直线分布点电荷体系的电场线方程中曲线簇参数取值范围的确定

对于沿直线分布的n个点电荷体系的电场线方程,给出了一种逐步调整的算法,由此可确定电场线方程中曲线簇参数C的取值范围.     

沿曲线的超奇异积分算子的Lp有界性

文章着重研究R~2中的超奇异积分算子H_(α,β)f(x,y)=p.v.∫_(-1)~1f(x-t,y-γ(t))e~(-i|t|~(-β))(dt)/(t|t|~α) (α,β>0)沿曲线Γ(t)=(t,γ(t))的L~p有界性,推广了Chandarana,陈杰诚,范大山等的结果.此外也得到了R~2中沿变曲线的超奇异积分算子T_(α,β)f(x,y)的L~p估计.     

Irreducible polynomials over F2r with three prescribed coefficients

For any positive integers $n\ge 3$ and $r\ge 1$, we prove that the number of monic irreducible polynomials of degree n over ${\mathbb{F}}_{2^r}$ in which the coefficients of $T^{n-1}$, $T^{n-2}$ and $T^{n-3}$ are prescribed has period 24 as a function of n, after a suitable normalization. A similar result holds over ${\mathbb{F}}_{5^r}$, with the period being 60. We also show that this is a phenomena unique to characteristics 2 and 5. The result is strongly related to the supersingularity of certain curves associated with cyclotomic function fields, and in particular it complements an equidistribution result of Katz.     

Pressure effects on EXAFS Debye-Waller factor and melting curve of solid krypton

The pressure effects on atomic mean-square displacement, extended X-ray absorption fine structure (EXAFS) Debye-Waller factor and melting temperature of solid krypton have been investigated in within the statistical moment method scheme in quantum statistical mechanics. By assuming the interaction between atoms can be described by Buckingham potential, we performed the numerical calculations for krypton up to pressure 120?GPa. Our calculations show that the atomic mean-square displacement and EXAFS Debye-Waller factor of krypton crystal depend strongly on pressure. They make the robust reduction of the EXAFS peak height. Our results are in good and reasonable agreements with available experimental data. This approach gives us a relatively simple method for qualitatively calculating high-pressure thermo-physical properties of materials. Moreover, it can be used to verify future high-pressure experimental and theoretical works.     

The value semiring of an algebroid curve

Abstract

We study the value semiring Γ, equipped with the tropical operations, associated to an algebroid curve. As a set, Γ determines and is determined by the well-known value semigroup S and we prove that Γ is always finitely generated in contrast to S. In particular, for a plane curve, we present a straightforward way to obtain Γ in terms of the semiring (or the semigroup) of each branch of the curve and the mutual intersection multiplicity of its branches. In the analytic case, this allows us to relate the results of Zariski and Waldi that characterize the topological type of the curve.     

Accretive growth kinematics via null evolution curve

It is known that the kinematics on the Lorentzian surfaces changes according to the casual characters of the vector fields. Suspicions, the character of the generator curve affects the surface growth. Therefore, we determine the model of the growth function in the three-dimensional Minkowski spacetime with a null generating curve. Moreover, the proposed method is illustrated with various examples.     

The possible equation of state of dark matter in low surface brightness galaxies

The observed rotation curves of low surface brightness (LSB) galaxies play an essential role in studying dark matter, and indicate the existence of a central constant density dark matter core. However, the cosmological N-body simulations of cold dark matter predict an inner cusped halo with a power-law mass density distribution, and cannot reproduce a central constant-density core. This phenomenon is called cusp-core problem. When dark matter is quiescent and satisfies the condition for hydrostatic equilibrium, the equation of state can be adopted to obtain the density profile in the static and spherically symmetric space-time. To address the cusp-core problem, we assume that the equation of state is independent of the scaling transformation. Its lower order approximation for this type of equation of state can naturally lead to a special case, i.e., \begin{document}$p=\zeta\rho+2\epsilon V_{\rm rot}^{2}\,\rho$\end{document}, where p and \begin{document}$\rho$\end{document} represent the pressure and density, respectively, \begin{document}$V_{\rm rot}$\end{document} depicts the rotation velocity of galaxy, and \begin{document}$\zeta$\end{document} and \begin{document}$ \epsilon$\end{document} are positive constants. It can obtain a density profile that is similar to the pseudo-isothermal halo model when \begin{document}$\epsilon$\end{document} is approximately 0.15. To obtain a more universally used model, let the equation of state include the polytropic model, i.e. \begin{document}$p= \frac{\zeta}{\rho_{0}^{s}}\rho^{1+s}+ 2\epsilon V_{\rm rot}^{2}\,\rho$\end{document}, from which we can obtain other types of density profiles, such as the profile that is nearly same as the Burkert profile, where s and \begin{document}$\rho_{0}$\end{document} are positive constants.