results from in vitro works suggest that 1,25- and 24,25-dihydroxyvitamin D3 (1,25-(OH)2D3 and 24,25-(OH)2D3) act on bone via different mechanisms. The present investigation was performed to study the effect of these two metabolites and of their precursor 25-hyxdroxyvitamin D3 (25-(OH)D3) on bone cAMP content in vitro. Rats' paired half calvaria were incubated under sterile conditions with one vitamin D3 derivative (10−13 to 10−9 M) or with ethanol (0.005 ml for 15 min to 24 h in 1 ml medium containing 0, 0.2, 1, 2, or 3 mM calcium. In some experiments: (a) cycloheximide (10−5M) was added simultaneously with the vitamin D3 metabolites; (b) 1–84 bPTH (5 × 10−8 M) was added for 5 or 15 min at the end of the 24 h incubation. Calvaria were immersed in 1 ml TCA 5% 4°C and homogenized. The cAMP was extracted with diethylether and measured by a competitive protein binding assay. Results bring further evidence for a particular effect of low doses of 24,25-(OH)2D3 (10−9 to 10−12M) and of 25-(OH)D3 (10−9 to 10−11M) on bone, different from that of 1,25-(OH)2D3: cAMP content was higher in 24,25-(OH)2D3- or 25-(OH)D3-treated and lower in 1,25-(OH)2D3-treated calvaria than in ethanol-treated ones with 1 mM calcium. The 1,25-(OH)2D3 effect persisted in calcium-free medium whereas 25-(OH)D3 and 24,25-(OH)2D3 effects could not be observed with 0 mM nor with 3 mM calcium. The required duration of the preincubation (over 1 h) as well as the inhibitory action of cycloheximide may suggest an involvement of protein synthesis in the vitamin D3 metabolites effects. Neither 1,25-(OH)2D3 nor 24,25-(OH)2D3 affected the PTH-induced increase in bone cAMP content.
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  • 12
    ISSN: 1432-0827
    Keywords: Hydroxyapatite ; Dissolution ; Pyrophosphate, Diphosphonates ; Calcium ; Phosphate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary Pyrophosphate and diphosphonate ions have been said to diminish the dissolution of hydroxyapatite crystals, because they lower the equilibrium concentrations of calcium and phosphate ions in the bulk solution around hydroxyapatite crystals in a closed system. However, in a closed system these effects are not necessarily due to an effect on dissolution alone. In this paper we have used a continuous flow system to study the effects of pyrophosphate and two diphosphonates, ethane-1-hydroxy-1,1-diphosphonate and dichloromethane diphosphonate, on the dissolution of hydroxyapatite. All three compounds decreased markedly the rate of dissolution of hydroxyapatite as well as the exchangeable pools of calcium and phosphate ions around the cystals.
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  • 13
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    Calcified tissue international 31 (1980), S. 231-238 
    ISSN: 1432-0827
    Keywords: Magnesium ; Bone ; Calcium ; Parathyroid gland
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary Calcium homeostasis and bone pathology were studied in weanling rats fed a low (70 ppm) magnesium diet for 2–21 days. The rats developed significant, progressive hypercalcemia after 6 days on the diet. The increase in blood calcium was accompanied by progressive hypoactivity of the parathyroid gland (PTG), as determined by histologic and morphometric analyses. Thus hyperactivity of the PTG could not have been responsible for the hypercalcemia observed. Histologic examination of femora and humeri from magnesium-deficient rats showed progressive subperiosteal hyperplasia, consisting of undifferentiated osteoprogenitor cells and fibrous tissue, after 7 days of deficiency. The presence of unmineralized osteoid tissue in the metaphyses indicated that mineralization was not proceeding normally. The alterations in differentiation of osteoprogenitor cells, together with the failure of mineralization, resulted in significantly lower rates of bone formation (as measured by fluorochrome labeling) in the magnesium-deficient rats. Basophilic cementing lines and inactive osteocytes in the cortices of bones from magnesium-deficient rats indicated that bone resorption was also severely reduced in magnesium deficiency. We postulate that bone magnesium depletion (66% by day 21) has a direct negative effect on osteoblastic and osteocytic activity, and may explain, in part, the decreased responsiveness of bone to parathyroid hormone (PTH) that has been observed in magnesium-deficient animals.
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  • 14
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    Calcified tissue international 32 (1980), S. 45-53 
    ISSN: 1432-0827
    Keywords: Dentin ; Periodicity ; Allometry ; Calcium ; Sulfur
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary We have described differences in the aspects of biological rhythms for calcium and sulfur deposition on the labial and lingual sides of the growing rabbit incisor, where growth occurs along a spiral axis. The calcium oscillations appear to be smoother on the labial side than on the lingual side. The lingual side is characterized by high-frequency rhythms with high amplitudes which possess the greatest percent of the power (Fourier analysis). These observations also reflect a difference in behavior of the mean Ca concentration across the labial and lingual sides. Sulfur rhythms on the labial side have higher amplitudes than those on the lingual side, but systematic differences in distribution of power between high and low frequencies is not as pronounced as in the case of Ca. The differences in Ca rhythms reflect differences in the growth rates of incisors on either side of the spiral axis. The labial side grows slightly faster than the lingual side, and its odontoblasts secrete Ca along the spiral axis and toward the pulp cavity at the same time. Thus the resultant direction of growth is more nearly opposite the extension of the occlusal end on the labial side, and Ca is consequently deposited over a wider area relative to that on the lingual surfaces. On the lingual side, Ca is deposited within a more limited area, and growth must therefore be continuous at high frequencies. The distribution of Ca on both sides of the tooth reflects these differences in growth rate and periodicity in two ways. First, given a unit area of tooth, the calcium concentration on the labial side is less than that of the lingual side. Second, whereas the calcium concentration on the labial side declines rapidly from the enamel-dentin junction to the pulp cavity, it is uniformly high across the lingual side because its growth is more continuous at high frequencies.
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  • 15
    ISSN: 1432-0827
    Keywords: 1α-Hydroxy vitamin D3 ; 1,25-Dihydroxyvitamin D3 ; Calcium ; Transport ; Intestine
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary The timed sequence of events following the oral administration of 1α-hydroxy vitamin D3 (1αOHD3) to rachitic chicks was compared to that following a comparable dose of 1α,25-dihydroxyvitamin D3 (1,25(OH)2D3). RNA polymerase activity was maximally increased 20% by 1αOHD3 within 1 to 2 h and returned to control values after 8 h. Alkaline phosphatase activity was stimulated by 4 h and was maximal (3- to 5-fold increase) at 24 h. Calcium binding protein (CaBP) was detected initially within epithelial cells at the proximal end of the villus (just above the crypt) 6 to 8 h after 1αOHD3 administration, in epithelial cells lining the proximal half of the villus by 24 h, and in epithelial cells along nearly the entire villus by 48 h. At no time did goblet cells contain CaBP. Serum calcium concentrations were significantly elevated in 2 h and maximal by 12 h (an increase of 3.6 mg/dl). Calcium accumulation by the intestinal mucosa in vitro was increased by 6 to 8 h and maximal (60% increase over controls) at 24 h. Phosphate accumulation by the intestinal mucosa in vitro was increased by 6 h and maximal (105% increase over controls) between 8 and 24 h. 1,25(OH)2D3 increased CaBP and calcium accumulation by 4 h, 2 h sooner than did 1αOHD3. 1,25(OH)2D3 decreased serum calcium levels and increased serum phosphate levels at 2 h unlike 1αOHD3. No difference in the effects of these compounds on alkaline phosphatase activity, RNA polymerase activity, and phosphate accumulation could be demonstrated. These results are consistent with the possibility that 1αOHD3 may not require conversion to 1,25(OH)2D3 for all of its biological effects.
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  • 16
    ISSN: 1432-0827
    Keywords: Perifusion ; Parathyroid hormone ; In vitro ; Calcium ; Beta regulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary An in vitro perifusion system was used to study parathyroid hormone (PTH) secretion in response to calcium (Ca) and beta-adrenergic agents. Perifused parathyroid tissue responded to changes in Ca within the physiologic range during experiments up to 5 h. There was rapid secretory stimulation after exposure to low Ca, with the maximum response being observed at 20 min. Normal bovine glands showed a Ca-independent nonsuppressible component of PTH release at concentrations of Ca above physiologic. 1-isoproterenol produced rapid stimulation of PTH release, the response being blocked by a beta antagonist. The maximum secretory response to either low Ca (0.5 mM) or 1-isoproterenol (10−5 M) was enhanced when the two stimuli were applied simultaneously. The response to isoproterenol was blocked by raising Ca to 2.5 mM. Although d,l-propranolol (10−4 M) caused mild suppression of PTH release at a Ca of 1.25 mM, it did not cause additional suppression at 2.5 mM Ca nor did it decrease the response to 0.5 mM Ca stimulation. The secretory response of the gland to low Ca was sustained at a level more than double the baseline rate. The response to isoproterenol was more transient, with a return to or toward baseline secretion within 60 min. These results suggest that beta agonists and low Ca have separate but related mechanisms for stimulating PTH release and may affect different pools of hormone. The perifusion system described is a relatively simple technique for assessing the kinetics and interactions of various stimulators of PTH secretion.
