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  • 1980-1984
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  • 1950-1954
  • 1977  (43,877)
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  • 1975-1979  (43,877)
  • 1950-1954
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  • 101
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    European journal of nutrition 16 (1977), S. 92-97 
    ISSN: 1436-6215
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary The thermal inactivation of lipase out of Geotrichum candidum and of lipoxigenase out of soybeans was investigated in phosphate buffer solution. Comparable to peroxidase, a sharp bend was observed in the inactivation curves of both enzymes. The z-value of 19 °C for lipase out of Geotrichum candidum was higher than the values indicated in the pertinent literature for pancreas lipase and milk lipase. The z-value for soy lipoxigenase was found to be 9.8 °C.
    Notes: Zusammenfassung Die thermische Inaktivierung von Lipase aus Geotrichum candidum und von Lipoxigenase aus Sojabohnen wurde in Phosphatpufferlösung untersucht. Ähnlich wie bei Peroxidase wurde ein Knickpunkt bei den Inaktivierungskurven beider Enzyme beobachtet. Dabei ergab Lipase aus Geotrichum candidum einen z-Wert von 19 °C, der größer war als die in der Literatur angegebenen Werte für Pankreaslipase und Milchlipase. Für die Sojalipoxigenase wurde ein z-Wert von 9,8 °C ermittelt.
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  • 102
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    European journal of nutrition 16 (1977), S. 81-91 
    ISSN: 1436-6215
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary The thermal inactivation and storage behaviour for horseradish and spinach peroxidases were investigated in defined systems, in spinach also within its natural environment. The inactivation curves of either enzyme show a sharp bend which is clearly visible at low, but not at higher temperatures. The D-values were taken from the inactivation curves. z-values resulting from the D-values were 25.5 °C for horseradish peroxidase, 13 °C for isolated peroxidase and 18 °C for peroxidase in spinach extract. Horseradish peroxidase was relatively heat-resistent at pH 6.0, spinach peroxidase at pH 5.0–6.0; both enzymes were found to be highly susceptible to heat at pH 4.0. Peroxidase isolated from spinach responded differently to heating than the enzyme in spinach extract or suspension. This discrepancy indicates that certain model experiments cannot be transferred to foods. Heated peroxidase from horseradish and spinach were found to regenerate during storage; the extent of regeneration depended on the pH.
    Notes: Zusammenfassung Die thermische Inaktivierung und das Lagerungsverhalten von Peroxidase aus Meerrettich und Spinat wurden in definierten Systemen, bei Spinat auch innerhalb des natürlichen Verbandes, untersucht. Die Inaktivierungskurven wiesen bei beiden Enzymen einen Knickpunkt auf, der bei niedrigen Temperaturen deutlich, bei höheren Temperaturen dagegen nicht mehr erkennbar war. Aus den Inaktivierungskurven wurdenD-Werte ermittelt, aus denen sich z-Werte von 25,5 °C für Meerrettich-Peroxidase, von 13 °C für isolierte Peroxidase und von 18 °C für Peroxidase im Spinatextrakt ergaben. Meerrettich-Peroxidase war bei pH 6,0 und Spinat-Peroxidase zwischen pH 5,0 und 6,0 besonders hitzeresistent; bei pH 4,0 waren beide sehr hitzelabil. Die aus Spinat isolierte Peroxidase verhielt sich beim Erhitzen anders als das Enzym in Spinat-Extrakt oder -Suspension. Die beobachtete Diskrepanz deutet die Nichtübertragbarkeit gewisser Modelluntersuchungen auf Lebensmittel an. Erhitzte Peroxidasen aus Meerrettich und Spinat zeigten eine Regenerierung während der Lagerung, die vom pH-Wert abhängig war.
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  • 103
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    European journal of nutrition 16 (1977), S. 107-114 
    ISSN: 1436-6215
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary The thermal reaction of a lipid-acyl-hydrolase which seems to be important for the quality preservation of vegetable foods, was investigated in spinach. The authors applied a simple in-situ method using thin-layer chromatography which had been developed for the enzyme determination, to follow the thermal inactivation of the lipid-acyl-hydrolase by measuring the decomposition of lecithine, mono- und digalactosyl diglycerides. According to the incactivation curves, the enzyme is relatively little resistant to heat. Since the D- and z-values resulting from the inactivation curves for phospholipase, mono- and digalactolipase activities are almost the same, it can be assumed that the lipid-acyl-hydrolase is a multi-function enzyme in spinach.
    Notes: Zusammenfassung Das thermische Verhalten einer Lipid-Acyl-Hydrolase, die für die Qualitätserhaltung pflanzlicher Lebensmittel wichtig erscheint, wurde im Falle von Spinat näher untersucht. Zur Enzymbestimmung wurde eine einfache dünnschichtchromatographische „In situ“-Methode entwickelt und mit deren Hilfe die thermische Inaktivierung der Lipid-Acyl-Hydrolase durch Messung des Abbaus von Lecithin, Mono- und Digalaktosyldiglycerid verfolgt. Nach Ausweis der Inaktivierungskurven besitzt das Enzym eine relativ geringe Hitzestabilität. Da die aus den Inaktivierungskurven für Phospholipase-, Mono- und Digalaktolipase-Aktivitäten ermittelten D- und z-Werte nahezu gleich sind, wird angenommen, daß die Lipid-Acyl-Hydrolase im Spinat ein multifunktionelles Enzym ist.
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  • 104
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    European journal of nutrition 16 (1977), S. 98-106 
    ISSN: 1436-6215
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary The influence of milieu factors on the thermal inactivation of peroxidase and lipoxigenase was investigated. Cationogenic, anionogenic, non-ionogenic and amphoteric tensides were more or less effective in inactivating horseradish peroxidase. Most effective in this respect were lecithine and monoglyceride, both capable of swelling in water. In presence of lecithine, peroxidase was inactivated already at 0 °C and pH 4.0. Linoleic acid was more efficient in an oxygen stream than in presence of nitrogen, in a stream of nitrogen its influence was comparable to oleic acid. This suggests an additional effect by lipid peroxides which are formed of linoleic acid under the heating process. Tensides prevented the regeneration of the heated peroxidase. In the case of lipoxigenase, the authors investigated the influence of lecithine and various fatty acids on the thermal inactivation at 60 ° and pH 7.0. Lecithine accelerated the inactivation less distinctly than with peroxidase. The accelerated the inactivation less distinctly than with peroxidase. The accelerating effect of the fatty acids decreased in the order oleic acid, linoleic acid, palmitic acid, myristic acid and stearic acid.
    Notes: Zusammenfassung Der Einfluß von Milieufaktoren auf die thermische Inaktivierung von Peroxidase und Lipoxigenase wurde untersucht. Kationogene, anionogene, nichtionogene und amphotere Tenside hatten einen mehr oder weniger großen Effekt auf die Inaktivierung der Meerrettich-Peroxidase. Dabei wirkten die in Wasser quellenden Stoffe Lecithin und Monoglycerid am stärksten. Peroxidase wurde in Anwesenheit von Lecithin schon bei 0 °C und pH 4,0 stark inaktiviert. Linolsäure hatte im Sauerstoffstrom einen größeren Einfluß auf die Peroxidaseinaktivierung als in Anwesenheit von Stickstoff, im Stickstoffstrom aber einen ähnlichen Einfluß wie Ölsäure. Daraus ist auf einen zusätzlichen Effekt von Lipidperoxiden zu schließen, die während der Erhitzung aus Linolsäure entstehen. Die Regenerierung der erhitzten Peroxidase wurde durch die Anwesenheit von Tensiden verhindert. Im Falle der Lipoxigenase wurde der Einfluß des Lecithins und verschiedener Fettsäuren auf die thermische Inaktivierung bei 60 °C und pH 7 untersucht. Lecithin beschleunigte die Inaktivierung weniger stark, als dies bei Peroxidase der Fall war. Die beschleunigende Wirkung der Fettsäuren nahm in der Reihenfolge Ölsäure, Linolsäure, Palmitinsäure, Myristinsäure, Stearinsäure ab.
