两类多输出逻辑函数的关系

首次给出了多输出广义部分Bent函数的定义并论证了其的存在,得到了多输出广义部分Bent函数的等价判别条件,给出了多输出p值广义部分Bent函数与多输出p值广义Bent函数的关系,并讨论了这两者的广义一阶Chrestenson谱的关系,为多输出p值广义部分Bent函数的构造提供了一种方法。     

Gbent函数的构造

基于研究布尔函数在子空间的限制,得到关于Gbent函数的一个充分必要条件。给出了两类简单的正则的Gbent函数。在此基础上,通过间接构造Bent函数的方法,利用已知的Gbent函数构造出了更多的Gbent函数。     

The use of walsh functions in multivariable limit cycle prediction

The describing function method has played a leading role in the prediction of limit cycles in scalar systems; in recent years this approach has been extended to the multivariable case. Derived techniques assume the nonlinearity inputs to be sinusoidal. However, this condition is not always satisfied, and as an alternative, the present paper considers the use of a method which is based on a set of non-sinusoidal functions. Novel concepts related to the characteristic loci are defined and employed for the derivation of new graphical tests.     

Analytical and numerical results onM-variable generalized Bessel functions

Recently, some multivariable special functions have been obtained by generalizing functions of Bessel type. Here, we continue the treatment of these functions starting fromJ _n (x, y; i), which is of noticeable practical interest. Finally, we consider the cases of functionsJ _n(x₁, x₂,..., x_M) and the related modified version,I _n(x₁, x₂,..., x_M), with two significant physical applications. Calculations of multivariable generalized Bessel functions are discussed and numerical results are given forJ _n(x₁,x₂;i), withn=0, 1, in a region of interest.     

奇数变元plateaued函数代数免疫性质研究

Plateaued函数是包含Bent函数和部分Bent函数的更大函数类,具有许多优良的密码学性质。基于布尔函数非线性度与代数免疫阶之间的关系,利用Walsh谱等工具,讨论奇数变元的plateaued函数的代数免疫性质,得到其存在低次零化子的一个充分条件,并进一步刻画变元个数n与plateaued函数的阶r之间的具体关系,利用此关系可确定函数代数免疫阶的上界。     

基于广义松弛方法的快速均值偏移算法的研究

针对均值偏移算法收敛性慢的缺点,通过对加速均值偏移方法的研究,将优化算法中的松弛方法扩展为广义的松弛方法,并给出确定对角矩阵参数的方法;然后对收敛准则进行了修改．在此基础上,提出了基于广义松弛方法的均值偏移算法,并通过大量的聚类实验和图像分割实验验证了所提出算法的有效性．     

Generation of sign Walsh spectra from disjoint cubes of Boolean functions

A new algorithm is given that converts a reduced representation of Boolean functions in the form of disjoint cubes to sign Walsh spectra. Since the known algorithms that generate sign Walsh spectra always start from the truth table of Boolean functions, the method presented computes faster with a smaller computer memory. The method is especially efficient for such Boolean functions that are described by only few disjoint cubes.     

The global avalanche characteristics of two Boolean functions and algebraic immunity

The global avalanche characteristics criterion of two Boolean functions was introduced by Zhou et al. [On the global avalanche characteristics criterion of two Boolean functions and the higher order nonlinearity, Inform. Sci. 180(2) (2010), pp. 256–265] to measure the cryptographic behaviour in a global characteristic. The two indicators σ _{f, g} and Δ _{f, g} of Boolean functions f and g were presented. In this paper, a new upper bound on σ _{f, g} is derived, and a technique on constructing Boolean functions to attain the lower bound on the sum-of-squares indicator is described by using the disjoint spectra method. Some new upper bounds on Δ _{f, g} and σ _{f, g} are deduced for two special Boolean functions. Two relationships between σ _{f, g} and algebraic immunity of the two Boolean functions are obtained. Finally, some links among different cryptographic indicators are shown.     

On renamable Horn and generalized Horn functions

A Boolean function in disjunctive normal form (DNF) is aHorn function if each of its elementary conjunctions involves at most one complemented variable. Ageneralized Horn function is constructed from a Horn function by disjuncting a nested set of complemented variables to it. The satisfiability problem is solvable in polynomial time for both Horn and generalized Horn functions. A Boolean function in DNF is said to berenamable Horn if it is Horn after complementation of some variables. Succinct mathematical characterizations and linear-time algorithms for recognizing renamable Horn and generalized Horn functions are given in this paper. The algorithm for recognizing renamable Horn functions gives a new method to test 2-SAT. Some computational results are also given.The authors were supported in part by the Office of Naval Research under University Research Initiative grant number N00014-86-K-0689. Chandru was also supported by NSF grant number DMC 88-07550.The authors gratefully acknowledge the partial support of NSF (Grant DMS 89-06870) and AFOSR (Grant 89-0066 and 89-0512).     

