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  • Springer  (211,911)
  • Oxford University Press  (13,342)
  • National Academy of Sciences  (6,306)
  • 1975-1979  (231,559)
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Year
  • 201
    Electronic Resource
    Electronic Resource
    Buchbesprechungen (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 81-92 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01470940
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  • 202
    Electronic Resource
    Electronic Resource
    Almost-topological representation theorems for dynamical systems (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 93-108 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For topological dynamical systems (X, T) representation theorems into shift dynamical systems are proved where the representing map φ is a homeomorphism between residual sets. φ can be endowed with additional properties so that the entropies of a measurem and its transport φm are arbitrary close.
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    URL: http://dx.doi.org/10.1007/BF01305909
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  • 203
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    Eine kinematische Kennzeichnung der gleichseitigen Paraboloide (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 69-80 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a given quadric exist (in general) ∞ generating methods by means of cones. In the case of the equilateral hyperbolic paraboloid we know, due toH. Brauner, an explicit generation by an equilateral hyperbola. More general we show: The only quadrics which can be generated with cones by a cylindrical vibration are the equilateral paraboloids. The generating cones are equilateral hyperbolas or parabolas, resp. Some special properties are demonstrated.
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    URL: http://dx.doi.org/10.1007/BF01470939
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  • 204
    Electronic Resource
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    Absolut stetige Maße auf lokalkompakten Halbgruppen (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 109-121 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetS be a locally compact semigroup. It is shown that if a measure μ is “absolutely continuous” and ifS is cancellative, then the measure ν concentrated on a Borel subsetB ofS (i. e. ν=μ(B∩.)) is also “absolutely continuous”. Other properties of “absolutely continuous” measures will be obtained. Moreover we will answer the question when “absolutely continuous” probability measures exist. This is the case ifS admits an invariant integral on the space of all continuous functions onS with compact support. Another result is the following: If the compact semigroupS has a connected kernel then there exist “absolutely continuous” probability measures if and only ifS is amenable.
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    URL: http://dx.doi.org/10.1007/BF01305910
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  • 205
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    Zur simultanen Diophantischen Approximation. II (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 133-143 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An important problem in the field of Diophantine Approximation was solved in 1891 byHurwitz. He could show that any irrational number can be approximated by infinitely many rationals in such a way that the modulus of the difference multiplied with the square of the denominator is less than 5−1/2, and here 5−1/2 is best possible. The generalization of this problem in the direction of simultaneous Diophantine Approximation is still unsolved.Furtwängler in 1925 gave lower bounds for the maximum difference, conjecturing that these were best possible. Here this conjecture is disproved by showing the existence of an infinite number of counterexamples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01305912
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  • 206
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    Contributions to diophantine approximation in fields of series (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 145-165 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The following topics are taken up: (i) the dimension of certain vector spaces defined in terms of denominations of differential polynomials, (ii) examples of series for which a Thue-Siegel-Roth type theorem holds, (iii) approximation of linear forms whose coefficients satisfy algebraic differential equations, and (iv) rational approximations to solutions of algebraic difference-differential equations.
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    URL: http://dx.doi.org/10.1007/BF01305913
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  • 207
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    Eine mehrdimensionale Version der Ungleichung von le Veque (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 167-169 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this short note we give a proof of le Veque's inequality $$D_N \leqq (6/\pi ^2 )\sum\limits_{h = 1}^\infty {h - 2\left| {(1/N)\sum\limits_{k = 1}^N {e^{2\pi ihx_k } |2)1/3} } \right|} $$ for dimensions≧2.
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    URL: http://dx.doi.org/10.1007/BF01305914
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  • 208
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    Die totale mittlere Krümmung gewisser Hyperflächen im ℝ5 (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 123-131 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The integrated square of the mean curvature of the standard torus (anchor-ring) in euclidean three-space is greater or equal to 2π2 with equality precisely for radii with the ratio $$\sqrt 2 :1$$ . The same lower bound holds for flat tori in euclidean four-space which are products of two circles. Here equality stands for the Clifford-tori having radii with the ratio 1∶1. Several authors have generalized this result to a larger class of surfaces of the torus-type (Willmore, Chen, Shiohama andTakagi). In this note we consider the same situation for certain submanifolds of the type ofS 1×S 3 andS 2×S 2. We consider not only the trace of the second fundamental tensor (mean curvature) but also the second elementary function of its eigenvalues, which intrinsically is just the scalar curvature. The results differ from the case of the tori: at first the minimal ratio of radii is not always algebraic, secondly the lower bounds are not the same for hypersurfaces and products.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01305911
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  • 209
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    Buchbesprechungen (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 171-180 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01305915
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  • 210
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    Banach convolution algebras of functions II (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 181-207 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetG be a noncompact, locally compact group. By means of “generalized dyadic decompositions” ofG, translation invariant Banach spacesF(B, B, X) of (classes of) measurable functions onG are constructed, e. g. certain weighted amalgams ofL p -spaces. Basic properties of these spaces are derived and connections with spaces considered in the literature are indicated. As a main result, sufficient conditions are given which imply that a space of this type is a Banach algebra with respect to convolution.
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    URL: http://dx.doi.org/10.1007/BF01303075
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  • 211
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    A class of flows with quasi discrete spectrum (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 209-228 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A class of minimal actions of finitely generated abelian groups is constructed. The class contains many non-trivial actions with quasi discrete spectrum and is used to give an ergodic theoretic proof of Weyl's theorem on uniform distribution of polynomials of finitely many variables.
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    URL: http://dx.doi.org/10.1007/BF01303076
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  • 212
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    A mean value theorem for the Dedekind zeta-function of a quadratic number field (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 229-239 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let $$K = \mathbb{Q}(\sqrt d )$$ be any quadratic number field with discriminantd. ζ K (s) denotes the Dedekind zeta-function. The purpose of this note is to prove the following asymptotic formula: $$\int\limits_0^T {|\zeta _K ({1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2} + it)|^2 dt = ({6 \mathord{\left/ {\vphantom {6 {\pi ^2 }}} \right. \kern-\nulldelimiterspace} {\pi ^2 }})} \prod\limits_{p/d} {(1 + {1 \mathord{\left/ {\vphantom {1 p}} \right. \kern-\nulldelimiterspace} p})^{ - 1} \cdot R_K^2 \cdot T \cdot \log ^2 T + O_\varepsilon \left\{ {\left| d \right|1 + \varepsilon \cdot T \cdot \log T} \right\},} $$ where the implied constant depends only on ε. HereR K, denotes the residue of ζ K (s) ats=1.
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    URL: http://dx.doi.org/10.1007/BF01303077
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  • 213
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    Quasinormalität in topologischen Gruppen (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 241-245 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetQ be a subgroup of the locally compact groupG. Q is called a topologically quasinormal subgroup ofG, ifQ is closed and $$\overline {QA} = \overline {AQ} $$ for each closed subgroupA ofG. We prove: If the compact elements ofG form a proper subgroup, compact topologically quasinormal subgroups ofG are subnormal of defect 2. IfG is connected, compact topologically quasinormal subgroups ofG are normal. IfG/G 0 is compact, connected topologically quasinormal subgroups ofG are normal.
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    URL: http://dx.doi.org/10.1007/BF01303078
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  • 214
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    On the existence of uniformly distributed sequences in compact topological spaces II (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 247-260 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We characterize those probability measures on the Bohr compactification of a metrizable, abelian group which admit a u. d. sequence in the original group. We show that the set of u. d. sequences on a nonmetrizable compact space can have the measure zero or one or it can be non-measurable. Finally we show that the existence of a u. d. sequence does not imply the existence of a well distributed sequence.
