A Construction of 1-Resilient Boolean Functions with Good Cryptographic Properties

This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic immunity are also considered. A sufficient condition of the modified functions with optimal algebraic degree in terms of the Siegenthaler bound is proposed. The authors obtain a lower bound on the nonlinearity of the Tang-Carlet-Tang functions, which is slightly better than the known result. If the authors do not break the “continuity” of the support and zero sets, the functions constructed in this paper have suboptimal algebraic immunity. Finally, four specific classes of 1-resilient Boolean functions constructed from this construction and with the mentioned good cryptographic properties are proposed. Experimental results show that there are many 1-resilient Boolean functions have higher nonlinearities than known 1-resilient functions modified by Tu-Deng and Tang-Carlet-Tang functions.     

On Software Development of Characteristic Set Method

1　IntroductionIn mathematics,there are two distinctsystem ofthoughts and methods:axiomatic methodand mechanical method. As consequences,there are two kinds of major activities,one istheorem proving and another is equation solving.In contrast to the Eucli…     

Elimination Theory in Differential and Difference Algebra

Elimination theory is central in differential and difference algebra. The Wu-Ritt characteristic set method, the resultant and the Chow form are three fundamental tools in the elimination theory for algebraic differential or difference equations. In this paper, the authors mainly present a survey of the existing work on the theory of characteristic set methods for differential and difference systems,the theory of differential Chow forms, and the theory of sparse differential and difference resultants.     

水平集方法中窄带构造技术

提出了距离模板方法并从时间复杂度、窄带宽度以及零水平集点数对窄带生成的影响等方面与快进方法、快速扫描方法进行了比较;在分析快进方法的基础上,给出了一种窄带构造算法;改进了全局快速扫描算法,以用于生成窄带。2D图像分割与3D表面重建的仿真实验表明,距离模板方法能够较快地分割图像;快进和快速扫描方法适合于表面重建等3D应用。     

Recent progress on controllability/observability for systems governed by partial differential equations

<正> The main purpose of this paper is to overview some recent methods and results on controllability/observability problems for systems governed by partial differential equations.First,the authorsreview the theory for linear partial differential equations,including the iteration method for the nullcontrollability of the time-invariant heat equation and the Rellich-type multiplier method for the exactcontrollability of the time-invariant wave equation,and especially a unified controllability/observabilitytheory for parabolic and hyperbolic equations based on a global Carleman estimate.Then,the authorspresent sharp global controllability results for both semi-linear parabolic and hyperbolic equations,based on linearization approach,sharp observability estimates for the corresponding linearized systemsand the fixed point argument.Finally,the authors survey the local null controllability resultfor a class of quasilinear parabolic equations based on the global Carleman estimate,and the localexact controllability result for general hyperbolic equations based on a new unbounded perturbationtechnique.     

Resultant elimination via implicit equation interpolation

It is well known that resultant elimination is an effective method of solving multivariate polynomial equations. In this paper, instead of computing the target resultants via variable by variable elimination, the authors combine multivariate implicit equation interpolation and multivariate resultant elimination to compute the reduced resultants, in which the technique of multivariate implicit equation interpolation is achieved by some high probability algorithms on multivariate polynomial interpolation and univariate rational function interpolation. As an application of resultant elimination, the authors illustrate the proposed algorithm on three well-known unsolved combinatorial geometric optimization problems. The experiments show that the proposed approach of resultant elimination is more efficient than some existing resultant elimination methods on these difficult problems.     

B-spline patches and transfinite interpolation method for PDE controlled simulation

This paper is to discuss an approach which combines B-spline patches and transfinite interpolation to establish a linear algebraic system for solving partial differential equations and modify the WEB-spline method developed by Klaus Hollig to derive this new idea.First of all,the authors replace the R-function method with transfinite interpolation to build a function which vanishes on boundaries. Secondly,the authors simulate the partial differential equation by directly applying differential operators to basis functions,which is similar to the RBF method rather than Hollig’s method.These new strategies then make the constructing of bases and the linear system much more straightforward.And as the interpolation is brought in,the design of schemes for solving practical PDEs can be more flexible. This new method is easy to carry out and suitable for simulations in the fields such as graphics to achieve rapid rendering.Especially when the specified precision is not very high,this method performs much faster than WEB-spline method.     