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  • 105
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    European journal of nutrition 16 (1977), S. 115-119 
    ISSN: 1436-6215
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Zusammenfassung Mongolische Gerbils bilden Cholesterolgallensteine, wenn sie mit einer Diät gefüttert werden, der Cholesterol und Cholinsäure zugefügt sind. Die Veränderung der Gallenzusammensetzung, die die Gallensteinbildung begleitet, besteht aus einer Steigerung der Cholesterolfraktion auf Kosten der Gallensäurefraktion der Summe von Gallensäuren und -lipiden. Die fünf Tiermodelle für Gallensteinbildung, über welche man jetzt zuverlässige Auskünfte hat, wurden verglichen. Alle fünf Modelle zeigten dieselbe Veränderung. Die Phospholipidfraktion zeigte eine Tendenz zu höheren Werten. In allen fünf Tiermodellen sank die Gallensäuren-/Phospholipid-Quote, wenn Gallensteine sich entwickelten.
    Notes: Summary Mongolian gerbils form cholesterol gallstones when fed with chow supplemented with cholesterol and cholic acid. The change in bile composition accompanying gallstone formation was found to consist of an increase of the cholesterol fraction at the expense of the bile acid fraction of the total sum of bile acids and lipids. The five animals models for gallstone formation on which reliable information regarding bile composition is now available, were compared. A similar change was found in all five models while the phospholipid fraction showed a tendency to higher values. In all five models the bile acid/phospholipid ratio decreases when gallstones are induced.
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  • 106
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    European journal of nutrition 16 (1977), S. 153-157 
    ISSN: 1436-6215
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Notes: Summary Under the effect of carbon-disulfide intoxication on serum levels of zinc, iron, calcium, magnesium, potassium, and sodium of albino rats, five groups of rats were injected with daily doses of carbon disulfide over a period of 50 days. The extent of regression of the developed biochemical derangement was also studied. A significant decrease was observed in the levels of serum zinc, iron, calcium, and magnesium, while a slight elevation in the level of serum potassium. No definite correlation could be found between the level of serum sodium in control and carbon-disulfide intoxicated rats. By stoppage of dosage at 20 days, most of these derangements started to be normal.
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  • 107
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    European journal of nutrition 16 (1977), S. 158-162 
    ISSN: 1436-6215
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Notes: Summary The vitamin content, namely vitamin C, carotene, riboflavin and nicotinic acid, of some popular vegetables and fruits was determined. It was found that the green parts of the plants were the most rich in these four vitamins. Trigonella foenum-graecum (Helba) was the richest of all vegetables and fruits in vitamin C (207 mg%). Scandicium stellatum (Shabat contains the highest value for carotene (57.3 mg%). Solanum tuberosum (Batatis) was the richest in riboflavin (0.3 mg%) and Pisum sativum (Busselah) in niacin (1.8 mg%).
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  • 108
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    Monatshefte für Mathematik 83 (1977), S. 9-23 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Two quantitative forms of the inverse function theorem giving estimates on the size of balls covered biholomorphically are proved for holomorphic mappings of a ball in a Banach space into the space. Also, a Bloch theorem forK-quasiconformal mappings on the open unit ball of a Banach space is given and some mapping properties ofK-quasiconformal mappings are deduced.
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  • 109
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    Monatshefte für Mathematik 83 (1977), S. 1-8 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Starting from Problem 4 on p. 36 ofK. Wagner's book “Graphentheorie” the following question is investigated: Suppose an (undirected) graphG having its edges valuated with nonnegative integers; does there exist a closed walk inG such that each 0-valuated edge is passed the same number of times in both directions, while ak-valuated edge fork〉0, is passed exactlyk times in one direction and not at all in the other direction (without having the direction prescribed)? A general criterion and a sufficient condition for the existence of such “value-true walks” are proved. For the analogous question for directed graphs an algorithm for the construction of such walks is established.
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  • 110
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    Monatshefte für Mathematik 83 (1977), S. 25-36 
    ISSN: 1436-5081
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    Topics: Mathematics
    Notes: Abstract In 1953L. Fejes Tóth published the following conjecture: Among all triangle-faced convex polyhedra with a given inradius the regular tetrahedron and octahedron have the least possible total edge-length. In the following this conjecture is proved.
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  • 111
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    Monatshefte für Mathematik 83 (1977), S. 37-41 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Consider the functional differential equations (1)x (n) (t)+a(t)f(x(g(t)))=Q(t) and (2)x (n) (t)+s(t)f(x(t))=0 wheres(t)≧γa(t) for all sufficiently larget, sayt≧T〉0 and for some γ, 0〈γ〈1. Recently,E. D. True proposed a new comparison theorem for equations (1) and (2) with which he proved some results on the oscillation of (1). The purpose of the present paper is to extend them to the more general case. The examples indicate that the results are applicable to interesting problems.
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  • 112
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    Monatshefte für Mathematik 83 (1977), S. 53-58 
    ISSN: 1436-5081
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    Topics: Mathematics
    Notes: Abstract Let (S,·) be a semi-group having the following properties: (1)S=∪S α where α is in some index setI andS α are subgroups isomorphic to each other, (2)S α∩S β=Ø, a void set for α≠β and (3) the identity ofS α is a left identity ofS for each α inI. Then the automorphism group Aut (S) ofS is studied from the point of category theory. It is proved that Aut (S) is determined by Aut (S α) and right multiplications by the identities of groupsS α.
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  • 113
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    Monatshefte für Mathematik 83 (1977), S. 43-52 
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    Topics: Mathematics
    Notes: Abstract LetG=H 1* A H 2 a free product with amalgamation with $$H_1 = \left\langle {s_1 ,...,s_m |s_1^{\alpha _1 } = ... = s_m^{\alpha _m } = 1} \right\rangle ,\alpha _i \geqslant 2,m \geqslant 2,$$ a free product ofm cyclic groups. If we ask for the generation ofG, the following questions are significant: 1) For which α i andm there is a set {x 1, ...,x m } of. generators ofH 1 withx 1=(s 1...s m )α, α≥2, and what can we say about α andx 2, ...,x m ? 2) for which α i andm there is a set {x 1, ...,x m } of generators ofH 1 withx 1=(s 1...s m )α x 2=h(s 1...s m )β h −1, α〉0, β〉0,h∈H 1, and what can we say about α, β,h andx 3, ...,x m ? In this note we give a complete solution of these questions.
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    Monatshefte für Mathematik 83 (1977), S. 59-63 
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    Topics: Mathematics
    Notes: Abstract The following theorem is going to be proved. Letp m be them-th prime and putd m :=p m+1−p m . LetN(σ,T), 1/2≤σ≤1,T≥3. denote the number of zeros ϱ=β+iγ of the Riemann zeta function which fulfill β≥σ and |γ|≤T. Letc≥2 andh≥0 be constants such thatN(σ,T)≪T c(1−σ) (logT) h holds true uniformly in 1/2≤σ≤1. Let ε〉0 be given. Then there is some constantK〉0 such that
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  • 115
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    Monatshefte für Mathematik 83 (1977), S. 65-75 
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    Topics: Mathematics
    Notes: Abstract An undirected graph Γ of valencyd and girth γ is called a (d, γ)-cage if its automorphism group acts transitively on the set of alls-paths in Γ ands≥(γ+1)/2. We discuss an elementary construction of two known families of cages which allows us to prove easily some facts about their automorphism groups. We give, for example, a new proof of the fact that the automorphism group ofSp 4(2 n ) contains elements which are not induced by ΓSp 4(2 n ).
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  • 116
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    Monatshefte für Mathematik 83 (1977), S. 93-97 
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    Topics: Mathematics
    Notes: Abstract LetX be a vector space over a totally ordered fieldF and Λ a subset ofF. Necessary and sufficient conditions are obtained on Λ for a join defined bya·b={λa+(1−λ)b|λ∈Λ} to make (X,·) (i) a convexity space (ii) a join system and (iii) a join space. For (X,·) to be a convexity space Λ is necessarily the set of elements between 0 and 1 for some ordered subfield ofF. In this setting join systems and join spaces are essentially the same but they remain quite distinct from convexity spaces.
