The Inverse Problem of the Calculus of Variations for Sixth- and Eighth-order Scalar Ordinary Differential Equations

On the equation manifold of the 2nth-order scalar ordinary differential equation, n3,

非齐次守恒律方程分片光滑解的粘性方法

1　引　　言考虑非齐次守恒律方程ut+f(u) x =g(u) ,　　 -∞ 0 ,(1 .1 )u(x,0 ) =u0 (x) ,　　 -∞ 0 , (1 .5)g∈ C3且 g是 Lipschitz连续的 ,Lipschitz系数为 L . (1 .6 )对于一般守恒律齐次方程 ,粘性解逼近熵解的收敛阶为 O(ε ) [1 ] .在 f严格凸的条件下 ,其收敛速度可以提高到 O(ε|lnε|+ε) [2 ] ,[3] .本文考虑具有条件 (1 .5) (1 .6 )的非齐次方程(1 .1 ) ,在较广泛的一类初值条件下…     

On fillable contact structures up to homotopy

Let be a closed, oriented -manifold. The set of homotopy classes of positive, fillable contact structures on is a subtle invariant of , known to always be a finite set. In this paper we study under the assumption that carries metrics with positive scalar curvature. Using Seiberg-Witten gauge theory, we prove that two positive, fillable contact structures on are homotopic if and only if they are homotopic on the complement of a point. This implies that the cardinality of is bounded above by the order of the torsion subgroup of . Using explicit examples we show that without the geometric assumption on such a bound can be arbitrarily far from holding.

     

Fast MAS total through-bond correlation spectroscopy

Mixing sequences for total through-bond correlation spectroscopy in solids (TOBSY) were developed. The motivation is the design of broadband, effective, and robust sequences adapted for "fast" MAS. Possible sequences with the desired Hamiltonian (the homonuclear isotropic J interaction) were identified using lowest order average Hamiltonian theory. Numerical simulations as a function of the MAS frequency were then employed to further characterize the performance. An experimental TOBSY spectrum of a uniformly (13)C-labeled decapeptide at 20 kHz MAS was obtained using one of the new sequences. The spectrum allows us to assign the (13)C resonances to the respective spin systems.     

Horizon-less Spherically Symmetric Vacuum-Solutions in a Higgs Scalar-Tensor Theory of Gravity

The exact static and spherically symmetric solutions of the vacuum field equations for a Higgs Scalar-Tensor theory (HSTT) are derived in Schwarzschild coordinates. It is shown that in general there exists no Schwarzschild horizon and that the fields are only singular (as naked singularity) at the center (i.e. for the case of a point-particle). However, the Schwarzschild solution as in usual general relativity (GR) is obtained for the vanishing limit of Higgs field excitations.     

How exact are simplified scalar approaches to optical fields in oxide-confined stripe-geometry diode lasers?

Optical model, scalar or vectorial one, describing behaviour of an optical field within a diode-laser cavity, is one of the most important parts of modelling of a diode-laser operation. As compared to more accurate vectorial optical approaches, scalar ones are known to be less exact but simultaneously they need much less computation time. Besides, they have been sometimes found to be surprisingly exact even beyond their confirmed range of validity. Therefore, in this paper, real validity limits of their application have been determined by comparing their simplified results with more exact results obtained with the aid of vectorial models. The analysis comprises a comparison of an application of the most popular scalar approach to optical properties of diode lasers, i.e., the effective index method, and the vectorial method of lines for the standard 1.3-μm GaAs-based stripe-geometry diode laser. The scalar model has been found to be quite exact in the case of a determination of the effective refractive index, i.e., the wavelength of emitted radiation, whereas its exactness in the lasing threshold analysis is much worse, especially in the case of higher-order modes. Our analysis is concluded with a determination of the regions where both models give satisfactorily close results.     

Scaling,Renormalization and Statistical Conservation Laws in the Kraichnan Model of Turbulent Advection

We present a systematic way to compute the scaling exponents of the structure functions of the Kraichnan model of turbulent advection in a series of powers of ξ, adimensional coupling constant measuring the degree of roughness of the advecting velocity field. We also investigate the relation between standard and renormalization group improved perturbation theory. The aim is to shed light on the relation between renormalization group methods and the statistical conservation laws of the Kraichnan model, also known as zero modes.     

The conformal status of o = ‐3/2 Brans‐Dicke cosmology

Following recent fit of supernovae data to Brans‐Dicke theory which favours the model with o = ‐ 3/2 [1] we discuss the status of this special case of Brans‐Dicke cosmology in both isotropic and anisotropic framework. It emerges that the limit o = ‐3/2 is consistent only with the vacuum field equations and it makes such a Brans‐Dicke theory conformally invariant. Then it is an example of the conformal relativity theory which allows the invariance with respect to conformal transformations of the metric. Besides, Brans‐Dicke theory with o = ‐3/2 gives a border between a standard scalar field model and a ghost/phantom model. In this paper we show that in o = ‐3/2 Brans‐Dicke theory, i.e., in the conformal relativity there are no isotropic Friedmann solutions of non‐zero spatial curvature except for k=‐1 case. Further we show that this k=‐1 case, after the conformal transformation into the Einstein frame, is just the Milne universe and, as such, it is equivalent to Minkowski spacetime. It generally means that only flat models are fully consistent with the field equations. On the other hand, it is shown explicitly that the anisotropic non‐zero spatial curvature models of Kantowski‐Sachs type are admissible in o = ‐3/2 Brans‐Dicke theory. It then seems that an additional scale factor which appears in anisotropic models gives an extra deegre of freedom and makes it less restrictive than in an isotropic Friedmann case.     

用振幅比值方法预言中性粲介子衰变到CP本征态的CP不对称性

用振幅比之方法计算了中性粲介子衰变到CP本征态的CP不对称性. 计算了时间相关和时间积分的CP不对称性. 结果表明, 时间积分的CP不对称参数约为千分之一的量级. 还讨论了在BESⅢ和B工厂上实验检验的可能性.     

Probing new physics in B→J/ψπ0 decay

We calculate the branching ratio of B→J/ψπ0 with a mixed formalism that combines the QCD-improved factorization and the perturbative QCD approaches. The result is consistent with experimental data.The quite small penguin contribution in B→J/ψπ0 decay can be calculated with this method. We suggest two methods to extract the weak phase β. One is through the dependence of the mixing induced CP asymmetry SJ/ψπ0 on the weak phase β, the other is from the relation of the total asymmetry ACP with the weak phase β. Our results show that the deviation △SJ/ψπ0 of the mixing induced CP asymmetry from sin(-2β) is of O(10-3) and has much less uncertainty. The above O(10-3) deviation can provide a good reference for identifying new physics.