The Set of Hausdorff Continuous Functions— The Largest Linear Space of Interval Functions

Hausdorff continuous (H-continuous) functions are special interval-valued functions which are commonly used in practice, e.g. histograms are such functions. However, in order to avoid arithmetic operations with intervals, such functions are traditionally treated by means of corresponding semi-continuous functions, which are real-valued functions. One difficulty in using H-continuous functions is that, if we add two H-continuous functions that have interval values at same argument using point-wise interval arithmetic, then we may obtain as a result an interval function which is not H-continuous. In this work we define addition so that the set of H-continuous functions is closed under this operation. Moreover, the set of H-continuous functions is turned into a linear space. It has been also proved that this space is the largest linear space of interval functions. These results make H-continuous functions an attractive tool in real analysis and provides a bridge between real and interval analysis.     

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。     

Humanoid walking pattern generation based on model predictive control approximated with basis functions

This paper proposes a real-time walking pattern generator (WPG) based on model predictive control (MPC). Since reducing the calculation time is a crucial problem in real-time WPG, we consider introducing basis functions to reduce the number of control input. The control inputs in the MPC are described by a series of basis functions. Compared with the standard discrete-time MPC formulation, the approach with basis functions requires fewer optimization variables at the cost of decreasing precision. In order to find an appropriate trade-off, two basis functions named Laguerre functions and Haar functions, are tested in this paper. MPC with Laguerre functions decreases more computational load while MPC with Haar functions offers a more accurate solution. The approach is not restricted to Laguerre functions or Haar functions, users can select their own basis functions for different applications and preferences.     

Nearly bent functions

In this paper, we define a large class of almost balanced Boolean functions called nearly bent functions. These functions lie at large Hamming distance to all affine functions and preserve a high level of algebraic degree. Then a construction of nearly bent functions is described. It is shown that the constructed functions have good global avalanche characteristic properties. In the concluding remarks, we show that nearly bent functions have good stability.     

基于AHP模型的政府系统职能评价方法的研究

政府人力资源系统与政府职能密切相关,研究政府人力资源必须从政府职能的视角对政府系统的要素与职能的关系进行分析.在政府系统的环境适应性概念模型的基础之上,通过对政府系统的政治职能、经济职能、社会职能、文化职能的分析,研究了政府系统要素与职能、规模关系,明确了政府系统的目标是政府系统内部结构分析的出发点,是政府系统目的的具体化的特征,确定了政府系统的目标集,构建了政府职能评价的递级层次结构模型,并通过AHP方法,构建了政府系统职能评价模型.     

周期B样条基函数系数的并行算法

在现有周期B样条插值方法中,需要用迭代算法确定B样条基函数系数。针对现有方法的不足,建立B样条基函数系数的并行算法。首先构造周期区域的正交B样条基,得出正交B样条基函数系数的并行算法;进一步利用正交B样条基函数系数与B样条基函数系数的关系,得出B样条基函数系数的并行算法;最后推导二阶、三阶、四阶周期插值B样条基函数系数及插值点函数值的显式算式。实验证明了该方法在实现B样条基函数系数快速并行算法的同时保持了B样条基函数简单的函数关系。     

The novel generating algorithm and properties of hybrid-P-ary generalized bridge functions

1 Introduction Copy theory is a kind of signal generation technology, built on the research of Walsh function. The main content of the copy theory includes generating non-sine orthogonal functions, utilizing shift and symmetric copy methods and control in…     

互补对称布尔函数的非线性度

互补对称布尔函数是一类特殊的对称布尔函数。在所有代数免疫最优的对称布尔函数中,有相当的比例均属此类函数。特别是当变元数量为2m元时,有2/3比例的代数免疫最优对称布尔函数都是互补对称布尔函数。通过布尔函数非线性度、Walsh谱和Krawtchouk多项式间的关系,计算出互补对称布尔函数的非线性度。结果表明,任意n元互补对称布尔函数的非线性度为2n-1-1/2[nn/2]     

