A characteristic set method for solving boolean equations and applications in cryptanalysis of stream ciphers*

This paper presents a characteristic more efficient and has better properties than the set method for solving Boolean equations, which is general characteristic set method. In particular, the authors give a disjoint and monic zero decomposition algorithm for the zero set of a Boolean equation system and an explicit formula for the number of solutions of a Boolean equation system. The authors also prove that a characteristic set can be computed with a polynomial number of multiplications of Boolean polynomials in terms of the number of variables. As experiments, the proposed method is used to solve equations from cryptanalysis of a class of stream ciphers based on nonlinear filter generators. Extensive experiments show that the method is quite effective.     

A triangular decomposition algorithm for differential polynomial systems with elementary computation complexity

In this paper, a new triangular decomposition algorithm is proposed for ordinary differential polynomial systems, which has triple exponential computational complexity. The key idea is to eliminate one algebraic variable from a set of polynomials in one step using the theory of multivariate resultant. This seems to be the first differential triangular decomposition algorithm with elementary computation complexity.     

A note on two classes of Boolean functions with optimal algebraic immunity

Tu and Deng proposed a class of bent functions which are of optimal algebraic immunity under the assumption of a combinatorial conjecture.In this paper,the authors compute the dual of the Tu-Deng functions and then show that they are still of optimal algebraic immunity under the assumption of the same conjecture.For another class of Boolean functions constructed by Tang,et al.which are of optimal algebraic immunity with similar forms to Tu-Deng functions,the authors show that they are not bent functions by using some basic properties of binary complete Kloosterman sums.     

Nonlinear Inverse Relations of the Bell Polynomials via the Lagrange Inversion Formula(Ⅱ)

In this paper, by means of the classical Lagrange inversion formula, the authors establish a general nonlinear inverse relation as the solution to the problem proposed in the paper [J. Wang,Nonlinear inverse relations for the Bell polynomials via the Lagrange inversion formula, J. Integer Seq.,Vol. 22(2019), Article 19.3.8]. As applications of this inverse relation, the authors not only find a short proof of another nonlinear inverse relation due to Birmajer, et al.(2012), but also set up a few ...     

2-D algebraic test for robust stability of time-delay systems with interval parameters

1. INTRODUCTION The robust stability test of time-delay systems with interval parameters is to determine whether the eigenvalues of the characteristic polynomials of the systems are located at open left half complex plane. Different from classical 1-D systems, the eigenvalues of the characteristic polynomials are infinite, classical robust stability results (Kharitonov extreme test and Edge test) for 1-D systems are not suitable for the stability test of the characteristic polynomials of…     

任务主体二元约束下作战任务分解EVA方法

针对复杂作战任务分解中存在的随意性、不确定性问题, 综合考虑任务主体能力属性和结构特征等二元约束, 提出了一种由子任务集提取(extraction, E)、约束检验(verification, V)、子任务集调整(adjustment, A)等步骤递进循环形成的任务分解EVA方法。首先, 构建了全局任务空间, 提出基于任务匹配的子任务集提取方法; 其次, 针对任务主体能力属性和结构特征的二元约束, 建立了子任务集调整模型, 通过改进精英保留策略, 引入任务分解粒度和交叉变异概率动态调整策略, 提出了一种引进的非支配排序遗传算法-Ⅱ(improved non-dominated sorting genetic algorithm-Ⅱ, INSGA-Ⅱ)算法; 最后, 进行仿真实验, 验证了算法相较于传统多目标优化算法在解集多样性、收敛性和时间性能上的优势。研究结果表明, 所提方法能够使决策者依据任务主体实际自主调控任务分解结果, 在一定程度上克服了传统方法过度依赖主观经验, 忽略任务主体能力属性、结构特征约束的问题。     

THE MULTIPLICITY OF ZERO AND LIMIT CYCLES FOR ABEL EQUATIONS

In [1], AlwaSh and Lloyd investigated the nUmber of hot cycles surrounding a critical pointof focus take for polynOInial two dimensional systems. Under polar coordinates, the discussedsystems can be transformed into Abel equstion of the form:2 = a(t)z' g(t)z' 7(t)z, (1)with periodic boundary condition:z(0) = z(W). (2)When multiplicity p of solution z = 0 for equation (1) is larger than one, without lOss ofgeneralityt we can assume 7(t) = 0 for t E [0, w]. Let pm denote the m~ multiplic…     

Adaptive variational models for image decomposition combining staircase reduction and texture extraction

New models for image decomposition are proposed which separate an image into a cartoon, consisting only of geometric objects, and an oscillatory component, consisting of textures or noise. The proposed models are given in a variational formulation with adaptive regniarization norms for both the cartoon and texture parts. The adaptive behavior preserves key features such as object boundaries and textures while avoiding staircasing in what should be smooth regions. This decomposition is computed by minimizing a convex functional which depends on the two variables u and v, alternatively in each variable. Experimental results and comparisons to validate the proposed models are presented.     