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    URL: http://dx.doi.org/10.1007/BF01303079
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  • 215
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    Buchbesprechungen (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 261-268 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01303080
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  • 216
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    Eine Bemerkung zur Verteilung der pythagoräischen Zahlentripel (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 269-271 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Letr(n) be the number of decompositions of a natural numbern into a sum of two squares. In this note we give an asymptotic formula for $$\mathop \sum \limits_{0 \leqq n \leqq x} r(n^2 )$$ , that is, the number of pythagorean triangles with hypotenuse less thanx.
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    URL: http://dx.doi.org/10.1007/BF01637029
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  • 217
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    On the number of subgroups of given index in the modular group (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 273-280 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new recurrence for the number of subgroups of given index in the modular group is derived. The proof requires the derivation of a recurrence for a sequencea nbn from recurrences for thea n andb n. We show that this is always possible if thea n andb n satisfy polynomial recurrences. We also include a short proof of a result ofW. W. Stothers on the parity of the number of subgroups of given index in the modular group.
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  • 218
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    Über die Anzahl der Gitterpunkte in verallgemeinerten Kreissektoren (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 297-307 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we consider lattice points in domains bounded by algebraic curves of the formx n+yn=Rn fulfilling the additional condition $$\alpha \leqq y/x \leqq \beta $$ where α and β are fixed positive real numbers. The number of these lattice points is estimated for largeR and it appears that for rational or “badly approximable” α and β the error term in the final result can be made smaller (at least forn≧3) than it is best possible when counting the lattice points without the additional condition indicated above.
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    URL: http://dx.doi.org/10.1007/BF01637032
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  • 219
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    An asymmetric inequality for non-homogeneous ternary quadratic forms (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 281-295 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetQ(x,y,z) be an indefinite ternary quadratic form of type (2,1) and determinantD(〈0). Let 0≤t≤1/3 and $$f(t) = \frac{4}{{(1 + t)^2 (1 + 5t)}}$$ . Then given any real numbersx 0,y 0,z 0 there exist integersx,y,z satisfying $$ - t(f(t)|D|)^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}}〈 Q (x + x_0 ,y + y_0 ,z + z_0 ) \leqslant (f(t)|D|)^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} $$ All the cases when equality holds are also obtained.
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    URL: http://dx.doi.org/10.1007/BF01637031
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  • 220
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    On some truncated units in algebraic number fields of degreen≧3 (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 309-312 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we present a partial answer to the following question. What algebraic number fields have truncated units others than of the form 1+xw+yw 2.
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    URL: http://dx.doi.org/10.1007/BF01637033
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  • 221
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    Zur Metrik der Diskrepanz (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 313-316 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetI=[0,1),dω the product measure onI ℕ of the Lebesgue measure onI, D N (ω) the discrepancy ofω ∈I ℕ. We show that for α〉0 $$\mathop {\lim }\limits_{N \to \infty } N^{\alpha /2} \mathop \smallint \limits_{I^\mathbb{N} } D_N^\alpha (\omega ) d\omega = 4.2 - (3\alpha /2)(2\alpha - 1 - 1) \zeta (\alpha ) \Gamma (\alpha /2 + 1)$$ Furthermore we sharpen and generalize this result.
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    URL: http://dx.doi.org/10.1007/BF01637034
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  • 222
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    Diskrepanz von Ketten (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 317-324 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper the discrepancy of chains is studied. The main result is an estimation of the discrepancy of chains likeRoth's estimation for usual sequences.
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  • 223
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    Zur Konvergenz derL n -Diskrepanz gegen die extreme Diskrepanz (1979)
    Springer
    Monatshefte für Mathematik 88 (1979), S. 1-6 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper gives bounds for the rate of convergence of theL n -discrepancy of a sequence of points of thes-dimensional space ℝ s (s∈ℕ. Further, a formula to calculate theL n -discrepancy for even numbersn is given.
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    URL: http://dx.doi.org/10.1007/BF01305853
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  • 224
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    Buchbesprechungen (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 325-342 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
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  • 225
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    Multiplizitäten “unendlich-ferner” Spitzen (1979)
    Springer
    Monatshefte für Mathematik 88 (1979), S. 7-26 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetX be the quotient of a bounded symmetric domainD by an arithmetically defined subgroup Γ of all analytic automorphisms ofD and letX * be theSatake-compactification ofX. In the present note, the multiplicities of the local rings of the zero-dimensional boundary components ofX * will be computed in a completely elementary manner using reduction-theory in selfadjoint homogeneous cones.
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  • 226
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    Best coapproximation in normed linear spaces (1979)
    Springer
    Monatshefte für Mathematik 88 (1979), S. 27-44 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider, in normed linear spaces, a kind of “approximation” by elements of linear subspaces, introduced byC. Franchetti andM. Furi [5], which we call best coapproximation. We obtain some results on characterization and existence of elements of best coapproximation in arbitrary normed linear spaces and in spaces of continuous functions. We give some characterizations of strict convexity in terms of best coapproximation and we study some properties of the setvalued operators of best coapproximation.
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  • 227
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    Weakly almost periodic functions on semisimple Lie groups (1979)
    Springer
    Monatshefte für Mathematik 88 (1979), S. 55-68 
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    Topics: Mathematics
    Notes: Abstract IfG is a semisimple analytic group with finite center, it is proved thatG admits only the “obvious” weakly almost periodic functions. The analysis yields also an intrinsic proof of Moore's ergodicity theorem [7].
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  • 228
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    Über eine Klasse von Brezelknoten (1979)
    Springer
    Monatshefte für Mathematik 88 (1979), S. 69-79 
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    Topics: Mathematics
    Notes: Abstract The paper gives a classification of pretzel knots (p,qq,rr) with one even cross number. The Alexander polynomial is computed in general and it is proved that its degree is always twice the genus of the knot. The classification does not include amphicheirality.
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  • 229
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    Über zweiparametrige ebene Bewegungsvorgänge (1979)
    Springer
    Monatshefte für Mathematik 88 (1979), S. 45-54 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract TheBlaschke-Grünwald-map associates to each surface β in the quasielliptic space a planar euclidean two-parameter motion $$\mathfrak{B}$$ . Using this map we find kinematic meanings of the Gaussian quasielliptic curvature and furthermore some theorems about the asymptotic motions of $$\mathfrak{B}$$ . The kinematic equivalent of the relation of left-conjugated tangents in points of β is a regular or singular projectivity σ on each poleline of $$\mathfrak{B}$$ . This projectivities have been studied already byH. J. E. Beth andW. v.d. Woude. We show that in every position the quadratic curvature transformations of almost all one-parameter motions of $$\mathfrak{B}$$ are determined by σ.
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    Buchbesprechungen (1979)
    Springer
    Monatshefte für Mathematik 88 (1979), S. 81-86 
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    Topics: Mathematics
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  • 231
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    Operatormethoden fürq-Identitäten (1979)
    Springer
    Monatshefte für Mathematik 88 (1979), S. 87-105 
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    Topics: Mathematics
    Notes: Abstract We use some simple operator methods in order to give more insight intoq-identities.
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  • 232
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    Analytische Vektoren von Faltungshalbgruppen II. Funktionenräume, auf lokalkompakten Gruppen (1979)
    Springer
    Monatshefte für Mathematik 88 (1979), S. 107-122 
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    ISSN: 1436-5081
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    Topics: Mathematics
    Notes: Abstract In this paper the investigations of [3], [4], [5] are continued. LetG be a locally compact group. First we show that in general there is no rich subspace of functions of the Bruhat-spaceD (G), whose, elements are analytical vectors for any convolution semigroup of probability measures. On the other hand we are able to construct dense subspaces ofC 0 (G) of analytical vectors, ifG is a Moore-group or a symmetric Riemannian space. We study properties of these subspaces and their relations to the structure, of the groupG.