Results on permutation symmetric Boolean functions

This paper provides a systematic method on the enumeration of various permutation symmetric Boolean functions. The results play a crucial role on the search of permutation symmetric Boolean functions with good cryptographic properties. The proposed method is algebraic in nature. As a by-product, the authors correct and generalize the corresponding results of St?nic? and Maitra (2008). Further, the authors give a complete classification of block-symmetric bent functions based on the results of Zhao and Li (2006), and the result is the only one classification of a certain class of permutation symmetric bent functions after the classification of symmetric bent functions proposed by Savicky (1994).     

Well-Posedness of Fully Coupled Linear Forward-Backward Stochastic Differential Equations

This paper studies the well-posedness of fully coupled linear forward-backward stochastic differential equations(FBSDEs). The authors introduce two main methods-the method of continuation under monotonicity conditions and the unified approach-to ensure the existence and uniqueness of solutions of fully coupled linear FBSDEs. The authors show that the first method(the method of continuation under monotonicity conditions) can be deduced as a special case of the second method(the unified approach). An example is given to illustrate it in linear FBSDEs case. And then, a linear transformation method in virtue of the non-degeneracy of transformation matrix is introduced for cases that the linear FBSDEs can not be dealt with by the the method of continuation under monotonicity conditions and the unified approach directly. As a powerful supplement to the the method of continuation under monotonicity conditions and the unified approach, linear transformation method overall develops the well-posedness theory of fully coupled linear forward-backward stochastic differential equations which have potential applications in optimal control and partial differential equation theory.     

Maximum principle for partially-observed optimal control problems of stochastic delay systems

This paper is concerned with partially-observed optimal control problems for stochastic delay systems. Combining Girsanov’s theorem with a standard variational technique, the authors obtain a maximum principle on the assumption that the system equation contains time delay and the control domain is convex. The related adjoint processes are characterized as solutions to anticipated backward stochastic differential equations in finite-dimensional spaces. Then, the proposed theoretical result is applied to study partially-observed linear-quadratic optimal control problem for stochastic delay system and an explicit observable control variable is given.     

基于矩阵分解的惯导安装误差矩阵解耦方法

针对捷联惯性导航系统级标定中安装误差矩阵存在3组耦合关系问题,提出一种基于矩阵分解的解耦方法。该方法将安装误差矩阵分解为对称误差矩阵和斜对称误差矩阵后,推导其对惯性导航姿态方程和速度方程的影响,揭露系统级标定中安装误差矩阵存在耦合的原因——陀螺仪表组和加速度计仪表组的斜对称误差对误差方程的影响是耦合的,进而提出适当选取体坐标系使得陀螺仪表组的斜对称误差矩阵为0的解耦方法。该解耦方法是一种均值分配方法,与传统解耦方法相比能减少系统运算中的二阶舍项误差。仿真实例说明了该解耦方法是有效的。     

基于拟牛顿算法的自由下落猫的非完整运动规划

研究猫在自由下落时四肢着地的姿态运动规划问题。自由落体的猫在空中转体运动由于角动量守恒，姿态运动方程呈现为非完整形式。系统的控制问题可转化为无漂移系统的非完整运动规划问题。首先导出由两个对称刚体组成的力学模型的非完整姿态运动方程。利用最优控制理论和最优化技术，采用输入参数化的方法将连续的最优控制问题转化为离散的最优控制问题。基于拟牛顿方法，给出自由落体猫在空中姿态非完整运动规划算法。最后对自由落体猫作了数值仿真试验，仿真结果验证了该算法的有效性。     

SET COVERING-BASED TOPSIS METHOD FOR SLOVING SUP-T EQUATION CONSTRAINED MULTI-OBJECTIVE OPTIMIZATION PROBLEMS

This paper considers solving a multi-objective optimization problem with sup-r equation constraints.A set covering-based technique for order of preference by similarity to the ideal solution is proposed for solving such a problem.It is shown that a compromise solution of the sup-r equation constrained multi-objective optimization problem can be obtained by solving an associated set covering problem.A surrogate heuristic is then applied to solve the resulting optimization problem.Numerical experiments on solving randomly generated multi-objective optimization problems with sup-T equation constraints are included.Our computational results confirm the efficiency of the proposed method and show its potential for solving large scale sup-T equation constrained multi-objective optimization problems.     