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    Monatshefte für Mathematik 83 (1977), S. 89-91 
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    Topics: Mathematics
    Notes: Abstract It is shown by a simple induction that any square-free natural number is the square-free kernel of Euler's φ-function of infinitely many natural numbers. Furthermore every square-free natural number 〉1 is the square-free kernel of Euler's φ-function of infinitely many square-numbers.
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  • 118
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    Monatshefte für Mathematik 83 (1977), S. 77-88 
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  • 119
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    Monatshefte für Mathematik 83 (1977), S. 99-112 
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    Topics: Mathematics
    Notes: Abstract Letr *(x) denote the maximum number of pairwiserelatively prime integers which can exist in an interval (y,y+x] of lengthx, and let ϱ*(x) denote the maximum number ofprime integers in any interval (y,y+x] wherey≥x. Throughout this paper we assume the “primek-tuples hypothesis.” (This hypothesis could be avoided by using an alternative sievetheoretic definition of ϱ*(x); cf. the beginning of Section 1.) We investigate the differencer *(x)—ϱ*(x): that is we ask how many more relatively prime integers can exist on an interval of lengthx than the maximum possible number of prime integers. As a lower bound we obtainr *(x)—ϱ*(x)〈x c for somec〉0 (whenx→∞). This improves the previous lower bound of logx. As an upper bound we getr *(x)—ϱ*(x)=o[x/(logx)2]. It is known that ϱ*(x)—π(x)〉const.[x/(logx)2];.; thus the difference betweenr *(x) and ϱ*(x) is negligible compared to ϱ*(x)—π(x). The results mentioned so far involve the “upper bound” or “maximizing” sieve. In Section 2, similar comparisons are made between two types of “minimum” sieves. One of these is the “erasing” sieve, which completely eliminates an interval of lengthx; and the other, introduced by Erdös and Selfridge [1], involves a kind of “minimax” for sets of pairwise relatively prime numbers. Again these two sieving methods produce functions which are found to be closely related.
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  • 120
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    Monatshefte für Mathematik 83 (1977), S. 113-119 
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    Topics: Mathematics
    Notes: Abstract LetX denote a reflexive Banach space and {A(t)|t∈[0,T]} a time dependent family of accretive operators defined onX. Conditions are placed on {A(t)|t∈[0,T]} which are sufficient to guarantee the existence of solutions to the Cauchy initial value problem:u′(t,x)+A(t)u(t,x)=0; u(0,x)=x. These solutions are obtained via the method of product integration; however limits for the infinite product are taken with respect to the weak topology.
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    Monatshefte für Mathematik 83 (1977), S. 121-131 
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    Topics: Mathematics
    Notes: Abstract Results byW. Mader and the authors on the connectivity of finite graphs are generalized to include infinite graphs. In the infinite case a distinction must be made concerning the distribution of finite and infinite components with respect to the separating sets. Results are obtained relating these components to the atoms.
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    Monatshefte für Mathematik 83 (1977), S. 133-146 
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    Notes: Abstract Let ℜ={e(u)|u∈I} be a one-parameter family of straight lines forming a ruledC r-2-surface Φ⊂E n (n≥2,r≥1) without singular generatorse(u) (u∈I). As a synopsis, a generalization and an improvement of various results already known about the strictional properties of ruled surfaces Φ⊂E n (especially in the casen=3) the author demonstrates a uniform geometrical way of defining and uniquely obtaining thestriction point S(u) and theparameter of distribution d(u) of a generatore(u)∈ℜ under the minimal assumptions thate(u)∈ℜ⊂E n (n≥2) be noncylindrical andr≥1. Other methods of obtainingS(u) andd(u) are discussed in comparison, and special strictional properties ofskew ruled surfaces Φ⊂E n are proved.
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    Monatshefte für Mathematik 83 (1977), S. 147-153 
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    Notes: Abstract We give a new proof of the non uniqueness of the equilibrium state inF. Hofbauer's example. We extend it to obtain examples with any finite number of ergodic equilibrium states.
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    Monatshefte für Mathematik 83 (1977), S. 159-162 
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    Notes: Abstract We consider linear differential equations $$w^{(n)} + \sum\limits_{i = 0}^{n - 1} {\sigma _i w^{(i)} = 0 in |z|}〈 1.$$ If the coefficients σi inH ∞ the solutions of theis equations have only a finite number of zeros and therefore these solutions are multivalent in |z|〈1.
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    Monatshefte für Mathematik 83 (1977), S. 155-157 
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    Notes: Abstract By means of results due toKlieman andFlor it is shown that a Galois-polynomial of degree greater than two over a formally real field is determined uniquely by its root polynomials except for the degenerate case where the roots are linearly dependent.
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  • 126
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    Monatshefte für Mathematik 83 (1977), S. 163-166 
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    Topics: Mathematics
    Notes: Abstract By means of the Hoheisel—Montgomery prime number theorem it is shown that for every α≥1 the inequality $$|(\sigma (n)/n) - \alpha | \leqslant {1 \mathord{\left/ {\vphantom {1 {n^{({2 \mathord{\left/ {\vphantom {2 5}} \right. \kern-\nulldelimiterspace} 5}) - \varepsilon } }}} \right. \kern-\nulldelimiterspace} {n^{({2 \mathord{\left/ {\vphantom {2 5}} \right. \kern-\nulldelimiterspace} 5}) - \varepsilon } }}(\varepsilon 〉 0,\sigma (n) = \sum\limits_{d/n} d )$$ has infinitely many solutionsn∈N. It is highly probable that the exponent 2/5 can be replaced by 1.
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    Monatshefte für Mathematik 83 (1977), S. 191-200 
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    Notes: Abstract Corresponding to a graduation of the comprehension predicateC there arise two systems PC1 and PC2. PC1 represents constructive mathematics whereas PC2 as a restricted enlargement of PC1 enables one to deal with full set theory. Unnatural definitions likeKuratowski's ordered pair and identification of 0 and $$\not 0$$ are avoided. In PC1 the postulate introduced for ordered pairs holds not only for sets but for classes generally. The comprehension condition in PC1 implicitly contains a set axiom for at most denumerable calsses and for ordered pairs. By introduction of the concept “ordered self-pair” the real numbers are interpreted as self-pairs of (non denumerable) equivalence classes of concentrated ratioal sequences and they can be shown to be sets in PC1.
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    Monatshefte für Mathematik 83 (1977), S. 177-189 
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    Notes: Abstract Using symmetric forms $$M_{k_1 ,...,k_p } : = (1/A(n))\,\sum\limits_{v_1 ,...,v_p } {a_{v_1 }^{k_1 } ...a_{v_p }^{k_p } } $$ A(n)=number of terms of the sum,a ν〉0,k i≠0,i=1,...,n) the meansm k 1,...,kp:=(Mk 1,...,kp1/(k1+...+kp)(k1+...+kp≠0) are formed and investigated as to monotonicity under the hypothesis that the exponentsk 1,...,k p are certain linear functions of only one parameterk(k i =λ i k+β 1,λ i 〉0,β 1+...β p =0). (The means $$m_{\lambda _1 k_1 ,...,\lambda _1 k_p } $$ , e. g., are increasing ifk is increasing.) The proofs are elementary and use the known method of positive logarithmically convex (or concave) sequences and certain generalizations of Muirhead's theorem.
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    Monatshefte für Mathematik 83 (1977), S. 201-205 
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    Notes: Abstract This note is concerned with the existence of a weak solution for a degenerate Cauchy problem of parabolic type in then-dimensional spaceR n. The degenerate property is in the sense that the matrix (a ij(t,x)) involved in the differential operator is not necessarily positive definite. The essential idea is the construction of a suitable function spaceH and to prove the existence of a weak solution inH.
