Maximum norm stability of difference schemes for parabolic equations on overset nonmatching space-time grids

In this paper, theoretical results are described on the maximum norm stability and accuracy of finite difference discretizations of parabolic equations on overset nonmatching space-time grids. We consider parabolic equations containing a linear reaction term on a space-time domain which is decomposed into an overlapping collection of cylindrical subregions of the form , for . Each of the space-time domains are assumed to be independently grided (in parallel) according to the local geometry and space-time regularity of the solution, yielding space-time grids with mesh parameters and . In particular, the different space-time grids need not match on the regions of overlap, and the time steps can differ from one grid to the next. We discretize the parabolic equation on each local grid by employing an explicit or implicit -scheme in time and a finite difference scheme in space satisfying a discrete maximum principle. The local discretizations are coupled together, without the use of Lagrange multipliers, by requiring the boundary values on each space-time grid to match a suitable interpolation of the solution on adjacent grids. The resulting global discretization yields a large system of coupled equations which can be solved by a parallel Schwarz iterative procedure requiring some communication between adjacent subregions. Our analysis employs a contraction mapping argument.

Applications of the results are briefly indicated for reaction-diffusion equations with contractive terms and heterogeneous hyperbolic-parabolic approximations of parabolic equations.

     

On primitive ideals

We extend two well-known results on primitive ideals in enveloping algebras of semisimple Lie algebras, the Irreducibility theorem for associated varieties and Duflo theorem on primitive ideals, to much wider classes of algebras. Our general version of the Irreducibility Theorem says that if A is a positively filtered associative algebra such that gr A is a commutative Poisson algebra with finitely many symplectic leaves, then the associated variety of any primitive ideal in A is the closure of a single connected symplectic leaf. Our general version of the Duflo theorem says that if A is an algebra with a triangular structure, see § 2, then any primitive ideal in A is the annihilator of a simple highest weight module. Applications to symplectic reflection algebras and Cherednik algebras are discussed.     

On linear congruence relations for Kubota-Leopoldt 2-adic L-functions

Our purpose in the paper is to find the most general linear congruence relation of the Hardy-Williams type for linear combinations of special values of Kubota-Leopoldt 2-adic L-functions L₂(k,χω^1−k) with k running over any finite subset of not necessarily consisting of consecutive integers (see Acta Arith. 47 (1986) 263; Publ. Math. Fac. Sci. Besançon, Théorie des Nombres, 1995/1996; Publ. Math. Debrecen 56 (2000) 677 and cf. Mathematics and Its Applications, Vol. 511, Kluwer Academic Publishers, Dordrecht, Boston, London, 2000). If k runs over finite subsets of consisting of consecutive integers see Compositio Math. 111 (1998) 289; Publ. Math. Debrecen 56 (2000) 677; Hardy and Williams, 1986; Compositio Math. 75 (1990) 271; Acta Arith. 71 (1995) 273; 52 (1989) 147; J. Number Theory 34 (1990) 362. In order to obtain the most general congruences of this type we make use of divisibility properties of the generalized Vandermonde determinants obtained in Spie? et al. (Divisibility properties of generalized Vandermonde and Cauchy determinants, Preprint 627, Institute of Mathematics, Polish Academy of Sciences, Warsaw, 2002). This allows us to simplify our main Theorem 2 and obtain Theorem 3 where the most general form of the linear congruence relation is given.     

The genus fields of Kummer function fields

In this paper, we give a definition of genus field of function field with one variable over finite fields. And we explicitly describe the genus fields of Kummer function fields. For quadratic function fields case, our results are analogous to the genus fields of quadratic number fields.     

Limits of tangents and minimality of complex links

We show that the complex link of a large class of space germs (X,x₀) is characterized by its “simplicity”, among the Milnor fibres of functions with isolated singularity on X. This amounts to the minimality of the Milnor number, whenever this number is defined. Such a phenomenon has been first pointed out in case (X,x₀) is an isolated hypersurface singularity, by Teissier (Cycles évanescents, sections planes et conditions de Whitney, in: Singularités à Cargèse 1972, Asterisque, Nos. 7 et 8, Soc. Math. France, Paris, 1973, pp. 285-362).     

锂原子同位素位移的计算(英文)

本文应用Grasp92程序包计算了~(5,7)LiI的2~2P_(3/2)到2~2S_(1/2)和2~2P_(1/2)到2~2S_(1/2)跃迁的同位素位移.2~2P_(3/2)到2~2S_(1/2)跃迁的同位素位移为10307 MHz,2~2P_(1/2)到2~2S_(1/2)跃迁的同位素位移为10207 MHz.这些理论结果和实验是相符合的.     

A solvent-governed surface state strategy for rational synthesis of N and S co-doped carbon dots with multicolour fluorescence

ABSTRACT

Multicolour emissive carbon dots (CDs) are widely investigated by virtue of their merits on fluorescent properties. Method on heteroatom doping assisted with various solvents has been proved efficient in achieving multiple-colour-emissive CDs, especially long-wavelength emission. Herein, a synthesis of multicolour-emissive CDs by controlled surface function is reported. By tuning the thermal-pyrolysis temperature and molar ratio of reactants, optimal emission of the resulted CDs gradually shifts from blue to yellow light with the assistance of different solvents. According to the emissive relationship dependent on excitation, fluorescence lifetimes, and FT-IR of these CDs, the different surface states participated with S and N elements on the surface of carbogenic core govern fluorescent colours of the CDs. In terms of the applications, blue CDs (B-CDs) exhibits high sensitivity for ion detections of Ag⁺ and Fe³⁺, which is further illustrated to have different quenching mechanisms each other because that these ions have the affinity interaction with different surface groups of the CDs. Moreover, blue and yellow CDs solutions are mixed with PVP water solution to fabricate white-light CDs/PVP film, which exhibits stable fluorescence with a CIE coordinate of (0.32, 0.33) and endows these CDs as potentially fluorescent nanomaterial in the solid state lighting field.     

Fractional Fourier transform and geometric quantization

Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of the phase-space: no linear structure is necessary. It is shown that the “fractional Fourier transform” provides a simple example of this construction. As an application of this technique we show that for any linear Hamiltonian system, its quantum dynamics can be obtained exactly as the lift of the corresponding classical dynamics by means of the above transformation. Moreover, it can be deduced from the free quantum evolution. This way new, unknown symmetries of the Schrödinger equation can be constructed. It is also argued that the above construction defines in a natural way a connection in the bundle of quantum states, with the base space describing all their possible representations. The non-flatness of this connection would be responsible for the non-existence of a quantum representation of the complete algebra of classical observables.