RESEARCH ANNOUNCEMENTS ON “RIGIDITY OF THURSTON’S SPHERE PACKINGS ON3-DIMENSIONAL MANIFOLDS”

1 Introduction and Main Results In the study of hyperbolic metrics on 3-dimensional manifolds,Thurston(see[9],Chapter 13)introduced Thurston’s circle packing on surfaces,which allows the circles to intersects with non-obtuse angles and is a natural generalization of the tangential circle packing studied by Andreev[1,2]and Koebe[6].Thurston further proved the Andreev-Thurston theorem.

Super-sensitive phase estimation with coherent boosted light using parity measurements

We consider a passive and active hybrid interferometer for phase estimation, which can reach the sub-shot-noise limit in phase sensitivity with only the cheapest coherent sources. This scheme is formed by adding an optical parametric amplifier before a Mach-Zehnder interferometer. It is shown that our hybrid protocol can obtain a better quantum Cramer- Rao bound than the pure active （e.g., SU（1, I）） interferometer, and this precision can be reached by implementing the parity measurements. Furthermore, we also draw a detailed comparison between our scheme and the scheme suggested by Caves [Phys. Rev. D 23 1693 （1981）], and it is found that the optimal phase sensitivity gain obtained in our scheme is always larger than that in Caves＇ scheme.

Variational Methods to Nonlinear Differential Equations with Non-instantaneous Impulses

The author aimed to investigate the solvability for nonlinear differential equations with not instantaneous impulses.Variational approach was adopted to obtain the existence of weak solutions as critical points. The findings of this study may serve as a reference for multiplicity of impulsive problems.

Generalized gravitomagnetic field and gravitational waves

Synge was the first to derive the geodesic deviation entirely mathematically (1)Only later did people realize its importance [2] for describing the physical behavior of curved spacetime [3], particularly that it can unambiguously manifest gravitational waves (4, 5)The geodesic deviation relates purely to the 'electric' part of a curved spacetime, while the complementary 'magnetic' part is related to the way gyroscopes adapt to geodesics. For Ricci flat spacetimes.

On limit behavior of quasi-local mass for ellipsoids at spatial infinity

We discuss the spatial limit of the quasi-local mass for certain ellipsoids in an asymptotically flat static spherically symmetric spacetime.These ellipsoids are not nearly round but they are of interest as an admissible parametrized foliation defining the Arnowitt–Deser–Misner mass.The Hawking mass of this family of ellipsoids tends to-∞.In contrast,we show that the Hayward mass converges to a finite value.Moreover,a positive mass type theorem is established.The limit of the mass has a uniform positive lower bound no matter how oblate these ellipsoids are.This result could be extended for asymptotically Schwarzschild manifolds.And numerical simulation in the Schwarzschild spacetime illustrates that the Hayward mass is monotonically increasing near infinity.

Review of Mathematical Methodology for Electric Power Optimization Problems

Electric power system is a physical energy system consisting of power generation,substations,transmission,distribution,and consumption.The objective of power system optimization is to improve power system security,economy,and reliability.This paper summarizes the classical mathematical optimization methods and modeling techniques of power system optimization associated with system planning,operation,and control.Along with the development of electric power industry,the concept of Energy Internet is addressed,which consists of power network,gas network,and transportation network.Under such new environments,electric power optimization faces some challenging with respect to the cooperation of multi-energy networks.According to the design structure and operational characteristics of the Energy Internet,some research areas of electric power optimization are presented from the viewofmathematical optimization modeling and calculation.The aim is to provide some optimization methodology to solve the optimal issues of power system under the background of Energy Internet.

Coupled MRT Lattice Boltzmann Study of Electrokinetic Mixing of Power-Law Fluids in Microchannels with Heterogeneous Surface Potential

The electrokinetic mixing,as a powerful technique in microfluidic devices,is widely used in many applications.In this study,a more general dynamic model,which consists of Poisson equation,Nernst-Planck equation and Navier-Stokes equations,is used to describe the electrokinetic mixing of non-Newtonian fluids in microchannels.Furthermore,a coupled multiple-relaxation-time(MRT)lattice Boltzmann(LB)framework is developed to solve this complicated multi-physics transport phenomenon.In numerical simulations,we mainly consider the effects of the arrangement of nonuniform surface potentials and the power-law index on the mixing efficiency and the volumetric flow rate.Numerical results show that the mixing efficiency and the volumetric flow rate of shear-thinning fluids are higher than that of shear-thickening fluids under the same condition.It is also shown that for both types of fluids,there should be a balance between the mixing and liquid transport in electrokinetic microfluidics.

The Commuting Graphs on Dicyclic Groups

For a group G and a non-empty subsetΩof G,the commuting graph C(G,Ω)ofΩis a graph whose vertex set isΩand any two vertices are adjacent if and only if they commute in G.Define T4n=(a,b|a^(2)n=b^(4)=1,an=b2,b^(−1)ab=a^(−1)),the dicyclic group of order 4n(n≥3),which is also known as the generalized quaternion group.We mainly investigate the properties and metric dimension of the commuting graphs on the dicyclic group T4n.

Binary black hole systems do not interact in the Kastor-Traschen spacetime

The laser-interferometer gravitational-wave observatory (LIGO) has reported several observations of binary black hole mergers. Unfortunately, no exact solutions to the equations describing binary black hole systems exist. In particular, no exact solutions are available for the case in which a binary black hole system undergoes a merger;hence, we must rely on numerical calculations of the Maxwell-Einstein equations to construct the templates used to analyze gravitational wave data about suspected binary black hole systems [1,2].