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  • Articles  (46,518)
  • 1980-1984  (46,518)
  • Mathematics  (46,518)
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  • Books  (164)
  • Articles  (46,518)
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  • 1
    Electronic Resource
    Electronic Resource
    On the boundedness and the asymptotic behaviour of the non-negative solutions of Volterra-Hammerstein integral equations (1980)
    Springer
    Manuscripta mathematica 31 (1980), S. 379-412 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study the Volterra-Hammerstein integral equation $$U(t,x) = U_O (t,x) + \mathop \smallint \limits_O^t \mathop \smallint \limits_D f(y, U (t - s,y)) h (x,y,s)dsdy,$$ t≥0, x∈D. We derive sufficient conditions for the boundedness of all non-negative solutions U. We show that, for bounded non-negative solutions U, U(t,.) is positive on D for sufficiently large t〉0, if we impose appropriate positivity assumptions on f and h. If we additionally assume that, for y∈D, rf(y,r) strictly monotone increases and f(y,r)/r strictly monotone decreases as r〉0 increases, the following alternative holds for any bounded non-negative solution U: Either U(t,.) converges toward zero for t→∞, pointwise on D, or U(t,.) converges, for t→∞, toward the unique bounded positive solution of the corresponding Hammerstein integral equation, uniformly on D. We indicate conditions for the occurrence of each of the two cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02320701
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  • 2
    Electronic Resource
    Electronic Resource
    Eine geometrische Bemerkung zu Sätzen über harmonische Abbildungen, die ein Dirichletproblem lösen (1980)
    Springer
    Manuscripta mathematica 32 (1980), S. 51-57 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let BM(p) be a geodesic ball in a Riemannian manifold with radius $$M〈 \frac{\pi }{{2\sqrt K }}$$ , where κ is an upper bound of the sectional curvature. The cut locus condition on BM(p) occuring in several theorems on harmonic mappings which map into BM(p) can be weakened by proving uniqueness of geodesics contained in BM(p).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01298181
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  • 3
    Electronic Resource
    Electronic Resource
    Primitive holomorphic maps of curves (1980)
    Springer
    Manuscripta mathematica 32 (1980), S. 59-80 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let t: X→Y be a proper morphism of non-singular irreducible affine curves over ℌ. This paper shows that there is seldom a holomorphic function f such that (t,f): X → Y × ℌ is a holomorphic embedding.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01298182
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  • 4
    Electronic Resource
    Electronic Resource
    Automatic continuity of generalized local linear operators (1980)
    Springer
    Manuscripta mathematica 32 (1980), S. 263-294 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this note, we present a general automatic continuity theory for linear mappings between certain topological vector spaces. The theory applies, in particular, to local operators between spaces of functions and distributions, to algebraic homomorphisms between certain topological algebras, and to linear mappings intertwining generalized scalar operators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01299605
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  • 5
    Electronic Resource
    Electronic Resource
    A quick proof of Singhof's cat(M ×S1)=cat(M)+1 theorem (1983)
    Springer
    Manuscripta mathematica 42 (1983), S. 49-52 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a topological space X, the Lusternik-Schnirelmann category, cat(X), is the smallest number N such that X can be covered by N open subsets each of which is contractible in X. W. Singhof [6] proved that the minimal number of n-balls which suffice to cover a closed PL n-manifold M coincides with the Lusternik-Schnirelmann category if the latter is not too small compared with the dimension of M. As a consequence, one obtains in this case that cat(M×1)=cat(M)+1, thus establishing a special case of a long-standing conjecture. The purpose of this paper is to give a quick proof of Singhof 's results by exploiting the linear structure between the k-skeleton of a polyhedron and its dual skeleton.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01171745
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  • 6
    Electronic Resource
    Electronic Resource
    A note on prime k-th power nonresidues (1983)
    Springer
    Manuscripta mathematica 42 (1983), S. 285-288 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Bounds for the second and third smallestprime k-th power nonresidues of odd primes p have been given by Alfred Brauer, Clifton Whyburn, and L. K. Hua. Bounds for the n-th prime residue, n≥4, do not appear in the literature and it would be difficult to obtain bounds as sharp as p1/4 if n is large and k is small. In this note we use the character sum estimates of D. A. Burgess to show that there are on the order of log p/log log pprime k-th power nonresidues less than p1/4 +∈ for every ∈〉0 and sufficiently large p.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01169590
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  • 7
    Electronic Resource
    Electronic Resource
    Geometric applications of euclidean Jordan triple systems (1983)
    Springer
    Manuscripta mathematica 42 (1983), S. 265-272 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The article presents a result about the trace form of Jordan triple systems and as application the classification of the pseudo-umbilical symmetric submanifolds of hyperbolic space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01169588
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  • 8
    Electronic Resource
    Electronic Resource
    On subseries convergent series and m-quasi-bases in topological linear spaces (1982)
    Springer
    Manuscripta mathematica 38 (1982), S. 87-98 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove that the algebraic dimension of the linear span of sums of a subseries convergent series in a Hausdorff topological linear space is either finite or equals 2ℵ°. This result is applied to represent every infinite-dimensional metrizable linear spaee of cardinality 2ℵ° as the direct sum of a sequence of dense subspaces with a strange summability property. Moreover, we show that every infinite-dimensional separable metrizable linear space admits an m-quasi-basis which is not a quasi-basis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01168388
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  • 9
    Electronic Resource
    Electronic Resource
    Die 3-Weierstrass-Punkte über dem Teichmüller-Raum T2 (1982)
    Springer
    Manuscripta mathematica 38 (1982), S. 201-223 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The set of k-Weierstraß-points (k≥3) belonging to the universal family π2∶V2→T2 of compact Riemann surfaces of genus 2 consists of the set of 1-Weierstraß-points, being devided into six submanifolds of V2, and of a further analytic subset, which covers the Teichmüller space T2 relative to the restriction π* of π2 but does not contain a global sheet. The aim of this paper is the investigation of those 3-Weierstraß-points that are not 1-Weierstraß-points, i. e. the investigation of the covering π*.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01168591
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  • 10
    Electronic Resource
    Electronic Resource
    Probabilistic topologies induced by L-fuzzy uniformities (1982)
    Springer
    Manuscripta mathematica 38 (1982), S. 289-323 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Basic properties of probabilistic topologies associated with L-fuzzy uniformities are studied, e.g. regularity, uniform continuity and 1-completeness. The main result is the existence and uniqueness of the probabilistic completion of L-fuzzy uniform spaces. Moreover with respect to the applicability of this theory we also give concrete representations of the probabilistic completion of compact as well as of Polish spaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01170928
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