Semiparametric analysis of isotonic errors-in-variables regression models with randomly right censored response

This paper considers the estimation of a semiparametric isotonic regression model when the covariates are measured with additive errors and the response is randomly right censored by a censoring time. The authors show that the proposed estimator of the regression parameter is rootn consistent and asymptotically normal. The authors also show that the isotonic estimator of the functional component, at a fixed point, is cubic root-n consistent and converges in distribution to the slope at zero of the greatest convex minorant of the sum of a two-sided standard Brownian motion and the square of the time parameter. A simulation study is carried out to investigate the performance of the estimators proposed in this article.     

Discovering non-terminating inputs for multi-path polynomial programs

This paper investigates the termination problems of multi-path polynomial programs （MPPs） with equational loop guards. To establish sufficient conditions for termination and nontermination simultaneously, the authors propose the notion of strong/weak non-termination which under/over- approximates non-termination. Based on polynomial ideal theory, the authors show that the set of all strong non-terminating inputs （SNTI） and weak non-terminating inputs （WNTI） both correspond to tile real varieties of certain polynomial ideals. Furthermore, the authors prove that the variety of SNTI is computable, and under some sufficient conditions the variety of WNTI is also computable. Then by checking the computed SNTI and WNTI varieties in parallel, termination properties of a consid- ered MPP can be asserted. As a consequence, the authors establish a new framework for termination analysis of MPPs.     

Normalization in Riemann Tensor Polynomial Ring

It is one of the oldest research topics in computer algebra to determine the equivalence of Riemann tensor indexed polynomials. However, it remains to be a challenging problem since Grbner basis theory is not yet powerful enough to deal with ideals that cannot be finitely generated. This paper solves the problem by extending Grbner basis theory. First, the polynomials are described via an infinitely generated free commutative monoid ring. The authors then provide a decomposed form of the Grbner basis of the defining syzygy set in each restricted ring. The canonical form proves to be the normal form with respect to the Grbner basis in the fundamental restricted ring, which allows one to determine the equivalence of polynomials. Finally, in order to simplify the computation of canonical form, the authors find the minimal restricted ring.     

Detecting JPEG image forgery based on double compression

Detecting the forgery parts from a double compressed image is very important and urgent work for blind authentication. A very simple and efficient method for accomplishing the task is proposed. Firstly, the probabilistic model with periodic effects in double quantization is analyzed, and the probability of quantized DCT coefficients in each block is calculated over the entire image. Secondly, the posteriori probability of each block is computed according to Bayesian theory and the results mentioned in first part. Then the mean and variance of the posteriori probability are to be used for judging whether the target block is tampered. Finally, the mathematical morphology operations are performed to reduce the false alarm probability. Experimental results show that the method can exactly locate the doctored part, and through the experiment it is also found that for detecting the tampered regions, the higher the second compression quality is, the more exact the detection efficiency is.     

An Efficient Multiple Imputation Approach for Estimating Equations with Response Missing at Random and High-Dimensional Covariates

Empirical-likelihood-based inference for parameters defined by the general estimating equations of Qin and Lawless(1994) remains an active research topic. When the response is missing at random(MAR) and the dimension of covariate is not low, the authors propose a two-stage estimation procedure by using the dimension-reduced kernel estimators in conjunction with an unbiased estimating function based on augmented inverse probability weighting and multiple imputation(AIPW-MI) methods. The authors show that the resulting estimator achieves consistency and asymptotic normality. In addition, the corresponding empirical likelihood ratio statistics asymptotically follow central chi-square distributions when evaluated at the true parameter. The finite-sample performance of the proposed estimator is studied through simulation, and an application to HIV-CD4 data set is also presented.     

