We present a probabilistic approach which proves blow-up of solutions of the Fujita equation in the critical dimension . By using the Feynman-Kac representation twice, we construct a subsolution which locally grows to infinity as . In this way, we cover results proved earlier by analytic methods. Our method also applies to extend a blow-up result for systems proved for the Laplacian case by Escobedo and Levine (1995) to the case of -Laplacians with possibly different parameters .
We analyze the approximation and smoothness properties of quincunx fundamental refinable functions. In particular, we provide a general way for the construction of quincunx interpolatory refinement masks associated with the quincunx lattice in . Their corresponding quincunx fundamental refinable functions attain the optimal approximation order and smoothness order. In addition, these examples are minimally supported with symmetry. For two special families of such quincunx interpolatory masks, we prove that their symbols are nonnegative. Finally, a general way of constructing quincunx biorthogonal wavelets is presented. Several examples of quincunx interpolatory masks and quincunx biorthogonal wavelets are explicitly computed.
We find generators of the group of birational automorphisms of the Hessian surface of a general cubic surface. Its nonsingular minimal model is a K3 surface with the Picard lattice of rank 16 which embeds naturally in the even unimodular lattice of rank 26 and signature . The generators are related to reflections with respect to some Leech roots. A similar observation was made first in the case of quartic Kummer surfaces in the work of Kondo. We shall explain how our generators are related to the generators of the group of birational automorphisms of a general quartic Kummer surface which is birationally isomorphic to a special Hessian surface.
The application of transient nutations in EPR spectroscopy of condensed media is considered. The main methods of formation and observation of transient nutations are presented. The laws governing this phenomenon in twolevel and multilevel spin systems and also in inhomogeneous broadening of EPR lines are described. Recent advances in the use of transient nutations to separate overlapping spectra, identify quantum numbers and quantum transitions, investigate the kinetics of photoinduced paramagnetic centers, and determine relaxation times for a wide range of crystalline and disordered media are presented. 相似文献
Using the Pirogov–Sinai theory, we study finite-size effects for the ferromagnetic q-state Potts model in a cube with boundary conditions that interpolate between free and constant boundary conditions. If the surface coupling is about half of the bulk coupling and q is sufficiently large, we show that only small perturbations of the ordered and disordered ground states are dominant contributions to the partition function in a finite but large volume. This allows a rigorous control of the finite-size effects for these weak boundary conditions. In particular, we give explicit formulæ for the rounding of the infinite-volume jumps of the internal energy and magnetization, as well as the position of the maximum of the finite-volume specific heat. While the width of the rounding window is of order L–d, the same as for periodic boundary conditions, the shift is much larger, of order L–1. For strong boundary conditions—the surface coupling is either close to zero or close to the bulk coupling—the finite size effects at the transition point are shown to be dominated by either the disordered or the ordered phase, respectively. In particular, it means that sufficiently small boundary fields lead to the disordered, and not to the ordered Gibbs state. This gives an explicit proof of A. van Enter's result that the phase transition in the Potts model is not robust. 相似文献
The semi-infinite Toda lattice is the system of differential equations dn(t)/dt = n(t)(bn+1(t) – bn(t)), dbn(t)/dt = 2(n2(t) – n–12(t)), n = 1, 2, ..., t > 0. The solution of this system (if it exists) is a pair of real sequences n(t), bn(t) which satisfy the conditions n(0) = n,, bn(0) = bn, where n > 0 and bn are given sequences of real numbers. It is well known that the system has a unique solution provided that both sequences n and bn are bounded. When at least one of the known sequences n and bn is unbounded, many difficulties arise and, to the best of our knowledge, there are few results concerning the solution of the system. In this letter we find a class of unbounded sequences n and bn such that the system has a unique solution. The results are illustrated with a typical example where the sequences i(t), bi(t), i = 1, 2, ... can be exactly determined. The connection of the Toda lattice with the semi-infinite differential-difference equation d2/dt2 log hn = hn+1 + hn–1 – 2hn, n = 1, 2, ... is also discussed and the above results are translated to analogous results for the last equation. 相似文献
The concentration profiles of monomers and counterions in star-branched polyelectrolyte micelles are calculated through Monte
Carlo simulations, using the freely jointed chain model. We have investigated the onset of different regimes corresponding
to the spherical and Manning condensation of counterions as a function of the strength of the Coulomb coupling. The Monte
Carlo results are in fair agreement with the predictions of Self-Consistent-Field analytical models. We have simulated a real
system of diblock copolymer micelles of (sodium-polystyrene-sulfonate)(NaPSS)-(polyethylene-propylene)(PEP) with f = 54 hydrophilic branches of N = 251 monomers at room temperature in salt-free solution. The calculated form factor compares nicely with our neutron scattering
data.
Received 18 July 2002 and Received in final form 11 October 2002
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ID="a"e-mail: roger@drecam.saclay.cea.fr 相似文献
We present a new pump probe laser beams configuration for the nonlinear optical characterization of microemulsions. We detect
the variation of the on-axis optical intensity of the probe beam as generated by the concentration profile induced in an optically
thin film of microemulsion by the pump beam. A mathematical model has been introduced to describe the phenomenon. The technique
allows the determination of both Kerr-like optical nonlinearity and time constants and, therefore, it gives information both
on cluster dimension and their shape. We discuss its application to WAD (water/AOT/decane, where AOT denotes sodium-bis-di-ethyl-sulfosuccinate)
with the application of a strong electric field of optical source. Comparison between theoretical predictions and experimental
results confirms the presence of giant optical nonlinearity in the absence of turbidity divergence. Chainlike shape of clusters,
of the kind already reported with the application of strong electric field, could justify this result.
Received 26 October 2002
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ID="a"e-mail: vicari@na.infn.it 相似文献
Soliton interactions in systems modelled by coupled nonlinear Schr?dinger (CNLS) equations and encountered in phenomena such
as wave propagation in optical fibers and photorefractive media possess unusual features: shape changing intensity redistributions,
amplitude dependent phase shifts and relative separation distances. We demonstrate these properties in the case of integrable
2-CNLS equations. As a simple example, we consider the stationary two-soliton solution which is equivalent to the so-called
partially coherent soliton (PCS) solution discussed much in the recent literature.
Received 1st October 2001 / Received in final form 4 February 2002 Published online 2 October 2002
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ID="a"e-mail: lakshman@bdu.ernet.in 相似文献
We compare the Hamiltonian properties of the N-soliton solutions of the NLSE in the adiabatic approximation and show how it matches the Hamiltonian formulation for the
complex Toda chain which describes the adiabatic N-soliton interactions.
Received 21 October 2001 Published online 2 October 2002
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ID="a"e-mail: gerjikov@inrne.bas.bg 相似文献