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    Monatshefte für Mathematik 83 (1977), S. 253-264 
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    Monatshefte für Mathematik 83 (1977), S. 207-221 
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    Notes: Abstract Let ℂ〚X〛=ℂ〚X 1,...,X n 〛 be the ring of formal power series inn indeterminates over ℂ. LetF:X→AX+B(X)=(F (1)(X),...,F (n)(X))∈(ℂ〚X〛) n denote an automorphism of ℂ〚X〛 and let ϱ1,...,ϱ n be the eigenvalues of the linear partA ofF. We will say thatF has an analytic iteration (a. i.) if there exists a family (F t (itX)) t∈ℂ of automorphisms such thatF t(X) has coefficients analytic int and such thatF 0=X,F 1=F,F t+t′=FtℴFt′ for allt,t′∈ℂ. Let now a setΛ=(lnϱ1,...,lnϱ n ) of determinations of the logarithms be given. We ask if there exists an a. i. ofF such that the eigenvalues of the linear partA(t) ofF t(X) are $$e^{\ln \varrho _1 t} ,...,e^{\ln \varrho _n t} $$ . We will give necessary and sufficient conditions forF to have such an a. i., namely thatF is conjugate to a semicanonical formN=T −1ℴFℴT such that inN (k)(X) there appear at most monomialsX 1 α1 ...X n n $$\ln \varrho _k = \sum\limits_{i = 1}^n {\alpha _i \ln } \varrho _i $$ . This generalizes a result of Shl.Sternberg.
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    Monatshefte für Mathematik 83 (1977), S. 265-278 
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    Notes: Abstract A sofic system is a symbolic flow defined by a finite semigroup. We exhibit finite procedures, involving only the defining semigroup, for answering cetain questions about a sofic system and for constructing certain subshifts of finite type associated with a sofic system.
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    Monatshefte für Mathematik 83 (1977), S. 223-251 
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    Notes: Abstract This paper presents a general investigation of the relations between structural properties of a totally ordered abelian semigroupS and the properties of various “topological” structures, such as topologies, bitopologies and (semi-)uniformities on a spaceX induced byS-valued distance functionsd∶X×X→S satisfyingd(x,y)=0 iffx=y and the triangular inequalityd(x,z)≤d(x,y)+d(y,z), for allx,y,z∈X. Since a linearly ordered abelian semigroupS need not be a topological semigroup with respect to its order topology we have to consider two cases: the case where addition inS is continuous at 0∈S, and the case where it is not. For both cases, we state several metrization theorems, examples and applications. In this connection, we are also concerned with some special basis-properties of topological spaces. Closely connected is the program stated byAlexandroff-Bourbaki (amongst others) to investigate to what extent countability inherent in matrization theory can be replaced by order-theoretic properties.—Distinguishing between symmetric and not necessarily symmetric distancesd S we obtain a theory containing the theory ofω µ -metrics andω µ- quasimetrics.—As far as it concerns not necessarily symmetric distancesd onX, it seems adequate to study the bitopological structure (τ e ,τ r ) induced onX byd and the “inverse” distanced −1 respectively. This is done in § 4 where, in this respect, we also generalize a well-known theorem ofSion andZelmer.
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    Monatshefte für Mathematik 83 (1977), S. 309-313 
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    Notes: Abstract In [1], semi-concentric circles have been defined and considered, also their special nets and pencils.—The isochordal curve and the isogonal curve of two circles, the isochordal lines and the isogonal points of three circles show many differences according to whether the two or three circles are semiconcentric or not. Results for semi-concentric circles are developed here, while results for other circles have been given in [2] and [5].
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    Monatshefte für Mathematik 83 (1977), S. 279-307 
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    Notes: Abstract We shall consider positive definite quadratic formsQ inr≥2 variables of the “almost diagonal shape” $$Q{\mathbf{ }}(u) = \sum\limits_{1 \leqslant j{\mathbf{ }} \leqslant \sigma } {\alpha j{\mathbf{ }}(u^{(j)} )} $$ where ϖ≥2, and for 1≤j≤ϖ,Q j is a positive definite quadratic form with integral coefficients inr j variables, α j is a positive real number,r j≥1 andr 1+...+r α=r Letb 1,...,b r be a system of real numbers with 0≤b j〈1. For x〉0 letA(x) be the number of lattice points in the ellipsoidQ(u+b)≤x, letV(x) be the volume of this ellipsoid and letP(x)=A(x)-V(x). Our purpose is to find the exact order ofP(x); i. e., the numberf for which for each ɛ〉0P(x)=O(xf+ε) andP(x)=Ω(x f−ε).
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    Monatshefte für Mathematik 83 (1977), S. 315-329 
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    Notes: Abstract LetX be a compact metric space, λ a probability measure onX, T a measure preserving transformation ofX into itself. Furthermore, letZ be a compact abelian group, andS the skew-product defined onX×Z by the formula:S(x,z)=(T x,z+ϕ(x)) where ϕ is some map fromX toZ. It is known that under the hypothesis of unique ergodicity for the triple (X, λ,T) and some suitable conditions of continuity onT and ϕ, the triple (X×Z,m,S) wherem is the product measure of λ by the Haar measure onZ is uniquely ergodic if and only if an associated functional equation has no non trivial solution.—We introduce here a generalization of unique ergodicity (which appears quite naturally when studying well distributed sequences) and prove about it the same kind of results.
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    Monatshefte für Mathematik 83 (1977), S. 331-337 
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    Notes: Abstract For any set ofn+1 pointsx 1, ...,x n+1F we denote byv(C(x 1,...,x n+1∈ℝ)) then-dimensional oriented volume of the convex hullC(x 1,...,x n+1) of these points. With a fixed symmetric functionf: ℝ→〉ℝ〉 strictly monotone increasing on the nonnegative real line, we consider the real functional RODEL on the set of all convex bodiesK of ℝn with absolute volume |v(K)|=1 and assert, that it takes its minimal value on the ellipsoids with absolute volume 1.
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    Monatshefte für Mathematik 83 (1977), S. 348-348 
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    Monatshefte für Mathematik 84 (1977), S. 13-19 
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    Notes: Abstract Let γ(n) be the largest squarefree divisor of a natural numbern. In this note we give an asymptotic formula for $$\sum\limits_{n \leqslant x} {\gamma (n)/n^k } $$ wherek is an arbitrary integer.
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    Monatshefte für Mathematik 84 (1977), S. 29-35 
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    Notes: Abstract LetF 2 be the free group with two generatorsa, b andP be a probability measure onF 2 with support {a, a −1,b, b −1}. The asymptotic behavior forn→∞ of the convolution powersP n (e) at the identitye is found.
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    Monatshefte für Mathematik 84 (1977), S. 1-11 
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    Notes: Abstract Let $$f(z) = \sum\limits_{h = 0}^\infty {f_h z^h } $$ be a power series with positive radius of convergenceR f ≤1,f h algebraic and lacunary in the following sense: Let {r n }, {s n } be two infinite sequences of integers, satisfying $$0 = s_0 \leqslant r_1〈 s_1 \leqslant r_2〈 s_2 \leqslant r_3〈 s_3 \leqslant ..., \mathop {lim}\limits_{n \to \infty } (s_n /F(n)) = \infty $$ such that $$f_h = 0 if r_n〈 h〈 s_n ,f_{r_n } \ne 0,f_{s_n } \ne 0 for n = 1,2,3,...;$$ F(n) denotes a certain function ofn, dependent onr n and $$f_0 ,f_1 ,f_2 , \ldots f_{r_n } $$ . Using ideas from a note ofK. Mahler, among other results the following main theorem is proved: The function valuef(α) (with α algebraic, 0〈|α|〈R f ) is algebraic if and only if there exists a positive integerN=N(α) such that $$P_n (\alpha ): = \sum\limits_{h = s_n }^{r_{n + 1} } {f_h \alpha ^h = 0 for all n \geqslant N.} $$
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    Monatshefte für Mathematik 84 (1977), S. 21-28 
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    Notes: Abstract LetQ(u) be a positive definite quadratic form inr≥2 variables with a real symmetric coefficient matrix of determinantD. Given a real vectorb with 0≤b j 〈1, forx〉0 letA(x) be the number of lattice points in the ellipsoidQ(u+b)≤x, letV(x) be the volume of this ellipsoid andP(x)=A(x)−V(x). Let $$M(x) = \int\limits_0^x {P^2 (y)dy} $$ . By introduction of a parameter ϖ we shall show how the treatment of estimates onP(x) and onM(x) can be unified.
