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  • Articles  (18)
  • 81R10  (8)
  • numerical methods  (6)
  • Chebyshev
  • mathematics
  • 2020-2023
  • 2010-2014
  • 1990-1994  (10)
  • 1980-1984  (2)
  • 1970-1974  (6)
  • 1965-1969
  • Mathematics  (18)
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  • Articles  (18)
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  • 1
    Electronic Resource
    Electronic Resource
    Error estimates of Hermite interpolation (1973)
    Springer
    BIT 13 (1973), S. 338-343 
    Details
    ISSN: 1572-9125
    Keywords: Hermite interpolation ; Chebyshev ; order of continuity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents a procedure for obtaining error estimates for Hermite interpolation at the Chebyshev nodes {cos ((2j+1)π/2n)} j =0n−1 −1≦x≦1, for functionsf(x) of various orders of continuity. The procedure is applicable in many cases when the usual Lagrangian error bound is not, and is a better bound, in general, when both are applicable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01951944
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  • 2
    Electronic Resource
    Electronic Resource
    Quantum groups and diagonalization of the braid generator (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 183-196 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that the braid generator is diagonalizable on arbitrary tensor product modules V ⊗ V, V an irreducible module for a quantum group. A generalization of the Reshetikhin form for the braid generator is thereby obtained in the general case. As an application, a general closed formula is determined for link polynomials.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402893
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  • 3
    Electronic Resource
    Electronic Resource
    Two variable link polynomials from quantum supergroups (1992)
    Springer
    Letters in mathematical physics 26 (1992), S. 187-198 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract New two variable link polynomials are constructed corresponding to a one-parameter family of representations of the quantum supergroup U q [gl(2 | 1)]. Their connection with the Kauffman polynomials is also investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00420752
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  • 4
    Electronic Resource
    Electronic Resource
    Baxterization of ther-matrix for the adjoint representation of U q [D(2, 1;α)] (1993)
    Springer
    Letters in mathematical physics 27 (1993), S. 51-58 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The Baxterization procedure is applied to the Braid group representation arising from the adjoint representation of the quantum supergroup U q [D(2, 1;α)]. This yields a two-parameter family of solutions to the (parameter dependent) Yang-Baxter equation of interest in supersymmetric lattice models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00739589
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  • 5
    Electronic Resource
    Electronic Resource
    On universalR-matrix for quantized nontwisted rank 3 affine KM algebras (1993)
    Springer
    Letters in mathematical physics 29 (1993), S. 19-31 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Explicit formulas of the universalR-matrix are given for all quantized nontwisted rank 3 affine KM algebras U q (A 2 (1) ), U q (C 2 (1) ) and U q (G 2 (1) ).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00760855
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  • 6
    Electronic Resource
    Electronic Resource
    Quantized affine Lie algebras and diagonalization of braid generators (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 267-277 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Let U q $$(\hat{\mathcal{G}})$$ be a quantized affine Lie algebra. It is proven that the universal R-matrix R of U q $$(\hat{\mathcal{G}})$$ satisfies the celebrated conjugation relationR + =TR withT the usual twist map. As applications, the braid generator is shown to be diagonalizable on arbitrary tensor product modules of integrable irreducible highest weight U q $$(\hat{\mathcal{G}})$$ -module and a spectral decomposition formula for the braid generator is obtained which is the generalization of Reshetikhin and Gould forms to the present affine case. Casimir invariants are constructed and their eigenvalues computed by means of the spectral decomposition formula. As a by-product, an interesting identity is found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00751063
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  • 7
    Electronic Resource
    Electronic Resource
    Casimir invariants for quantized affine Lie algebras (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 77-83 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Casimir invariants for quantized affine Lie algebras are constructed and their eigenvalues computed in any irreducible highest-weight representation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00751173
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  • 8
    Electronic Resource
    Electronic Resource
    Quantum affine algebras and universalR-matrix with spectral parameter (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 101-110 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Using the previously obtained universalR-matrix for the quantized nontwisted affine Lie algebras U q (A 1 (1) ) and U q (A 2 (1) ), we determine the explicitly spectral dependent universalR-matrix for the corresponding quantum Lie algebras U q (A 1) and U q (A 2). As applications, we reproduce the well known results in the fundamental representations and we also derive an extremely explicit formula of the spectral-dependentR-matrix for the adjoint representation of U q (A 2), the simplest nontrivial case when the tensor product decomposition of the representation with itself has nontrivial multiplicity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750144
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  • 9
    Electronic Resource
    Electronic Resource
    Diagonalization of the braid generator on unitary irreps of quantum supergroups (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 231-240 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that the braid generator σ associated with the universalR-matrix is diagonalizable on all unitary representations of quantum supergroups. An example is considered using U q (gl(2|1)) and a family of eight-dimensional typical representations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750665
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  • 10
    Electronic Resource
    Electronic Resource
    Attractors and transients for a perturbed periodic KdV equation: A nonlinear spectral analysis (1993)
    Springer
    Journal of nonlinear science 3 (1993), S. 477-539 
    Details
    ISSN: 1432-1467
    Keywords: nearly integrable systems ; spectral transform ; attractors ; traveling waves ; stability ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary In this paper we rigorously show the existence and smoothness inε of traveling wave solutions to a periodic Korteweg-deVries equation with a Kuramoto-Sivashinsky-type perturbation for sufficiently small values of the perturbation parameterε. The shape and the spectral transforms of these traveling waves are calculated perturbatively to first order. A linear stability theory using squared eigenfunction bases related to the spectral theory of the KdV equation is proposed and carried out numerically. Finally, the inverse spectral transform is used to study the transient and asymptotic stages of the dynamics of the solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02429875
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