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  • 17
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    Calcified tissue international 32 (1980), S. 29-44 
    ISSN: 1432-0827
    Keywords: Rabbit ; Dentin ; Calcium ; Sulfur ; Periodicity ; Circadian ; Ultradian
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary We have identified a variety of biological rhythms involved in the apposition and mineralization of dentin in the rabbit incisor. Animals were injected during the day or night with lead acetate at 2-week intervals—to provide biological time markers in forming dentin—and transverse undecalcified sections of the lower incisors were prepared for electron microprobe analysis. The positions of the lead markers were identified, and the continuous distribution of calcium and sulfur was measured at 1 µm intervals between the markers. In thin sections stained with hematoxylin after decalcification, the widths of a series of structural increments (bands) were measured with an ocular micrometer. Fourier analysis of the data revealed spectra of structural and compositional rhythms with a range of periodicities which extended from a matter of hours [ultradian (〈24 h)] to days [infradian (〉24 h) and circadian (approximately 24 h)]. The structural and compositional rhythms appeared to be independent to the extent that they did not necessarily have the same periods, or amplitudes. Nor were there simple phase relationships between all of the rhythms. At some times, Ca and S fluctuations are inversely proportional (180° out of phase), but in other cases they are directly proportional or out of phase by varying degrees other than 180°. The analyses thus suggest that calcium and sulfur deposition (representing mineral and glycosaminoglycan deposition, respectively) are not simply inversely proportional, and that the hematoxylin-stained structural increments did not solely reflect differences in the distribution of the mineral components in dentin.
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  • 18
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    Calcified tissue international 34 (1982), S. 253-257 
    ISSN: 1432-0827
    Keywords: Prednisolone ; Calcium ; Bone ; Corticoid osteopenia ; Vitamin D metabolites
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary Adult male rats were fed a diet containing 0.15% calcium, 0.3% phosphorus, and either 100, 50, or 20 mg of prednisolone per kg of diet. All these levels of prednisolone led to osteopenia, decreased intestinal absorption of calcium, slightly lower serum calcium and phosphorus, and a decreased level of serum 1,25-dihydroxyvitamin D3. Exogenous parenteral 1,25-dihydroxyvitamin D3 corrected steroid-induced changes in serum calcium and phosphorus, but could not completely correct the low intestinal calcium transport; nor did it prevent the development of osteopenia. The prednisolone-induced osteopenia seems at least in part to be caused by impaired intestinal calcium transport. The impaired calcium transport may be the result of low levels of 1,25-dihydroxyvitamin D3 and a direct effect of presnisolone on the intestine.
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  • 19
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    Calcified tissue international 35 (1983), S. 107-110 
    ISSN: 1432-0827
    Keywords: Calcium ; Glucocorticoid ; Vitamin D ; Osteoporosis ; Rat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary Eighty-eight adult male Sprague-Dawley rats were given a diet with either (a) 0.5% Ca and 0.6% P or (b) 0.01% Ca and 0.6% P. Osteopenia was created by adding prednisolone to the diet. The prophylactic effect of oral 1,25(OH)2D3 on the osteopenia was studied. It was found that prednisolone osteopenia in the rat was associated with defective Ca absorption. By giving an oral dose of 1,25(OH)2D3, it was possible to maintain normal Ca absorption during prednisolone treatment and to prevent the bone loss. No significant hypercalcemia or any kidney calcifications were seen. These results are in contrast to earlier findings, in which subcutaneous administration of 1,25(OH)2D3 failed to prevent prednisolone osteopenia because of its tendency to increase bone resorption.
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  • 20
    ISSN: 1432-0827
    Keywords: 31P NMR spectroscopy ; Phosphoprotein ; Dentin ; Calcium ; Inorganic orthophosphate ; Bovine
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary The single phosphoprotein of fetal calf dentin, having a molecular weight of approximately 94,000 and a phosphorus content of 8% (w/w), was examined by31P NMR spectroscopy. The single resonance at 3.7 ppm at pH 10 and its chemical shift during acid titration established the phosphomonoester nature of the organic phosphorus moiety. During titration of the phosphoprotein with CaCl2 in the presence of inorganic orthophosphate ions, line broadening for the orthophosphate resonance was both phosphoprotein- and calcium-dependent, indicating ternary complex formation. The data indicate that the phosphoprotein of fetal calf dentin binds both calcium and inorganic orthophosphate ions and therefore has the requisite physical chemical properties necessary for it to facilitate the heterogeneous nucleation of a Ca-PO4 solid phase from solution during tissue mineralization.
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  • 21
    ISSN: 1432-0827
    Keywords: Calcitonin ; Parathyroid hormone ; Calcium ; Newborn ; Fracture
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Summary Determinations of serum calcium (Ca), phosphorus (P), calcitonin (CT), and parathyroid hormone (PTH) were carried out in 36 full-term newborn infants with fracture of the clavicle (CF) and in 46 normal neonates (N). At the 6th hour of life the CF neonates demonstrated lower serum Ca and higher serum CT in comparison with normal infants. In the hours following, no significant differences between the two groups for the Ca levels were found, whereas serum CT remained significantly higher in the CF newborns at the 24th, 48th, and 72nd hour of life. Significant differences between normal and CF infants in the PTH serum levels were detected only at the 48th hour, when PTH was lower in the CF newborns. The results of this investigation indicate that the fracture of the clavicle is a significant and peculiar factor in stimulating CT secretion. Serum Ca level appeared to be controlled by CT rather than auto-regulating the secretion of the hormone.
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    Calcified tissue international 33 (1981), S. 409-416 
    ISSN: 1432-0827
    Keywords: Bone Cells ; Cyclic AMP ; Calcium ; Parathyroid hormone ; Prostaglandin
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    Topics: Biology , Medicine , Physics
    Notes: Summary We have examined the influence of extracellular Ca2+ on cyclic AMP metabolism in an osteoblast-enriched population of bone cells isolated from the calvaria of rat fetuses. The cyclic AMP1 response to stimulators of cyclic AMP formation (PTH and PGE2), but not basal cyclic AMP levels, increased progressively as the extracellular Ca2+ concentration was raised from 0.2 to 4.0 mM. The response to changes in extracellular Ca2+ were rapid (within 3.5 min), and the level of responsivity that characterized each Ca2+ concentration persisted for at least 6 h when the Ca2+ concentration was kept constant. The effect of Ca2+ spanned the entire time course of PTH action, was not accompanied by altered excretion of cyclic AMP from the cells, and was evident at low as well as at high hormone concentrations. Ca2+ augmented the action of PTH in the presence as well as in the absence of cyclic AMP phosphodiesterase inhibitors, and failed to decrease cyclic AMP phosphodiesterase activity in the short term. Mn2+ and, to a smaller degree, Ba2+ substituted for Ca2+ in promoting the cyclic AMP response to PTH. Verapamil, an inhibitor of Ca2+ penetration, blunted the Ca2+-mediated increments in the cyclic AMP response, and the divalent cation ionophore A23187 enhanced these increments. These results indicate that Ca2+ and other cations are positive effectors of the stimulated cyclic AMP response in isolated bone cells. Accumulation into an as yet unknown cellular compartment may be required for the cation effect. The data are most consistent with enhancement of adenylate cyclase reactivity as the mode of cation action.
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    Calcified tissue international 32 (1980), S. 201-206 
    ISSN: 1432-0827
    Keywords: Magnesium ; Parathyroid hormone ; Secretion ; In vitro ; Calcium
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    Topics: Biology , Medicine , Physics
    Notes: Summary In a well-defined in vitro perifusion system, the effects of extracellular magnesium concentration (Mg) on parathyroid hormone (PTH) secretion by bovine parathyroid tissue were examined. At Mg less than 0.8 mM, the ability of the glands to secrete hormone maximally in response to low calcium (Ca) stimulation was progressively impaired. Low Mg also impaired the ability of isoproterenol, dibutyryl cyclic AMP and theophylline to stimulate hormone release. The defect in hormone release at low Mg observed in vitro was analogous to the well-documented inhibition of secretion observed in vivo. Increases in Mg from 0 to 0.8 mM rapidly repaired the defect in hormone secretion. At Mg above 1.0 mM there was a Ca-like effect on hormone release, with a progressive decrease in secretion at increased Mg. Although its mechanism is not yet clear, the low Mg effect appears to impair principally the process of hormone release rather than its biosynthesis or storage.
