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121.
The aim of this paper is to formulate a conjecture for an arbitrary simple Lie
algebra g in terms of the geometry of principal nilpotent pairs. When g is specialized to sln,
this conjecture readily implies the n! result and it is very likely that, in fact, it is equivalent
to the n! result in this case. In addition, this conjecture can be thought of as generalizing an
old result of Kostant. In another direction, we show that to prove the validity of the n! result
for an arbitrary n and an arbitrary partition of n, it suffices to show its validity only for the
staircase partitions. 相似文献
122.
We study the chromatic polynomials for m×n square-lattice strips, of width 9m13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed us also to extract the limiting curves when n. In this limit we have also obtained the isolated limiting points for these square-lattice strips and checked some conjectures related to the Beraha numbers. 相似文献
123.
At zero temperature, the 3-state antiferromagnetic Potts model on a square lattice maps exactly onto a point of the 6-vertex model whose long-distance behavior is equivalent to that of a free scalar boson. We point out that at nonzero temperature there are two distinct types of excitation: vortices, which are relevant with renormalization-group eigenvalue 1/2 and non-vortex unsatisfied bonds, which are strictly marginal and serve only to renormalize the stiffness coefficient of the underlying free boson. Together these excitations lead to an unusual form for the corrections to scaling: for example, the correlation length diverges as J/kT according to Ae
2
(1+be
–
+···), where b is a nonuniversal constant that may nevertheless be determined independently. A similar result holds for the staggered susceptibility. These results are shown to be consistent with the anomalous behavior found in the Monte Carlo simulations of Ferreira and Sokal. 相似文献
124.
Peter G. Casazza Ole Christensen 《Proceedings of the American Mathematical Society》2001,129(1):145-154
A Weyl-Heisenberg frame
for allows every function to be written as an infinite linear combination of translated and modulated versions of the fixed function . In the present paper we find sufficient conditions for to be a frame for , which, in general, might just be a subspace of . Even our condition for to be a frame for is significantly weaker than the previous known conditions. The results also shed new light on the classical results concerning frames for , showing for instance that the condition A>0$">is not necessary for to be a frame for . Our work is inspired by a recent paper by Benedetto and Li, where the relationship between the zero-set of the function and frame properties of the set of functions is analyzed.
for allows every function to be written as an infinite linear combination of translated and modulated versions of the fixed function . In the present paper we find sufficient conditions for to be a frame for , which, in general, might just be a subspace of . Even our condition for to be a frame for is significantly weaker than the previous known conditions. The results also shed new light on the classical results concerning frames for , showing for instance that the condition A>0$">is not necessary for to be a frame for . Our work is inspired by a recent paper by Benedetto and Li, where the relationship between the zero-set of the function and frame properties of the set of functions is analyzed.
125.
Time-temperature superposition in viscous liquids 总被引:1,自引:0,他引:1
Dielectric relaxation measurements on supercooled triphenyl phosphite show that time-temperature superposition (TTS) is obeyed for the primary relaxation process at low temperatures. Measurements on other molecular liquids close to the calorimetric glass transition indicate that TTS is linked to an omega(-1/2) high-frequency decay of the loss, while the loss peak width is nonuniversal. 相似文献
126.
Ole Christensen 《Journal of Fourier Analysis and Applications》2000,6(1):79-91
A frame in a Hilbert space
allows every element in
to be written as a linear combination of the frame elements, with coefficients called frame coefficients. Calculations of
those coefficients and many other situations where frames occur, requires knowledge of the inverse frame operator. But usually
it is hard to invert the frame operator if the underlying Hilbert space is infinite dimensional. In the present paper we introduce
a method for approximation of the inverse frame operator using finite subsets of the frame. In particular this allows to approximate
the frame coefficients (even inl
2) using finite-dimensional linear algebra. We show that the general method simplifies in the important cases of Weil-Heisenberg
frames and wavelet frames. 相似文献
127.
Ball G Vant K Christensen N 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》2000,61(2):1299-1311
We present a detailed numerical study of a chaotic classical system and its quantum counterpart. The system is a special case of a kicked rotor and for certain parameter values possesses cantori dividing chaotic regions of the classical phase space. We investigate the diffusion of particles through a cantorus. A quantum analysis confirms that the cantori act as barriers. We numerically estimate the classical phase space flux through the cantorus per kick and relate this quantity to the behavior of the quantum system. We introduce decoherence via environmental interactions with the quantum system and observe the subsequent increase in the transport of quantum particles through the boundary. 相似文献
128.
129.
An increasing number of proficiency testing schemes (PT schemes) related to occupational and environmental health have been
organised. Most schemes emphasise the importance of the validation of analytical results. With regards to harmonisation of
the schemes, there are many differences between the schemes at many levels. These include factors concerning their relationship
with legislation, national status, type and quality of proficiency testing material, analytical range and priorities for future
development. Since differences between PT schemes have been recognised at the European level by organisers of PT schemes and
external quality assessment schemes (EQASs) it seems appropriate to reinforce collaboration between scheme organisers in order
to improve the quality of analytical performance in occupational and environmental health. 相似文献
130.
We construct spectral triples and, in particular, Dirac operators, for the algebra of continuous functions on certain compact metric spaces. The triples are countable sums of triples where each summand is based on a curve in the space. Several fractals, like a finitely summable infinite tree and the Sierpinski gasket, fit naturally within our framework. In these cases, we show that our spectral triples do describe the geodesic distance and the Minkowski dimension as well as, more generally, the complex fractal dimensions of the space. Furthermore, in the case of the Sierpinski gasket, the associated Dixmier-type trace coincides with the normalized Hausdorff measure of dimension log3/log2. 相似文献