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  • Articles  (11)
  • Articles: DFG German National Licenses  (11)
  • Springer  (11)
  • Blackwell Science Ltd
  • 1995-1999  (5)
  • 1980-1984  (6)
  • Mathematics  (11)
  • 1
    Electronic Resource
    Electronic Resource
    A partially ordered extention of the integers (1995)
    Springer
    Studia logica 54 (1995), S. 303-332 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract This paper presents a monotonic system of Post algebras of order ω+ω* whose chain of Post constans is isomorphic with 0≤1≤2≤ ... ≤-3≤-2≤-1. Besides monotonic operations, other unary operations are considered; namely, disjoint operations, the quasi-complement, succesor, and predecessor operations. The successor and predecessor operations are basic for number theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01053003
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  • 2
    Electronic Resource
    Electronic Resource
    Aligning simulation models: A case study and results (1996)
    Springer
    Computational & mathematical organization theory 1 (1996), S. 123-141 
    Details
    ISSN: 1572-9346
    Keywords: Simulation ; replication ; computational models ; alignment ; culture
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper develops the concepts and methods of a process we will call “alignment of computational models” or “docking” for short. Alignment is needed to determine whether two models can produce the same results, which in turn is the basis for critical experiments and for tests of whether one model can subsume another. We illustrate our concepts and methods using as a target a model of cultural transmission built by Axelrod. For comparison we use the Sugarscape model developed by Epstein and Axtell. The two models differ in many ways and, to date, have been employed with quite different aims. The Axelrod model has been used principally for intensive experimentation with parameter variation, and includes only one mechanism. In contrast, the Sugarscape model has been used primarily to generate rich “artificial histories”, scenarios that display stylized facts of interest, such as cultural differentiation driven by many different mechansims including resource availability, migration, trade, and combat. The Sugarscape model was modified so as to reproduce the results of the Axelrod cultural model. Among the questions we address are: what does it mean for two models to be equivalent, how can different standards of equivalence be statistically evaluated, and how do subtle differences in model design affect the results? After attaining a “docking” of the two models, the richer set of mechanisms of the Sugarscape model is used to provide two experiments in sensitivity analysis for the cultural rule of Axelrod's model. Our generally positive experience in this enterprise has suggested that it could be beneficial if alignment and equivalence testing were more widely practiced among computational modelers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01299065
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  • 3
    Electronic Resource
    Electronic Resource
    On-Line and Off-Line Approximation Algorithms for Vector Covering Problems (1998)
    Springer
    Algorithmica 21 (1998), S. 104-118 
    Details
    ISSN: 1432-0541
    Keywords: Key words. Approximation algorithm, Worst case ratio, Competitive analysis, On-line algorithm, Packing problem, Covering problem.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. This paper deals with vector covering problems in d -dimensional space. The input to a vector covering problem consists of a set X of d -dimensional vectors in [0,1] d . The goal is to partition X into a maximum number of parts, subject to the constraint that in every part the sum of all vectors is at least one in every coordinate. This problem is known to be NP-complete, and we are mainly interested in its on-line and off-line approximability. For the on-line version, we construct approximation algorithms with worst case guarantee arbitrarily close to 1/(2d) in d≥ 2 dimensions. This result contradicts a statement of Csirik and Frenk in [5] where it is claimed that, for d≥ 2 , no on-line algorithm can have a worst case ratio better than zero. Moreover, we prove that, for d≥ 2 , no on-line algorithm can have a worst case ratio better than 2/(2d+1) . For the off-line version, we derive polynomial time approximation algorithms with worst case guarantee Θ(1/ log d) . For d=2 , we present a very fast and very simple off-line approximation algorithm that has worst case ratio 1/2 . Moreover, we show that a method from the area of compact vector summation can be used to construct off-line approximation algorithms with worst case ratio 1/d for every d≥ 2 .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009203
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  • 4
    Electronic Resource
    Electronic Resource
    Core points in double Heyting algebras and dissectable lattices (1983)
    Springer
    Algebra universalis 16 (1983), S. 204-218 
    Details
    ISSN: 1420-8911
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01191769
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  • 5
    Electronic Resource
    Electronic Resource
    Fixed points of Feigenbaum's type for the equationf p (λx)≡λf(x) (1984)
    Springer