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  • 233
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    Invariante Markoff-Kerne und der Vergleich von Translationsexperimenten (1979)
    Springer
    Monatshefte für Mathematik 88 (1979), S. 123-135 
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    Topics: Mathematics
    Notes: Abstract LetX andY be two experiments invariant with respect to an amenable measureable group. By a theorem of C. Boll which is proved with the help of a well-known fixed point theorem, the decision theoretical comparison relationX ≻Y introduced by LeCam can be characterized in terms of invariant Markov kernels. Applying this result to translation (invariant) experiments one obtains, an explicit analysis of the comparison relationship in the special case of Gaussian experiments.
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    Weierstraßscher Approximationssatz und Gleichverteilung (1979)
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    Monatshefte für Mathematik 88 (1979), S. 137-170 
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    Topics: Mathematics
    Notes: Abstract Using uniformly distributed sequences modulo 1 polynomials are formed which approximate continuous functions ofJ, whereJ is at first a compact interval inR s . The error of the approximation is estimated using the discrepancy of the sequences. Some cases of unbounded intervals are also studied. Furthermore trigonometric polynomials are considered which approximate periodic continuous functions inR s .
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    Über Hamiltonsche Kreise und unabhängige Ecken in Graphen (1979)
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    Monatshefte für Mathematik 88 (1979), S. 195-210 
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    Topics: Mathematics
    Notes: Abstract Two sufficient conditions for a graph to allow a hamiltonian circuit are proved. These conditions involve the connectivity, the stability number and the minimum valence ofG.
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    Buchbesprechungen (1979)
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    Monatshefte für Mathematik 88 (1979), S. 189-194 
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    Topics: Mathematics
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    Products of random varibles depending on a random walk (1979)
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    Monatshefte für Mathematik 88 (1979), S. 171-187 
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    Topics: Mathematics
    Notes: Abstract LetX=(X n ) n≥0 denote an irreducible random walk (“ergodic” in the sense of [7]) on a compact metrizable abelian groupG. In this paper we characterize completely the limit distributions of the productsY n =X 0...X n . In particular we find necessary and sufficient conditions forX and/orG to imply that the products are asymptotically equidistributed in the mean, i. e. {im171-1} holds for all open,m G -regular subsetsA ofG (m G : normalized Haar measure).—For example ifG is monothetic and connected or ifX is asymptotically equidistributed (not merely in the mean) then the products are asymptotically equidistributed in the mean.
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    On bicompact extensions of tychonoff spaces (1979)
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    Monatshefte für Mathematik 88 (1979), S. 211-218 
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    Topics: Mathematics
    Notes: Abstract Necessary and sufficient conditions for existence of the minimal elements in some subsets of the partially-ordered set of all Hausdorff bicompact extensions of the completely regularT 1 spaces are given.
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    Mittelwert der Eulerschen φ-Funktion und des Quadrates der Dirichletschen Teilerfunktion in algebraischen Zahlkörpern (1979)
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    Monatshefte für Mathematik 88 (1979), S. 219-228 
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    Topics: Mathematics
    Notes: Abstract LetK be an algebraic number field, and for every integer γ∈K let φ(γ) andd(γ), respectively, denote the number of relatively prime residue classes and the number of divisors of the principal ideal (γ). Asymptotic equalities are proved for the sums Σφ(γ) and Σd 2(γ), where γ runs through certain finite sets of integers ofK.
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    Factors and extensions of full shifts (1979)
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    Monatshefte für Mathematik 88 (1979), S. 239-247 
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    Topics: Mathematics
    Notes: Abstract Let ∑ A be an irreducible shift of finite type with entropy logn. Then ∑ A is a continuous extension of the fulln-shift. Also, if ∑ A is a continuous factor of the fulln-shift, then it is shift equivalent to the fulln-shift.
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    Duals of orbit spaces in groups with relatively compact inner automorphism groups are hypergroups (1979)
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    Monatshefte für Mathematik 88 (1979), S. 229-238 
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    Topics: Mathematics
    Notes: Abstract For a locally compact groupG and a groupB of topological automorphisms containing the inner automorphisms ofG and being relatively compact with respect to Birkhoff topology (that isG∈[FIA] B,B $$ \supseteq $$ I(G)) the spaceG B of $$\bar B$$ -orbits is a commutative hypergroup (=commutative convo inJewett's terminology) in a natural way asJewett has shown. Identifying the space of hypergroup characters ofG B withE(G, B) (the extreme points ofB-invariant positive definite continuous functionsp withp (e)=1, endowed with the topology of compact convergence) we prove thatE(G, B) is a hypergroup, the “hypergroup dual” ofG B.
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    On asymptotic values of meromorphic functions (1979)
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    Monatshefte für Mathematik 88 (1979), S. 249-251 
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    Topics: Mathematics
    Notes: Abstract The following theorem ofLindelöf is known: Iff (z) is meromorphic in |z|〈1, and iff (z) admits two distinct asymptotic values at some pointP of |z|=1, thenf (z) assumes infinitely often in any neigh borhood ofP all values of the extended complex plane with at most two possible exceptions. The purpose of this note is to extend Lindelöf's theorem to Riemannian surfaces. Our extension of Lindelöf's theorem includes the fact that the conclusion of Lindelöf's theorem holds, iff (z) is meromorphic in |z|〈∞, and iff (z) admits two distinct asymptotic values atz=∞.
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    Buchbesprechungen (1979)
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    Monatshefte für Mathematik 88 (1979), S. 265-274 
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    Topics: Mathematics
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    Group automorphisms with finite entropy (1979)
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    Monatshefte für Mathematik 88 (1979), S. 275-285 
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    Topics: Mathematics
    Notes: Abstract A compact metrie abelian group X with the normalized Haar measure is a Lebesgue probability space. A group automorphism σ ofX is an invertible measure preserving transformation of the probability space. This paper is to show that if the entropy of σ is finite, then there exist totally disconnected subgroupsH andN, a finite-dimensional subgroupS and a subgroupT satisfying the conditions: (i)H, N, S andT are strictly σ-invariant, (ii)N=H∩S∩T, (iii)h(σ| N )=0, (iv) ifS/N is non-trivial then it is a finite-dimensional solenoidal group with condition (**) (see the definition in §1), (v) ifT/N is non-trivial then it is connected and locally connected, such thatX/N splits into a direct sumX/N=H/N⊕S/N⊕T/N. This result characterizes the structure of finite entropy automorphisms.
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    Zyklische Orientierungen endlicher bewerteter Graphen (1979)
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    Monatshefte für Mathematik 88 (1979), S. 253-263 
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    Topics: Mathematics
    Notes: Abstract Starting from problem 4 ofK. Wagner [2],H. Fleischner andP. D. Vestergaard [1] introduce the notion of a value-true walk in a finite, connected graph, the edges of which are valuated with nonnegative integers. Their main theorem states that the existence of such a walk is equivalent to the existence of an orientation of the edges with the following property: For every vertex the sum of the valuations of the incoming edges equals the sum of the valuations of the outgoing edges. Let us call such an orientation a cyclic one. In the present paper we study finite, valuated graphs that admit a cyclic orientation. First, we give two necessary conditions for a valuated graphG to admit a cyclic orientation concerning the stars and the bonds ofG, respectively. (The starS (v) of a vertexv is the set of all edges ofG incident withv.) Then, as the main part of the paper we give a characterization of those graphs for which the star- and the bond-condition is sufficient, respectively (for any valuation of the graph). These characterizations are in terms of constructability from trees andK 3, respectively, as well as in terms of forbidden subgraphs.
