A De Giorgi Type Result to Divergence Degenerate Elliptic Equation with Bounded Coefficients Related To Hörmander's Vector Fields

In this paper, we consider the divergence degenerate elliptic equation with bounded coefficients constructed by Hörmander's vector fields. We prove a De Giorgi type result, i.e., the local Hölder continuity for the weak solutions to the equation by providing a De Giorgi type lemma and extending the Moser iteration to the setting here. As a consequence, the Harnack inequality of weak solutions is also given.     

Asymptotic analysis of Emden–Fowler type equation with an application to power flow models

Emden–Fowler type equations are nonlinear differential equations that appear in many fields such as mathematical physics, astrophysics and chemistry. In this paper, we perform an asymptotic analysis of a specific Emden–Fowler type equation that emerges in a queuing theory context as an approximation of voltages under a well-known power flow model. Thus, we place Emden–Fowler type equations in the context of electrical engineering. We derive properties of the continuous solution of this specific Emden–Fowler type equation and study the asymptotic behavior of its discrete analog. We conclude that the discrete analog has the same asymptotic behavior as the classical continuous Emden–Fowler type equation that we consider.     

Complex geometrical optics of Kerr type nonlinear media

The paper generalizes paraxial complex geometrical optics (PCGO) for Gaussian beam (GB) propagation in nonlinear media of Kerr type. Ordinary differential equations for the beam amplitude and for complex curvature of the wave front are derived, which describe the evolution of axially symmetric GB in a Kerr type nonlinear medium. It is shown that PCGO readily provides the solutions of NLS equation obtained earlier from diffraction theory on the basis of the aberration-free approach. Besides reproducing classical results of self-focusing PCGO readily describes an influence of the initial curvature of the wave front on the beam evolution in a medium of Kerr type including a nonlinear graded-index fiber. The range of applicability of the PCGO theory is discussed as well which is helpful for avoiding nonphysical solutions.     

Heat Content Asymptotics for Oblique Boundary Conditions

We consider the short-time heat content asymptotics for oblique boundary conditions. The first few coefficients in the asymptotic expansion are calculated.     

温度对应变式位移传感系统灵敏系数的影响

应变式位移传感系统的工作原理是基于电阻应变效应,该系统具有精度高﹑稳定性好等优点,但温度尤其是极端低温环境将影响该系统的灵敏系数,进而影响其测量精度.本文介绍了一种可用于低温环境的应变式位移传感系统,理论分析和实验研究了温度对该系统灵敏系数的影响,研究结果为其在低温环境中的应用提供了一定基础。     

Optical design for enhanced prism type fingerprint scanner image contrast with asymmetrical aspheric lens

The design of optical prism fingerprint scanner with aspheric lens is researched. We propose a modified structure for optical prism fingerprint scanner, which has an asymmetrical aspheric lens on the output plane. It is numerically shown under elliptic valley similar fingerprint model that the optical image qualities of such a scanner are better than the scanner with symmetrical aspheric lens. When the fingerprint range is 15 mm, the results show that the minimum image contrast is 0.49 for an optical prism with asymmetrical aspheric lens, much better than a symmetrical aspheric lens with 0.20. The relative illumination variation is from 0.62 to 1.00 for optical prism with asymmetrical aspheric lens, and for the symmetrical aspheric lens it is 0.35 to 1.00. We conclude that an optical prism with asymmetrical aspheric lens is better than an optical prism with symmetrical aspheric lens.     

Freudenthal duality and generalized special geometry

Freudenthal duality, introduced in Borsten et al. (2009) [1] and defined as an anti-involution on the dyonic charge vector in d=4 space-time dimensions for those dualities admitting a quartic invariant, is proved to be a symmetry not only of the classical Bekenstein-Hawking entropy but also of the critical points of the black hole potential.Furthermore, Freudenthal duality is extended to any generalized special geometry, thus encompassing all N>2 supergravities, as well as N=2 generic special geometry, not necessarily having a coset space structure.     

一类带有回馈控制的捕食-食饵模型正周期解的存在性(英文)

研究了一类具有Hassell-Varely功能性反应函数的食饵-捕食模型的回馈控制系统,利用比较连续定理和一致度定理,证明了系统正周期解的存在性,并通过构造Lyapunov函数给出了系统全局稳定性的充分条件和证明.