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    Monatshefte für Mathematik 84 (1977), S. 37-48 
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    Notes: Abstract LetV be an ergodic automorphism of a probability space $$(X,\mathfrak{S},\mu )$$ and letA be a locally compact abelian group. Iff:X→A is a measurable function, one defines a “skew product” automorphismV f of the product spaceX×A byV f (x,α)=(Vx,α+f(x)) for every point (x,α) inX×A. In this paper we prove thatV f is ergodic for “most” functionsf.
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    Monatshefte für Mathematik 84 (1977), S. 49-53 
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    Notes: Abstract Let $$n = p_1^{\alpha _1 } \ldots p_r^{\alpha _r } $$ be the factoring of a natural numbern into primes. In 1969Niven found the average order of the functionsh(n)= min {α1,...α r } andH(n)= max {α1,...α r }. In this note a generalization ofNiven's results is discussed, namely the average order of the corresponding functions in certain arithmetical semigroups.
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    Monatshefte für Mathematik 84 (1977), S. 69-78 
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    Notes: Abstract Let {z k } be a Blaschke-sequence and $$E_1 = \{ e^{i\theta _k } :z_k = r_k e^{i\theta _k } \} $$ the “radial projection” of the sequence on the unit circleT. Some sufficient conditions concerning the arguments of the sequence {z k } are established, so thatE 1 is a Carleson-set relative to a modulus of continuity ω(t).
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    Monatshefte für Mathematik 84 (1977), S. 55-68 
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    Notes: Abstract LetG=〈a 1,b 1, ...,a q ,b q | (W 1 (a 1,b 1) ...W q (a q b q ))γ=1〉,q≥1, γ≥2,W j (a j ,b j )≠1. We solve the isomorphism problem forG inasmuch as we can decide in finitely many steps, if any arbitrary one-relator group is isomorphic toG or not. FurthermoreG turns out to have a finitely generated automorphism group. Forq=1 this was proved byS. J. Pride. Forq≥2 the proof is based onNielsen's reduction method. There are some other interesting results on subgroup problems for one-relator groups obtained by this method.
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    Monatshefte für Mathematik 84 (1977), S. 89-90 
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    Notes: Abstract This note contains a criterion for the existence of fixed points under the operation of a real Lie group on a symmetric space of non-compact type. This generalizes results of [2] and [4] and gives a shorter proof for the special case considered in [2] and [4].
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    Monatshefte für Mathematik 84 (1977), S. 91-108 
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    Notes: Abstract In this note several conditions are developed which together guarantee that an element of the Markov spectrum is an accumulation point of the Lagrange spectrum. Every known limit point of the Lagrange spectrum which is the Markov value of an attained non-completely periodic sequence satisfies these criteria. Examples are given to show that the removal of any one of the conditions can result in an element of the Markov spectrum which is not a limit point of the Lagrange spectrum. New elements of the Markov spectrum satisfying these conditions have been included.
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    Monatshefte für Mathematik 84 (1977), S. 109-124 
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    Notes: Abstract The Jacobsthal functiong(n) is defined as the maximal distance between two integers relatively prime ton. Letk, l,... be natural numbers, letp 1,p 2,... be primes. From $$3 \leqq l \leqq p_1〈 ...〈 p_{l - 1}〈 k + 2 - l \leqq p_l〈 ...〈 p_k $$ followsTheorem 1. g(p 1 ...p k )≦g(p 1 ...p l−1 )g(p l ...p k )=l(k+2−l), ifkl is large enough.Theorem 1′. From (1) and12≦l followsg(p 1 ...p k )≦l(k+2−l).
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    Monatshefte für Mathematik 84 (1977), S. 125-131 
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    Notes: Abstract We generalize a result ofHlawka about sums of the form $$\sum\limits_{n = 1}^N {(f(x_n + 1/N) - f(n)} ),$$ where (x n ) n ∈ℕ is a uniformly distributed sequence mod 1.
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    Monatshefte für Mathematik 84 (1977), S. 133-142 
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    Notes: Abstract The definitions of weak and very weak Bernoulli are reformulated to allow conditioning with respect to the entire past. For skew products which are measurable with respect to an independent generator of the base this reformulation allows one to state simple necessary and sufficient conditions for weak and very weak Bernoulli. We use these ideas to give a simple example of a partition which is very weak but not weak Bernoulli.
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    Monatshefte für Mathematik 84 (1977), S. 143-153 
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    Notes: Abstract This paper is devoted to the study of dominant operators with an emphasis on their spectral properties. In particular the equation (T−λ)f(λ)≡ ≡x (T a dominant or hyponormal operator on the Hilbert space ℌ,x∈ℌ andf a function from the open setU to ℌ) is investigated in an effort to discover necessary and/or sufficient conditions for the analyticity off.
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    Monatshefte für Mathematik 84 (1977), S. 155-163 
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    Notes: Abstract We define an infinite class of conditionsC and derive a formula for the numberp C (n) of non-isomorphic relations satisfyingC over a set ofn elements. This formula we directly get from some syntactical normal form ofC and the cycle-index of the symmetric group of degreen.
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    Monatshefte für Mathematik 84 (1977), S. 177-195 
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    Notes: Abstract It is shown that ifC is a convex surface, in euclidean space of dimension at least 3, having the property that all shortest paths onC between pairs of its points are planar, thenC is a sphere, a hyperplane or the boundary of an intersection of two half-spaces. No smoothness assumptions are made.
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    Monatshefte für Mathematik 84 (1977), S. 213-217 
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    Notes: Abstract Arithmetic formulae and an asymptotic expression for the order of magnitude of the arithmetic function $$\psi (n) = \mathop \sum \limits_{s \le n} $$ ged (s, n) and of a generalisation of it are derived.
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    Monatshefte für Mathematik 84 (1977), S. 197-208 
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    Notes: Abstract The miquelian Minkowski-planes can be characterized by cycle-reflections. More exactly: If is a non degenerate quadric of index 2 in a 3-dimensional pappian projective space, and if is the set of plane intersections of , which don't contain a line of (the elements of are called cycles), then the incidence-structure is a miquelian Minkowski-plane. In these hold: (*) there exists a reflection on every cycle (i. e. a non-identical automorphism of the Minkowski-plane, which fixes the points of the cycle) and (**) the product of three reflections on cycles through two fixed points fixes the points of a cycle. It is shown, that the properties (*) and (**) characterize the miquelian Minkowski-planes under the Minkowski-planes (i. e. incidence-structures, which are generalizations of intersection-geometries of quadrics mentioned above). Counter-examples show, that miquelian Minkowski-planes could not be characterized only by property (*).
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    Monatshefte für Mathematik 84 (1977), S. 209-212 
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    Notes: Abstract The strong law of large numbers for independent and identically distributed random variablesX i ,i=1, 2, 3,... with finite expectationE|X 1| can be stated as, for any ɛ〉0, the number of integersn such that $$|n^{ - 1} \mathop {\mathop \sum \limits_{i \le n} }\limits^n X_i ---EX_1 | 〉 \varepsilon $$ ,N ɛ is finite a. s. It is known thatEN ɛ〈∞ iffEX 1 2 〈∞ and that ε2 ENε → var X1 as ɛ→0, ifE X 1 2 〈∞. Here we consider the asymptotic behaviour ofEN ɛ(n) asn→∞, whereN ɛ(n) is the number of integersk≤n such that $$|k^{ - 1} \mathop {\mathop \sum \limits_{i \le 1} }\limits^k X_i ---EX_1 | 〉 \varepsilon $$ andE N 1 2 =∞.
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    Monatshefte für Mathematik 84 (1977), S. 219-235 
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    Notes: Abstract LetA be an operator on a finite dimensional unitary space. This paper contains results on the set of values taken on by the conjugate bilinear functional (A x, y) asx andy range over all unit vectors with prescribed inner product. By analyzing the same problem for the induced functional on the Grassmannian, results on non-principal subdeterminants are also obtained.