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    Über eine Verallgemeinerung der Nicoletti-Aufgabe für Funktional-Differentialgleichungen mit voreilendem Argument (1979)
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    Monatshefte für Mathematik 88 (1979), S. 287-291 
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    Topics: Mathematics
    Notes: Abstract We consider a functional differential equation (1) ϕ′(t)=F(t,ϕ) fort∈[0,+∞) together with a generalized Nicoletti condition (2)H(ϕ)=η. The functionF: [0,+∞)×C 0[0,+∞)→B is given (whereB denotes the Banach space) and the value ofF (t, ϕ) may depend on the values of ϕ (t) fort∈[0,+∞);H: C 0[0,+∞)→B is a given linear operator and η∈B. Under suitable assumptions we show that when the solution ϕ:[0,+∞)→B satisfies a certain growth condition, then there exists exactly one solution of the problem (1), (2).
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    Inhomogeneous minimum of indefinite quadratic forms in five variables of type (3,2) or (2,3): A conjecture of watson (1979)
    Springer
    Monatshefte für Mathematik 88 (1979), S. 305-320 
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    Topics: Mathematics
    Notes: Abstract LetQ(x,y,z,t,u) be a real indefinite quadratic form in five variables of type (3,2) or (2,3) and determinantD≠0. The given any real numbersx 0,y 0,z 0,t 0,u 0 we can find integersx,y,z,t,u, satisfying $$|Q(x + x_0 ,y + y_0 ,z + z_0 ,t + t_0 ,u + u_0 )| \leqslant (\frac{1}{4}|D|)^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 5}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$5$}}} .$$ All the cases when the sign of equality holds are also determined.
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    Gleichverteilte Doppelfolgen und eine Abschätzung der C-Diskrepanz (1979)
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    Monatshefte für Mathematik 88 (1979), S. 321-330 
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    Topics: Mathematics
    Notes: Abstract In this paper a criterion forC-uniformly distributed differentiable functions is given by using uniformly distributed double sequences. This criterion allows to find lower bounds of theC-discrepancy of differentiable functions.
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    Zum Approximationssatz von Dirichlet (1979)
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    Monatshefte für Mathematik 88 (1979), S. 331-333 
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    Topics: Mathematics
    Notes: Abstract In this paper we improve the estimation in Dirichlet's Approximation Theorem for systems of linear forms using a method ofG. Raisbeck andG. Kaindl.
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    Zwei Bemerkungen über transzendente Zahlen (1979)
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    Monatshefte für Mathematik 88 (1979), S. 293-304 
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    Topics: Mathematics
    Notes: Abstract In the first part theorems ofBaker are used to prove the transcendence of special values of power series whose coefficients are values of certain ordinary Dirichlet series with coefficients forming a periodic sequence of algebraic numbers. Especially the transcendence of Ψ(z)+C is shown for all rationalz which are not integers, Ψ denoting the logarithmic derivative of the gamma function andC Euler's constant. In the second part the intimate connection betweenSchanuel's conjecture and the arithmetic nature of $$\sum\limits_{n = 2}^\infty {\gamma (n)n^{ - s} }$$ ,s=3,4,5... is studied where γ (n) denotes the number of distinct representation ofn in the forma b with positive integersa, b. This function was recently introduced byGolomb.
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    Eingegangene Bücher (1979)
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    Monatshefte für Mathematik 88 (1979), S. 350-354 
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    On regular rings and V-rings (1979)
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    Monatshefte für Mathematik 88 (1979), S. 335-344 
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    Topics: Mathematics
    Notes: Abstract In this note, certain generalisations of strongly regular rings are considered in connection with regular rings andV-rings. The result that strongly regular rings are left (and right)V-rings [11] is extended. A condition for prime leftV-rings to be primitive with non-zero socle is given (this is related to a question ofFisher [7, Problem 3]. IfA is an ALD (almost left duo) ring, then (1) a simple leftA-module is injective iff it isp-injective; (2)A is von Neumann regular iff every maximal essential right ideal ofA isf-injective. Characterisations of semi-simple Artinian and simple Artinian rings are given in terms of regular andV-rings.
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    Buchbesprechungen (1979)
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    Monatshefte für Mathematik 88 (1979), S. 345-350 
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    Chemical and biological studies on banana fruit (1979)
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    European journal of nutrition 18 (1979), S. 8-15 
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    ISSN: 1436-6215
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Notes: Summary Chemical and biological evaluation of both the edible and nonedible portion of banana fruit was carried out. The possibility of using the nonedible portion (peel) as animal feed was also explored. The results showed a remarkable difference concerning the chemical composition of both the edible and nonedible portions. The amino acid contents were proved to be vastly deficient with regard to the indispensable amino acids with exception of phenylalanine which was found in good amounts in the edible portion (pulp). The biological results demonstrated that neither the pulp nor the peel portions yielded good P.E.R. values when used at 6% protein level. The P.E.R values showed negative values which amounted to −1.75, −5.85 and −4.67 for the pulp and peel diets respectively. Incorporation of the stock diet to the peel diet resulted in a slight increase which amounted to 6% in both male and female rat groups.
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    Chemical analysis of linseed meal produced in Egypt (1979)
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    European journal of nutrition 18 (1979), S. 23-25 
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    ISSN: 1436-6215
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Zusammenfassung Repräsentative Stichproben von Leinsamen-Mehl der 19 produktiven Mühlen in ägypten wurden gesammelt. Der prozentuale Anteilswert der Nährstoffe dieser Stichproben betrug: 6,55±0,22 Feuchtigkeit, 93,45±0,22 Trockensubstanz, 11,19±0,60 ätherextrakt, 26,97±0,59 Eiweiß, 11,18±0,43 Rohfaser, 36,10±0,60 freier N, 8,00±0,38 Asche, 0,39±0,03 Kalzium, 0,89±0,04 Phosphor. Der durchschnittliche Brennwert des Mehls betrug 435,81±3,16 kcal pro 100 g.
    Notes: Summary Representative samples of linseed meal were collected from the productive nineteen oil mills of Egypt. The averages of nutrients in the mentioned samples Were 6.55±0.22, 93.45±0.22, 11.19±0.60, 26.97±0.59, 11.18±0.43, 36.10±0.60, 8.00±0.38, 0.39±0.03 and 0.89±0.04 for moisture, dry matter, ether extract, crude protein, crude fiber, nitrogen-free extract, ash, calcium and phosphorus respectively. The average of the calculated calorific value was 435.81±3.16 kcal per 100 gram of the meal.
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    Editorial (1979)
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    OR spectrum 1 (1979), S. 1-1 
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    Topics: Mathematics , Economics
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    Strukturierung von Entscheidungsprozessen bei mehrfacher Zielsetzung (1979)
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    OR spectrum 1 (1979), S. 3-26 
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    Topics: Mathematics , Economics
    Description / Table of Contents: Summary This paper focusses on some alternative structures of a goal formation and decision process in order to select a compromise alternative for a multiple-criteria decision problem. It is illustrated, that resolving a multiple-criteria decision conflict on the basis of a decision model with several objective functions in the sense that the decision maker finds an acceptable compromise alternative within an acceptable span of time constitutes not only a theoretical but a practicable possibility.
    Notes: Zusammenfassung In diesem Beitrag werden einige Alternativen zur Strukturierung von Entscheidungsprozessen auf der Grundlage konkreter Planungsmodelle mit mehrfacher Zielsetzung vorgestellt, die zu einer Lösung von Planungsproblemen bei mehrfacher Zielsetzung beitragen können.
