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  • Articles  (115)
  • Mathematics  (115)
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  • Articles  (115)
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  • 1
    Electronic Resource
    Electronic Resource
    Sieve algorithms for perfect power testing (1993)
    Springer
    Algorithmica 9 (1993), S. 313-328 
    Details
    ISSN: 1432-0541
    Keywords: Perfect powers ; Number theoretic algorithms ; Riemann hypothesis ; Newton's method ; Sieve algorithms ; Parallel algorithms ; Average-case analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A positive integern is a perfect power if there exist integersx andk, both at least 2, such thatn=x k . The usual algorithm to recognize perfect powers computes approximatekth roots fork≤log 2 n, and runs in time O(log3 n log log logn). First we improve this worst-case running time toO(log3 n) by using a modified Newton's method to compute approximatekth roots. Parallelizing this gives anNC 2 algorithm. Second, we present a sieve algorithm that avoidskth-root computations by seeing if the inputn is a perfectkth power modulo small primes. Ifn is chosen uniformly from a large enough interval, the average running time isO(log2 n). Third, we incorporate trial division to give a sieve algorithm with an average running time ofO(log2 n/log2 logn) and a median running time ofO(logn). The two sieve algorithms use a precomputed table of small primes. We give a heuristic argument and computational evidence that the largest prime needed in this table is (logn)1+O(1); assuming the Extended Riemann Hypothesis, primes up to (logn)2+O(1) suffice. The table can be computed in time roughly proportional to the largest prime it contains. We also present computational results indicating that our sieve algorithms perform extremely well in practice.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01228507
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  • 2
    Electronic Resource
    Electronic Resource
    Zur Weylschen Relativitätstheorie und der Weylschen Erweiterung des Krümmungstensorbegriffs (1921)
    Springer
    Mathematische Zeitschrift 9 (1921), S. 110-135 
    Details
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01378338
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  • 3
    Electronic Resource
    Electronic Resource
    Weil Bounds for Singular Curves (1996)
    Springer
    Applicable algebra in engineering, communication and computing 7 (1996), S. 289-298 
    Details
    ISSN: 1432-0622
    Keywords: Keywords Algebraic space curves ; Genus ; Singularities ; Riemann hypothesis for function fields.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics , Technology
    Notes: Abstract  We give explicit bounds useful in estimating the number of points on a (possibly singular) space curve defined over a finite field. Our estimates involve the degrees of the polynomials defining the curve set-theoretically, and reduce to Weil’s well-known estimate for nonsingular complete intersection curves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01195534
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  • 4
    Electronic Resource
    Electronic Resource
    Private health insurance, 2nd ed.
    Amsterdam : Elsevier
    Insurance Mathematics and Economics 13 (1993), S. 171 
    Details
    ISSN: 0167-6687
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1016/0167-6687(93)90946-M
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  • 5
    Electronic Resource
    Electronic Resource
    Return to equilibrium (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 3985-4060 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study an atom with finitely many energy levels in contact with a heat bath consisting of photons (blackbody radiation) at a temperature T〉0. The dynamics of this system is described by a Liouville operator, or thermal Hamiltonian, which is the sum of an atomic Liouville operator, of a Liouville operator describing the dynamics of a free, massless Bose field, and a local operator describing the interactions between the atom and the heat bath. We show that an arbitrary initial state that is normal with respect to the equilibrium state of the uncoupled system at temperature T converges to an equilibrium state of the coupled system at the same temperature, as time tends to +∞ (return to equilibrium). © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533334
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  • 6
    Electronic Resource
    Electronic Resource
    Accuracy of the Hartree–Fock approximation for the Hubbard model (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 2072-2083 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A lower bound 0≥(Egs(n)−Ehf(n))/|Λ|≥−const[n2/3U4/3(|ln U|+1) +Un1/2|Λ|−1/2d(|ln(|Λ|−1/2)|1)] to the difference of the ground state and the Hartree–Fock energy of the Hubbard model is derived. Here |Λ| is the lattice size, U is the coupling parameter, and n is the electron density per site. This estimate holds for all dimensions d≥2 and all densities. Thus the Hartree–Fock approximation becomes exact (even beyond terms of order U) for small U and large |Λ|. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531922
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  • 7
    Electronic Resource
    Electronic Resource
    Error bound for the Hartree-Fock energy of atoms and molecules (1992)
    Springer
    Communications in mathematical physics 147 (1992), S. 527-548 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We estimate the error of the Hartree-Fock energy of atoms and molecules in terms of the one-particle density matrix corresponding to the exact ground state. As an application we show this error to be of orderO(Z 5/3−δ) for any δ〈2/21 as the total nuclear chargeZ becomes large.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02097241
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  • 8
    Electronic Resource
    Electronic Resource
    Positive Commutators and the Spectrum¶of Pauli--Fierz Hamiltonian of Atoms and Molecules (1999)
    Springer
    Communications in mathematical physics 207 (1999), S. 557-587 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: In this paper we study the energy spectrum of the Pauli–Fierz Hamiltonian generating the dynamics of nonrelativistic electrons bound to static nuclei and interacting with the quantized radiation field. We show that, for sufficiently small values of the elementary electric charge, and under weaker conditions than those required in [3], the spectrum of this Hamiltonian is absolutely continuous, except possibly in small neighbourhoods of the ground state energy and the ionization thresholds. In particular, it is shown that (for a large range of energies) there are no stable excited eigenstates. The method used to prove these results relies on the positivity of the commutator between the Hamiltonian and a suitably modified dilatation generator on photon Fock space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050737
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  • 9
    Electronic Resource
    Electronic Resource
    A characterization of the classical states of the quantum harmonic oscillator by means of de Finetti's theorem (1989)
    Springer
    Communications in mathematical physics 123 (1989), S. 453-462 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Integral representations of statistical operators in terms of coherent states are derived by means of a quantum version of the Poisson limit of de Finetti's theorem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01238810
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  • 10
    Electronic Resource
    Electronic Resource
    The simplex structure of the classical states of the quantum harmonic oscillator (1986)
    Springer
    Communications in mathematical physics 107 (1986), S. 553-560 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that the convex set of classical states of the quantum harmonic oscillator is a simplex generated as the closed convex hull of the coherent states in the weak topology of the Banach space of trace class operators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01205485
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