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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Set-valued analysis 1 (1993), S. 47-63 
    ISSN: 1572-932X
    Keywords: 34A60 ; 54C65 ; Lipschitz multifunction ; directional continuity ; Hölder continuous selection
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider two continuous selection problems related to the differential inclusion $$\dot x$$ ∈F(t, x). Assuming thatF is Hölder or Lipschitz continuous with compact, not necessarily convex values, we provide estimates on the modulus of continuity of these selections.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear differential equations and applications 3 (1996), S. 305-322 
    ISSN: 1420-9004
    Keywords: 34 C 20 ; 47 A 20 ; 57 R 25 ; Homogeneous vector fields ; Nonlinear vector fields ; Normal forms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Homogenous vector fields of degree one with respect to an arbitrary dilation δ ε r may be regarded as a natural extension of the linear vector fields. This paper is concerned with the problem of computing normal forms for vector fields that can be expanded in terms of homogeneous fields of degree greater than or equal to one with respect to an arbitrary dilation δ ε r . In particular, necessary and sufficient conditions are given for the existence of a local coordinate change that transforms an analytic field into a homogeneous field of degree one with respect to an arbitrary dilation δ ε r .
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Neural computing & applications 5 (1997), S. 152-159 
    ISSN: 1433-3058
    Keywords: Digital neural processor ; Generalisation ; Hardware implementation ; Probabilistic neural networks ; Random optimisation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A modified PNN training algorithm is proposed. The standard PNN, though requiring a very short training time, when implemented in hardware exhibits the drawbacks of being costly in terms of classification time and of requiring an unlimited number of units. The proposed modification overcomes the latter drawback by introducing an elimination criterion to avoid the storage of unnecessary patterns. The distortion in the density estimation introduced by this criterion is compensated for by a crossvalidation procedure to adapt the network parameters. The present paper deals with a specific realworld application, i.e. handwritten character classification. The proposed algorithm makes it possible to realise the PNN in hardware and, at the same time, compensates for some inadequacies arising from the theoretical basis of the PNN, which does not perform well with small training sets.
    Type of Medium: Electronic Resource
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