THE RATIONALITY OF THE DISCRETE ORDINATES METHOD FOR TIME DEPENDENT NEUTRON TRANSPORT EQUATION

ＴＨＥＲＡＴＩＯＮＡＬＩＴＹＯＦＴＨＥＤＩＳＣＲＥＴＥＯＲＤＩＮＡＴＥＳＭＥＴＨＯＤＦＯＲＴＩＭＥＤＥＰＥＮＤＥＮＴＮＥＵＴＲＯＮＴＲＡＮＳＰＯＲＴＥＱＵＡＴＩＯＮＬＩＸｕｅｚｈｉ；ＺＨＵＧｕａｎｇｔｉａｎ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉ...     

ON THE THEORY OF RESOLVENTS AND ITS APPLICATIONS

1.IntroductionSomefrequentlyusedalgebraicalgorithmssharethesamepropertythattheytransformasetofpolynomialequationstoasinglepolynomialequationsuchthatthezerosetofthepolynomialsetandthehypersurfacedefinedbythesinglepolynomialareequivalentincertainsense.FOralgorithmswiththisproperty,wemaymention'thealgorithmtofindaprimitiveelementforafinitelygeneratedalgebraicextensionfield[1],thealgorithmtofindaplanecurvewhichisbirationaltoaspacealgebraiccur.e[2]!etc.Inthispaper,wepresentageneralalgorithmwhichcan…     

A Legendre Galerkin spectral method for optimal control problems

This paper considers the Legendre Galerkin spectral approximation for the unconstrained optimal control problems. The authors derive a posteriori error estimate for the spectral approximation scheme of optimal control problem. By choosing the appropriate basis functions, the stiff matrix of the discretization equations is sparse. And the authors use the Fast Legendre Transform to improve the efficiency of this method. Two numerical experiments demonstrating our theoretical results are presented.     

An Additive-Multiplicative Cox-Aalen Subdistribution Hazard Model for Competing Risks Data

This paper proposes a flexible additive-multiplicative Cox-Aalen hazard model which allows time-varying covariate effects for the subdistribution in a competing risks study. Weighted estimating equation approaches under an covariates-dependent adjusted weight by fitting the Cox proportional hazard model for the censoring distribution are established for inference on the model parametric and nonparametric components. In addition, large number properties are presented and the finite sample behavior of the proposed estimators is evaluated through simulation studies, estimators from the proposed method perform satisfactorily on reduction of the bias. The authors apply our model to a competing risks data set from a tamoxifen trail for breast cancer study.     

矿井通风网络最小独立路集不交化可靠度的计算

运用可靠性工程理论及不交型积之和定律 ,在大型网络系统可靠度计算的基础上 ,提出了矿井通风网络系统最大线性无关最小独立路集予以真子集涤除的不交化可靠度计算的实现方法 .根据不交化可靠度计算法 ,当最小独立路集按所含网络分支的多少进行升序排列时 ,还可进一步减少中间过程的计算量 ,从而达到最佳不交化简化计算的效果 .实例分析表明 :采用升序排列的最小独立路集并按不交型积之和定理予以真子集涤除的不交化处理后 ,不仅计算值等同于一般网络分析中用全概率公式计算的矿井通风网络系统可靠度 ,而且 ,计算工作量大为简化 .     

Optimal Output Tracking Control and Stabilization of Networked Control Systems with Packet Losses

This paper studies the optimal output tracking control and stabilization for networked control systems with packet losses via output feedback control. Both finite-horizon and infinite-horizon cases are considered. For the finite-horizon case, the authors introduce an augmented system according to the state variable and the reference trajectory for the first time. Based on a set of difference Riccati equations, an optimal output feedback tracking controller is proposed by applying the stochastic maximum principle. And an optimal estimator is presented. For the infinite-horizon case, a necessary and sufficient condition for the stabilization of the system is provided. And an optimal output feedback stabilizing tracking controller is obtained by establishing a set of algebraic Riccati equations. Finally,numerical examples are given to verify the proposed results.     

A matrix construction of Boolean functions with maximum algebraic immunity

Boolean functions used in a cryptographic system should have high algebraic immunity to resist algebraic attacks.This paper presents a matrix method for constructing balanced Boolean functions achieving maximum algebraic immunity.