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    Calcified tissue international 36 (1984), S. 77-82 
    ISSN: 1432-0827
    Keywords: Osteogenesis ; Diffusion chambers ; Alkaline phosphatase ; Calcium ; Phosphorus
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    Topics: Biology , Medicine , Physics
    Notes: Summary The alkaline phosphatase activity and the calcium and phosphorus content of osteogenic tissue formedin vivo following the implantation of diffusion chambers loaded with rabbit bone marrow cells is reported. (In this study the term osteogenic includes osteoblastic and chondroblastic.) Chambers examined 14–70 days after implantation revealed progressive accumulation of mineral. Alkaline phosphatase activity increased until day 30 and declined thereafter. The osteogenic potential of the marrow cells decreased with increasing weight (age) of the cell donor rabbit when measured either as the percentage of chambers containing osteogenic tissue or as the amount of calcium, phosphorus, or alkaline phosphatase activity within the chambers. The results confirm that measurements of these parameters in tissue formed by cells incubated in diffusion chambersin vivo may be used as a method for assay of osteogenesis.
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  • 25
    ISSN: 1432-0827
    Keywords: Calcium ; Vitamin D deficiency ; 1,25(OH)2D3 ; Parathyroidectomy ; Parathyroid hormone
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    Topics: Biology , Medicine , Physics
    Notes: Summary Studies presented here were designed to investigate further the basis for an impaired cAMP response to parathyroid hormone (PTH) in osteoblastlike calvarial bone cells isolated from vitamin D-deficient rat pups. The goal was to perturb Ca, PTH, and vitamin Din vivo in order to see which factors might be responsible for the impairedin vitro bone cell cAMP response. Pups either were parathyroidectomized (PTX) 3–5 days, implanted with osmotic minipumps delivering high doses of PTH, given repeated, high doses of 1,25(OH)2D3, or were D-deficient (-D, i.e., born and suckled by D-deficient mothers). Osteoblastlike bone cells, isolated by sequential enzyme digestion and centrifugation, were exposed to PTH for 5 min in the presence of a phosphodiesterase inhibitor. In bone cells isolated from -D rat pups, both basal and PTH-induced cAMP accumulation were significantly lower than in +D bone cells. Earlier, we had shown that two daily injections of -D pups with 50 ng 1,25(OH)2D3 restores this reduced bone cAMP response of -D pups toward normal. In the present study, neither basal nor PTH-induced bone cell cAMP accumulation was affected by subjecting D-replete pups to PTX, PTH infusion, or repeated high doses of 1,25(OH)2D3 despite the fact that each treatment markedly changed serum Ca or serum immunoreactive PTH. The results indicate that the impaired bone cell cAMP response seen in -D pups is not a direct result of chronic hypocalcemia and that the “heterologous desensitization” seenin vitro with added 1,25(OH)2D3 could not be duplicated byin vivo treatment of +D pups with supraphysiologic doses of 1,25(OH)2D3. Finally the lack of alteration in the bone cell cAMP response to PTHin vitro after chronic PTH infusionin vivo fails to support the notion that the impaired response in -D bone cells can be explained entirely by “homologous desensitization” induced by high circulating levels of PTH in the hypocalcemic, -D rat pup.
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    Calcified tissue international 33 (1981), S. 485-488 
    ISSN: 1432-0827
    Keywords: 1,25-(OH)2-D ; Hypophysectomy ; Calcium ; Phosphorus
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    Topics: Biology , Medicine , Physics
    Notes: Summary The mechanism by which dietary phosphate deprivation elevates plasma 1,25-(OH)2-D levels is not known. To evaluate the role of the pituitary in regulating plasma 1,25-(OH)2-D concentrations, the responses of plasma 1,25-(OH)2-D to dietary phosphate deprivation and, separately, to dietary calcium deprivation were evaluated in intact and hypophysectomized male rats. Among intact and hypophysectomized rats eating normal diets, plasma 1,25-(OH)2-D levels averaged 228±76 and 148±62 pmol/1, respectively (P〈0.01). During dietary phosphate deprivation, plasma 1,25-(OH)2-D levels rose to 1160±260 in intact rats and fell to 90±26 pmol/l in hypophysectomized rats (P〈0.001). By contrast, during dietary calcium deprivation, plasma 1,25-(OH)2-D levels rose in both intact and hypophysectomized animals to 856±107 and 742±279 pmol/l, respectively (NS). In response to dietary phosphate deprivation, serum calcium concentrations rose as 1,25-(OH)2-D concentrations rose in intact rats but remained at control levels in hypophysectomized rats. These results support the hypothesis that a pituitary hormone acting either directly or indirectly on the kidney mediates the increase in plasma 1,25-(OH)2-D during dietary phosphate deprivation. The hypercalcemia that occurs in rats during dietary phosphate deprivation appears to depend on the elevation of plasma 1,25-(OH)2-D.
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    Calcified tissue international 30 (1980), S. 27-34 
    ISSN: 1432-0827
    Keywords: Ultrastructure ; Calcium ; Cartilage ; Vesicles
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    Topics: Biology , Medicine , Physics
    Notes: Summary The potassium pyroantimonate technique was utilized for the selective subcellular localization of calcium in the mandibular condylar cartilage of 1-day-old rats. Electron dense calcium pyroantimonate precipitates were localized principally in mitochondria and at the cell membrane of the chondrocytes. In addition, small intracellular vesicles 0.1–0.2µm in diameter were observed in proximity to the cell membrane of chondrocytes of the mid-hypertrophic zone. The results suggest that these vesicles were being extruded from the cell into the extracellular matrix. Energy-dispersive analysis by X-rays confirmed that calcium is the principal cation of the electron-dense precipitates.
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    Calcified tissue international 36 (1984), S. 269-273 
    ISSN: 1432-0827
    Keywords: Bone loss (osteopenia) ; Calcium ; Corticosteroids (glucocorticosteroids) ; Fluoride ; Vitamin D
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    Topics: Biology , Medicine , Physics
    Notes: Summary To evaluate the effect of prednisone and triple treatment (sodium fluoride, calcium, and vitamin D) on trabecular and cortical bone serial bone mineral content (BMC) measurements were made at a metaphyseal (BMCD) and diaphyseal (BMCP) site on the forearm on 31 consecutive and previously bone-healthy patients scheduled for at least 24 weeks high-dose prednisone treatment. The patients were randomized into two further treatment groups: group I (n=16) received prednisone plus triple treatment and group II (n=15) received only prednisone. The two groups were similar with regard to age, sex, prednisone dose, and initial BMC. During 24 weeks treatment, BMCD (partially representing trabecular bone) and BMCP (mainly representing cortical bone) fell significantly and similarly, demonstrating that there is no preventive effect on bone mineral loss on the triple regimen. The BMC fall after 12 weeks was significantly more pronounced for metaphyseal (partially trabecular) than for diaphyseal (cortical) bone, whereas the values did not differ significantly after 24 weeks; this indicates a greater sensitivity to the hormone treatment of trabecular bone. In the entire group, the fall in BMC correlated positively with individual prednisone dose, significant at the diaphyseal site (r=0.39,P〈0.05), but not at the metaphyseal site (r=0.31, P=0.08). It is concluded that corticosteroid-induced osteopenia is a diffuse bone disease which affects trabecular as well as cortical bone, suggesting that BMC measured on the forearm reflects changes in bone mineral at other locations.
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    Calcified tissue international 36 (1984), S. 392-400 
    ISSN: 1432-0827
    Keywords: Vitamin D ; Chick embryo ; Bone ; Calcium ; Phosphate
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    Topics: Biology , Medicine , Physics
    Notes: Summary Chick embryos were injected in the yolk sac at various ages with various doses of different vitamin D3 metabolites. Serum concentrations of total calcium and inorganic phosphate were determined 24 h after the injection and histological and electron microscopic studies of the tibiae were conducted 3–6 days after. Confirming previous results, the injection of 1,25(OH)2D3 was found to produce significant hypercalcemia and hypophosphatemia. The dose required to produce these effects decreased with age: 100 ng on the 9th day, 50 ng on the 11th, and 10 ng on the 15th. This finding is interpreted as resulting from the fact that the specialized cells in the chorionic epithelium which are considered to be involved in mineral resorption from the shell differentiate between the 11th and 13th days. Although no bone changes were observed in embryos injected before the 11th day, a rim of unmineralized trabeculae (osteoid) was observed at the periphery of the cortex of the tibial diaphysis in the embryos which had been injected after that age. Thus, in embryos injected on the 11th day with 100 ng 1,25(OH)2D3, the trabeculae formed between the 11th and 14th day remained unmineralized until the 15th or 16th day at which time they completed their mineralization. In the embryos injected on the 14th day, the alterations were more severe and could be produced with doses 10 times smaller than those required when the injections were made on the 11th day. At all ages, the doses that produced an osteoid rim also induced hypercalcemia and hypophosphatemia. The electron microscopical study of the osteoid trabeculae showed that osteoblasts and osteocytes had normal cytological characteristics and that the bone matrix did not present changes other than the reduction in mineral deposition. While the above findings do not exclude a direct action of 1,25(OH)2D3 on bone cells as the mechanism of osteoid formation, they do underline the importance of the humoral changes at least as partial determinants of this phenomenon. The activities of various vitamin D metabolites were compared using as parameter the threshold-dose required to produce a rim of unmineralized trabeculae in the tibia of 14–15 days embryos (T-D). The most active metabolite appeared to be 1,25(OH)2D3 (T-D: 10 ng); it was followed by 1,24,25(OH)3D3 (T-D: 100 ng) and 1,25,26(OH)3D3 (T-D: 100 ng). Vitamin D3 itself (T-D: 100 µg), 25(OH)D3 (T-D: 2.5µg) and 24,25(OH)2D3 (T-D: 5 µg) produced similar responses but only when administered in much larger doses.
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    Calcified tissue international 36 (1984), S. 596-603 
    ISSN: 1432-0827
    Keywords: Calcium ; Ameloblasts ; X-ray microanalysis ; Transport ; Frozen
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    Topics: Biology , Medicine , Physics
    Notes: Summary Energy dispersive X-ray microanalysis was applied to freeze-dried blocks of enamel organ tissue to determine levels of calcium in various celular regions. The tissue blocks were dissected free from adjacent forming enamel following injection of cobalt or fluoride ions, both of which temporarily inhibit enamel mineralization. In all control and experimental specimens there was an increasing gradient of calcium from the stratum intermedium cells to the distal ends of the ameloblasts. Calcium levels were significantly reduced near the distal ends of the ameloblasts following cobalt or fluoride injection as compared with controls. It is suggested that evidence of an intercellular buildup of calcium near the distal ends of the ameloblast supports a controlling function of these cells. The changes in calcium levels are correlated with alterations in mineralization known to occur in the adjacent enamel of the model systems employed.
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    ISSN: 1432-0827
    Keywords: Saliva ; Calcium ; Phosphate ; Ion-binding ; Supersaturation
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    Topics: Biology , Medicine , Physics
    Notes: Summary Previous ultrafiltration studies indicated that up to one-half of the calcium and two-thirds of the phosphate in human salivary secretions may be bound by salivary proteins. Since this binding is an important variable in determining the extent of salivary supersaturation with respect to calcium phosphate salts, and since the amount of binding reported is surprisingly large, calcium and phosphate ion-binding by salivary macromolecules has been reexamined. From experiments using equilibrium dialysis, it was found that (1) the fraction of salivary calcium involved in macromolecular complexes ranges from a few percent for unstimulated secretions, to no more than about 10% for stimulated glandular salivas, and (2) salivary proteins do not bind phosphate ions to any significant extent. These findings, and experiments using an improved ultrafiltration membrane, indicate that the earlier results were artifacts of the ultrafiltration technique. Fractionation of salivary proteins, followed by equilibrium dialysis measurements, showed that the anionic proline-rich proteins and a basic proline-rich glycoprotein are responsible for most of the calcium binding now observed. The finding that macromolecular complexes of salivary calcium and phosphate have been overestimated in the past, leads to the conclusion that salivary calcium and phosphate ion activities in stimulated salivary secretions may be up to 50 to 100% higher than previously thought. Revised values were therefore used to recalculate the degree of salivary supersaturation with respect to calcium phosphate salts. The results indicate that stimulated salivary secretions are supersaturated with respect to dicalcium phosphate dihydrate; this is a substantially greater degree of supersaturation than previously reported.
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    Numerische Mathematik 41 (1983), S. 255-279 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L15 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Some methods for evaluating the characteristic exponents in connection with Newton's iteration are applied for solving the eigenvalue problem related to the finite Hill's differential equation or, in particular, Mathieu's equation. By using these methods a high accuracy is achieved, furthermore a complete error analysis, which yields rather realistic error bounds, is possible.
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    Numerische Mathematik 41 (1983), S. 373-398 
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    Keywords: AMS(MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The paper introduces a new semi-implicit extrapolation method especially designed for the numerical solution of stiff systems of ordinary differential equations. The existence of a quadratic asymptotic expansion in terms of the stepsize is shown. Moreover, the new discretization is analyzed in the light of well-known stability models. The efficiency of the new integrator is clearly demonstrated by solving a series of challenging test problems including real life examples.
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    Numerische Mathematik 41 (1983), S. 345-371 
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    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Maximum-norm stability and error estimates of best approximation and nonsmooth data types are derived for the approximate solution of a parabolic equation in one space variable, using the continuous in time Galerkin method based on piecewise polynomial approximating functions on a quasi-uniform mesh.
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    Numerische Mathematik 42 (1983), S. 119-123 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N10 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Many difference methods for the numerical solution of elliptic boundary value problems lead to systems of linear equations whose matrices areM-matrices and which therefore have nonnegative inverses. In this paper it is shown, that these difference methods are at most consistent of second order.
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    Numerische Mathematik 42 (1983), S. 271-290 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65J10, 65L20, 65M10 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Consider a linear autonomous system of ordinary differential equations with the property that the norm |U(t)| of each solutionU(t) satisfies |U(t)|≦|U(0)| (t≧0). We call a numerical process for solving such a system contractive if a discrete version of this property holds for the numerical approximations. A givenk-step method is said to be unconditionally contractive if for each stepsizeh〉0 the numerical process is contractive. In this paper a general theory is given which yields necessary and sufficient conditions for unconditional contractivity. It turns out that unconditionally contractive methods are subject to an order barrierp≦1. Further the concept of a contractivity threshold is studied, which makes it possible to compare the contractivity behaviour of methods with an orderp〉1 as well. Most theoretical results in this paper are formulated for differential equations in arbitrary Banach spaces. Applications are given to numerical methods for solving ordinary as well as partial differential equations.
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    Numerische Mathematik 42 (1983), S. 299-310 
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    Keywords: AMS(MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary A new approach to the problem of numerically integrating stiff differential systems is described. In this approach a linear multistep method (the basic method) is split into a kind of predictor-corrector scheme, where the predictor is also implicit. If this splitting is done in an appropriate manner, the modified method has considerably better stability properties than the basic method. As a result, splitting methods are particularly useful for problems where conventional integration methods experience stability difficulties. In particular some highly stable split linear multistep methods based on backward differentiation formulae are derived and a highly stable variable step implementation is proposed.
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    Numerische Mathematik 42 (1983), S. 311-322 
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    Keywords: AMS(MOS): 65 N 30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary This paper presents Galerkin approximations for solutions of two dimensional interface problems by solving corresponding boundary integral equations. These are obtained by simple layer potential operators only. Due to the strong ellipticity of the integral equations the Galerkin procedure converges with optimal order. Smoothness of the given data implies high convergence rates for the layers.
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    Numerische Mathematik 42 (1983), S. 349-357 
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    Keywords: AMS(MOS) 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary In this paper theD-stability properties of some classes of perturbed collocation methods are investigated. Among others we show the implicit Runge-Kutta methods described by Ehle-Chipman to beD-stable. We also give implicit Runge-Kutta methods that are bothD-stable andA-stable but notB-stable. Finally we indicate in what senseB-stability is stronger thanA-stability together withD-stability. The results of this paper are based on recent results of Nørsett and Wanner on perturbed collocation methods.
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    Numerische Mathematik 42 (1983), S. 359-377 
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    Keywords: AMS 65L05 ; 65L07 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary This paper is concerned with the stability of multistep methods for ordinary initial-value problems on grids with variable mesh-sizes. A necessary and sufficient condition for stability is given from which generalizations of recent results by Gear et al. and by Zlatev can be obtained as special cases. As an application the stability of the variable BDF-formulas is treated.
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    Numerische Mathematik 42 (1983), S. 379-389 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L20 ; 15A60 ; 65M20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary If the field of values of a matrixA is contained in the left complex halfplaneH and a functionf mapsH into the unit disc then ∥f(A)∥2≦1 by a theorem of J.v. Neumann. We prove a theorem of this type, only the field of values ofA is used for functions which are absolutely bounded by one in only part ofH. An extension can be used to show norm-stability of single step methods for stiff differential equations. The results are applicable among others to several subdiagonal Padé approximations which are notA-stable.
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    Numerische Mathematik 43 (1984), S. 105-119 
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    Keywords: AMS (MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary A new formulation of the Dirichlet problem for the biharmonic operator is presented. This gives rise to a simple numerical method to solve the above problem. Convergence is proved in the unidimensional case. Numerical results in one and two dimensional test problems are presented.
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    Numerische Mathematik 43 (1984), S. 175-198 
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    Keywords: AMS(MOS): 65 L 10 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We present a difference scheme for solving a semilinear singular perturbation problem with any number of turning points of arbitrary orders. It is shown that a solution of the scheme converges, uniformly in a perturbation parameter, to that of the continuous problem.
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    ISSN: 0945-3245
    Keywords: AMS (MOS): 65 N 30 ; CR: 5.17
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    Topics: Mathematics
    Description / Table of Contents: Summary This paper uses Augmented Lagrangian techniques for the numerical solution of equilibrium problems of compressible hyperelastic bodies subjected to large deformations. The resulting method is illustrated by several numerical examples.
    Notes: Résumé Cet article applique les techniques de Lagrangien Augmenté à la résolution numérique des problèmes d'équilibre de corps hyperélastiques compressibles soumis à de grandes déformations. La méthode obtenue est illustrée par plusieurs exemples numériques.
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    Numerische Mathematik 39 (1982), S. 449-463 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L65 ; CR: 5.17 ; AMS (MOS): 65L65 ; CR: 5.17
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    Topics: Mathematics
    Description / Table of Contents: Summary In [10] a general procedureV is presented to obtain spline approximations by collocation for the solutions of initial value problems for first order ordinary differential equations. In this paper the attainable order of convergence with respect to the maximum norm is characterized in dependence of the parameters involved inV; in particular the appropriate choice of the collocation points is considered.
    Notes: Zusammenfassung In [10] ist ein allgemeines VerfahrenV beschrieben, das die Lösungen von Anfangswertproblemen bei gewöhnlichen Differentialgleichungen erster Ordnung durch Splines approximiert. Die Konstruktion der Splines erfolgt hierbei mittels Kollokation. In dieser Arbeit wird die maximal erreichbare Konvergenzordnung vonV bezüglich der Maximumnorm in Abhängigkeit aller Parameter vonV charakterisiert, insbesondere wird auf die geeignete Wahl der Kollokationsknoten eingegangen.
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    Numerische Mathematik 40 (1982), S. 169-177 
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    Keywords: AMS(MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The stability and accuracy of some explicit nonlinear methods for the numerical integration of stiff systems of ordinary differential equations are investigated. It is shown, that in the general case they can produce the essential error. The special class of stiff systems is singled out, for which these methods are highly efficient. Some numerical results are also presented.
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    Numerische Mathematik 40 (1982), S. 179-199 
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; Primary 65N30 ; Secondary 35R35 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Two problems are considered in the paper: the first of them is connected with elliptic variational inequalities and consists in developing a moving obstacle algorithm for approximating the unknown free boundary; the other problem is linked with numerical solution of the Stefan problem, which is formulated in the similar way as in the elliptic case. Some computational aspects are also discussed in the paper.
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    Numerische Mathematik 40 (1982), S. 207-227 
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    Keywords: AMS(MOS): 65M30 ; CR: 5.17
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    Notes: Summary Several regularization methods for parabolic equations backwards in time together with the usual additional constraints for their solution are considered. The error of the regularization is estimated from above and below. For a “boundary value problem in time”-method, finite elements as well as a time discretization are introduced and the error with respect to the regularized solution is estimated, thus giving an overall error of the discrete regularized problem. The algorithm is tested in simple numerical examples.
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    Numerische Mathematik 40 (1982), S. 319-328 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65J05, 65L15 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Although multiparameter eigenvalue problems, as for example Mathieu's differential equation, have been known for a long time, so far no work has been done on the numerical treatment of these problems. So in this paper we extend the spectral theory for one parameter (cf. [7, II, VII]) to multiparameter eigenvalue problmes, formulate in the framework of discrete approximation a convergent numerical treatment, establish algebraic bifurcation equations for the intersection points of the eigenvalue curves and illustrate this with some numerical examples.
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    Numerische Mathematik 40 (1982), S. 373-406 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30, 65M20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We extend in this paper the analysis of a posteriori estimates of the space discretization error presented in a previous paper [3] for time-independent space meshes. In the context of the model problem studied there, results are given relating the effectiveness of the error estimator to properties of the solution, space meshes, and manner in which the meshes change. A procedure based upon this theory is presented for the adaptive construction of time-dependent meshes. The results of some computational experiments show that this procedure is practically very effective and suggest that it can be used to control the space discretization error in more general problems.
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    Numerische Mathematik 40 (1982), S. 329-337 
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    Keywords: AMS (MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary A widely used technique for improving the accuracy of solutions of initial value problems in ordinary differential equations is local extrapolation. It is well known, however, that when using methods appropriate for solving stiff systems of ODES, the stability of the method can be seriously degraded if local extrapolation is employed. This is due to the fact that performing local extrapolation on a low order method is equivalent to using a higher order formula and this high order formula may not be suitable for solving stiff systems. In the present paper a general approach is proposed whereby the correction term added on in the process of local extrapolation is in a sense a rational, rather than a polynomial, function. This approach allows high order formulae with bounded growth functions to be developed. As an example we derive anA-stable rational correction algorithm based on the trapezoidal rule. This new algorithm is found to be efficient when low accuracy is requested (say a relative accuracy of about 1%) and its performance is compared with that of the more familiar Richardson extrapolation method on a large set of stiff test problems.
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    Numerische Mathematik 40 (1982), S. 339-371 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; 65M20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary In this first of two papers, computable a posteriori estimates of the space discretization error in the finite element method of lines solution of parabolic equations are analyzed for time-independent space meshes. The effectiveness of the error estimator is related to conditions on the solution regularity, mesh family type, and asymptotic range for the mesh size. For clarity the results are limited to a model problem in which piecewise linear elements in one space dimension are used. The results extend straight-forwardly to systems of equations and higher order elements in one space dimension, while the higher dimensional case requires additional considerations. The theory presented here provides the basis for the analysis and adaptive construction of time-dependent space meshes, which is the subject of the second paper. Computational results show that the approach is practically very effective and suggest that it can be used for solving more general problems.
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    Numerische Mathematik 41 (1983), S. 55-62 
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    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The finite element method with Laplace transform of time variable is proposed for the solution of hyperbolic equations. Error estimates in Hardy spaces of functions with values in Sobolev spaces are derived. Due to the isometric isomorphism of Hardy spaces with weighted Hilbert spaces these estimates are valid also for original formulations of hyperbolic equations.
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    Numerische Mathematik 41 (1983), S. 165-175 
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    Keywords: AMS(MOS): 65LO5 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The extrapolated midpoint rule is a popular way to solve the initial value problem for a system of ordinary differential equations. As originally formulated by Gragg, the results are smoothed to remove the weak instability of the midpoint rule. It is shown that this smoothing is not necessary. A cheaper smoothing scheme is proposed. A way to exploit smoothing to increase the robustness of extrapolation codes is formulated.
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
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    Notes: Summary We study the difference equations obtained when a linear multistep method is applied to the scalar test equationdy/dt=λy and constant stepsizeh. LetS be the region of the absolute stability of the method, and letD be a closed subset ofS (on the Riemann sphere $$\mathbb{C}$$ ). It is shown that the solutions of these difference equations are bounded forn≧0, uniformly for λh∈D.S is itself closed in $$\mathbb{C}$$ iff ∂S is free of cusps. The question is studed by means of contractivity analysis and a matrix theorem, derived from the matrix theorem of Kreiss.
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    Numerische Mathematik 41 (1983), S. 399-422 
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    Keywords: AMS(MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The paper presents a new theory for joint order and stepsize control in extrapolation methods. This theory defines a locally optimal order that can be determined along any trajectory to be computed. In addition, Shannon's information theory is applied to derive some ideal convergence model that is expected to describe the behavior of an extrapolation method over a large set of test problems. Extensive numerical comparisons document a drastic acceleration in stiff integration and a mild acceleration in non-stiff integration by the new device. Moreover, a significant increase in reliability, robustness, and portability of the extrapolation codes is achieved.
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    Numerische Mathematik 42 (1983), S. 15-30 
    ISSN: 0945-3245
    Keywords: AMS: 65L10 ; 34C25 ; 34K10 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary An iterative method is presented which starting from a lower or from an upper periodic solution, provides a monotone sequence converging to a periodic solution of (1). With some restrictions on the growth off, the method extends to functional differential equations of type (1′). Two numerical examples with an “a posteriori” error analysis are given.
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    Numerische Mathematik 42 (1983), S. 51-64 
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    Keywords: AMS (MOS): 65N99 ; 35L05 ; CR: 5.17
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    Notes: Summary Engquist and Majda [3] proposed a pseudodifferential operator as asymptotically valid absorbing boundary condition for hyperbolic equations. (In the case of the wave equation this boundary condition is valid at all frequencies.) Here, least-squares approximation of the symbol of the pseudodifferential operator is proposed to obtain differential operators as boundary conditions. It is shown that for the wave equation this approach leads to Kreiss well-posed initial boundary value problems and that the expectation of the reflected energy is lower than in the case of Taylor- and Padé-approximations [3, 4]. Numerical examples indicate that this method works even more effectively for hyperbolic systems. The least-squares approach may be used to generate the boundary conditions automatically.
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    Numerische Mathematik 42 (1983), S. 77-95 
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    Keywords: AMS(MOS): 65N99 ; CR: 5.17
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    Notes: Summary Brakhage and Werner, Leis and Panich suggested to reduce the exterior Dirichlet boundary value problem for the Helmholtz equation to an integral equation of the second kind which is uniquely solvable for all frequencies by seeking the solution in the form of a combined double- and single-layer potential. We present an analysis of the appropriate choice of the parameter coupling the double- and single-layer potential in order to minimize the condition number of the integral operator.
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    Numerische Mathematik 42 (1983), S. 65-76 
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    Keywords: AMS(MOS): 65 N 20 ; CR: 5.17
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    Notes: Summary We consider here a general class of algorithms for the numerical solution of variational inequalities. A convergence proof is given and in particular a multi-grid method is described. Numerical results are presented for the finite-difference discretization of an obstacle problem for minimal surfaces
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    Numerische Mathematik 42 (1983), S. 173-194 
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    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We consider the stationary Navier-Stokes equations, written in terms of the primitive variables, in the case where both the partial differential equations and boundary conditions are inhomogeneous. Under certain conditions on the data, the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed. A conforming finite element method is presented and optimal estimates for the error of the approximate solution are proved. In addition, the convergence properties of iterative methods for the solution of the discrete nonlinear algebraic systems resulting from the finite element algorithm are given. Numerical examples, using an efficient choice of finite element spaces, are also provided.
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    Development genes and evolution 189 (1980), S. 57-67 
    ISSN: 1432-041X
    Keywords: Drosophila ; Ecdysone deficient mutants ; Ecdysteroid titer ; Ring gland ; Fine structure
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    Topics: Biology
    Notes: Summary This paper describes two ecdysone-deficient, recessive-lethal mutants,lethal(1)giant ring gland (grg) andlethal(1)suppressor of forked mad-ts (mad-ts: Jürgens and Gateff 1979) and compares their ecdysteroid titers with that of the wild-type. Mutant larvae show a much reduced ecdysteroid content, amounting to 1/10 to 1/30 of the wild-type values, but never a true titer peak. They fail to pupate and die after 1–3 weeks. Ecdysteroid feeding elicits different responses in the larvae of the two mutants.mad-ts larvae pupate within 24 h, thus showing that their low ecdysteroid titer is directly connected to their inability to pupate.mad-ts resembles the mutantlethal (3)ecdysone-1 ts (Garen et al. 1977). Thegrg mutant larvae, on the other hand, fail to pupate after 20-hydroxyecdysone feeding as well as injection. The primary defect of thegrg mutant is not entirely clear. Thegrg larval salivary gland cells appear to possess normal ecdysteroid receptors. Furthermore, the low ecdysteroid titer ingrg is not the result of an increased ecdysteroid catabolism. The primary defect in the mutant may lie in the malfunctioning neurosecretory cells which do not show neurosecretion in histological preparations. Further support for this notion comes from electronmicrographs of the enlargedgrg ring glands which, in contrast to the wild-type, do not possess nerve endings. In the wild-type three ecdysteroid peaks were found: one shortly before puparium formation, the second at approximately 12 h and the third at about 30 h after pupation. The ecdysteroid titer peak in late third instar, wild-type larvae is mainly due to the presence of 20-dydroxyecdysone as shown by radioimmunoassays after thin layer chromatography and derivatization followed by gas liquid chromatography and mass spectroscopy. In addition, a number of unidentified polar and apolar metabolites were also present.
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    Development genes and evolution 190 (1981), S. 11-21 
    ISSN: 1432-041X
    Keywords: Drosophila ; Imaginal discs ; Ecdysteroid ; Lethal mutant ; Morphogenesis
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    Topics: Biology
    Notes: Summary Imaginal disc development in the non-pupariating lethall(1)npr-1, a mutant that maps to an ecdysone early puff site, is studied in situ, in vitro and in transplanted discs. Disc development is slightly abnormal from the middle of the third instar with severe abnormalities appearing after the rise in 20-hydroxyecdysone that triggers metamorphosis. The mutant discs only partly evaginate and do not undergo any of the detailed morphological changes characteristic of metamorphosis. Treatment of the mutant dises in vitro with colcemid and trypsin facilitates evagination but the appendages remain morphologically abnormal. A number of differentiative processes occur in mutant discs in situ and in discs transplanted into wild type hosts in spite of the absence of normal morphogenesis. Implications of the observations for normal disc development are discussed. Possible modes of action of thel(1)npr-1 gene are also discussed in light of the observation that the mutant gene maps to a locus which is thought to have a regulatory function in development.
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    Development genes and evolution 190 (1981), S. 132-138 
    ISSN: 1432-041X
    Keywords: Maternal effect mutant ; Homeotic-mutants ; Pattern formation ; Drosophila
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    Topics: Biology
    Notes: Summary The temperature sensitive mutationfs(l)h is characterized at the restrictive temperature of 29°C by both a maternal effect responsible for the early embryonic lethality and pupal zygotic lethality. The two phenotypes are inseparable and map at a short deletion in the X chromosome (7Dl, 7D5-6). At semipermissive temperatures, hemizygous mutant females produce adults with morphological defects, such as organ deficiencies and homeotic transformations of haltere to wing and third leg to second leg. These defects depend on the maternal genotype and are governed by an early temperature sensitive period, which covers the end of oogenesis and the first hours of embryogenesis. Furthermore, this maternal effect mutation interacts with some dominant mutations of the bithorax system. These properties suggest thatfs(l)h is somehow involved in segmental determination.
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    Development genes and evolution 192 (1983), S. 164-170 
    ISSN: 1432-041X
    Keywords: Drosophila ; Imaginal disc ; Morphogenesis ; Tissue culture
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    Topics: Biology
    Notes: Summary The early morphogenesis of the eye-antennal disc ofDrosophila in response to 20-hydroxy ecdysone involves the curling of the eye anlagen dorsally over the antenna. During this process, the area of the peripodial membrane is substantially reduced. The peripodial membrane is taut at this stage, and if it is cut the curling of the disc cannot continue, and the eye anlagen returns to its original position within one minute of the operation. In contrast, cutting the columnar epithelium between the eye and antennal anlagen does not disrupt curling, but actually facilitates it. During curling, the cells of the peripodial membrane appear healthy, and exhibit basal extensions. We suggest that the curling of the eye is mediated by the conversion of cuboidal peripodial membrane cells into pseudostratified columnar epithelium at the edges of the peripodial membrane. Subsequently, cells of the peripodial membrane secrete first a pupal cuticle, and then an imaginal cuticle.
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    Development genes and evolution 193 (1984), S. 267-282 
    ISSN: 1432-041X
    Keywords: Drosophila ; Larval cuticle ; Pattern formation ; Embryonic lethal mutations
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    Topics: Biology
    Notes: Summary In a search for embryonic lethal mutants on the second chromosome ofDrosophila melanogaster, 5764 balanced lines isogenic for an ethyl methane sulfonate (EMS)-treatedcn bw sp chromosome were established. Of these lines, 4217 carried one or more newly induced lethal mutations corresponding to a total of 7600 lethal hits. Eggs were collected from lethal-bearing lines and unhatched embryos from the lines in which 25% or more of the embryos did not hatch (2843 lines) were dechorionated, fixed, cleared and scored under the compound microscope for abnormalities of the larval cuticle. A total of 272 mutants were isolated with phenotypes unequivocally distinguishable from wild-type embryos on the basis of the cuticular pattern. In complementation tests performed between mutants with similar phenotype, 48 loci were identified by more than one allele, the average being 5.4 alleles per locus. Complementation of all other mutants was shown by 13 mutants. Members of the complementation groups were mapped by recombination analysis. No clustering of loci with similar phenotypes was apparent. From the distribution of the allele frequencies and the rate of discovery of new loci, it was estimated that the 61 loci represent the majority of embryonic lethal loci on the second chromosome yielding phenotypes recognizable in the larval cuticle.