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    Anpassung von Lenkkosten (1979)
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    OR spectrum 1 (1979), S. 27-33 
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    Topics: Mathematics , Economics
    Description / Table of Contents: Summary An adaptive (s,S)-inventory model being implemented in industry is compared with a Wagner-Whitin (WW)-model. Three criteria are taken into account: mean stock on hand, order frequency, and service level. It is shown that cost parameters can be chosen for the WW-model such that this model leads to dominant values for all 3 criteria. These results not only hold for the empirical time series of the company studied but also for more general time series generated by simulation.
    Notes: Zusammenfassung Ein in der Industrie implementiertes (s,S)-Lagerhaltungsmodell wird mit einem Wagner-Whitin (WW)-Modell verglichen. Drei Kriterien werden dazu herangezogen: Mittlerer Lagerstand, Bestellhäufigkeit und Servicegrad. Es zeigt sich, daß sich im WW-Modell Lenkkostenparameter angeben lassen, für die das WW-Modell in allen Zielen dominant ist. Diese Untersuchungen bestätigen sich nicht nur an den gegebenen empirischen Nachfragezeitreihen, sondern auch an allgemeineren durch Simulation generierten Zeitreihen.
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    Optimale Investitionsstrategien im Tankermarkt (1979)
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    OR spectrum 1 (1979), S. 35-49 
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    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Summary The main objective of this study consists in making a contribution to overcome the crisis on the tanker-market. A simulation model has been developed to describe the specific problems of this market. The main parts of model are the demand sector, the supply sector, the capital sector, the sector of the tanker-market, and the sector of ship construction. The data used in the model are based on statistic and explorations of Intertanko, OECD, Exxon, United Nations, “Yearbook of International Trade Statistics”, Shipping Statistics and Economics etc. This simulation model is integrated into an optimization procedure. The freight rate as one of the most important variables is defined as the objective variable which is controlled (optimized) by the investment decisions of the tanker-shipowner. The Razor Search algorithm is applied to optimize the model of the tanker-market.
    Notes: Zusammenfassung Das wesentliche Ziel dieser Arbeit besteht darin, Einsichten und Entscheidungshilfen zur Bewältigung der komplexen Investitionssituation auf dem Tankermarkt zu vermitteln. Das entwickelte Simulationsmodell umfaßt den Angebots- und Nachfragesektor, den Tankermarkt- und den Schiffbausektor sowie den Kapitalsektor. Die im Modell benötigten Daten basieren auf Statistiken und Prognosen von Intertanko, OECD, Exxon, United Nations, “Jahrbuch der internationalen Handelsstatistiken”, Shipping Statistics and Economics usw. Zur Modelloptimierung wird das Simulationsmodell in eine Regelkreisstruktur integriert. Die Frachtrate wird als Zielgröße definiert und durch Investitionsentscheidungen der Tankreeder beeinflußt, die durch den heuristischen Optimierungsalgorithmus “Razor Search” in bestmöglicher Form gesteuert werden.
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    Semi-infinite quadratic programming (1979)
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    OR spectrum 1 (1979), S. 51-55 
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    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Eine Methode zur Minimierung einer positiv definiten quadratischen Funktion unter unendlich vielen linearen Nebenbedingungen wird vorgestellt. Diese Methode hat die Eigenschaft, daß eine Folge von zulässigen Lösungen des Problems sowie eine Folge von Basislösungen gleichzeitig erzeugt wird. Auf diese Weise erhält man Einschließungen des Zielfunktions-wertes der Lösung des Problems. Zudem weist die Methode hervorragende Stabilitätseigenschaften auf.
    Notes: Summary A method is presented for minimizing a definite quadratic function under an infinite number of linear inequality restrictions. Special features of the method are that it generates a sequence of feasible solutions and a sequence of basic solutions simultaneously and that it has very favourable properties concerning numerical stability.
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    Tagungen (1979)
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    OR spectrum 1 (1979), S. 73-73 
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    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
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    Die Simulation zeitdiskreter Systeme mit GPSS-FORTRAN (1979)
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    OR spectrum 1 (1979), S. 69-73 
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    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Summary The properties of the software-package GPSS-FORTRAN are described. It gives the user an opportunity to implement into programs written in FORTRAN IV additional macros and subroutines in order to make all the features of GPSS available. Other simulation languages and tools for the analysis of discrete systems such as GPSS, SIMULA, SIMSCRIPT and GASP are compared with GPSS-FORTRAN.
    Notes: Zusammenfassung Es wird das Programmpaket GPSS-FORTRAN vorgestellt, das sich zur Simulation zeitdiskreter Systeme eignet. Die wesentlichen Eigenschaften von GPSS-FORTRAN werden beschrieben. Ein beurteilender Vergleich zwischen GPSS-FORTRAN und GPSS sowie den Simulationssprachen SIMULA, SIMSCRIPT und GASP ermöglicht dem Anwender von Simulationssprachen eine allgemeine Übersicht.
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    On theory and algorithms for Markov decision problems with the total reward criterion (1979)
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    OR spectrum 1 (1979), S. 57-67 
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    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Im ersten Teil dieser Übersichtsarbeit werden unter schwachen Voraussetzungen, die keine Kontraktion garantieren, eine Reihe wichtiger Existenz- und Konvergenzaussagen für Markoffsche Entscheidungs-prozesse gewonnen. Im zweiten Teil der Arbeit werden Bedingungen untersucht, die einen Zugang mit Hilfe kontrahierender Abbildungen erlauben. Diese Bedingungen sind recht schwach, insbesondere sind unbeschränkte Erträge zugelassen. Am Ende der Arbeit wird beschrieben, wie man mit Hilfe aktionsabhängiger Stopzeiten verschiedene Verfahren der sukzessiven Approximation zur Lösung Markoffscher Entscheidungsprozesse gewinnen kann.
    Notes: Summary The first part of this survey paper is devoted to derive under rather weak conditions, which don't guarantee contraction, a number of important existency and convergency results in Markov decision theory. In the second part of the paper conditions that guarantee that the contraction mapping approach can be used are analysed. These conditions are rather weak and allow for unbounded rewards. The generation of successive approximation methods for solving Markov decision processes by using action depending stopping times is described at the end of the paper.
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    Eingegangene Bücher (1979)
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    OR spectrum 1 (1979), S. 74-74 
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    Topics: Mathematics , Economics
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    Performance of the LINK System: 1970 versus 1975 base year trade share matrix (1979)
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    Empirical economics 4 (1979), S. 11-41 
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    ISSN: 1435-8921
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract Within the LINK world model different national econometric models are linked through a trade share matrix. Until recently the last observation of the matrix available to Project LINK was from 1970. The objective of this paper is to analyse the performance of the LINK world model when employing the newly availably 1975 trade share matrix.
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    A minimum dimension state-space representation for deterministic economic system, instrument instability, and the design of stable feedback policy (1979)
    Springer
    Empirical economics 4 (1979), S. 1-10 
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    ISSN: 1435-8921
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Summary A minimum dimension realization theory in applications to economic policy model is investigated in this paper. The relative effectiveness of two different realization methods for the optimal stabilization purposes is numerically examined in relation to the problem of instrument instability. Finally, certain simpler design method of stable feedback policy is presented using a minimum dimension state-space representation for linear deterministic economic system.
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    Model estimation and verification — Some recent approaches (1979)
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    Empirical economics 4 (1979), S. 87-99 
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    ISSN: 1435-8921
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    Topics: Economics
    Notes: Summary In this paper, data analysis methodologies and procedures are applied to economic data. The appropriateness of this approach to model development and verification is also addressed. Models and data addressing United States housing purchases between the years 1948–1975 are used as a case study. The data and several candidate models of relationships are explicitly examined. Residuals, as well as the data matrix of the independent variables, are examined in some detail.
