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Dec 1998

Volume 39, Issue 12, pp. 6247-6756

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Integrable discretizations of the Euler top

A. I. Bobenko, B. Lorbeer, and Yu. B. Suris

J. Math. Phys. 39, 6668 (1998); http://dx.doi.org/10.1063/1.532648 (16 pages) | Cited 9 times

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Discretizations of the Euler top sharing the integrals of motion with the continuous time system are studied. Those of them which are also Poisson with respect to the invariant Poisson bracket of the Euler top are characterized. For all these Poisson discretizations a solution in terms of elliptic functions is found, allowing a direct comparison with the continuous time case. We demonstrate that the Veselov–Moser discretization also belongs to our family, and apply our methods to this particular example. © 1998 American Institute of Physics.
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45.05.+x General theory of classical mechanics of discrete systems
05.45.-a Nonlinear dynamics and chaos
02.30.Cj Measure and integration

On harmonic maps into gauge groups

Qing Ding

J. Math. Phys. 39, 6684 (1998); http://dx.doi.org/10.1063/1.532649 (12 pages)

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We continue the work of the paper [J. Math. Phys. 37, 4076 (1996)] on the existence of globally defined harmonic maps from the Minkowski plane R1,1 into an infinite-dimensional Hilbert Lie group. We prove that the Cauchy problem for harmonic maps from R1,1 into Hilbert loop groups Hs(LG) can be solved globally for all remaining cases ½<s ⩽ ¾ and we obtain similar results for harmonic maps from R1,1 into certain Hilbert Lie gauge groups Hs(Sn,G) (n ≥ 2). These answer the two questions remaining from the above paper. © 1998 American Institute of Physics.
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11.15.-q Gauge field theories
02.20.Qs General properties, structure, and representation of Lie groups

The topological structure of the space–time disclination

Yishi Duan and Sheng Li

J. Math. Phys. 39, 6696 (1998); http://dx.doi.org/10.1063/1.532650 (10 pages) | Cited 2 times

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The space–time disclination is studied by making use of the decomposition theory of gauge potential in terms of the antisymmetric tensor field and ϕ-mapping method. It is shown that the self-dual and anti-self-dual parts of the curvature compose the space–time disclinations which are classified in terms of topological invariants—winding number. The projection of space–time disclination density along an antisymmetric tensor field is quantized topologically and characterized by Brouwer degree and Hopf index. © 1998 American Institute of Physics.
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98.80.Jk Mathematical and relativistic aspects of cosmology
98.80.Qc Quantum cosmology
04.60.-m Quantum gravity

Maximum entropy in the generalized moment problem

M. Frontini and A. Tagliani

J. Math. Phys. 39, 6706 (1998); http://dx.doi.org/10.1063/1.532651 (9 pages) | Cited 3 times

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The generalized moment problem in the framework of the maximum entropy approach is considered. A proof for the existence conditions of the solution is provided. © 1998 American Institute of Physics.
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02.50.Cw Probability theory

On the use of a new integral theorem for the quantum mechanical treatment of electric circuits

W. Magnus and W. Schoenmaker

J. Math. Phys. 39, 6715 (1998); http://dx.doi.org/10.1063/1.532652 (5 pages) | Cited 6 times

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We present a new integral theorem based on the well-known Gauss and Stokes theorems which provides a straightforward physical interpretation of the quantum mechanical energy balance equation governing the steady-state propagation of charge carriers through closed electric circuits. © 1998 American Institute of Physics.
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84.30.Bv Circuit theory
85.35.Ds Quantum interference devices
73.23.-b Electronic transport in mesoscopic systems
02.30.Rz Integral equations

Solving Poisson’s equation with interior conditions

J. E. McCarthy, E. Yu. Backhaus, and J. Fajans

J. Math. Phys. 39, 6720 (1998); http://dx.doi.org/10.1063/1.532653 (10 pages) | Cited 2 times

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We consider the problem of extending the solution of a particular two-dimensional Poisson equation to a larger domain. This problem is related to the problem of putting a non-neutral plasma into equilibrium by applying a suitable wall potential, and to similar problems in two-dimensional fluid dynamics. While one cannot always find an exact solution, one can always find an approximate solution if the plasma has no holes. © 1998 American Institute of Physics.
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52.55.Dy General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
47.10.-g General theory in fluid dynamics
52.40.Hf Plasma-material interactions; boundary layer effects

On the triple sum formula for Wigner 9j-symbols

Hjalmar Rosengren

J. Math. Phys. 39, 6730 (1998); http://dx.doi.org/10.1063/1.532634 (15 pages) | Cited 5 times

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We give a new proof of the triple sum formula for Wigner 9j-symbols due to Ališauskas and Jucys. The proof uses explicit expressions for the coupling kernels recently introduced by the author. Parts of our results generalize to general recoupling coefficients. © 1998 American Institute of Physics.
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03.65.Ca Formalism

Lie symmetry and integrability of ordinary differential equations

R. Z. Zhdanov

J. Math. Phys. 39, 6745 (1998); http://dx.doi.org/10.1063/1.532654 (12 pages)

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Combining a Lie algebraic approach that is due to Wei and Norman [J. Math. Phys. 4, 475 (1963)] and the ideas suggested by Drach [Compt. Rend. 168, 337 (1919)], we have constructed several classes of systems of linear ordinary differential equations that are integrable by quadratures. Their integrability is ensured by integrability of the corresponding stationary cubic Schrödinger, KdV, and Harry–Dym equations. Next, we obtain a hierarchy of integrable reductions of the Dirac equation of an electron moving in the external field. Their integrability is shown to be in correspondence with integrability of the stationary mKdV hierarchy. © 1998 American Institute of Physics.
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41.20.Jb Electromagnetic wave propagation; radiowave propagation
02.30.Hq Ordinary differential equations
02.10.Ud Linear algebra
02.10.Xm Multilinear algebra
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