Commutators of fractional integral operators on Vanishing-Morrey spaces

In this note we prove a sufficient condition for commutators of fractional integral operators to belong to Vanishing Morrey spaces VL ^p,λ. In doing this we use an extension on Morrey spaces of an inequality by Fefferman and Stein concerning the sharp maximal function and the fractional maximal function and related Morrey inequalities.      

Barth type vanishing theorem

In this paper we give a vanishing result for cohomology groups of symmetric powers of the co-normal bundle of a non-degenerate smooth subvariety X of projective space, then we use this theorem to give a Barth type vanishing theorem.      

Fundamental error analysis and geometric interpretation for block truncation coding techniques

Various variants and hybrid approaches evolved from the origin of Delp and Mitchell's block truncation coding (BTC) or moment preserving quantizer (MPQ) have formed a niche as an effective and simple image compression methodology with attractive coding performance achieved at moderate bitrates. As BTC is still lacking a fundamental error analysis, in this paper we present some fundamental insights regarding one-bit (or two-level) BTC's truncation error by providing mathematical analysis as well as novel geometric interpretation. We further show that the mean-square error (MSE) of Lema and Mitchell's absolute moment block truncation coding (AMBTC) is always bounded below (i.e., less than or equal to) that of BTC. Therefore, with additional advantages in computation and implementation, AMBTC is always superior. Furthermore, we developed a new adaptive equal sign position optimization (ESPO) algorithm for optimum pixel classification. Our quantization error analysis shows that incorporating the ESPO algorithm into conventional AMBTC or BTC achieves minimum MSE in either case.     

复杂环境中短波天线的MoM/FDTD混合法分析

利用电磁场数值计算方法中的矩量法/时域有限差分（MoM/FDTD）混合方法,分析了复杂环境中短波天线的电磁辐射性能,建立了短波双极天线的自由空间模型。采用矩量法和时域有限差分法相结合,对其模型进行仿真计算,并将计算结果和已有的文献进行比较,验证了混合方法计算结果的可行性、准确性。总结了该模型对短波天线远区场影响的有益经验,为改善短波天线性能提供了设计参考。     

A numerical model for multigroup radiation hydrodynamics

We present in this paper a multigroup model for radiation hydrodynamics to account for variations of the gas opacity as a function of frequency. The entropy closure model (M₁) is applied to multigroup radiation transfer in a radiation hydrodynamics code. In difference from the previous grey model, we are able to reproduce the crucial effects of frequency-variable gas opacities, a situation omnipresent in physics and astrophysics. We also account for the energy exchange between neighbouring groups which is important in flows with strong velocity divergence. These terms were computed using a finite volume method in the frequency domain. The radiative transfer aspect of the method was first tested separately for global consistency (reversion to grey model) and against a well-established kinetic model through Marshak wave tests with frequency-dependent opacities. Very good agreement between the multigroup M₁ and kinetic models was observed in all tests. The successful coupling of the multigroup radiative transfer to the hydrodynamics was then confirmed through a second series of tests. Finally, the model was linked to a database of opacities for a Xe gas in order to simulate realistic multigroup radiative shocks in Xe. The differences with the previous grey models are discussed.     

Partially harmonic forms and models of H-series

Let G   be a real reductive Lie group, let H=TA$H=TA$ be the identity component of a Cartan subgroup, and let h$\mathfrak{h}$ be the corresponding Cartan subalgebra. This leads to a parabolic subgroup of G whose identity component is MAN. The unitary G-representations induced by MAN are known as the H  -series. We study symplectic geometry of G×h$G\times \mathfrak{h}$ and apply geometric quantization to construct unitary G-representations by partially harmonic forms. They are direct integrals of the H-series, indexed by the image of the moment map. We also perform symplectic reduction and symplectic induction, and consider their analogues in representation theory via geometric quantization.     

Delta-shocks and vacuum states in the vanishing pressure limit of solutions to the isentropic Euler equations for modified Chaplygin gas

The phenomena of concentration and cavitation and the formation of δ-shocks and vacuum states in solutions to the isentropic Euler equations for a modified Chaplygin gas are analyzed as the double parameter pressure vanishes. Firstly, the Riemann problem of the isentropic Euler equations for a modified Chaplygin gas is solved analytically. Secondly, it is rigorously shown that, as the pressure vanishes, any two-shock Riemann solution to the isentropic Euler equations for a modified Chaplygin gas tends to a δ-shock solution to the transport equations, and the intermediate density between the two shocks tends to a weighted δ-measure that forms the δ-shock; any two-rarefaction-wave Riemann solution to the isentropic Euler equations for a modified Chaplygin gas tends to a two-contact-discontinuity solution to the transport equations, the nonvacuum intermediate state between the two rarefaction waves tends to a vacuum state. Finally, some numerical results exhibiting the formation of δ-shocks and vacuum states are presented as the pressure decreases.