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    Quotas and the structure of consumer demand (1979)
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    Empirical economics 4 (1979), S. 101-109 
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    ISSN: 1435-8921
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract In the direct utility function, quantities axe exogenous, while prices and total expenditure are endogenous. Consequently, this utility function is appropriate for analyzing the impact on prices and total expenditure from an exogenous change in the quantity of a commodity. Such an exogenous change in quantity could occur when quotas change. The direct translog utility function is estimated for a four commodity breakdown of U.S. expenditure. Estimates of quantity elasticities of price and expenditure indicate that domestically produced non-durables are necessities. As a result, the imposition of quotas on these goods will be particularly deleterious to lower income consumers.
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    Modeling equilibrium trends and interventions in commodity markets (1979)
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    Empirical economics 4 (1979), S. 111-134 
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    ISSN: 1435-8921
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    Topics: Economics
    Notes: Abstract The monthly spot prices in the international tin and copper and U.S. domestic lead markets are modeled based on the “supply of storage” concept. In all cases the lag-1 natural logS/C (stocks/consumption) was highly important in the final fitted equation. For copper and lead, trend directions in the U.S. Index of Leading Economic Indicators modified theS/C dependency. Disaggregation of the tin stocks showed the special model sensitivity to the level of the ITC buffer stock. The underlying econometric models are used to estimate the price intervention effects of international political-economic crises, and commodity producer cartel actions.
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    A monte carlo study of the small sample properties of various estimators of Solow's distributed lag model (1979)
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    Empirical economics 4 (1979), S. 167-186 
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    ISSN: 1435-8921
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    Topics: Economics
    Notes: Abstract The results of some Monte Carlo experiments investigating the small sample properties of estimators ofSolow's distributed lag model are presented. In general, the relative efficiency of an estimation technique depends on the true values of the parameters being estimated. But if the assumptions of the model are not violated, then the maximum and mean likelihood and the Bayesian estimators are best.
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    The economic development of the FRG and USA a principal-components-analysis (1979)
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    Empirical economics 4 (1979), S. 187-198 
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    ISSN: 1435-8921
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Summary The economic development of the FRG and the USA has been analysed for the years 1965–75 using the principal components method. This method not only served to combine information but also to test hypotheses regarding different cyclical data-pattern as well as different degrees of interdependence in time for the FRG and the USA. This was done by the introduction of synthetic regular statistical series and by subdivision of the mentioned period. It was shown that the direct link between both countries via trade has been weakened but the simultaneity of economic development after the oil-price shock has been strengthened.
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    Some tests for money illusion and distribution effects in the aggregate consumption function (1979)
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    Empirical economics 4 (1979), S. 221-234 
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    ISSN: 1435-8921
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    Topics: Economics
    Notes: Abstract The hypothesis that the aggregate consumption displays money illusion in the sense that consumers mistake an increase in nominal incomes for an increase in real incomes and thus consume more out of given real incomes in response to a rise in the price level and the hypothesis that the aggregate consumption depends on the distribution of income are tested using Finnish annual and quarterly data. The money illusion hypothesis is rejected by annual data, while it meets success with quarterly data. The hypothesis of distribution effects in the aggregate consumption is supported by annual data. Particularly, equalizing the distribution of income would increase the aggregate consumption. In view of the quality of data on personal income distribution this conclusion cannot be regarded as more than tentative.
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    Employment, factor income distribution, and economic growth: Theory and planning (1979)
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    Empirical economics 4 (1979), S. 247-279 
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    ISSN: 1435-8921
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    Topics: Economics
    Notes: Summary The object of the paper is to present models of economic growth based on the idea that consumption is determined by the number of workers employed, and investment by the sales of final goods. It is shown that these assumptions lead to growth paths in which the rates of growth of employment and of technological change are determined by the parameters of production, consumption and investment functions, without reference to exogenous rates of growth of the labor force or of technology. The basic model is extended to study the effects of considering the distribution of income between capital and labor as one of the determinants of consumption, and to study open economies. Finally, the open models are applied to the analysis of the economies of Mexico and Venezuela, both in the case where past growth is studied, and when it is assumed that a decision-maker sets targets for the rate of growth of GDP.
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    An economic model of mental hospitals (1979)
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    Empirical economics 4 (1979), S. 293-301 
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    ISSN: 1435-8921
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    Topics: Economics
    Notes: Summary The aim of the paper is to study the composition of intermediate products supplied by non profit institutions. In case the institution is financed according to part of the intermediate products supplied by it, we expect it to choose distorted composition of production factors. We studied Israeli mental hospitals. The aim of mental hospitals is to maximize the probability of curing but it produces both medication and maintenance. We measured the output by the number of patients discharged back home and assumed Cobb-Douglas production function. Data were collected for fifteen hospitals seventeen years back. Hospitals are financed according to the bed days they supply. The econometric study shows that while the marginal product of medical factors: doctors, nurses and medicines are significantly positive, the marginal product of the factors used for maintenance: capital and food, are significantly negative.
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    An input-output approach to the estimation of employment requirements in Europe (1979)
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    Empirical economics 4 (1979), S. 149-165 
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    ISSN: 1435-8921
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    Topics: Economics
    Notes: Abstract This study reports the results of an attempt to analyse the employment requirements per one million dollars of final demand on the basis of an input-output model, in which the standard technology matrix is partitioned into domestic and import input coefficient matrices for twelve European countries. International comparisons of employment requirements indicate that the labour productivity is higher for high income countries while employment requirements per one million dollars of final demand is less closely associated with the size of the country. Our results demonstrate that the total employment requirements estimated on the basis of the total input coefficients matrix or the domestic coefficients matrix retain the same ordinal ranking of the sectors. For developing countries, where the data are not available for domestic and import coefficients matrix separately, the methodology of estimating employment requirements (per unit of final demand) through total coefficients matrix may be adopted since our experience indicates that ranking of the sectors in terms of labour productivity is not altered between two approaches for twelve European countries.
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    A structural econometric model of Czechoslovakia: 1954–1975 (1979)
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    Empirical economics 4 (1979), S. 199-219 
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    ISSN: 1435-8921
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Summary This paper describes an econometric model of the Czechoslovak economy. The model is based on a macroeconomic theory of the planned economy and the hypothesis that planners' behavior is relatively stable over time and reflects the policy options implied by the macroeconomic theory. Parameter estimates of the model are presented and discussed. We find both macroeconomic relationships consistent with hypothesis derived from our macroeconomic theory and stable planners' behavior. We thus conclude that models of both planned economies and planners' behavior can be constructed on the basis of theory rather on the basis of ad hoc searches for the existence of regularities in the data.
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    Polymerization of propylene over titanium exchanged Y-zeolite (1979)
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    Polymer bulletin 1 (1979), S. 665-670 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary It was found that isotactic polymerization of propylene took place over titanium ion-exchanged Y-zeolite without organometallic compounds. The results obtained have led to the conclusions that Ti4+ species as well as Ti3+ species are active for the polymerization and that neither Ti-alkyl bonds nor Cl ligands are necessarily essential for polymerization of propylene.
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    Copolymers from 1-phenyl-2-(3-vinylphenylthio)-diazen and styrene and grafting with acrylonitrile (1979)
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    Polymer bulletin 1 (1979), S. 679-684 
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    ISSN: 1436-2449
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary A new azo monomer (2) was synthesized and copolymerized with styrene. The resulting azo copolymer could be used as an initiator for the acrylonitrile polymerisation yielding grafted copolymers. Quantitative treatment of the grafting experiments leads to the conclusion that the intermediate thiyl radicals show less reactivity towards monomers than phenyl radicals.
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    Polymeric coordination complexes of some bipositive metal ions with 5,5′-(benzidinebisazo)-8-hydroxyquinoline (1979)
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    Polymer bulletin 1 (1979), S. 685-690 
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    ISSN: 1436-2449
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Coordination chain polymers of Mn(II), Fe(II), Co(II), Ni(II), Cu(II), zn(II), and Cd(II) with 5,5-(benzidinebisazo)-8-hydroxyquinoline were synthesized by refluxing a mixture of metal acetate hydrates and ligand (1∶1) in DMSO. From analytical data an empirical formula of ML.2H2O is indicated. Ir spectra reveal coordination through O and N of oxine units, thus forming the polymeric chain; presence of coordinated water is also indicated. Magnetic moments and electronic spectra suggest octahedral geometry around the central metal ion. Besides the presence of 2H2O, TGA shows the order of thermal stability as : Cd∼Zn〉 Mn〉 Co∼Ni∼Cu〉Fe.
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    Poly(amidine)s and poly(guanidine)s — synthesis and some properties (1979)
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    Polymer bulletin 1 (1979), S. 715-722 
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    ISSN: 1436-2449
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Synopsis Several poly(amidine) and poly(guanidine) copolymers and their hydrochloride salts were synthesized by introducing the functional groups into suitable polymers. The properties of the resulting copolymers were investigated by base and acid titration.
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    Load transfer through chain molecules after interpenetration at interfaces (1979)
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    Polymer bulletin 1 (1979), S. 697-707 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A series of PMMA samples of different molecular weights and degrees of copolymerisation have been tested for their crack-healing behavior. Slightly above Tg, a diffusional interpenetration of chain segments takes place. The fracture toughness in the plane of the interpenetrated interface was measured in short- and longtime experiments. After very short penetration times of only 5 min, full material resistance was regained in short-time experiments, whereas the long-time properties were not restored. A qualitative explanation of these effects, based on structural parameters, is given.
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    Radiation grafting of acrylic acid onto polypropylene fibres (1979)
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    Polymer bulletin 1 (1979), S. 727-731 
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    ISSN: 1436-2449
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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    Synthesis of some new divalent metal salts of mono(hydroxyethyl)phthalate (1979)
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    Polymer bulletin 1 (1979), S. 723-725 
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    ISSN: 1436-2449
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Divalent metal salts of mono(hydroxyethyl)phthalate (HEP) were considered to be of interest as difunctional ionic monomers and are useful for the preparation of condensation polymers. Recently, Matsuda1 reported the preparation of Ca, Mg and Zn salts of mono-(hydroxyethyl)phthalate and their polymers2–7. He prepared these salts by the reaction of HEP with the respective divalent metal oxides. But so far there was no report on the preparation of Pb2+ and Mn2+ salts of HEP. Since metal dicarboxylates can be obtained by the reaction of organic dibasic acids and metal acetates8, Pb2+ and Mn2+ acetates can similarly react with HEP to give their respective salts at the optimum temperature. We report here the synthesis and characterisation of Pb2+ and Mn2+ salts of mono(hydroxyethyl)-phthalate (HEP).
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    Effect of cooling rate on the viscoelastic properties in the plastic zone of solid polymers (1979)
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    Polymer bulletin 1 (1979), S. 743-748 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract PMMA and PC samples were subjected to several cooling rates from the glass transition temperature. Stress-relaxation data, obtained with these samples under strains larger than the yield strain, were not influenced by the cooling rate previously experienced by the material. This shows that after yielding the effect of previous aging is quickly erased; similar indications, drawn from calorimetric measurements, were already available in (11–12).
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    The use of graft copolymers as enzyme supports (1979)
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    Polymer bulletin 1 (1979), S. 749-753 
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    ISSN: 1436-2449
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary A new type of polymer support for immobilizing enzymes, a copolymer grafted onto nylon was investigated. Polyacrylamide was used and successfully coupled to β-galactosidase (from yeast and bacteria) using two different methods to give activities of the order of 5 units/g of polymer for the yeast enzyme, and 156 units/g for the E.coli enzyme. Lactose did not affect the yield. The azide method gave better results than the glutaraldehyde method. β-galactosidase coupled enzyme was fairly stable but not as good as the free enzyme. Papain was also coupled to the polyacrylamide grafted nylon using both methods; the glutaraldehyde gave better results with 1.5mg of enzyme being coupled for each gram of polymer.
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    Polymerization via zwitterion. 23. Terpolymerization among 2-phenyl-1,3,2-dioxaphospholane, methyl acrylate, and carbon disulfide (1979)
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    Polymer bulletin 1 (1979), S. 243-251 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The present paper describes the terpolymerization involving 2-phenyl-1,3,2-dioxaphospholane, methyl acrylate, and carbon disulfide, which took place without any added initiator in benzonitrile or dimethylformamide. The structure and composition of terpolymer were determined by NMR and IR spectra, as well as by elemental analysis. A reaction scheme proceeding via zwitterion was proposed (Eq. 2–5).
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    Preparation of poly(vinyl chloride-g-isobutylene) by BCl3 (1979)
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    Polymer bulletin 1 (1979), S. 253-258 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Poly(vinyl chloride-g-isobutylene) has been synthesized using mildly dehydrochlorinated (NaOH treated) PVC in conjunction with BCl3 coinitiator. Treatment of PVC with NaOH increases initial thermal dehydrochlorination rate and renders the polymer suitable for efficient grafting. Untreated PVC produces negligible grafting.
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    Theory of thermal decomposition and volatilization of normal alkanes and linear polyethylene (1979)
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    Polymer bulletin 1 (1979), S. 347-354 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The fragmentation of linear polyethylene of high molecular weight, of normal alkanes, and of other nonbranched poly- α- olefins in a pyrolyzer connected with a gas chromatograph was studied previously. From the evaluation of the fragments longer than C11 or than the respective pentamer random decomposition process was suggested for these polymers. This process was described with characteristic cleavage probabilities for the C-C-bonds in the backbone of the chain. It is not possible to apply this simple model to the decomposition of normal alkanes without consideration of the volatilization. An approach to this problem is presented in this paper.
