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  • 1990-1994  (4)
  • 1985-1989  (3)
  • 1950-1954  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    Misinformation (1993)
    [s.l.] : Nature Publishing Group
    Nature 362 (1993), S. 509-509 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] INFORMATION theory and molecular biology are both large and important fields. In this book, H. P. Yockey tries to link the two. Quite often the word 'information' is used with different meanings, but from the very beginning he sticks to a single interpretation — Shannon information. This ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/362509a0
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    An explicit construction of a class of suspensions and autonomous differential equations for diffeomorphisms in the plane (1987)
    Springer
    Communications in mathematical physics 111 (1987), S. 63-74 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract From a large class of diffeomorphisms in the plane, which are known to produce chaotic dynamics, we explicitly construct their continuous suspension on a three dimensional cylinder. This suspension is smooth (C 1) and can be characterized by the choice of two smooth functions on the unit interval, which have to fulfill certain boundary conditions. For the case of entire Cremona transformations, we are able to construct the corresponding autonomous differential equations of the flow explicitly. Thus it is possible to relate properties of discrete maps to those of ordinary differential equations in a quantitative manner. Furthermore, our construction makes it possible to study the exact solutions of chaotic differential-equations directly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01239015
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Zum Identitätsproblem bei Gruppen (1952)
    Springer
    Mathematische Zeitschrift 56 (1952), S. 335-362 
    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/BF01686754
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Quasiperiodicity involving twin oscillations in the complex Lorenz equations describing a detuned laser (1990)
    Springer
    The European physical journal 81 (1990), S. 457-461 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Quasiperiodical motion in the complex Lorenz equations describing a detuned laser is shown to consist of twin oscillations: the first oscillation originates from Hopf bifurcation and the second is a parastic oscillation of the first one. Equations for the twin asymptotic oscillations are analytically derived in the center manifold, showing explicitly the parastic property of the second oscillation: its frequency is proportional to the square of the amplitude of the first one. The phase of the second oscillation shows also certainanholonomy which is very similar to the characteristics of Berry's phase. Numerical results show further that the first oscillation follows the sequence of bifurcations from simple periodic through period-doubling to chaos, as one continuously increases the control parameter, whereas the frequency of the parastic oscillation does not change qualitatively during the bifurcation process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390829
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Unbiased determination of forces causing observed processes (1992)
    Springer
    The European physical journal 88 (1992), S. 95-103 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Using measured short time correlation functions of a stochastic process as constraints in the maximum calibre principle of Jaynes, we formulate the joint probability distribution function of the process. The Lagrange multipliers which hereby occur are determined by minimizing a time-dependent form of the (Kullback) information gain. This step can alternatively be interpreted as if our system builds a neural network which “learns” the Lagrange multipliers. Next, we proceed to determine explicit formulas-expressed in terms of the Lagrange multipliers-for the drift and diffusion coefficients appearing in the corresponding Ito-Langevin equation, which describe the forces underlying the process. Computer-simulations of two processes are presented, showing good confirmation of the theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01573843
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  • 6
    Electronic Resource
    Electronic Resource
    Generalized Ginzburg-Landau equation for self-pulsing instability in a two-photon laser (1989)
    Springer
    The European physical journal 77 (1989), S. 163-174 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A nonlinear analysis is made for a degenerate two-photon ring laser near its critical point corresponding to a self-pulsing instability by using the slaving principle and normal form theory. It turns out that the system undergoes two kinds of transitions, a usual Hopf bifurcation to a stable or unstable limit cycle and a co-dimension two Hopf bifurcation where the limit cycles disappear. An analytical criterion is given to distinguish the super-from the sub-critical bifurcation. We have also solved the equations numerically to confirm and to supplement our analytical results. In the case of super-critical bifurcation, a period-doubling bifurcation sequence to chaos is also observed with the decrease in pumping.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01313634
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  • 7
    Electronic Resource
    Electronic Resource
    Instability in degenerate two-photon running wave laser (1989)
    Springer
    The European physical journal 77 (1989), S. 157-162 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The stability of the homogeneously broadened and degenerate two-photon running wave laser is analysed by using the full set of matter-field equations. The stability depends on the relative size of the relaxation constants. For 2k〉1+r(k=κ/γ⊥,r=γ∥/γ⊥; κ is the cavity loss of the field and γ∥,γ⊥ are the longitudinal and transversal decay constants, respectively) no stable lasing state exists. Forr〈k〈(1+r)/2 an instability occurs. With the decrease in pumping the stable lasing state loses its stability due to Hopf-bifurcation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01313633
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Learning the dynamics of two-dimensional stochastic Markov processes (1992)
    Springer
    Open systems & information dynamics 1 (1992), S. 311-326 
    Details
    ISSN: 1573-1324
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Natural Sciences in General
    Notes: Abstract We show that it is possible to “learn” the forces causing an observed two-dimensional stochastic Markov process. Hereby, we extend the ideas presented in our earlier work [1–3], where we discussed one-dimensional processes. Appropriate short-time correlation function measurements are used as constraints in the maximum information principle of Jaynes, allowing us to formulate the joint probability distribution function of the process. This is done using the method of Lagrange multipliers, which we determine by means of a dynamical learning method. Next, we derive explicit formulas expressing the drift- and diffusion coefficients of the Ito-Langevin equation corresponding to the process in terms of the Lagrange multipliers. This provides us with the sought for underlying deterministic and stochastic dynamics. The method was tested on a simulated Ornstein-Uhlenbeck process, showing good confirmation of the theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02228842
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