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  • 1.
    Guariglia, Emanuel
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Qi, Xiaomin
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    A spectral analysis of the Weierstrass-Mandelbrot function on the Cantor set2016Conference paper (Other academic)
    Abstract [en]

    In this paper, the Weierstrass-Mandelbrot function on the Cantor set is presented with emphasis on possible applications in science and engineering. An asymptotic estimation of its one-sided Fourier transform, in accordance with the simulation results, is analytically derived. Moreover, a time-frequency analysis of the Weierstrass-Mandelbrot function is provided by the numerical computation of its continuous wavelet transform.

  • 2.
    Nazir, Talat
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, COMSATS Institute of Information Technology.
    Qi, Xiaomin
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Linear and Nonlinear Classifiers of Data withSupport Vector Machines and GeneralizedSupport Vector Machines2016In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016, p. 377-396Chapter in book (Refereed)
    Abstract [en]

    The support vector machine for linear and nonlinear classification of datais studied. The notion of generalized support vector machine for data classifications is used. The problem of generalized support vector machine is shown to be equivalent to the problem of generalized variational inequality and various results for the existence of solutions are established. Moreover, examples supporting the results are provided.

  • 3.
    Nazir, Talat
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, COMSATS Institute of Information Technology.
    Qi, Xiaomin
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Linear Classification of data with Support Vector Machines and Generalized Support Vector Machines2016In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Chapter in book (Refereed)
    Abstract [en]

    In this paper, we study the support vector machine and introduced the notion of generalized support vector machine for classification of data. We showthat the problem of generalized support vector machine is equivalent to the problem of generalized variational inequality and establish various results for the existence of solutions. Moreover, we provide various examples to support our results.

  • 4.
    Nazir, Talat
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, COMSATS Institute of Information Technology, Pakistan.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Qi, Xiaomin
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Fractals of Generalized F-Hutchinson Operator in b-Metric Spaces2016In: Journal of Operators, ISSN 2314-5064, Vol. 2016, p. 9 pp-, article id 5250394Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is to construct a fractal with the help of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the setup of b-metric space. Consequently, we obtain a variety of results for iterated function system satisfying a different set of contractive conditions. Our results unify, generalize, and extend various results in the existing literature.

  • 5.
    Qi, Xiaomin
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Fixed points, fractals, iterated function systems and generalized support vector machines2016Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis, fixed point theory is used to construct a fractal type sets and to solve data classification problem. Fixed point method, which is a beautiful mixture of analysis, topology, and geometry has been revealed as a very powerful and important tool in the study of nonlinear phenomena. The existence of fixed points is therefore of paramount importance in several areas of mathematics and other sciences. In particular, fixed points techniques have been applied in such diverse fields as biology, chemistry, economics, engineering, game theory and physics. In Chapter 2 of this thesis it is demonstrated how to define and construct a fractal type sets with the help of iterations of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the context of b-metric space. This leads to a variety of results for iterated function system satisfying a different set of contractive conditions. The results unify, generalize and extend various results in the existing literature. In Chapter 3, the theory of support vector machine for linear and nonlinear classification of data and the notion of generalized support vector machine is considered. In the thesis it is also shown that the problem of generalized support vector machine can be considered in the framework of generalized variation inequalities and results on the existence of solutions are established.

  • 6.
    Qi, Xiaomin
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Nazir, Talat
    Department of Mathematics, COMSATS Institute of Information Technology.
    Data classification with support vector machine and generalized support vector machine2017In: AIP Conference Proceedings, Volume 1798 / [ed] Seenith Sivasundaram, 2017, Vol. 1798, p. 020126-1-020126-9, article id 020126Conference paper (Refereed)
    Abstract [en]

    In the paper, we study the theory of support vector machine and the using for linear and nonlinear classification of data. And we also used the notion of generalized support vector machine for data classifications. We show that the problem of generalized support vector machine is equivalent to the problem of generalized variational inequality and establish various results for the existence of solutions.

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