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41.
The Reshetikhin–Turaev invariants arising from the quantum groups associated with the exceptional Lie algebras G2, F4 and E8 at odd roots of unity are constructed and explicitly computed for all the lens spaces. 相似文献
42.
Let T be an extension of a one to one normal operator A by a nilpotent operator N. In this paper we calculate the defect of reflexivity of T. We give a necessary and sufficient condition to insure the reflexivity of such extensions. In particular, it is shown that T is reflexive when N is reflexive. 相似文献
43.
44.
M. Azram 《Acta Mathematica Hungarica》2003,101(3):217-226
A theoretic and diagrammatic relationship between knots and planar graphs has enabled us to establish necessary condition
for achirality. It is shown that the regions, crossings and consequently the number of vertices, edges, and faces in the corresponding
LR-graph are same and invariant. Establishment of new but pivotal moves such as R*-move, 2π-twist and π-twist enabled us to prove that the black regions can be changed into white regions via Reidemeister
moves. Consequently, the equivalence of the companion graphs, necessary and sufficient conditions for achirality.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
45.
Regina Aragn 《Mathematical Logic Quarterly》1995,41(4):485-504
We consider the theory Thprin of Boolean algebras with a principal ideal, the theory Thmax of Boolean algebras with a maximal ideal, the theory Thac of atomic Boolean algebras with an ideal where the supremum of the ideal exists, and the theory Thsa of atomless Boolean algebras with an ideal where the supremum of the ideal exists. First, we find elementary invariants for Thprin and Thsa. If T is a theory in a first order language and α is a linear order with least element, then we let Sentalg(T) be the Lindenbaum-Tarski algebra with respect to T, and we let intalg(α) be the interval algebra of α. Using rank diagrams, we show that Sentalg(Thprin) ? intalg(ω4), Sentalg(Thmax) ? intalg(ω3) ? Sentalg(Thac), and Sentalg(Thsa) ? intalg(ω2 + ω2). For Thmax and Thac we use Ershov's elementary invariants of these theories. We also show that the algebra of formulas of the theory Tx of Boolean algebras with finitely many ideals is atomic. 相似文献
46.
Varghese Mathai 《Proceedings of the American Mathematical Society》1996,124(8):2585-2588
In this paper, we prove that the Novikov-Shubin invariants satisfy a sequence of inequalities and deduce some useful consequences of this result.
47.
David Cohen Ernst Hairer Christian Lubich 《Foundations of Computational Mathematics》2003,3(4):327-345
Modulated Fourier expansions are developed as a tool for gaining insight into the long-time behavior of Hamiltonian systems with highly oscillatory solutions. Particle systems of Fermi–Pasta–Ulam type with light and heavy masses are considered as an example. It is shown that the harmonic energy of the highly oscillatory part is nearly conserved over times that are exponentially long in the high frequency. Unlike previous approaches to such problems, the technique used here does not employ nonlinear coordinate transforms and can therefore be extended to the analysis of numerical discretizations. 相似文献
48.
In this paper we present an approach for modelling and analyzing flexible manufacturing systems (FMSs) using Petri nets. In this approach, we first build a Petri net model (PNM) of the given FMS in a bottom-up fashion and then analyze important qualitative aspects of FMS behaviour such as existence/absence of deadlocks and buffer overflows. The basis for our approach is a theorem we state and prove for computing the invariants of the union of a finite number of Petri nets when the invariants of the individual nets are known. We illustrate our approach using two typical manufacturing systems: an automated transfer line and a simple FMS.A shorter version of this paper was presented at the 1st ORSA/TIMS Special Interest Conference on FMSs, University of Michigan, Ann Arbor, August 1984. 相似文献
49.
In this paper we present an invariant moving frame, in the group theoretical sense, along curves in the Möbius sphere. This moving frame will describe the relationship between all conformal differential invariants for curves that appear in the literature. Using this frame we first show that the Kac-Moody Poisson bracket on can be Poisson reduced to the space of conformal differential invariants of curves. The resulting bracket will be the conformal analogue of the Adler-Gel'fand-Dikii bracket. Secondly, a conformally invariant flow of curves induces naturally an evolution on the differential invariants of the flow. We give the conditions on the invariant flow ensuring that the induced evolution is Hamiltonian with respect to the reduced Poisson bracket. Because of a certain parallelism with the Euclidean case we study what we call Frenet and natural cases. We comment on the implications for completely integrable systems, and describe conformal analogues of the Hasimoto transformation.
50.
F Alberto Grünbaum 《Journal of multivariate analysis》1976,6(3):392-396
In this paper, it is shown that the distribution of the spectrum of A + X gives (essentially) a complete set of orthogonal invariants for the (real nonsymmetric) matrix A. 相似文献