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1.
The ultraviolet band systemsA
1Π-X
1Σ+ of P14N and P15N were excited in an electrodeless tube containing traces of phosphorus specpure nitrogen and neon using a microwave discharge
(2450 MHz). Bands of the isotopic species, P15N, were obtained using15N2 enriched to 95.5%. Rotational analyses of eleven bands of P14N and sixteen bands of P15N were carried out. Three perturbing statese
3Σ−,d
3Δ andb
3Π, arising from the lower valence configurations were identified from the observed perturbations in thev′=0–4 levels of theA
1Π state. Deperturbation studies led to the determination of molecular constants of the perturbing states. Vibrational assignments
of the perturbing states were made from isotope shift studies. 相似文献
2.
P. De Maesschalck 《Journal of Differential Equations》2007,238(2):338-365
By applying geometric techniques to real analytic singularly perturbed vector fields on the plane, we develop a way to give a bound on the Gevrey type of the Taylor development of canard manifolds at degenerate planar turning points. By blowing up the phase space at the turning point, we find asymptotic estimates even when such expansions w.r.t. traditional phase space variables do not exist. The asymptotic estimates are then used to give a sufficient and necessary condition on the existence of (local) canard solutions. 相似文献
3.
We introduce a random perturbed version of the classical fidelity and we show that it converges with the same rate of decay
of correlations, but not uniformly in the noise. This makes the classical fidelity unstable in the zero-noise limit. 相似文献
4.
V. Mukhanov 《International Journal of Theoretical Physics》2004,43(3):623-668
I derive analytically the spectrum of the CMB fluctuations. The final result for C
l is presented in terms of elementary functions with an explicit dependence on the basic cosmological parameters. This result is in a rather good agreement with CMBFAST for a wide range of parameters around concordance model. This allows us to understand the physical reasons for dependence of the particular features of the CMB spectrum on the basic cosmological parameters and to estimate the possible accuracy of their determination. I also analyze the degeneracy of the spectrum with respect to certain combinations of the cosmological parameters. 相似文献
5.
This work is devoted to near-optimal controls of large-scale discrete-time nonlinear dynamic systems driven by Markov chains; the underlying problem is to minimize an expected cost function. Our main goal is to reduce the complexity of the underlying systems. To achieve this goal, discrete-time control models under singularly-perturbed Markov chains are introduced. Using a relaxed control representation, our effort is devoted to finding near-optimal controls. Lumping the states in each irreducible class into a single state gives rise to a limit system. Applying near-optimal controls of the limit system to the original system, near-optimal controls of the original system are derived. 相似文献
6.
The theory of nonequilibrium potentials or quasipotentials is a physically motivated approach to small random perturbations of dynamical systems, leading to exponential estimates of invariant probabilities and mean first exit times. In the present article we develop the mathematical foundation of this theory for discrete-time systems, following and extending the work of Freidlin and Wentzell, and Kifer. We discuss strategies for calculating and estimating quasipotentials and show their application to one-dimensionalS-unimodal maps. The method proves to be especially suited for describing the noise scaling behavior of invariant probabilities, e.g., for the map occurring as the limit of the Feigenbaum period-doubling sequence. We show that the method allows statements about the scaling behavior in the case of localized noise, too, which does not originally lie within the scope of the quasipotential formalism. 相似文献
7.
A. V. Kravtsov 《Computational Mathematics and Mathematical Physics》2007,47(11):1875-1884
A linear problem of parametric oscillations of a low-viscous two-layer fluid in a closed vessel partially filled with a porous medium is studied. An asymptotic solution is constructed on the basis of combined application of boundary functions and averaging methods. Approximate formulas for boundaries of instability domains in the case of subharmonic and harmonic resonances are derived. 相似文献
8.
The paper deals with the global minimization of a differentiable cost function mapping a ball of a finite dimensional Euclidean space into an interval of real numbers. It is established that a suitable random perturbation of the gradient method with a fixed parameter generates a bounded minimizing sequence and leads to a global minimum: the perturbation avoids convergence to local minima. The stated results suggest an algorithm for the numerical approximation of global minima: experiments are performed for the problem of fitting a sum of exponentials to discrete data and to a nonlinear system involving about 5000 variables. The effect of the random perturbation is examined by comparison with the purely deterministic gradient method. 相似文献
9.
V. A. Demin 《Fluid Dynamics》2008,43(4):524-532
The free oscillations of a capillary bridge whose equilibrium shape is determined by the surface tension forces and the static gravity field are investigated. The values of 25 “lower” levels of the spectrum of natural oscillations of the capillary bridge are found for various control parameters in accordance with the experimental conditions. 相似文献
10.
Banach frames and atomic decompositions are sequences that have basis-like properties but which need not be bases. In particular, they allow elements of a Banach space to be written as linear combinations of the frame or atomic decomposition elements in a stable manner. In this paper we prove several functional — analytic properties of these decompositions, and show how these properties apply to Gabor and wavelet systems. We first prove that frames and atomic decompositions are stable under small perturbations. This is inspired by corresponding classical perturbation results for bases, including the Paley — Wiener basis stability criteria and the perturbation theorem el kato. We introduce new and weaker conditions which ensure the desired stability. We then prove quality properties of atomic decompositions and consider some consequences for Hilbert frames. Finally, we demonstrate how our results apply in the practical case of Gabor systems in weighted L2 spaces. Such systems can form atomic decompositions for L2w(IR), but cannot form Hilbert frames but L2w(IR) unless the weight is trivial. 相似文献