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Abstract. At the beginning of the paper, the fractional calculus is briefly presented. Then, the models of dielectric relaxation in supercapacitors are described. On the basis of the Cole-Cole model, a fractional-order model of supercapacitor impedance is formulated. The frequency characteristics of selected supercapacitors and their voltage response to a current step are assumed as a basis for the analysis of their dynamics. An example of the fractional dynamic model application was used for the critical assessment of the IEC standard recommendation on the conditions of supercapacitor capacitance measurements. The presented study shows some imperfections of the IEC standard recommendations, which probably result from the use of an inaccurate dynamics model. At the end of the paper, the authors propose a solution to this problem by changing the measurement conditions and introducing a concept of dynamic capacitance. The conclusions of the paper indicate that the models of fractional-order dynamics may be useful not only for the control purposes but also in other domains. At the beginning, after some information about fractional calculus, the models of dielectric relaxation in supercapacitors are described. On this basis, a fractional-order model of supercapacitor impedance is formulated. In accordance with the recommendation of the IEC standard concerning the requirements for supercapacitor capacitance measurement [21], the analyses of frequency characteristics of selected supercapacitor samples and their voltage responses to current steps were made. The study shows the imperfection of the IEC standard recommendations, which probably results from the use of an inaccurate dynamics model. At the end of the paper, the authors propose a solution to this problem by changing the measurement conditions and by introducing a concept of dynamic capacitance. Fractional-order dynamic modelsAs mentioned, most dynamic systems are described by the integer order models. The dynamics is described in many ways. One of the widely used methods is to employ the differential equation of general form: Abstract. At the beginning of the paper the fractional calculus is briefly presented. Then the models of dielectric relaxation in supercapacitors are described. On the basis of the Cole-Cole model a fractional-order model of supercapacitor impedance is formulated. The frequency characteristics of selected supercapacitors and their voltage response to a current step are assumed as basis to the analysis of their dynamics. An example of the fractional dynamic model application was used for a critical assessment of the IEC standard recommendation on the conditions of supercapacitor capacitance measurements. The presented study shows some imperfections of the IEC standard recommendations , which probably result from the use of inaccurate dynamics model. At the end of the paper the authors propose a solution to this problem by changing the measurement conditions and introducing a concept of dynamic capacitance. The conclusions of the paper ind...

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This paper locally classifies finite-dimensional Lie algebras of conformal and Killing vector fields on R 2 relative to an arbitrary pseudo-Riemannian metric. Several results about their geometric properties are detailed, e.g. their invariant distributions and induced symplectic structures. Findings are illustrated with two examples of physical nature: the Milne-Pinney equation and the projective Schrödinger equation on the Riemann sphere.

The general scheme for the fast, pipelined rst level trigger on high pt muons in the CMS detector at LHC is presented. The prototype PACT system was tested in the high momentum muon beams in the RD5 experiment during 1993/94 runs. The obtained eciency curves are shown.