Exact solution of the Landau-Lifshitz equations for a radiating charged particle in the Coulomb potential

We solve exactly the classical non-relativistic Landau-Lifshitz equations of motion for a charged particle moving in a Coulomb potential, including radiation damping. The general solution involves the Painlevè transcendent of type II. It confirms our physical intuition that a negatively charged classical particle will spiral into the nucleus, supporting the validity of the Landau-Lifshitz equation.     

Magnetic properties,electronic structure,and optical properties of the filled skutterudite BaFe4Sb12

The magnetic properties, electronic structure, and optical properties of the filled skutterudite BaFe₄Sb₁₂ are calculated by the first-principles full-potential linearized augmented plane wave (FPLAPW) plus local orbital method. It is found that the local spin density approximation (LSDA) method appears more accurate than the generalized gradient approximation (GGA) method in calculating the electronic structures and optical properties of this compound. Furthermore, our calculated lattice constant and spin magnetic moments with the LSDA method are in overall better agreement with experiment. In contrast with recent experiment, our calculations are in good agreement with experimental reflectivity spectra and optical conductivity spectrum.     

L1-type smoothness indicators based weighted essentially nonoscillatory scheme for Hamilton-Jacobi equations

This article presents an improved fifth-order finite difference weighted essentially nonoscillatory (WENO) scheme to solve Hamilton-Jacobi equations. A new type of nonlinear weights is introduced with the construction of local smoothness indicators on each local stencil that are measured with the help of generalized undivided differences in L¹-norm. A novel global smoothness measurement is also constructed with the help of local measurements from its linear combination. Numerical experiments are conducted in one- and two-dimensions to demonstrate the performance enhancement, resolution power, numerical accuracy for the proposed scheme, and compared it with the classical WENO scheme.     

Improved third‐order weighted essentially nonoscillatory scheme

A new third‐order WENO scheme is proposed to achieve the desired order of convergence at the critical points for scalar hyperbolic equations. A new reference smoothness indicator is introduced, which satisfies the sufficient condition on the weights for the third‐order convergence. Following the truncation error analysis, we have shown that the proposed scheme achieves the desired order accurate for smooth solutions with arbitrary number of vanishing derivatives if the parameter ε satisfies certain conditions. We have made a comparative study of the proposed scheme with the existing schemes such as WENO‐JS, WENO‐Z, and WENO‐N3 through different numerical examples. The result shows that the proposed scheme (WENO‐MN3) achieves better performance than these schemes.     

Weighted weak-type inequalities for the maximal function of nonnegative integral transforms over approach regions

The relation between approach regions and singularities of nonnegative kernels is studied, where , , , and is a homogeneous space. For , a sufficient condition on approach regions () is given so that the maximal function

is weak-type with respect to a pair of measures and . It is shown that this condition is also necessary for operators of potential type in the sense of Sawyer and Wheedon (Amer. J. Math. 114 (1992), 813-874).

     

On weighted inequalities for singular integrals

In this note we consider singular integrals associated to Calderón-Zygmund kernels. We prove that if the kernel is supported in then the one-sided condition, , is a sufficient condition for the singular integral to be bounded in , , or from into weak- if . This one-sided condition becomes also necessary when we require the uniform boundedness of the singular integrals associated to the dilations of a kernel which is not identically zero in . The two-sided version of this result is also obtained: Muckenhoupts condition is necessary for the uniform boundedness of the singular integrals associated to the dilations of a general Calderón-Zygmund kernel which is not the function zero either in or in .

     

Uniform boundedness of (<Emphasis Type="Italic">C</Emphasis>, 1) means of Jacobi expansions in weighted sup norms. II (Some necessary estimations)

The paper is concerned with bounds for integrals of the type

木质素磺酸盐的分离提纯

以粗木质素磺酸钠为原料, 采用树脂法、超滤法、长链胺法和溶剂萃取法对其进行了提纯. 红外光谱、元素分析、凝胶渗透色谱等测试结果表明, 溶剂萃取法不能达到提纯目的; 树脂法、超滤法、长链胺法可除去相对分子量小于1000的杂质, 粗木质素磺酸钠经提纯后木质素磺酸钠的质量分数从59.0%提高到90%左右, 且提纯产品的重均分子量和数均分子量均增大, 分子量分布更均一. 从产品收率、提纯效果及提纯工艺等3方面分析表明, 长链胺法除糖效果最好, 提纯后糖含量下降了50%; 超滤法的收率最高, 可达31%, 且其提纯产品的重均分子量较高, 达到12000, 比粗木钠提高了1倍以上.     

Ring geometries,two-weight codes,and strongly regular graphs

It is known that a projective linear two-weight code C over a finite field corresponds both to a set of points in a projective space over that meets every hyperplane in either a or b points for some integers a < b, and to a strongly regular graph whose vertices may be identified with the codewords of C. Here we extend this classical result to the case of a ring-linear code with exactly two nonzero homogeneous weights and sets of points in an associated projective ring geometry. We will introduce regular projective two-weight codes over finite Frobenius rings, we will show that such a code gives rise to a strongly regular graph, and we will give some constructions of two-weight codes using ring geometries. All these examples yield infinite families of strongly regular graphs with non-trivial parameters.