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    ISSN: 1432-041X
    Keywords: Drosophila ; Imaginal disc ; Morphogenesis ; Tissue culture
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    Topics: Biology
    Notes: Summary The thin region of the peripodial membrane is confined to the area overlying the distal anlagen in thoracic discs. During the early stages of evagination the peripodial membrane is greatly stretched, but does not rupture. The appendage then evaginates through the stalk, probably by means of a contraction of the peripodial membrane. The cells of the peripodial membrane of leg and wing discs persist and differentiate sheets of trichomes characteristic of the ventral and lateral thorax. This is discussed in relation to imaginal disc fate maps.
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    Numerische Mathematik 34 (1980), S. 1-13 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 34A45, 34A50, 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary In this paper Lie series are presented in Chebyshev form and applied to the iterative solution of initial value problems in differential equations. The resulting method, though algebraically complicated, is of theoretical interest as a generalisation of Taylor series methods and iterative Chebyshev methods. The theory of the method is discussed and the solutions of some simple scalar equations are analysed to illustrate the behaviour of the process.
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    Numerische Mathematik 34 (1980), S. 171-187 
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    Topics: Mathematics
    Notes: Summary Difference methods for the numerical solution of linear partial differential equations may often be improved by using a weighted right hand side instead of the original right hand side of the differential equation. Difference formulas, for which that is possible, are called “Mehrstellenformeln’ or Hermitian formulas. In this paper the Hermitian formulas for the approximation of Laplace's operator are characterized by a very simple condition. We prove, that in two-dimensional case for a Hermitian formula of ordern at leastn+3 discretization points are necessary. We give examples of such optimal formulas of arbitrary high-order.
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    Numerische Mathematik 34 (1980), S. 457-467 
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    Keywords: AMS(MOS): 65L05, 65Q05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary By employing a numerical method which uses only rather classical tools of Numerical Analysis such as Newton's method and routines for ordinary differential equations, unstable periodic solutions of differential-difference equations can be computed. The method is applied to determine bifurcation diagrams with backward bifurcation.
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    Numerische Mathematik 35 (1980), S. 13-20 
    ISSN: 0945-3245
    Keywords: AMS (MOS): primary 65M05 ; 65M10 ; 65M15 ; secondary: 35M05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We consider the numerical solution of the Tricomi problem. Using a weak formulation based on different spaces of test and trial functions, we construct a new Galerkin procedure for the Tricomi problem. Existence, uniqueness, and uniform stability of the approximate solution is proven, and a priori error bounds are given.
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    Numerische Mathematik 35 (1980), S. 21-33 
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    Keywords: AMS(MOS): 65B05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The trapezoidal rule with deferred corrections using uncentered end formulas is shown to converge. While the proof technique is more specialized than the standard asymptotic expansion approach, it has some advantages. In addition to providing a more complete theoretical justification for current implementations of deferred corrections with the trapezoidal rule, the approach given here will hopefully apply for several other discretization methods.
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    Numerische Mathematik 35 (1980), S. 57-68 
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    Keywords: AMS(MOS): 65L05 ; 65M20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary This paper discussesrational Runge-Kutta methods for stiff differential equations of high dimensions. These methods are explicit and in addition do not require the computation or storage of the Jacobian. A stability analysis (based onn-dimensional linear equations) is given. A second orderA 0-stable method with embedded error control is constructed and numerical results of stiff problems originating from linear and nonlinear parabolic equations are presented.
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    Numerische Mathematik 35 (1980), S. 127-142 
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    Keywords: AMS (MOS): 34G05, 65L05 ; CR: 5.17
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    Notes: Summary A class of approximation schemes of arbitrary accuracy, generated by a two-step recurrence relation, is devised for evolution equations of the second order. The schemes are effected via a specially constructed family of rational approximations to cos τ for τ≧0 and yield computationally efficient methods for systems of second-order ordinary differential equations and semidiscrete approximations for initial-boundary value problems for second-order hyperbolic equations.
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    Numerische Mathematik 35 (1980), S. 143-162 
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    Keywords: AMS(MOS): 65M15, 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We study the error due to the discretization in time of a nonlinear parabolic problem by a multistep method. Error estimates are obtained if the method is of the orderp (p〉1) and stronglyA(Θ)-stable $$\left( {0〈 \Theta〈 \frac{\pi }{2}} \right)$$ . The method is also applied to the Navier-Stokes equations in two dimensions.
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    Numerische Mathematik 35 (1980), S. 231-240 
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    Keywords: AMS(MOS): 65L10 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The homotopy method is a frequently used technique in overcoming the local convergence nature of multiple shooting. In this paper sufficient conditions are given that guarantee the homotopy process to be feasible. The results are applicable to a class of two-point boundary value problems. Finally, the numerical solution of two practical problems arising in physiology is described.
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    Numerische Mathematik 35 (1980), S. 257-276 
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    Keywords: AMS(MOS) ; 65M10 ; CR: 5.17
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    Topics: Mathematics
    Description / Table of Contents: Résumé Considérons une équation d'évolution parabolique linéaire associée à un opérateur linéaireA(t) dépendant du tempst. Nous développons dans cet article une méthode de discrétisation, basée sur les méthodes linéaires à pas multiples, traitant de manière implicite une partie de l'opérateurA(t) indépendante du temps, l'autre partie est traitée de manière explicite. Nous étudions la stabilité et la convergence de cette méthode.
    Notes: Summary Let us consider a linear parabolic equation which is associated with a time dependent operatorA(t). In this paper, we present a method, which is founded on linear multistep methods, which discretize a time-independent part of the operatorA(t) in an implicit way, and the other part in an explicit way. We study stability and convergence for this method.
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    Numerische Mathematik 35 (1980), S. 315-341 
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    Keywords: AMS(MOS) ; 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We present here some new families of non conforming finite elements in ℝ3. These two families of finite elements, built on tetrahedrons or on cubes are respectively conforming in the spacesH(curl) andH(div). We give some applications of these elements for the approximation of Maxwell's equations and equations of elasticity.
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    Numerische Mathematik 35 (1980), S. 381-404 
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    Topics: Mathematics
    Notes: Summary We study in this paper the convergence of a new mixed finite element approximation of the Navier-Stokes equations. This approximation uses low order Lagrange elements, leads to optimal order of convergence for the velocity and the pressure, and induces an efficient numerical algorithm for the solution of this problem.
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    Numerische Mathematik 36 (1980), S. 1-25 
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    Keywords: AMS(MOS): 65 N 30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We begin in this paper the study of a general method of approximation of solutions of nonlinear equations in a Banach space. We prove here an abstract result concerning the approximation of branches of nonsingular solutions. The general theory is then applied to the study of the convergence of two mixed finite element methods for the Navier-Stokes and the von Kármán equations.
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    Numerische Mathematik 36 (1980), S. 33-52 
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    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary A modified variational formulation, recently introduced by Taylor, Beresford and Wilson for solving second order problems, using the nonconforming Wilson element is here analysed. It is shown that the Patch Test is satisfied and that stresses and displacements are respectively first and second order accurate for arbitrary quadrilateral meshes.
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    Numerische Mathematik 36 (1980), S. 73-98 
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    Keywords: AMS: 35R35, 65P05, 76S05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary A new numerical method is used to solve stationary free boundary problems for fluid flow through porous media. The method also applies to inhomogeneous media, and to cases with a partial unsaturated flow.
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    Numerische Mathematik 36 (1980), S. 253-266 
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    Keywords: AMS(MOS): 65LO5 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Single step exponentially fitted integration formulae of orders 4 and 6 are derived. The final approximation to the required solution is obtained via a linear combination of asymptotically less accurate solutions obtained using conventional implicit integration formulae. This linear combination is performed in such a way that the final integration formula, as well as having an increased order of accuracy, integrates a certain pre-determined ordinary differential equation exactly. The algorithms developed are illustrated by means of some numerical examples.
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    Numerische Mathematik 36 (1980), S. 267-290 
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    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary In this paper, we present a finite element lumped mass scheme for eigenvalue problems of circular arch structures, and give error estimates for the approximation. They assert that approximate eigenvalues and eigenfuctions converge to the exact ones. Some numerical examples are also given to illustrate our results.