    Communications in mathematical physics 93 (1984), S. 495-516 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Existence and hyperbolicity of fixed points for the mapN p :f(x) →λ−1 f p (λx), withf p p-fold iteration and λ=f p (0) are given forp large. These fixed points come close to being quadratic functions, and our proof consists in controlling perturbation theory about quadratic functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01212292
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  • 6
    Electronic Resource
    Electronic Resource
    Analyticity properties of the Feigenbaum function (1981)
    Springer
    Communications in mathematical physics 81 (1981), S. 437-453 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Analyticity properties of the Feigenbaum function [a solution ofg(x)=−λ−1 g(g(λx)) withg(0)=1,g′(0)=0,g″(0)〈0] are investigated by studying its inverse function which turns out to be Herglotz or anti-Herglotz on all its sheets. It is found thatg is analytic and uniform in a domain with a natural boundary.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01209078
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  • 7
    Electronic Resource
    Electronic Resource
    Some analyticity properties arising from asymptotic completeness in quantum field theory (1981)
    Springer
    Communications in mathematical physics 80 (1981), S. 99-125 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is well-known that two-particle unitarity of the S-Matrix in quantum field theory implies (modulo regularity assumptions) second sheet analyticity for the 2-body scattering amplitude. Here this is first used to prove off-mass-shell analyticity for the 4 point function in a complex neighborhood of any real mass-shell point under the 3-particle threshold. Then this is applied to the study of the 5 and 6-point functions near the real mass-shell of 2→3 and 3→3 processes below the 4-particle threshold: the results are those suggested by perturbation theory apart from the 3-particle cut and away from some submanifolds. The advantage of this method, which could presumably be extended to the exploitation ofn-particle unitarity, is that the regularity assumptions only refer to the physical scattering amplitudes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01213597
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  • 8
    Electronic Resource
    Electronic Resource
    Perturbations of geodesic flows on surface of constant negative curvature and their mixing properties (1984)
    Springer
    Communications in mathematical physics 95 (1984), S. 61-112 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider one parameter analytic hamiltonian perturbations of the geodesic flows on surfaces of constant negative curvature. We find two different necessary and sufficient conditions for the canonical equivalence of the perturbed flows and the non-perturbed ones. One condition says that the “Hamilton-Jacobi equation” (introduced in this work) for the conjugation problem should admit a solution as a formal power series (not necessarily convergent) in the perturbation parameter. The alternative condition is based on the identification of a complete set of invariants for the canonical conjugation problem. The relation with the similar problems arising in the KAM theory of the perturbations of quasi periodic hamiltonian motions is briefly discussed. As a byproduct of our analysis we obtain some results on the Livscic, Guillemin, Kazhdan equation and on the Fourier series for the SL(2, ℝ) group. We also prove that the analytic functions on the phase space for the geodesic flow of unit speed have a mixing property (with respect to the geodesic flow and to the invariant volume measure) which is exponential with a universal exponent, independent on the particular function, equal to the curvature of the surface divided by 2. This result is contrasted with the slow mixing rates that the same functions show under the horocyclic flow: in this case we find that the decay rate is the inverse of the time (“up to logarithms”).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01215756
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  • 9
    Electronic Resource
    Electronic Resource
    The set of maps $$F_{a,b} :x \mapsto x + a + \tfrac{b}{{2\pi }}$$ sin(2πx) with any given rotation interval is contractiblewith any given rotation interval is contractible (1995)
    Springer
    Communications in mathematical physics 173 (1995), S. 313-333 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Consider the two-parameter family of real analytic maps $$F_{a,b} :x \mapsto x + a + \tfrac{b}{{2\pi }}$$ sin(2πx) which are lifts of degree one endomorphisms of the circle. The purpose of this paper is to provide a proof that for any closed intervalI, the set of mapsF a,b whose rotation interval isI, form a contractible set.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02101236
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  • 10
    Electronic Resource
    Electronic Resource
    On the existence of Feigenbaum's fixed point (1981)
    Springer
    Communications in mathematical physics 79 (1981), S. 261-302 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We give a proof of the existence of aC 2, even solution of Feigenbaum's functional equation $$g{\text{(}}x) = - \lambda _0^{ - 1} g{\text{(}}g( - \lambda _0 x)),g{\text{(0) = 1,}}$$ whereg is a map of [−1, 1] into itself. It extends to a real analytic function over ℝ.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01942063
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