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    Monatshefte für Mathematik 84 (1977), S. 259-264 
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    Monatshefte für Mathematik 84 (1977), S. 247-258 
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    Notes: Abstract Let $$E = (e_{\mu v} )_{\mu = 0,v = 0}^{m,n - 1} $$ be a fixed matrix with elements that are 0 or 1 and letX be a fixed set ofm+1 different knots. The problem is to find necessary and sufficient conditions for (E, X) to guarantee the existence of a quadrature formula with a remainder term of type $$R(f): = \int\limits_0^1 {w(t)f(t)dt---\sum\limits_{e_{\mu v} = 1} {a_{\mu v} } f(v)(x_\mu )} $$ for any choice of a weight functionw(t) and satisfyingR(f)=0 forf a polynomial of degree at mostn−1. The result generalizes the corresponding result ofI. J. Schoenberg for the special case of quasi-Lagrange-matricesE. —in case of the existence ofR it is possible to calculate the best quadrature formulaR * in the sense ofSard by integrating splines of degree 2n−1. But ifE contains onlyn ones it is sufficient to integrate polynomials of degreen−1.
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    Monatshefte für Mathematik 84 (1977), S. 237-246 
    ISSN: 1436-5081
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    Topics: Mathematics
    Notes: Abstract In a bounded simple connected region G ⊂ ℝ3 we consider the equation $$L\left[ u \right]: = k\left( z \right)\left( {u_{xx} + u_{yy} } \right) + u_{zz} + d\left( {x,y,z} \right)u = f\left( {x,y,z} \right)$$ where k(z)⪋ 0 whenever z ⪋ 0.G is surrounded forz≥0 by a smooth surface Γ0 with S:=Γ0 ⋂ {(x,y,z)|=0} and forz〈0 by the characteristic $$\Gamma _2 :---(x^2 + y^2 )^{{\textstyle{1 \over 2}}} + \int\limits_z^0 {(---k(t))^{{\textstyle{1 \over 2}}} dt = 0} $$ and a smooth surface Γ1 which intersect the planez=0 inS and where the outer normal n=(nx, ny, nz) fulfills $$k(z)(n_x^2 + n_y^2 ) + n_z^2 |_{\Gamma _1 } 〉 0$$ . Under conditions on Γ1 and the coefficientsk(z), d(x,y,z) we prove the existence of weak solutions for the boundary value problemL[u]=f inG with $$u|_{\Gamma _0 \cup \Gamma _1 } = 0$$ . The uniqueness of the classical solution for this problem was proved in [1].
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    Monatshefte für Mathematik 84 (1977), S. 265-273 
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    Topics: Mathematics
    Notes: Abstract Formulas for the class number of an imaginary quadratic number field are proved. Some of these formulas were previously established byBerndt and byGoldstein andRazar with the use of analytic methods. The proofs given here use Dirichlet's classical class number formula, but otherwise the proofs are completely elementary. A key ingredient in the proofs is the reciprocity theorem for Dedekind-Rademacher sums.
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    Monatshefte für Mathematik 84 (1977), S. 341-347 
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    Monatshefte für Mathematik 84 (1977), S. 275-288 
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    Topics: Mathematics
    Notes: Abstract This paper is concerned with the existence and stability of nonlinear Volterra equations which have infinite delay and are of the form: $$x (\varphi ) (t) = W (t, \tau ) \varphi (0) + \int\limits_\tau ^t {W (t, s)} F(s,x_s (\varphi )) ds, x_\tau (\varphi ) = \varphi \in C_u .$$ Here,X denotes a Banach space;W(t, s) is a linear evolution operator mappingX toX; C u is the space of uniformly continuous functions endowed with the supremum norm; andF(·,·) is a continuous mapping ofR×C u toX. The autonomous version of the preceding equation is also considered. A nonlinear semigroup is associated with its solutions and the infinitesimal generator of the semigroup is characterized. The generator is then used to represent and approximate solutions to the autonomous equation.
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    Monatshefte für Mathematik 84 (1977), S. 289-302 
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    Topics: Mathematics
    Notes: Abstract Let 〈V; ∪, ∩〉 be a lattice, thenF(V), the set of all functions fromV toV, becomes a lattice by defining the operations ∪ and ∩ pointwise. If we also consider the composition of functions as an operation onF(V), we get the function algebra 〈F(V); ∪, ∩,·〉. In this paper we give a characterization of the lattices with nonsimple function algebras. Moreover, the congruence lattice of these function algebras turns out to be a three-element chain.
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    Monatshefte für Mathematik 84 (1977), S. 303-339 
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    Topics: Mathematics
    Notes: Abstract One determines all the minimal surfaces Φ of the isotropic space, which simultaneously are affinminimal surfaces. A characteristic property of those surfaces Φ is that the isotropic spherical imagines of the asymptotic lines of Φ form two orthogonal pencils of circles. There are three types of such surfaces Φ: first the well known right helicoidΦ I , second an interesting transcendental surfaceΦ II , and third the isotropic analogyΦ III of the minimal surface ofEnneper. The surfaces Φ permit cinematic generations. EspeciallyΦ II andΦ ΦIII can be generated byClifford screws in a certain indefinite quasielliptic space. In the isotropic space conjugate to the surfaces Φ are isotropic minimal surfacesΦ * with plane lines of curvature. There are also three types of such surfaces:Φ I * is a logarithmic surface of revolution,Φ II * is an interesting transcendental surface, andΦ III * is again the isotropic minimal surface ofEnnerper.
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    Monatshefte für Mathematik 84 (1977), S. 348-348 
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    Papers in regional science 39 (1977), S. 85-98 
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    Topics: Geography , Economics
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    Papers in regional science 39 (1977), S. 128-135 
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    Topics: Geography , Economics
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    Papers in regional science 39 (1977), S. 137-156 
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    Papers in regional science 39 (1977), S. 157-171 
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    Empirical economics 2 (1977), S. 1-9 
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    Topics: Economics
    Notes: Abstract A two-stage standardization and grouping algorithm is applied to a 75×75 submatrix of the 86×86 1967 United States interindustry transaction table. The rows and columns of the submatrix are first adjusted so that they all have uniform sums. Entries of the adjusted table are maximum entropy estimates of flows in an idealized economy, in which all industries produce and consume an equal value of goods. Industries are then aggregated according to whether or not they are connected by chains of links with values equal to adjusted entries, all of which are greater than a given threshold level. Variation of the threshold yields a hierarchical aggregation scheme. Groups of functionally integrated industries can be identified through the examination of a tree diagram (dendrogram) which shows the aggregation results.
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    Empirical economics 2 (1977), S. 11-30 
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    Topics: Economics
    Notes: Abstract This paper deals with some problems of international factor mobility with respect to labor using the case of the German labor market. A quarterly macroeconometric model of the German labor market is developed and estimated. It consists of equations explaining labor supply and demand for men and women. Most equations distinguish between labor measured in persons and hours. After a determination of the variables of this model which are influenced by foreign employment two groups of foreign workers which differ according to their EC-member status are discussed separately. Because of several legal and institutional regulations a different treatment of each group with respect to employment policy is necessary. For foreigners from outside the EC alternative reaction functions of the government are discussed and estimated. As the officially published unemployment rate is not comparable intertemporally because of foreign involuntary remigration during recession a new unemployment series including these persons is constructed and explained. The influence of foreign employment on wages is examined and two wage equations are estimated. Finally, some simulation results of an enforced remigration policy are reported.
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    Empirical economics 2 (1977), S. 67-68 
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    Empirical economics 2 (1977), S. 109-122 
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    Topics: Economics
    Notes: Abstract Estimates of the average technical efficiency on the 2-digit industry-level for France (1962) are obtained by means of a maximum likelihood estimation of the Cobb-Douglas frontier production model with composed error. The theoretical and statistical implications of a possible relationship between technical efficiency and firm-size are discussed. The computations are carried out for each industry as a whole and the results are compared with the respective results for separate size-classes.