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    Numerische Mathematik 36 (1980), S. 319-331 
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    Keywords: AMS (MOS) ; 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Burrage and Butcher [1, 2] and Crouzeix [4] introduced for Runge-Kutta methods the concepts ofB-stability,BN-stability and algebraic stability. In this paper we prove that for any irreducible Runge-Kutta method these three stability concepts are equivalent.
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    Numerische Mathematik 36 (1981), S. 389-403 
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    Keywords: AMS(MOS): 65N 30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The paper deals with nonconforming finite element methods for the approximate solution of the interior boundary value problem for Maxwell equations in the time-harmonic case. The methods are based on penalization in the boundary conditions of total reflexion. Qualitative convergence results are obtained by a-priori estimates which are proven in the first part of this paper. The main object is to establish estimates for the global discretization error in various norms of the underlying spaces of approximating vector fields.
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  • 87
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    Keywords: AMS(MOS): 65N25 ; CR: 5.17
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    Notes: Summary In this paper we describe a nonconforming finite element method to compute the MHD spectrum of a plasma in a toroïdal configuration. We show that this method leads to a good approximation of the spectrum.
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    Numerische Mathematik 37 (1981), S. 1-28 
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    Keywords: AMS (MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We continue here the study of a general method of approximation of nonlinear equations in a Banach space yet considered in [2]. In this paper, we give fairly general approximation results for the solutions in a neighborhood of a simple limit point. We the apply the previous analysis to the study of Galerkin approximations for a class of variationally posed nonlinear problems and to a mixed finite element method for the NavierStokes equations.
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    Numerische Mathematik 37 (1981), S. 61-91 
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    Keywords: AMS(MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Stability regions of explicit “linear” time discretization methods for solving initial value problems are treated. If an integration method needsm function evaluations per time step, then we scale the stability region by dividing bym. We show that the scaled stability region of a method, satisfying some reasonable conditions, cannot be properly contained in the scaled stability region of another method. Bounds for the size of the stability regions for three different purposes are then given: for “general” nonlinear ordinary differential systems, for systems obtained from parabolic problems and for systems obtained from hyperbolic problems. We also show how these bounds can be approached by high order methods.
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    Numerische Mathematik 37 (1981), S. 105-120 
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    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary This study establishes an error estimate for a penalty-finite element approximation of the variational inequality obtained by a class of obstacle problems. By special identification of the penalty term, we first show that the penalty solution converges to the solution of a mixed formulation of the variational inequality. The rate of convergence of the penalization is ɛ where ɛ is the penalty parameter. To obtain the error of finite element approximation, we apply the results obtained by Brezzi, Hager and Raviart for the mixed finite element method to the variational inequality.
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    Numerische Mathematik 37 (1981), S. 157-166 
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    Keywords: AMS(MOS): 65L07 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Consider the systemy′=f(x,y),y(a)=η,x∈[a,b],y∈R n wheref is continuous and Lipschitzian with respect to the second argument. Very often linear multistep variable stepsize variable formula methods (LM VSVFM's) are used to computey k≈y(xk) on the points of the grid:a=x 0〈x1〈x2〈...〈xN=b. The general LM VSVFM is based on formulae of the following type $$y_k = \sum\limits_{i = 1}^{s_k } {\alpha _i (\bar h_k ,sk)y_{k - i} } + \sum\limits_{i = 0}^{s_k } {h_{k - i} \beta _i (\bar h_k ,s_k )f(x_{k - i} ,y_{k - i} )} $$ whereh k=xk−xk−1, $$\bar h_k = (h_k ,h_{k - 1} , \ldots ,h_{k - s_k } )$$ ,s k≦k, k=1(1)N. The coefficients α i and β i depend on the lasts k+1 stepsizes and on the formula used at stepk. Only the zero-stability properties of some special classes of LM VSVFM's (as for example those based on Adams formulae) were investigated in the literature. A class of three-ordinate LM VSVFM's is defined in this paper. Some results concerning the zero-stability properties of these methods are proved. It is shown that some well-known results are simple corollaries of the results found for the three-ordinate LM VSVFM's. It is easily seen that similar results hold for the corresponding one-leg VSVFM's. Finally, the use of the theoretical results in the practical implementations is briefly discussed.
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    Numerische Mathematik 37 (1981), S. 235-255 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; 65Q05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A class of numerical methods for the treatment of delay differential equations is developed. These methods are based on the wellknown Runge-Kutta-Fehlberg methods. The retarded argument is approximated by an appropriate multipoint Hermite Interpolation. The inherent jump discontinuities in the various derivatives of the solution are considered automatically. Problems with piecewise continuous right-hand side and initial function are treated too. Real-life problems are used for the numerical test and a comparison with other methods published in literature.
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    Numerische Mathematik 37 (1981), S. 257-277 
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    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary In theh-version of the finite element method, convergence is achieved by refining the mesh while keeping the degree of the elements fixed. On the other hand, thep-version keeps the mesh fixed and increases the degree of the elements. In this paper, we prove estimates showing the simultaneous dependence of the order of approximation on both the element degrees and the mesh. In addition, it is shown that a proper design of the mesh and distribution of element degrees lead to a better than polynomial rate of convergence with respect to the number of degrees of freedom, even in the presence of corner singularities. Numerical results comparing theh-version,p-version, and combinedh-p-version for a one dimensional problem are presented.
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    Numerische Mathematik 37 (1981), S. 355-370 
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    Keywords: AMS(MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Recently there has been considerable interest in the approximate numerical integration of the special initial value problemy″=f(x, y) for cases where it is known in advance that the required solution is periodic. The well known class of Störmer-Cowell methods with stepnumber greater than 2 exhibit orbital instability and so are often unsuitable for the integration of such problems. An appropriate stability requirement for the numerical integration of periodic problems is that ofP-stability. However Lambert and Watson have shown that aP-stable linear multistep method cannot have an order of accuracy greater than 2. In the present paper a class of 2-step methods of Runge-Kutta type is discussed for the numerical solution of periodic initial value problems.P-stable formulae with orders up to 6 are derived and these are shown to compare favourably with existing methods.
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    Numerische Mathematik 37 (1981), S. 405-421 
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    Keywords: AMS(MOS): 65 N 30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Abstract The discretization by finite elements of a model variational problem for a clamped loaded beam is studied with emphasis on the effect of the beam thickness, which appears as a parameter in the problem, on the accuracy. It is shown that the approximation achieved by a standard finite element method degenerates for thin beams. In contrast a large family of mixed finite element methods are shown to yield quasioptimal approximation independent of the thickness parameter. The most useful of these methods may be realized by replacing the integrals appearing in the stiffness matrix of the standard method by Gauss quadratures.
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    Numerische Mathematik 37 (1981), S. 387-404 
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    Keywords: AMS(MOS): 65N20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The treatment of a multigrid method in the framework of numerical analysis elucidates that regularity of the solution is not necessary for the convergence of the multigrid algorithm but only for fast convergence. For the linear equations which arise from the discretization of the Poisson equation, a convergence factor 0,5 is established independent of the shape of the domain and of the regularity of the solution.
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    Numerische Mathematik 45 (1984), S. 201-206 
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    Keywords: AMS(MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Bulirsch and Stoer have shown how to construct asymptotic upper and lower bounds on the true (global) errors resulting from the solution by extrapolation of the initial value problem for a system of ordinary differential equations. It is shown here how to do this for any one-step method endowed with an asymptotically correct local error estimator. The one-step method can be changed at every step.
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    Numerische Mathematik 38 (1982), S. 141-154 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 35 A 40 ; 35 K 05 ; 65 N 15 ; 65 K 05 ; 80 A 20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary A nonlinear approximation technique for the numerical solution of certain free boundary problems is proposed. The method is shown for a degenerate one-dimensional Stefan problem. For this problem, an error estimate, which is independent of the used algorithm, is derived. Numerical examples are discussed.
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    Numerische Mathematik 39 (1982), S. 221-230 
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    Keywords: AMS(MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary In this paper Adams type methods for the special case of neutral functional differential equations are examined. It is shown thatk-step methods maintain orderk+1 for sufficiently small step size in a sufficiently smooth situation. However, when these methods are applied to an equation with a “non-smooth” solution the order of convergence is only one. Some computational considerations are given and numerical experiments are presented.
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    Numerische Mathematik 39 (1982), S. 371-404 
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    Keywords: AMS (MOS): 65 N 30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The purpose of this paper is to study the approximation of the Von Karman equations by the mixed finite element scheme of Miyoshi and to follow the solutions arcs at a neighbourhood of the first eigenvalue of the linearized problem. This last problem is solved by a continuation method.
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