Convergence of an augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints

An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Löwner operator associated with a potential function for the optimization problems with inequality constraints. The favorable properties of both the Löwner operator and the corresponding augmented Lagrangian are discussed. And under some mild assumptions, the rate of convergence of the augmented Lagrange algorithm is studied in detail.     

Charge, Geometry, and Effective Mass

Charge, like mass in Newtonian mechanics, is an irreducible element of electromagnetic theory that must be introduced ab initio. Its origin is not properly a part of the theory. Fields are then defined in terms of forces on either masses—in the case of Newtonian mechanics, or charges in the case of electromagnetism. General Relativity changed our way of thinking about the gravitational field by replacing the concept of a force field with the curvature of space-time. Mass, however, remained an irreducible element. It is shown here that the Reissner-Nordström solution to the Einstein field equations tells us that charge, like mass, has a unique space-time signature.     

利用广义不确定关系计算Reissner-Nordstrm-de Sitter黑洞的统计力学熵

利用广义不确定关系修正的态密度方程并采用Wentzel-Kramers-Brillouin(WKB)近似方法,计算了Reissner-Nordstrm-de Sitter(RNdS)黑洞时空中标量场的统计力学熵.结果表明,由这种方法得到的黑洞熵与它的内、外视界面积和宇宙视界面积之和成正比,这与采用其他方法所得的结果一致,从而揭示了黑洞熵与视界面积之间的内在联系,也进一步表明了黑洞熵是视界面上量子态的熵,是一种量子效应.     

Two-Mode Harmonic Oscillator Model of Reissner-Nordström Black Hole

In this paper, we will assume that the Reissner-Nordström black hole can be dynamically expressed, at the classical level, in terms of a reduced phase space consisting of the physical observables and their canonical conjugates. More specifically, we propose that the phase space can be described by the black hole’s mass and charge along with their respective conjugates. In this four-dimensional phase space we perform a couple of canonical transformations to obtain a two-mode harmonic oscillator model of Reissner-Nordström black hole. By adopting this model, the quantum spectrum and wave function of horizon area are presented.     

Reissner-Nordstr?m de Sitter黑洞的量子隧穿效应

运用Parikh的量子隧穿模型，研究了Reissner-Nordstrm de Sitter黑洞的量子隧穿效应.结果表明，在能量守恒的条件下，黑洞外视界和宇宙视界处的粒子出射率与Bekenstein-Hawking熵有关，辐射谱不再是严格的纯热谱.     

Pre-B?tzinger复合体的从簇到峰放电的同步转迁及分岔机制

Pre-Bötzinger复合体是兴奋性耦合的神经元网络,通过产生复杂的放电节律和节律模式的同步转迁参与调控呼吸节律.本文选用复杂簇和峰放电节律的单神经元数学模型构建复合体模型,仿真了与生物学实验相关的多类同步节律模式及其复杂转迁历程,并利用快慢变量分离揭示了相应的分岔机制.当初值相同时,随着兴奋性耦合强度的增加,复合体模型依次表现出完全同步的“fold/homoclinic”,“subHopf/subHopf”簇放电和周期1峰放电.当初值不同时,随耦合强度增加,表现为由“fold/homoclinic”,到“fold/fold limit cycle”、到“subHopf/subHopf”与“fold/fold limit cycle”的混合簇放电、再到“subHopf/subHopf”簇放电的相位同步转迁,最后到反相同步周期1峰放电.完全(同相)同步和反相同步的周期1节律表现出了不同分岔机制.反相峰同步行为给出了与强兴奋性耦合容易诱发同相同步这一传统观念不同的新示例.研究结果给出了preBötzinger复合体的从簇到峰放电节律的同步转迁规律及复杂分岔机制,反常同步行为丰富了非线性动力学的内涵.     

Tunneling of Charged and Magnetized Fermions from the Reissner-Nordström Black Hole with Magnetic Charges

The Kerner-Mann fermions tunneling framework is extended to the spin particles with electric and magnetic charges in this paper. We rewrite the electromagnetic field tensor and the Lagrangian of the field corresponding to the source with electric and magnetic charges to redefine an equivalent charge. We only consider the case that the ratio of the electric charge and magnetic charge of the emission is constant and equal to the source. The result shows that when the energy conservation together with the electric charge and magnetic charge conservations are taken into account in the dynamical background space time, the emission rate agrees with the underlying unitary theory and the actual radiation spectrum of charged and magnetized fermions also derivates from the pure thermal one.     

Fermions’ Tunnelling from the Reissner- Nordström-Anti-de Sitter Black Hole

Very recent work of Kerner and Mann involving fermions tunnelling from the Rindler space-time and a general non-rotating black hole is extended to the case of Reissner-Nordström-anti-de Sitter black hole. Due to the couple between the gravity field and electromagnetic field, we introduce the Dirac equation of the charged particles to determine the action of the radiation. We further consider the correction of the thermal spectrum in the unfixed background space time. It is shown that when the energy and charge conservations are considered, the tunnelling rate of fermions is also related to the change of Bekenstein-Hawking entropy, implying the underlying unitary theory is satisfied.     

Theoretical investigation on optical properties of Möbius carbon nanobelts in one- and two-photon absorption

The first successful synthesis of fully fused and fully conjugated Möbius carbon nanobelts (CNBs) has attracted considerable attention. However, theoretical calculations based on such π-conjugated Möbius CNB are still insufficient. Herein, we theoretically investigated molecular spectroscopy of Möbius CNBs without and with n-butoxy groups via visualization methods. The results show that the presence of n-butoxy groups can significantly affect Möbius CNBs’ optical performance, changing electron-hole coherence and enhancing two-photon absorption cross-sections. Our work provides a deeper understanding of photophysical mechanisms of Möbius CNBs in one- and two-photon absorption and reveals possible applications on optoelectronic devices.     

Thermodynamic properties of Reissner-Nordstrm-de Sitter quintessence black holes

The mass,electric charge,and temperature of black holes in the Reissner-Nordstrm-de Sitter quintessence(RN-dSQ) spacetime are obtained.The heat capacities of the RN-dSQ black holes for certain electric charges and masses are analyzed.The electrostatic energy and dark energy in the RN-dSQ black holes are also calculated.