Certain classes of generating functions for the Jacobi and related hypergeometric polynomials

For a certain class of generalized hypergeometric polynomials, the authors first derive a general theorem on bilinear, bilateral, and mixed multilateral generating functions and then apply these generating functions in order to deduce the corresponding results for the classical Jacobi and Laguerre polynomials. They also consider several linear generating functions for these polynomials as well as for some multivariable Jacobi and multivariable Laguerre polynomials which were investigated in recent years. Some of the linear generating functions, presented in this paper, are associated with the Stirling numbers of the second kind.     

Constructions of q-ary functions with good global avalanche characteristics

In this paper, we construct two classes of q-ary balanced functions which have good global avalanche characteristics (GAC) measured in terms of sum-of-squares-modulus indicator (SSMI), modulus indicator(MI), and propagation criterion (PC). We show that the SSMI, MI, and PC of q-ary functions are invariant under affine transformations. Also, we give a construction of q-ary s-plateaued functions and obtain their SSMI. We provide a relationship between the autocorrelation spectrum of a cubic Boolean function and the dimension of the kernel of the bilinear form associated with the derivative of the function. Using this result, we identify several classes of cubic semi-bent Boolean functions which have good bounds on their SSMI and MI, and hence show good behaviour with respect to the GAC.     

A new recurslve method for the analysis of linear time invariant dynamic systems via double-term triangular functions （DTTF） in state space environment

This paper presents a new recursive method for system analysis via double-term triangular functions (DTTF) in state space environment. The proposed method uses orthogonal triangular function sets and proves to be more accurate as compared to single term Walsh series (STWS) method with respect to mean integral square error (MISE). This has been established theoretically and comparison of error with respect to MISE is presented for clarity. A numerical example is treated to establish the proposed method. Relevant curves for the solutions of states of the dynamic system are also presented with plots of percentage error for DTTF-based analysis.     

改进的广义隶属函数法及其FPGA实现

针对工程应用的实际,首先改进了广义隶属函数法,在Matlab中进行了算法仿真。将广义隶属函数法与FPGA的特点相结合,设计了一种广义隶属函数型模糊控制器,并将控制算法在FPGA上实现。     

The positive real lemma and construction of all realizations of generalized positive rational functions

We here extend the well known positive real lemma (also known as the Kalman-Yakubovich-Popov lemma) to a complex matrix-valued generalized positive rational function, when non-minimal realizations are considered. All state space realizations are partitioned into subsets, each is identified with a set of matrices satisfying the same Lyapunov inclusion. Thus, each subset forms a convex invertible cone, and is in fact is replica of all realizations of positive functions of the same dimensions. We then exploit this result to provide an easy construction procedure of all (not necessarily minimal) state space realizations of generalized positive functions. As a by-product, this approach enables us to characterize systems which can be brought, through a static output feedback, to be generalized positive.     

A new approach to the epsilon expansion of generalized hypergeometric functions

Assuming that the parameters of a generalized hypergeometric function depend linearly on a small variable ε$\epsilon$, the successive derivatives of the function with respect to that small variable are evaluated at ε=0$\epsilon =0$ to obtain the coefficients of the ε$\epsilon$-expansion of the function. The procedure, which is quite naive, benefits from simple explicit expressions of the derivatives, to any order, of the Pochhammer and reciprocal Pochhammer symbols with respect to their argument. The algorithm may be used algebraically, irrespective of the values of the parameters. It reproduces the exact results obtained by other authors in cases of especially simple parameters. Implemented numerically, the procedure improves considerably, for higher orders in ε$\epsilon$, the numerical expansions given by other methods.     

Error bound for the generalized complementarity problem with analytic functions

In this paper, we consider the global error bound for the generalized complementarity problem (GCP) with analytic functions. Based on the new technique, we establish computable global error bound under milder conditions, which refines the previously known results.     

Structural modification of systems using discretization and generalized sampled-data hold functions

This paper investigates the decentralized control of LTI continuous-time plants using generalized sampled-data hold functions (GSHF). GSHFs can be used to modify the structure of the digraph of the resultant discrete plant, by removing certain interconnections in the discrete-time equivalent model to form a hierarchical system model of the plant. This is a new application of discretization and has, as its motivation, the design of decentralized controllers using centralized methods.     

Some properties of functions related to the gamma, psi and tetragamma functions

In this paper, some properties associated with the complete monotonicity and the logarithmically complete monotonicity of functions related to the gamma, psi and tetragamma functions are obtained. Relevant connections of the results presented here with those derived in earlier works are also pointed out.     

UFPA器件的新型微桥结构设计及其有限元分析

提出一种应用于非致冷红外焦平面(UFPA)器件的U形三层微桥结构,其单元尺寸为25μm×25μm、占空比高达90%、支撑稳固且响应率高。采用有限元分析法对其进行力、热分析,并与雷神公司报导的微桥结构[1]进行比较,证明其具有稳定的力学支撑和良好的热性能;引入经典光学膜系分析方法,在8~14μm波段内获得80%以上平均红外吸收率。