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  • 1
    Digitale Medien
    Digitale Medien
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 396-403 
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: A general formula is given for the canonical decomposition of a homogeneous polynomial of order λ in m variables into a sum of harmonic polynomials. This formula, which involves successive applications of the generalized Laplace operator, is proved in the Appendix. It is shown that the group-theoretical method for constructing irreducible Cartesian tensors follows from the general formula for canonical decomposition. The relationship between harmonic polynomials and hyperspherical harmonics is discussed, and an addition theorem for hyperspherical harmonics is derived. An expansion of a many-dimensional plane wave in terms of Gegenbauer polynomials and Bessel functions is derived and used to construct bicenter expansions of arbitrary functions in many-dimensional spaces. Finally, a formula is derived for the 3λ coefficients of hyperspherical harmonics. These coefficients give the values of integrals involving the products of three harmonics.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    s.l. ; Stafa-Zurich, Switzerland
    Materials science forum Vol. 475-479 (Jan. 2005), p. 3165-3168 
    ISSN: 1662-9752
    Quelle: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Thema: Maschinenbau
    Notizen: A ferromagnetic monolayer with competing long-range dipolar interaction, short-range interaction and magnetic uniaxial anisotropy is studied using Monte Carlo simulation. Striped domain patterns are found and reveal the microstructure of the magnetization transition at the ground state via the competing between dipolar interaction and uniaxial anisotropy. We present the finite temperature phase diagram and find a temperature-induced magnetization reorientation from out-of-plane to in-plane phase. The influence of the various interactions on the structure of thestriped phase and reorientation behavior has been discussed
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 3
    Digitale Medien
    Digitale Medien
    s.l. ; Stafa-Zurich, Switzerland
    Advanced materials research Vol. 26-28 (Oct. 2007), p. 33-36 
    ISSN: 1662-8985
    Quelle: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Thema: Maschinenbau
    Notizen: The wear properties of TFHS-1 hot work steel developed by Tsinghua University formagnesium die casting application was studied at elevated temperature with the help of GWY-2000high temperature wear tester. The result showed that the oxidation wear is the main wear mechanismat high temperature with dry abrasion, which was also accompanied by some extent of adhesive wearand abrasive wear. Heat treatment conditions of TFHS-1 steel have an important effect on itsanti-abrasion properties. In this paper, the higher temperature of tempering may result in the betterwear resistance
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 4
    Digitale Medien
    Digitale Medien
    Springer
    Acta mechanica solida Sinica 1 (1988), S. 431-438 
    ISSN: 0894-9166
    Schlagwort(e): stagnation phenomenon ; inclined crack ; residual plastic zone ; crack initiating ; artificial notch ; fatigue crack
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 5
    Digitale Medien
    Digitale Medien
    s.l. ; Stafa-Zurich, Switzerland
    Materials science forum Vol. 561-565 (Oct. 2007), p. 1879-1882 
    ISSN: 1662-9752
    Quelle: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Thema: Maschinenbau
    Notizen: The mathematical models of compacting process in green sand molding were built upbased on the experiment results of molding sand property testing, in which the nonlinearityproblems involved in the molding sand material, the pattern geometry and the contact between sandand flask were considered. These models were then used to numerically simulate the compactingprocess of green sand and predict the hardness distribution of green sand mold. The effect of sandfilling on the initial sand density distribution was taken into account, which was obtained throughthe two phase flow simulation of sand filling. The predicted results were compared with themeasured ones and good agreement was obtained
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 6
    Digitale Medien
    Digitale Medien
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 717-738 
    ISSN: 0020-7608
    Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: A general formula for angular integrations in many-dimensional spaces (derived in a previous paper) is applied to several problems connected with solution of the Schrödinger equation for many-particle systems. Matrix elements of the Hamiltonian are derived for cases where the potential can be expressed in terms of functions of the generalized radius multiplied by polynomials in the m coordinates. The theory of hyperspherical harmonics is reviewed, and a sum rule is derived relating the sum over all the harmonics belonging to a particular eigenvalue of angular momentum to the Gegenbauer polynomial corresponding to that eigenvalue. A formula is derived for projecting out the component of an arbitrary function corresponding to a particular eigenvalue of generalized angular momentum, and the formula is applied to polynomials in the m coordinates. An expansion is derived for expressing a many-dimensional plane wave in terms of hyperspherical harmonics and functions which might be called “hyperspherical Bessel functions.” It is shown how this expansion may be used to calculate many-dimensional Fourier transforms. A formula is derived expressing the effect of a group-theoretical projection operator acting on a many-dimensional plane wave. Finally, the techniques mentioned above are used to expand the Coulomb potential of a many-particle system in terms of Gegenbauer polynomials.
    Zusätzliches Material: 1 Tab.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 7
    Buch
    Buch
    Boston [u.a.] :Kluwer Acad. Publ.,
    Titel: 3D face processing /
    Autor: Wen, Zhen
    Beteiligte Person(en): Huang, Thomas S.
    Verlag: Boston [u.a.] :Kluwer Acad. Publ.,
    Erscheinungsjahr: 2004
    Seiten: XVIII, 136 S. : , Ill., graph. Darst.
    Serie: Kluwer international series in video computing
    ISBN: 1-402-08047-6
    Materialart: Buch
    Sprache: Englisch
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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