“圆方率”的探究及应用

对于小学生来说，人人都知道：圆的周长与直径的比值就是圆周率。它是一个无限不循环小数，通常用字母π表示。但却未必知道：“圆方率”是怎么回事?

An approach to improving maneuver performance of coning algorithm

Aiming to improve the maneuver performance of the strapdown inertial navigation attitude coning algorithm a new coning correction structure is constructed by adding a sample to the traditional compressed coning correction structure. According to the given definition of classical coning motion the residual coning correction error based on the new coning correction structure is derived. On the basis of the new structure the frequency Taylor series method is used for designing a coning correction structure coefficient and then a new coning algorithm is obtained.Two types of error models are defined for the coning algorithm performance evaluation under coning environments and maneuver environments respectively.Simulation results indicate that the maneuver accuracy of the new 4-sample coning algorithm is almost double that of the traditional compressed 4-sample coning algorithm. The new coning algorithm has an improved maneuver performance while maintaining coning performance compared to the traditional compressed coning algorithm.

Azimuthal cement evaluation with an acoustic phased-arc array transmitter:numerical simulations and field tests

We developed a novel cement evaluation logging tool,named the azimuthally acoustic bond tool（AABT）,which uses a phased-arc array transmitter with azimuthal detection capability.We combined numerical simulations and field tests to verify the AABT tool.The numerical simulation results showed that the radiation direction of the subarray corresponding to the maximum amplitude of the first arrival matches the azimuth of the channeling when it is behind the casing.With larger channeling size in the circumferential direction,the amplitude difference of the casing wave at different azimuths becomes more evident.The test results showed that the AABT can accurately locate the casing collars and evaluate the cement bond quality with azimuthal resolution at the casing-cement interface,and can visualize the size,depth,and azimuth of channeling.In the case of good casingcement bonding,the AABT can further evaluate the cement bond quality at the cementformation interface with azimuthal resolution by using the amplitude map and the velocity of the formation wave.

A Public Verifiable Identity Based Signcryption in the Random Oracle Model

Since Libert and Quisquater's identity based signcryption scheme cannot provide public verifiability after research, the paper proposes a new identity based signcryption scheme. The scheme uses quadratic residue and pairings over elliptic curves to realize public verifiability. By analysis the scheme is proved to be more efficient than Libert and Quisquater's scheme. Moreover, a security proof of the original scheme is presented in the random oracle model.

A priori Estimates and Existence for a Class of Fully Nonlinear Elliptic Equations in Conformal Geometry

In this paper we prove the interior gradient and second derivative estimates for a class of fully nonlinear elliptic equations determined by symmetric functions of eigenvalues of the Ricci or Schouten tensors. As an application we prove the existence of solutions to the equations wb.en the manifold is locally conformally flat or the Ricci curvature is positive.

Strong Unique Continuation of Sub-elliptic Operator on the Heisenberg Group

In this paper, the Almgren＇s frequency function of the following sub-elliptic equation with singular potential on the Heisenberg group：-Cu＋V（z,t）u=Xi（aij（z,t）Xju）＋V（z,t）u=0 is introduced. The monotonicity property of the frequency is established and a doubling condition is obtained. Consequently, a quantitative proof of the strong unique continuation property for such equation is given.