An application of Chen’s theorem to convergence of Fourier multiplier transforms

Let V be a star shaped region. In 2006, Colzani, Meaney and Prestini proved that if function f satisfies some condition, then the multiplier transform with the characteristic function of tV as the multiplier tends to f almost everywhere, when t goes to∞. In this paper we use a Theorem established by K.K.Chen to show that if we change their multiplier, then the condition on f can be weakened.     

CONSERVATION LAWS FOR HEATED LAMINAR RADIAL LIQUID AND FREE JETS

The conserved quantities for the heated radial liquid jet and the heated radial free jet are established by using conservation laws. The flow in a heated radial jet is described by Prandtl's momentum boundary layer equation, the continuity equation and the energy equation. Viscous dissipation is neglected. The multiplier approach is used to derive the conservation laws for the system of three equations for the velocity components and the temperature and three conserved vectors are obtained. The conservation laws for the system of two partial differential equations for the stream function formulation are also computed by the multiplier approach and three conserved vectors are obtained. One of these is a non-local conserved vector for the system. The conserved quantities for the heated radial liquid jet and the heated radial free jet, emitted into a stationary fluid of uniform temperature θ_∞, are derived by integrating the conservation laws across the jet.     

Multiplier operators and extremal functions related to the dual dunkl-sonine operator

We study the dual Dunkl-Sonine operator ^tS_k,? on ?^d, and give expression of ^tS_k,?, using Dunkl multiplier operators on ?^d. Next, we study the extremal functions f^*_λ, λ >0 related to the Dunkl multiplier operators, and more precisely show that {f^*_λ} λ >0 converges uniformly to ^tS_k,?(f) as λ → 0+. Certain examples based on Dunkl-heat and Dunkl-Poisson kernels are provided to illustrate the results.     

Numerical simulations of systems of PDEs by variational iteration method

In this Letter, a general framework of the variational iteration method (VIM) is presented for solving systems of linear and nonlinear partial differential equations (PDEs). In VIM, a correction functional is constructed by a general Lagrange's multiplier which can be identified via a variational theory. VIM yields an approximate solution in the form of a rapid convergent series. Comparison with the exact solutions shows that VIM is a powerful method for the solution of linear and nonlinear systems of PDEs.     

QK乘子代数上的Corona定理和Wolff定理

本文给出对数K-Carleson测度的一个新特征,并以此为工具研究Q_K空间的乘子代数M(Q_K),给出乘子代数M(Q_K)的某些特征描述.利用对数K-Carleson测度及Q_K空间的一个新特征,建立乘子代数M(Q_K)上的Corona定理和Wolff定理.     

The Schur Multiplier of a Pair of Groups

In this article we develop the theory of a Schur multiplier for pairs of groups. The idea of such a multiplier is implicit in the work of J.-L. Loday (1978) and others on algebraicK -theory, and in the work of Eckmann et al. (1972) and others on group homology. In contrast to their work, we focus on the general group-theoretic properties of the multiplier. These properties are systematically derived from: 1) the functoriality of the multiplier; 2) an exact homology sequence; 3) and a transfer homomorphism.     

Gleason’s problem in weighted Bergman space on egg domains

It is shown that on the egg domains: