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  • 1
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    An Optimal Krasnosel'skii-Type Theorem for the Dimension of the Kernel of a Starshaped Set (1995)
    Oxford University Press
    Details
    Publication Date: 1995-05-01
    Print ISSN: 0024-6093
    Electronic ISSN: 1469-2120
    Topics: Mathematics
    Published by Oxford University Press
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  • 2
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    Representations of Starshaped Sets in Normed Linear Spaces (2000)
    Elsevier
    Details
    Publication Date: 2000-07-01
    Print ISSN: 0022-1236
    Electronic ISSN: 1096-0783
    Topics: Mathematics
    Published by Elsevier
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  • 3
    Electronic Resource
    Electronic Resource
    A Condition for Sets in R 3 to be Cones (2000)
    Springer
    Discrete & computational geometry 23 (2000), S. 147-154 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. Let S be a nonempty proper subset of R 3 . A point y in cl, S is clearly R -visible from a point x via S if and only if there exists a neighborhood N of y such that S contains all closed half-lines emanating from x through points of $S\cap N$ . The following Krasnosel'skii-type theorem is proved—if every two boundary points of S are clearly R -visible via S from a common point, then S is a cone. This improves an earlier result with the number three and answers an open question.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009488
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  • 4
    Electronic Resource
    Electronic Resource
    Estimating unique solutions of DC transistor circuits (1999)
    Bradford : Emerald
    Compel 18 (1999), S. 132-142 
    Details
    ISSN: 0332-1649
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: For each natural n let Fn denote the collection of mappings of Rn onto itself defined by: F ?Fn if and only if there exist n strictly monotone increasing functions fk mapping R onto itself such that for each x =[x1, ..., xn]T ? Rn, F(x) = [f1(x1), ..., fn(xn)]T. The following new property of the class P0 of matices is proved: a real n × n matrix A belongs to P0 if and only if for every G, H ? Fn the set S0 = { x ? Rn : - G(x) =Ax = - H(x) } is bounded. As an illustration of this property a method of estimating the unique solution of the nonlinear equation F(x) + A(x) =b describing the large class of DC transistor circuits is developed. This can improve the efficiency of known computation algorithms. Numerical examples of transistor circuits illustrate in detail how the method works in practice.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/03321649910264163
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  • 5
    Electronic Resource
    Electronic Resource
    A combinatorial method for computing bounds on solutions of active non-linear resistive networks (2000)
    Bradford : Emerald
    Compel 19 (2000), S. 805-811 
    Details
    ISSN: 0332-1649
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Let \cal N be a consistent connected network including independent voltage and current sources, positive linear resistors, multiterminal weakly no-gain non-linear resistors and equal numbers of nullators and norators, U(\cal N) a voltage appearing between a distinguished pair of nodes and I(\cal N) a current flowing in a distinguished branch in an equilibrium state of \cal N. It is proved that, under conditions detailed in the paper, U(\˜cal N1)= U(\cal N) = U(\˜cal N2) and I(\overline \cal N\raise1pt1) = I(\cal N) = I(\overline \cal N\raise1pt2) where \˜cal N1,\˜cal N2,\overline \cal N\raise1pt1, and \overline \cal N\raise1pt2, are networks derived from \cal N by replacing non-linear resistors by open- and/or short-circuit structures. An earlier combinatorial method of estimating solutions of non-linear resistive networks is extended to cover networks including active elements. The method is tested on simple examples of active diode-transistor circuits.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/03321640010334604
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  • 6
    Electronic Resource
    Electronic Resource
    Implicit descriptions of piecewise-linear configurations (2001)
    Bradford : Emerald
    Compel 20 (2001), S. 923-936 
    Details
    ISSN: 0332-1649
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: By a polyhedral or piecewise-linear configuration in Rn we mean the finite union of finite intersections of open or closed halfspaces. It is proved that every such configuration can be characterized by the single algebraic-like equation involving only addition, subtraction, multiplication, absolute value and signum operators. Next, all such simplest implicit characterizations are found for idealized diodes, the ideal step function and the hysteresis function. Finally, the one-dimensional infinite potential trough is analysed and the obtained equations are conjectured to be the simplest possible. All this allows among others to describe systems containing piecewise-linear elements in a compact form suitable for further analytic studies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/EUM0000000005761
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  • 7
    Electronic Resource
    Electronic Resource
    Simple proof of a criterion for cones in ℝ3 (1993)
    Springer
    Archiv der Mathematik 60 (1993), S. 494-496 
    Details
    ISSN: 1420-8938
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01202318
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  • 8
    Electronic Resource
    Electronic Resource
    Infinite-dimensional Krasnosel'skii-type criteria for cones (1993)
    Springer
    Archiv der Mathematik 61 (1993), S. 478-483 
    Details
    ISSN: 1420-8938
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01207547
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  • 9
    Electronic Resource
    Electronic Resource
    Determining dimension of the kernel of a cone (1992)
    Springer
    Monatshefte für Mathematik 114 (1992), S. 83-88 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Combinatorial conditions of Krasnosel'skii-type involving concepts ofR-visibility and clearR-visibility are given to ensure that the dimension of theR-kernel of a proper subset ofR d is greater than or equal tok, 0〈-k〈d.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01535573
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  • 10
    Electronic Resource
    Electronic Resource
    An Optimal Krasnosel'skii-type Theorem for an Open Starshaped Set (1997)
    Springer
    Geometriae dedicata 66 (1997), S. 293-301 
    Details
    ISSN: 1572-9168
    Keywords: starshaped set ; local nonconvexity points ; Krasnosel'skii-type theorems.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is shown that for an open connected nonconvex set S in a real topological linear space ker $$S = \cap $$ conv $$A_z :z \in $$ , where slnc S denotes the set of strong local nonconvexity points of S and % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa % aaleaacaWG6baabeaakiabg2da9iaacUhacaWGZbGaeyicI4Saam4u % aiaacQdacaWG6baaaa!3EFE! \[ A_z = \{ s \in S:z \] is clearly visible from s viaS . This formula, combined with familiar procedures, generates the Krasnosel'skii-type characterizations for the dimension of the kernel of S in complete separable real metric linear spaces and, provided slncS is bounded, in finite-dimensional Euclidean spaces. The latter generalizes a planar result and settles an open problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004907931405
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