基于Shifted Legendre正交多项式的迭代学习控制方法

考虑用迭代学习控制方法来解决一类线性时变连续系统的终端控制问题。运用ShiftedLegendre正交多项式的展开技术,利用其正交性和边值条件,将线性时变系统的微分方程转化为代数方程,避免了在判断误差收敛条件的过程中求解线性时变系统状态转移矩阵。并采用高阶学习律来求控制输入的ShiftedLegendre系数向量,仿真实例验证了该方法的有效性。     

基于分解进化多目标优化算法的火力分配问题

战前制定合理的火力分配方案,可以优化资源配置,用最小的代价获取最大的战场收益。综合考虑攻击、资源和毁伤概率等约束条件,建立了火力分配多目标优化数学模型。提出了一种求解火力分配模型的分解进化多目标优化算法,并设计了不可行解修复方法。仿真实验得出两个结论,一是不可行解修复方法可以显著提高算法的收敛性;二是在解决火力分配优化问题上,所提算法具有较好的收敛性和分散性,采用合适的分解方法可以有效提高算法的性能。     

HAJóS'''' CONJECTURE AND CONNECTIVITY OF EULERIAN GRAPHS

Hajos' conjecture asserts that a simple eulerian graph on n vertices can be decomposed into at most n-1/2 circuits. In this paper, we propose a new conjecture which is equivalent to Hajos' conjecture, and show that to prove Hajos' conjecture, it is sufficient to prove this new conjecture for 3-connected graphs. Furthermore, a special 3-cut is considered also.     

THE ASCENDING SUBGRAPH DECOMPOSITION OF K_n-H_(2n-1)

1.IntroductiollAlavi,Y.etal.presentedaconceptofsubgraphdecompositionin[1],whichiscalledascendingsubgraphdecomposition(abbreviatedASD).GivenagraphGwithqedges,C: ,5q5C: ,GissaidtohaveanASD,ifthereisnsuchthatGcanbedecomposedintonsubgraphsGIjGi,''3G.withouti…     

A New RCS Statistical Model of Radar Target

In this paper, the drawbacks of conventional target fluctuation models used in radar target modeling are set out. It is usually difficult to statistically model a real target because there are very few parameters which can be used to approximate the probability density function (PDF) of a real target's radar cross section (RCS) in conventional target models. A new method of statistical modeling is suggested, according to which the first nth central moment of real target's RCS, combined with the Legendre orthogonal polynomials, is used to reconstruct the PDF of the target's RCS. The relationship between the coefficients of the Legendre polynomials and the central moments of RCS are deduced mathematically. Through a practical computing example, the error-of-fit is shown as a function of the orders of Legendre coefficients. By comparing the errors-of-fit caused by both the new model and the conventional models, it is concluded that the new nonparametric method for statistical modeling of radar targets is s     

Variable Selection via Generalized SELO-Penalized Cox Regression Models

The seamless-L_0(SELO) penalty is a smooth function that very closely resembles the L_0 penalty, which has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selection. In this paper, the authors first generalize the SELO penalty to a class of penalties retaining good features of SELO, and then develop variable selection and parameter estimation in Cox models using the proposed generalized SELO(GSELO) penalized log partial likelihood(PPL) approach. The authors show that the GSELO-PPL procedure possesses the oracle property with a diverging number of predictors under certain mild, interpretable regularity conditions. The entire path of GSELO-PPL estimates can be efficiently computed through a smoothing quasi-Newton(SQN) with continuation algorithm. The authors propose a consistent modified BIC(MBIC) tuning parameter selector for GSELO-PPL, and show that under some regularity conditions, the GSELOPPL-MBIC procedure consistently identifies the true model. Simulation studies and real data analysis are conducted to evaluate the finite sample performance of the proposed method.     

On the nonexistence of nontrivial small cycles of the µ function in 3x+1 conjecture

This paper studies the property of the recursive sequences in the 3x+ 1 conjecture.The authors introduce the concept ofμfunction,with which the 3x + 1 conjecture can be transformed into two other conjectures:one is eventually periodic conjecture of theμfunction and the other is periodic point conjecture.The authors prove that the 3x + 1 conjecture is equivalent to the two conjectures above.In 2007,J.L.Simons proved the non-existence of nontrivial 2-cycle for the T function.In this paper,the authors prove that theμfunction has no l-periodic points for 2≤l≤12.In 2005, J.L.Simons and B.M.M de Weger proved that there is no nontrivial 2-cycle for the T function for l≤68,and in this paper,the authors prove that there is no nontrivial l-cycle for theμfunction for 2≤l≤102.