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    Empirical economics 2 (1977), S. 101-108 
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    Topics: Economics
    Notes: Summary This note describes the application of the variable projection (VP) algorithm developed byGolub andPereyra [1973], and successively modified byKrogh [1974] andKaufman [1975] to the iterated generalized least squares estimation of nonlinear systems of equations whose parameters separate into a linear part and a nonlinear part. The VP algorithm was originally applied to the least squares estimation of single-equation models having this structure. Recently an extension has been proposed [Corradi] for the estimation of seemingly unrelated nonlinear regressions, which has proved to be computationally more efficient than the standard methods as employed e.g. inGallant [1975]. In Section 1 we outline the proposed computational procedure and examine its relevant features, while in Section 2 we present some numerical results.
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    Empirical economics 2 (1977), S. 123-136 
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    Notes: Abstract The elasticity of imports with respect to final demand, calculated from the 1964 and 1970 input-output tables for Austria, is equal to 1.35. Input-output analysis makes it possible to show how the value of the import elasticity is related to following structural changes: i) Changes in the shares of final demand components (i.e. of consumption, capital formation and exports) on total final demand; ii) changes in the pattern of final demand components; iii) changes in the technology matrix; iv) substitution of domestic output by imports in the final demand; and v) substitution of the domestic output by imports in the intermediate demand.
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    Empirical economics 2 (1977), S. 213-223 
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    Topics: Economics
    Notes: Abstract In this paper a dynamic model is presented which describes the development of the demand for specialistic medical care in The Netherlands, during the period 1960–1972. The “regionally correlated, time-wise auto-regressive” model is consistently estimated from a time-series of cross-sections, using a modified Aitken estimator. The dependent variables are the number of publicly insured patients referred from general care to specialistic care, and the amount of care consumed per patient referred. As independent variables we took demographic factors, the supply of different levels of medical care and the insurance system. The estimation results show a.o. important substitution possibilities between general and specialistic care, and a significant influence of supply and supply-related variables on the demand for specialistic care.
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    Empirical economics 2 (1977), S. 225-243 
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    Notes: Abstract In this paper we discuss a multivariate generalization of autoregressive integrated moving average models. A methodology for constructing multivariate time series models is developed and the derivation of forecasts from such models is considered. A bivariate model for Austrian macroeconomic sequences is constructed. Furthermore it is discussed whether multivariate time series methods can be expected to lead to a significant increase in prediction accuracy when forecasting macroeconomic series.
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    Empirical economics 2 (1977), S. 253-277 
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    Topics: Economics
    Notes: Summary For market research and other purposes it is of interest to know the accumulation process of consumer durables, and in particular whether almost all households acquire durables in the same order or whether almost all households acquire a certain curable at the same level of the accumulation process. The first part of the article describes the accumulation process and its structure. In the second part estimation and test procedures are proposed for analyzing empirically the accumulation structure. The test procedure is compared withParoush's methods. In contrast toParoush's method the relation between “almost all households” and the test statistic is now intelligible. Numerical examples illustrate the difference of both approaches.
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    Empirical economics 2 (1977), S. 245-251 
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    Notes: Summary This note investigates various ways of specifying the state-adjustment model. It is shown that the value of the structural parameters depends on the discrete specification although the estimating form remains unchanged. Consequently, it is important that analysis involving those parameters be carried out using estimates obtained in a mutually consistent specification of the model; failures to do so may result in erroneous conclusions.
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    Mathematical programming 13 (1977), S. 116-118 
    ISSN: 1436-4646
    Keywords: Network flows ; Network interdiction ; Minimum paths
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    Topics: Computer Science , Mathematics
    Notes: Abstract Given a linear cost function for lengthening arcs, a technique is shown for maximizing, within a budget, the shortest source—sink path length in a graph. The computation is equivalent to the parametric solution of a minimum cost flow problem.
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    Mathematical programming 13 (1977), S. 156-166 
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    Keywords: Doubly stochastic matrix ; Permanent ; Van der Waerden Conjecture ; Reversed geometric program ; Dual program
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    Notes: Abstract LetD p be the set of all doubly stochastic square matrices of orderp i.e. the set of allp × p matrices with non-negative entries with row and column sums equal to unity. The permanent of ap × p matrixA = (a ij ) is defined byP(A) = Σ τ∈Sp II i=1 p a iτ(i) whereS p is the symmetric group of orderp. Van der Waerden conjectured thatP(A) ≥ p !/p p for all A ∈A∈D p with equality occurring if and only ifA = J p , whereJ p is the matrix all of whose entries are equal to 1/p. The validity of this conjecture has been shown for a few values ofp and for generalp under certain assumptions. In this paper the problem of finding the minimum of the permanent of a doubly stochastic matrix has been formulated as a reversed geometric program with a single constraint and an equivalent dual program is given. A related problem of reversed homogeneous posynomial programming problem is also studied.
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    Mathematical programming 13 (1977), S. 183-199 
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    Keywords: Multivalued convexity ; Quasi-convexity ; Convex programming ; Alternative theorems ; Generalized Slater condition ; Transposition theorems ; Lagrange multipliers
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    Notes: Abstract Multivalued functions satisfying a general convexity condition are examined in the first section. The second section establishes a general transposition theorem for such functions and develops an abstract multiplier principle for them. In particular both convex inequality and linear equality constraints are seen to satisfy the same generalized constraint qualification. The final section examines quasi-convex programmes.
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    Mathematical programming 12 (1977), S. 136-138 
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    Computing 19 (1977), S. 59-72 
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    Description / Table of Contents: Abstract In the present paper we discuss several steplength procedures from a general point of view. We consider their influence on the convergence of algorithms for the numerical treatment of optimization problems without constraints. We define efficient step-size functions and show that well known steplength procedures are efficient. Necessary and sufficient conditions for convergence of descent methods with efficient step-size functions and applications to conjugate gradient methods are given.
    Notes: Zusammenfassung Von einem allgemeinen Standpunkt aus werden verschiedene Schrittweitenfunktionen diskutiert und ihr Einfluß auf die Konvergenz von Verfahren der unrestringierten Optimierung betrachtet. Es werden effiziente Schrittweitenfunktionen definiert und gezeigt, daß die bekannten Schrittweitenalgorithmen effizient sind. Schließlich werden notwendige und hinreichende Konvergenzkriterien für Abstiegsverfahren angegeben und auf Verfahren der konjugierten Gradienten angewendet.
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    Computing 19 (1977), S. 95-110 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Da endliche Automaten nicht jedes Labyrinth bewältigen können (Budach [1]), werden endliche Automaten betrachtet, die eine zusätzliche Druckfähigkeit haben. Ein Algorithmus zur Bewältigung aller Labyrinthe, der fünf Druckzeichen verwendet, wird beschrieben. Durch Simulation dieses Algorithmus wird gezeigt, daß zur Labyrinthbewältigung ein Drucksymbol ausreichend ist und ein Löschen von Druckzeichen nicht erforderlich ist.
    Notes: Abstract Starting from the result of Budach [1] “No finite automaton can master every maze” automata with additional printing ability are considered. An algorithm for mastering every labyrinth using five print symbols is described. By simulation of this five-symbol-algorithm it is shown that a one-symbol print alphabet is sufficient for escaping from every labyrinth. Main result: A one-symbol, nonerasing print mouse can be constructed escaping from every labyrinth.
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    Computing 19 (1977), S. 141-147 
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    Description / Table of Contents: Zusammenfassung Das Konzept einer Grammatikform und deren Interpretation wurde eingeführt, um Familien von strukturell ähnlichen Grammatiken zu beschreiben. Im wesentlichen ist eine Grammatikform eine (kontext-freie) Grammatik, die als Muster dient und die über den Interpretationsoperator eine Familie strukturell verwandter Grammatiken definiert. In dieser Arbeit wird ein neuer Operator als Variante von eingeführt. Es werden zwei Hauptergebnisse nachgewiesen. Einerseits, daß bezüglich kommutativ ist und andererseits, daß für jede GrammatikformG unter den Grammatikfamilien G′, wennG′ alle Grammatiken in (G) durchläuft, nur endlich viele verschiedene auftreten.
