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  • 1
    Electronic Resource
    Electronic Resource
    Superposition formulas for rectangular matrix Riccati equations (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 530-535 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A system of nonlinear ordinary differential equations allowing a superposition formula can be associated with every Lie group–subgroup pair G&supuline;G0. We consider the case when G=SL(n+k,C) and G0=P(k) is a maximal parabolic subgroup of G, leaving a k-dimensional vector space invariant (1≤k≤n). The nonlinear ordinary differential equations (ODE's) in this case are rectangular matrix Riccati equations for a matrix W(t)∈Cn×k. The special case n=rk (n,r,k∈N) is considered and a superposition formula is obtained, expressing the general solution in terms of r+3 particular solutions for r≥2, k≥2. For r=1 (square matrix Riccati equations) five solutions are needed, for r=n (projective Riccati equations) the required number is n+2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527637
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  • 2
    Electronic Resource
    Electronic Resource
    Clebsch–Gordan coefficients for SU(5) unification models (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 258-271 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Clebsch–Gordan coefficients for the product (1001)⊗(1001), where (1001) is the adjoint representation of SU(5), with respect to the group basis and the subgroup basis in the reduction SU(5)&supuline;SU(3)×SU(2)×U(1) are computed. One of the basic tools in this computation is the exhaustive use of the Verma algorithm to find bases for the weight subspaces of dimension higher than 1. It allows for the construction of bases in a systematic way by using the so-called Verma inequalities. Only the coefficients for the dominant weights are calculated. The other ones can be obtained by using the elements of finite order (charge conjugation operators) of SU(5).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527655
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  • 3
    Electronic Resource
    Electronic Resource
    Moyal quantization of 2+1-dimensional Galilean systems (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3379-3386 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Stratonovich–Weyl kernels are constructed for some of the coadjoint orbits of the two-dimensional extended Galilean group G(2+1). As an intermediate step, the unitary irreducible representations associated with a given group orbit are obtained by using the Kirillov–Mackey theory. Star products are defined, in the sense of Moyal, for functions on each of these orbits. The central extension of G(2+1) with parameter k is also analyzed, which results from the commutator between the generators of boosts, to conclude that it originates a sort of nonrelativistic remainder of the Thomas precession.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529939
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  • 4
    Electronic Resource
    Electronic Resource
    Nonrelativistic conformal groups (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 3786-3809 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this work a systematic study of finite-dimensional nonrelativistic conformal groups is carried out under two complementary points of view. First, the conformal Killing equation is solved to obtain a whole family of finite-dimensional conformal algebras corresponding to each of the Galilei and Newton–Hooke kinematical groups. Some of their algebraic and geometrical properties are studied in a second step. Among the groups included in these families one can identify, for example, the contraction of the Minkowski conformal group, the analog for a nonrelativistic de Sitter space, or the nonextended Schrödinger group. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532067
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  • 5
    Electronic Resource
    Electronic Resource
    Classical deformations, Poisson–Lie contractions, and quantization of dual Lie bialgebras (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 631-640 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A Poisson–Hopf algebra of smooth functions is simultaneously constructed on the two dimensional Euclidean, Poincaré, and Heisenberg groups by using a classical r-matrix which is invariant under contraction. The quantization for this algebra of functions is developed, and its dual Hopf algebra is also computed. Contractions on these quantum groups are studied. It is shown that, within this setting, classical deformations are transformed into quantum ones by Hopf algebra duality and the quantum Heisenberg algebra is derived by means of a (dual) Poisson–Lie quantization that deforms the standard Moyal–Weyl *(h-dash-bar)-product. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531331
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  • 6
    Electronic Resource
    Electronic Resource
    Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 5916-5937 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Lie bialgebra contractions are introduced and classified. A non-degenerate coboundary bialgebra structure is implemented into all pseudo-orthogonal real algebras so(p,q) starting from the one corresponding to so(N+1). It allows us to introduce a set of Lie bialgebra contractions which leads to Lie bialgebras of quasi-orthogonal algebras. This construction is explicitly given for N=2,3,4. All Lie bialgebra contractions studied in this paper define Hopf algebra contractions for the Drinfel'd–Jimbo deformations Uzso(p,q). They are explicitly used to generate new non-semisimple quantum algebras as it is the case for the Euclidean, Poincaré, and Galilean algebras. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531368
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  • 7
    Electronic Resource
    Electronic Resource
    Four-dimensional quantum affine algebras and space–time q-symmetries (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4928-4940 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A global model of the q deformation for the quasiorthogonal Lie algebras generating the groups of motions of the four-dimensional affine Cayley–Klein (CK) geometries is obtained starting from the three-dimensional deformations. It is shown how the main algebraic classical properties of the CK systems can be implemented in the quantum case. Quantum deformed versions either of the space–time or space symmetry algebras [Poincaré (3+1), Galilei (3+1), 4-D Euclidean as well as others] appear in this context as particular cases. For some of these classical algebras several q deformations are directly obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530823
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  • 8
    Electronic Resource
    Electronic Resource
    Integrable systems based on SU(p,q) homogeneous manifolds (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 5118-5139 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The general theory of the separation of variables in Hamilton–Jacobi and Laplace–Beltrami equations on the SU(p,q) hyperboloid is used to introduce completely integrable Hamiltonian systems on O(p,q) hyperboloids. Each of the q+1 different Cartan subalgebras of su(p,q) leads to a different integrable O(p,q) potential. Different complete sets of integrals of motion are obtained for each of the integrable systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530346
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  • 9
    Electronic Resource
    Electronic Resource
    Nonrelativistic conformal groups. II. Further developments and physical applications (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 3810-3831 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The finite-dimensional conformal groups associated with the Galilei and (oscillating or expanding) Newton–Hooke space–time manifolds was characterized by the present authors in a recent work. Three isomorphic group families, one for each nonrelativistic kinematics, were obtained, whose members are labeled by a half-integer number l. Since the action of these groups on their corresponding space–time manifolds is only local, a linearization is introduced here such that the corresponding action is well defined everywhere. In particular, the (l=1)-conformal cases that can be obtained by contraction from the well-known Minkowskian conformal group are treated in more detail. As an application of physical interest, the conformal invariance of the Galilean electromagnetism is studied. In order to achieve it, the pertinent local representations of the Galilean conformal algebras are derived. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532068
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  • 10
    Electronic Resource
    Electronic Resource
    Spatial variations in oxygen precipitation in silicon after high temperature rapid thermal annealing (1997)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 70 (1997), S. 1572-1574 
    Details
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Spatial variations of oxygen precipitation have been studied in silicon wafers submitted to rapid thermal annealing (RTA) in nitrogen ambients at a temperature above 1150 °C prior to a two-step precipitation treatment. The samples submitted to high temperature preannealing show a consistent enhancement of oxygen precipitation, which is dependent on the RTA time and temperature. Oxygen precipitate density measurements show that oxygen precipitation is not homogeneous inside the wafer, but peaks near the surfaces, with a minimum in the bulk. The high treatment in N2 results in the formation of defects which act as precursors for the subsequent nucleation and growth of oxygen precipitates. There is strong evidence that these precursors are generated by the thermal nitridation of the silicon surface and subsequent vacancy injection into the bulk of the wafer. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.118620
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