47,828 research outputs found
Dynamics of charged fluids and 1/L perturbation expansions
Some features of the calculation of fluid dynamo systems in
magnetohydrodynamics are studied. In the coupled set of the ordinary linear
differential equations for the spherically symmetric dynamos, the
problem represented by the presence of the mixed (Robin) boundary conditions is
addressed and a new treatment for it is proposed. The perturbation formalism of
large expansions is shown applicable and its main technical steps are
outlined.Comment: 16 p
Parameterizable Views for Process Visualization
In large organizations different users or user groups usually have distinguished perspectives over business processes and related data. Personalized views on the managed processes are therefore needed. Existing BPM tools, however, do not provide adequate mechanisms for building and visualizing such views. Very often processes are displayed to users in the same way as drawn by the process designer. To tackle this inflexibility this paper presents an advanced approach for creating personalized process views based on well-defined, parameterizable view operations. Respective operations can be flexibly composed in order to reduce or aggregate process information in the desired way. Depending on the chosen parameterization of the applied view operations, in addition, different "quality levels" with more or less relaxed properties can be obtained for the resulting process views (e.g., regarding the correctness of the created process view scheme). This allows us to consider the specific needs of the different applications utilizing process views (e.g., process monitoring tools or process editors). Altogether, the realized view concept contributes to better deal with complex, long-running business processes with hundreds up to thousands of activities
Quantum star-graph analogues of PT-symmetric square wells
We pick up a solvable symmetric quantum square well on an
interval of (with an dependent
non-Hermiticity given by Robin boundary conditions) and generalize it. In
essence, we just replace the support interval (reinterpreted
as an equilateral two-pointed star graph with the Kirchhoff matching at the
vertex ) by a pointed equilateral star graph
endowed with the simplest complex-rotation-symmetric external
dependent Robin boundary conditions. The remarkably compact form of
the secular determinant is then deduced. Its analysis reveals that (1) at any
integer , there exists the same, independent and infinite
subfamily of the real energies, and (2) at any special , there
exists another, additional and dependent infinite subfamily of the real
energies. In the spirit of the recently proposed dynamical construction of the
Hilbert space of a quantum system, the physical bound-state interpretation of
these eigenvalues is finally proposed.Comment: 20 pp, 1 figur
Polygraphs for termination of left-linear term rewriting systems
We present a methodology for proving termination of left-linear term
rewriting systems (TRSs) by using Albert Burroni's polygraphs, a kind of
rewriting systems on algebraic circuits. We translate the considered TRS into a
polygraph of minimal size whose termination is proven with a polygraphic
interpretation, then we get back the property on the TRS. We recall Yves
Lafont's general translation of TRSs into polygraphs and known links between
their termination properties. We give several conditions on the original TRS,
including being a first-order functional program, that ensure that we can
reduce the size of the polygraphic translation. We also prove sufficient
conditions on the polygraphic interpretations of a minimal translation to imply
termination of the original TRS. Examples are given to compare this method with
usual polynomial interpretations.Comment: 15 page
PT symmetric models in more dimensions and solvable square-well versions of their angular Schroedinger equations
For any central potential V in D dimensions, the angular Schroedinger
equation remains the same and defines the so called hyperspherical harmonics.
For non-central models, the situation is more complicated. We contemplate two
examples in the plane: (1) the partial differential Calogero's three-body model
(without centre of mass and with an impenetrable core in the two-body
interaction), and (2) the Smorodinsky-Winternitz' superintegrable harmonic
oscillator (with one or two impenetrable barriers). These examples are solvable
due to the presence of the barriers. We contemplate a small complex shift of
the angle. This creates a problem: the barriers become "translucent" and the
angular potentials cease to be solvable, having the sextuple-well form for
Calogero model and the quadruple or double well form otherwise. We mimic the
effect of these potentials on the spectrum by the multiple, purely imaginary
square wells and tabulate and discuss the result in the first nontrivial
double-well case.Comment: 21 pages, 5 figures (see version 1), amendment (a single comment
added on p. 7
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