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    Stress and recovery maxima in LDPE melt elongation (1979)
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    Polymer bulletin 1 (1979), S. 397-402 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary By means of a new tensile rheometer for polymer melts, stress-strain curves σ(ε) and the elastic recovery εR(ε) of a low density polyethylene melt were measured up to total strains ε=7, i.e. stretch λ=1097, at 150°C and two strain rates, ε=0.03 and 0.1 s−1. Tensile tests up to very high strains e give relevant results only if the test performance is characterized by quality parameters which are defined and given in this paper. The test results show a maximum in a as well as in εR at about ε=5.5. Hence, in the range of ε investigated, a rheologically steady-state of flow does not exist.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00284409
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  • 290
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    Cis-trans isomerization of aromatic azo compounds built in the polyester segment of poly(ester urethanes) (1979)
    Springer
    Polymer bulletin 1 (1979), S. 517-522 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The photochemical and thermal cis-trans isomerization of 4,4 -(diamido)azobenzene derivative built in the polyester segment of a segmented poly(ester urethane) has been investigated. The photoisomerization in bulk proceeds more slowly than in solution and lower fractions of cis-isomers are reached in the photostationary state. The thermal cis-trans isomerization follows first order kinetics in polymers with amorphous soft phase but can only be described by two simultaneous first order processes in annealed samples. This is attributed to restrictions in the chain segmental mobility; it is assumed that the isomerization behaviour reflects different molecular motions in the bulk polymer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00255717
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  • 291
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    Correspondence between the theory of branching processes and the kinetic theory for random crosslinking in the post-gel stage (1979)
    Springer
    Polymer bulletin 1 (1979), S. 523-528 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The kinetic theory of crosslinking by step reactions (Kuchanov 1978) may be extended beyond the gel point, and the structure and amount of sol may be described. For random reactions, the kinetic theory yields results identical with the theory of branching processes based on cascade substitution (Gordon 1962, 1975, Dobson 1965). The extension of the kinetic theory may be employed in order to compare deviations between the two theories expected for the dependent reactivities of functional groups.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00254479
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  • 292
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    A new method for investigating the mechanism of initiation of radical polymerization (1979)
    Springer
    Polymer bulletin 1 (1979), S. 529-534 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The mechanism of initiation of polymerization of methyl acrylate by di-t-butyl peroxalate at 60°C, has been investigated using 2,2,6,6-tetramethylpiperidine-1-oxyl as a radical trapping agent and isolation of the resulting products. The following processes were identified: Tail addition of t-butoxy radicals to monomer, hydrogen abstraction from the methyl group of the monomer and fragmentation of the t-butoxy radicals to methyl radicals followed by tail addition of these to the methyl acrylate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00254480
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  • 293
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    Effect of hindered piperidine derivatives on polypropylene photooxidation (1979)
    Springer
    Polymer bulletin 1 (1979), S. 647-652 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The photostabilizing effect of a hindered piperidine derivative was studied in the photooxidation of polypropylene films by following the formation of carbonyl and hydroperoxide groups, as well as the change of concentration of the stabilizer. This additive — the tetramethylpiperidine sebacate — proved to be more effective than hydroxybenzophenone, hydroxybenztriazole or a sulphur containing nickel complex, since no oxidation products were formed after irradiation with 20O Mlxh dose. Addition of the piperidine derivative together with hydroxybenztriazole or with the organic nickel complex was less effective than with hydroxybenzophenone. In latter case concentration of both stabilizers under irradiation decreased at a slower rate than in the case of separate application. The effect of Cyasorb UV 531 and Tinuvin 770 was additive and the spontaneous rupture of the samples took place only after a long period of irradiation (∼ 250 Mlxh).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00254145
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    Functionalization of soluble polymers (1979)
    Springer
    Polymer bulletin 1 (1979), S. 691-695 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary In a second example of the functionalization of soluble polymers the conversion of the hydroxyl groups of poly (oxyethylene) into carboxyl groups is reported. As protected carboxyl component, 4-toluenesulfonyl lactic acid ethyl ester was synthesized and was allowed to react with sodium salt of poly(oxyethylene). Polymer-analogous hydrolysis of the di(lactic acid ethyl ester) poly(oxyethylene) yielded the carboxyl derivative of poly (oxyethylene).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00255444
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  • 295
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    Aqueous polymerization of acrylamide initiated by Ce(IV)-thiomalic acid redox system (1979)
    Springer
    Polymer bulletin 1 (1979), S. 671-678 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The use of a Ce (IV)-thiomalic acid (Ce4+-TMA) redox system as an initiator in the polymerization of acrylamide (M) in an aqueous medium has been investigated. The Ce4+ forms a 1∶1 complex with TMA, decomposing through free radical mechanism in an acid medium. From 5 to 15% conversion the rate equation is $$R_p = - \frac{{d[M]}}{{dt}} = k[M]^{3/2} [Ce^{4 + } ]^x [TMA]$$ where Rp is the rate of polymerization and x is 0.5 or 1.0 depending upon the concentration of monomer. The overall energy of activation has been calculated to be 9.12 k cal. deg−1 mol−1(38.12 kJ/mol) in the investigated range of temperature (25°–40°C) the degree of polymerization (P) of the polymer is directly proportional to [M]. The number of average molecular weight of the polymer remains unaffected at lower concentration of Ce4+ and is found to decrease at higher concentrations. In this investigation the kinetics and mechanism of the Ce(IV)-thiomalic acid (TMA) redox system to initiate the polymerization of acrylamide has been studied. Acrylamide (E. Merck) was purified by usual methods. Thiomalic acid and eerie ammonium sulfate were used without purification. All solutions were p repared in twice distilled water. The polymerization procedure adopted was similar to the one used by MISRA et al. [3, 4]. The polymerization was followed by quantitative estimation of the double bonds in acrylamide as described [8]. A small variable induction period was observed perhaps due tothe residual oxygen in the thiol solution. Curves were plotted after eliminating the induction period. The average molecular weights of the p olymers were determined by viscosity measurements at 30°C in an aqueous medium using the relationship of DAINTON et al. [2]. $$[\eta ] 30^\circ = 6.8 x 10^{ - 4} \bar Mn^{0.66} $$ Where [η]=intrinsic viscosity of the polymer solution and ¯Mn=molecular weight of the sample.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00255441
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    Ultrahigh-strength polyethylene filaments by solution spinning and hot drawing (1979)
    Springer
    Polymer bulletin 1 (1979), S. 733-736 
    Details
    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00256272
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  • 297
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    Environmental stress relaxation studies of polymers: effect of ketones on polyethylene and its temperature dependence (1979)
    Springer
    Polymer bulletin 1 (1979), S. 737-741 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The method of stress relaxation has been used to study the effect of ketones on polyethylene as it changes with temperature. From the observation of the stress relaxation in polyethylene under ketones and its temperature dependence, the activation energy of penetrant-enhanced relaxation of polyethylene caused by ketones were obtained and the effect of ketones on polyethylene were discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00256273
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    The use of graft copolymers as enzyme supports (1979)
    Springer
    Polymer bulletin 1 (1979), S. 755-761 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary β-Galactosidase and glucose oxidase have been immobilized on cellulose-polyacrylamide (C-PAM) graft copolymers, using the azide method or through glutaraldehyde. The original (C-PAM) copolymers were prepared via radiation-induced grafting under controlled conditions by both post-irradiation and simultaneous procedures. The optimum conditions for coupling of the copolymers to the enzymes were established as were the levels of activity of the immobilized enzymes. Grafting by the simultaneous route was seen to be more efficient than postirradiation grafting. Indirect evidence of grafting was found from elemental and thermal analysis. Binding of β-galactoside was found to be more successful than that of glucose oxidase. A relationship between the level of immobilized enzyme activity and the extent of grafting in the copolymer was established for the β-galactosidase system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00256276
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  • 299
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    Thermodynamic study on heat of mixing of polyisobutylene with ethylbenzene (1979)
    Springer
    Polymer bulletin 1 (1979), S. 763-770 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The heat of mixing of polyisobutylene with ethylbenzene was measured from 18.2 to 69.2° C with a Tian-Calvet twin micro-calorimeter, and the exchange enthalpy parameter X12 in Flory's theory was estimated. The X12 obtained was discussed also in comparison with the one based on Manzini model. Further combining with osmotic pressure data, temperature dependence of the entropy parameter Q12 was referred.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00256277
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  • 300
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    Effect of the chiral polymer chain in the anionic polymerization of styrene oxide (1979)
    Springer
    Polymer bulletin 1 (1979), S. 793-799 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Styrene oxide of different enantiomeric compositions was polymerized in bulk using a potassium alkoxide initiator. A preferential consumption of the enantiomer in excess was observed. The magnitude of this effect depends on the enantiomeric composition of the initial monomer: the more unbalanced is the latter, the stronger is the stereoelection observed. The stereoelective effect was almost completely suppressed by addition of complexing agents such as crown-ethers or cryptands. The observed phenomena are explained in terms of polymer-chain effects.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00256281
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