    Notes: Abstract The notions of a grammar form and its interpretations were introduced to describe families of structurally related grammars. Basically, a grammar formG is a (context-free) grammar serving as a master grammar and the interpretation operator defines a family of grammars, each structurally related toG. In this paper, a new operator yielding a family of grammars, is introduced as a variant of . There are two major results. The first is that and commute. The second is that for each grammar formG, the collection of all families of grammars ,G′ in , is finite. Expressed otherwise, the second result is that for each grammar formG there is only a bounded number of grammar forms in (G) no two of which are strongly equivalent.
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    Computing 19 (1977), S. 157-170 
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    Description / Table of Contents: Abstract Least-squares-solutions are defined and appropriate iterative methods are derived for the numerical solution of under-determined systems of non-linear equations. Especially an heuristic derivation of a damped Newton-like method is given in which the multiplicative damping factors are considered as additional unknowns to be computed during the iterations in the least-squares sense. A semilocal convergency theorem is proved for a related modification.
    Notes: Zusammenfassung Für die numerische Behandlung von unterbestimmten Systemen nichtlinearer Gleichungen werden Least-Squares-Lösungen definiert und geeignete Iterationsverfahren abgeleitet. Insbesondere wird ein gedämpftes Newton-ähnliches Verfahren heuristisch hergeleitet, bei dem die multiplikativen Dämpfungsfaktoren als zusätzliche Unbekannte betrachtet werden und im Least-Squares-Sinn im Verlaufe der Iterationen ermittelt werden. Für eine dazu verwandte Modifizierung wird ein semilokaler Konvergenzsatz bewiesen.
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    Computing 18 (1977), S. 51-58 
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    Description / Table of Contents: Zusammenfassung Durch ein einfaches Rechenverfahren werden asymptotische Approximationen für Laplace-Integrale erzeugt, die von höherer Ordnung sind als diejenigen, die man bei direkter Anwendung von Watsons Lemma erhält.
    Notes: Abstract A simple algorithm produces asymptotic approximations to Laplace integrals which are of higher order than those obtained by direct application of Watson's lemma.
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    Computing 18 (1977), S. 89-92 
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    Description / Table of Contents: Zusammenfassung Der Algorithmus erzeugt eine Liste von verschiedenen binärenn-Tupeln, so daß jedesn-Tupel sich vom vorhergehenden in genau einer Koordinate unterscheidet [1]. Der binäre Gray-Code wird oft zur Erzeugung aller Teilmengen einer gegebenen Menge verwendet [2]. Die gesamte Theorie kann leicht auf die Erzeugungr-närer Codes,r〉2, verallgemeinert werden [3].
    Notes: Abstract The algorithm generates a list of distinct binaryn-tuples such that eachn-tuple differs from the one preceding it in just one coordinate [1]. The binary Gray code is often used to generate all subsets of a given set [2]. The whole theory can easily be generalized to generatingr-ary codes,r〉2, [3].
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    Computing 18 (1977), S. 117-129 
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    Description / Table of Contents: Zusammenfassung Indem wir den aus den One-Step-Diskretierungsmethoden entstandenen dynamischen Systemen einige Bedingungen auferlegen, konstruieren wir einige nichtlineare One-Step-Methoden von erster und zweiter Ordnung, die nach der allgemeinen BezeichnungA-stabil oderL-stabil sind. Zahlenergebnisse an einigen „steifen” Test-Problemen, die vorgelegt werden, bestätigen die Brauchbarkeit dieser Methoden.
    Notes: Abstract By imposing some conditions on the discrete dynamical systems generated by one step discretization methods, we construct some non linear one step methods of the first and second order, which turn out to beA-stable orL-stable according to the current definitions. Numerical experiments are carried out on some common stiff test problems, confirming the validity of the methods.
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    Computing 18 (1977), S. 141-148 
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    Description / Table of Contents: Zusammenfassung Die Form der Flüssigkeitsoberfläche in einem zylindrischen Rohr mit allgemeinem Querschnitt wird mit Hilfe der einfachsten Methode der finiten Elemente approximiert. Einige a priori Abschätzungen für die Näherungslösung werden gezeigt. Dann wird Konvergenz einschließlich gleichmäßiger Abschätzungen wie bei gleichmäßig elliptischen Problemen bewiesen. Der Fall festen Flüssigkeitsvolumens ist hierbei eingeschlossen. Es werden einige numerische Ergebnisse angegeben.
    Notes: Abstract The shape of the surface of a liquid inside a cylindrical tube of general cross-section is approximated by the simplest finite element method. Some a priori estimates are obtained for the approximate solution. Then convergence including pointwise estimates is proved as for uniformly elliptic problems. The analysis also covers the case with a volume contraint. Some numerical results are given.
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    Computing 18 (1977), S. 167-176 
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    Description / Table of Contents: Zusammenfassung Verschiedene iterative Prozeduren zur numerischen Lösung des Problems der robusten Regression, genauer der robusten linearen Regression, wurden vorgeschlagen und entwickelt. Die hier beschriebenen Algorithmen sind modifizierte Fassungen der in der Veröffentlichung von Huber (1973, [8]) beschriebenen raffinierten („sophisticated”) Methode, die aber manchmal nicht konvergiert. In der vorliegenden Arbeit werden neue Algorithmen formuliert und Konvergenzbeweise gegeben. Das Verhalten der Prozeduren wird an einem numerischen Beispiel illustriert und mit dem eines einfachen („simple”) Algorithmus verglichen.
    Notes: Abstract Several iterative procedures have been proposed and developed to solve numerically the problem of robust regression, in particular, of robust linear regression. The algorithms described here are modified versions of the “sophisticated method” given by Huber (1973, [8]) which sometimes fail to converge. In this paper, the new algorithms are formulated and convergence proofs are given. The behavior of the procedures is illustrated by a numerical example and is compared to another (“simple”) algorithm.
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    Computing 18 (1977), S. 199-208 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir verwenden den in Golumbic [8, 9] eingeführten Begriff derG-Zerlegung, um eine Implementierung eines Algorithmus anzugeben, der einem transitiv orientierbaren Graphen eine transitive Orientierung in ZeitO(δ·|E|) und PlatzO(|E|) zuordnet, wobei δ der maximale Grad eines Knoten und |E| die Anzahl der Kanten ist. Wir zeigen eine Quotientenoperation, die den betrachteten Graphen reduziert undG-Zerlegung und transitive Orientierbarkeit bewahrt, und es werden effiziente Lösungen einigerNP-vollständiger Probleme diskutiert, die, für transitiv orientierbare Graphen, in Polynomzeit lösbar sind.
    Notes: Abstract Using the notion ofG-decomposition introduced in Golumbic [8, 9], we present an implementation of an algorithm which assigns a transitive orientation to a comparability graph inO(δ·|E|) time andO(|E|) space where δ is the maximum degree of a vertex and |E| is the number of edges. A quotient operation reducing the graph in question and preservingG-decomposition and transitive orientability is shown, and efficient solutions to a number ofNP-complete problems which reduce to polynomial time for comparability graphs are discussed.
    Type of Medium: Electronic Resource
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  • 200
    Electronic Resource
    Electronic Resource
    Springer
    Computing 18 (1977), S. 249-262 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract Generalizing the theory of linear innitial-value problems, formulated by Lax and Richtmyer [7], necessary conditions for solvability and convergence of a large class of implicit finite-difference methods for the numerical solution of certain quasilinear initial-value problems are given. In addition an equivalence theorem for these methods is proved.
    Notes: Zusammenfassung In Verallgemeinerung der von Lax und Richtmyer [7] formulierten Theorie linearer Anfangswertaufgaben werden hinreichende Bedingungen für Auflösbarkeit und Konvergenz einer großen Klasse impliziter Differenzenverfahren zur numerischen Lösung gewisser quasilinearer Anfangswertprobleme angegeben. Zusätzlich wird ein Äquivalenzsatz für diese Verfahren bewiesen.
    Type of Medium: Electronic Resource
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