罗丹明6G在醇溶液中的荧光频移特性分析

罗丹明6G在甲醇、乙醇、乙二醇溶液中均发出较强的荧光。当醇溶液浓度为33.3%时,基本不存在频移现象。当醇溶液浓度为99.7%时,荧光峰发生蓝移或红移,分析认为该频移是由罗丹明6G和醇类物质分子相互作用(如氢键、静电吸引)导致激发态能量升高、荧光峰蓝移,与醇类物质分子中羟基OH的孤对电子跃迁导致荧光能量降低、荧光峰红移,这两种因素相互竞争的结果,且在高浓度醇溶液中,羟基OH数量越多,红移越明显。     

Local foliations and optimal regularity of Einstein spacetimes

We investigate the local regularity of pointed spacetimes, that is, time-oriented Lorentzian manifolds in which a point and a future-oriented, unit timelike vector (an observer) are selected. Our main result covers the class of Einstein vacuum spacetimes. Under curvature and injectivity bounds only, we establish the existence of a local coordinate chart defined in a ball with definite size in which the metric coefficients have optimal regularity. The proof is based on quantitative estimates for, on one hand, a constant mean curvature (CMC) foliation by spacelike hypersurfaces defined locally near the observer and, on the other hand, the metric in local coordinates that are spatially harmonic in each CMC slice. The results and techniques in this paper should be useful in the context of general relativity for investigating the long-time behavior of solutions to the Einstein equations.     

Franck–Condon Factors and r‐Centroids for the B–, C–, F–, and G–X Band Systems of YF Molecule

The Franck–Condon factors and r‐centroids, which are very closely related to relative transition probabilities, have been evaluated by a more reliable numerical integration procedure for the B¹π–X¹Σ⁺, C¹Σ⁺–X¹Σ⁺, F¹Σ⁺–X¹Σ⁺, and G¹π–X¹Σ⁺ band systems of the YF molecule, using suitable potentials.     

Deformations of 2k-Einstein structures

It is shown that the space of infinitesimal deformations of 2k-Einstein structures is finite dimensional on compact non-flat space forms. Moreover, spherical space forms are shown to be rigid in the sense that they are isolated in the corresponding moduli space.     

Anisotropic Bianchi type V perfect fluid cosmological models in Lyra’s geometry

The law of variation for mean Hubble’s parameter with average scale factor, in an anisotropic Bianchi type V cosmological space–time, is discussed within the frame work of Lyra’s manifold. The variation of Hubble’s parameter, which gives a constant value of deceleration parameter, generates two types of solutions for the average scale factor; one is the power-law and the other one is of exponential form. Using these two forms, new classes of exact solutions of the field equations have been found for a Bianchi type V space–time filled with perfect fluid in Lyra’s geometry by considering a time-dependent displacement field. The physical and kinematical behaviors of the singular and non-singular models of the universe are examined. Exact expressions for look-back time, luminosity distance and event horizon versus redshift are also derived and their significance are discussed in detail. It has been observed that the solutions are compatible with the results of recent observations.     

A size-width inequality for distributive lattices

We show that every collection ofw sets such that none contains any other generates at least 3w-2 sets under the operations of taking intersections and unions. In particular, we prove that if the finite distributive lattice ? contains an antichain of sizew, then |?| ≧3w, forw≠1, 2, 3, 6, where the minimal exceptional cases arise from the Boolean algebras ?_n withn=0, 1, 2, 3, 4 atoms.     

Are linear algorithms always good for linear problems?

We exhibit linear problems for which every linear algorithm has infinite error, and show a (mildly) nonlinear algorithm with finite error. The error of this nonlinear algorithm can be arbitrarily small if appropriate information is used. We illustrate these examples by the inversion of a finite Laplace transform, a problem arising in remote sensing.     

Mathematical modelization of equatorial waves

Our purpose is to calculate waves propagating along the equator in an oceanic domain and the influence of a characteristic mean equatorial circulation on the nature of these waves. Equations satisfied by perturbations of currents and temperature are of the Navier-Stokes type and have been linearized around a stationary solution. Existence and uniqueness of the solution have been proved. Numerical experiments have been carried out and provided us with time-dependent values. The excited waves are exhibited by Fourier analysis of these time series.     

Extremum principles for a general class of saddle functionals

The usual notion of a saddle functional in the calculus of variations assumes a vex/concave structure over the product space of two inner product spaces. Here the ideas extended to include some convexity in both spaces whilst still retaining an overall saddle property. Dual extremum principles are established for these functionals. Examples include periodic solutions of Duffing's equation, an iterative scheme and a pair of simultaneous partial differential equations which arise in magnetohydrodynamics.     

B-convergence properties of defect correction methods. II

Summary B-convergence properties of defect correction methods based on the implicit Euler and midpoint schemes are discussed. The property ofB-convergence means that there exist global error bounds for nonlinear stiff problems independent of their stiffness. It turns out that the orders ofB-convergence of these methods coincide with the conventional orders of small (whereL is a Lipschitz constant of the right-hand side). In Part I these assertions are reduced to the validity of the so-called HypothesisA which is discussed in greater detail in Part II. Numerical experiments confirming the theoretical analysis are also given in Part II.