{
  "id": "1306.1327",
  "version": "v1",
  "published": "2013-06-06T07:55:50.000Z",
  "updated": "2013-06-06T07:55:50.000Z",
  "title": "Symmetric Quantum Calculus",
  "authors": [
    "Artur M. C. Brito da Cruz"
  ],
  "comment": "PhD thesis, Doctoral Programme in Mathematics and Applications (PDMA), University of Aveiro and University of Minho, 2012. Supervisor: Delfim F. M. Torres; co-supervisor: Natalia Martins. Defended and approved 12-Oct-2012 http://hdl.handle.net/10773/10467",
  "journal": "University of Aveiro, PhD thesis, 2012",
  "categories": [
    "math.CA",
    "math.OC"
  ],
  "abstract": "We generalize the Hahn variational calculus by studying problems of the calculus of variations with higher-order derivatives. The symmetric quantum calculus is studied, namely the $\\alpha,\\beta$-symmetric, the $q$-symmetric, and the Hahn symmetric quantum calculus. We introduce the symmetric quantum variational calculus and an Euler-Lagrange type equation for the $q$-symmetric and Hahn's symmetric quantum calculus is proved. We define a symmetric derivative on time scales and derive some of its properties. Finally, we introduce and study the diamond integral, which is a refined version of the diamond-$\\alpha$ integral on time scales.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-06T07:55:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34N05",
      "39A12",
      "39A13",
      "49K05",
      "49K15"
    ],
    "keywords": [
      "time scales",
      "hahn symmetric quantum calculus",
      "hahns symmetric quantum calculus",
      "symmetric quantum variational calculus",
      "hahn variational calculus"
    ],
    "tags": [
      "dissertation",
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.1327B"
    }
  }
}