C语言中函数编写方法的分析与探讨

函数是C语言学习的难点和重点,通过分析函数的结构,将函数编写中难以确定的问题进行分解、细化。按照返回值的个数将函数分为:无返回值函数、单反回值函数、多返回值函数三种类型。对这三种类型函数的设计方法分别举例分析和说明,详细阐述了函数编写的具体过程。     

二进神经网络中SP函数的一般判别和构造方法

SP函数是一类具有明确逻辑意义的线性可分结构系,PSP函数是SP函数的特殊子集. 文中讨论了二进神经元对SP函数和PSP函数的表达问题,通过研究PSP函数分类超平面的某 些性质,建立了SP函数和PSP函数的一般判别和构造方法.     

支持向量机的5阶光滑函数及其性能分析

光滑函数在支持向量机中起着重要作用,熊金志等人用插值函数的方法导出了一个递推公式,得到了一类新的光滑函数,解决了一个关于是否存在以及如何寻求性能更好的光滑函数的问题。然而其中五阶光滑的多项式函数还未进行性能分析。首先推导出了该光滑函数的表达式,然后分析了它的若干性能。结果表明,该光滑函数具有良好的逼近性能,其逼近精度高于以往的光滑函数。     

Set-based extended aggregation functions

Inspired by the Zadeh approach to fuzzy connectives in fuzzy set theory and by some applications, we introduce and study set-based extended functions, and in particular, set-based extended aggregation functions. These functions reflect neither reordering nor repetition of input values, and, linking different arities, they introduce serious constraints for extended functions. A complete characterization of set-based extended (aggregation) functions is given, and some constructions of such functions are also proposed, including several examples.     

Stabilization of Nonlinear Systems with Filtered Lyapunov Functions and Feedback Passivation

In this paper a generalized class of filtered Lyapunov functions is introduced, which are Lyapunov functions with time‐varying parameters satisfying certain differential equations. Filtered Lyapunov functions have the same stability properties as Lyapunov functions. Tools are given for designing composite filtered Lyapunov functions for cascaded systems. These functions are used to design globally stabilizing dynamic feedback laws for block‐feedforward systems with stabilizable linear approximation.     

Bivariate S-λ bases and S-λ surface patches

In this paper two kinds of bivariate S-λ basis functions, tensor product S-λ basis functions and triangular S-λ basis functions, are constructed by means of the technique of generating functions and transformation factors. These two kinds of bivariate S-λ basis functions have lots of important properties, such as non-negativity, partition of unity, linear independence and so on. The framework of the tensor product S-λ basis functions provides a unified scheme for dealing with several kinds of tensor product basis functions, such as the tensor product Bernstein basis functions, the tensor product Poisson basis functions and some other new tensor product basis functions. The framework of the triangular S-λ surface basis functions includes the triangular Bernstein basis functions, the rational triangular Bernstein basis functions and some other new triangular basis functions. Moreover, the corresponding two kinds of S-λ surfaces are constructed by means of these two kinds of bivariate basis functions, respectively. These two kinds of S-λ surface patches have the important properties of surface modeling, such as affine invariance, convex hull property and so on.     

Solution of variational problems using the Fourier series operational matrix

There are many functions having the property of orthogonality. Among them are Walsh functions, block-pulse functions, Chebyshev functions and Legendre functions. Recently, many scholars and researchers made new approaches to solving variational problems via orthogonal functions. This paper suggests a more simple and powerful orthogonal method—the Fourier series operational matrix for integration—which is derived and used to solve a variational problem.     

Semiconductor nanodevice simulation by multidomain spectral method with Chebyshev, prolate spheroidal and Laguerre basis functions

A new approach based on spectral method with efficient basis functions is proposed in the paper to simulate semiconductor nanodevice by solving the Schrödinger equation. The computational domain is partitioned at heterojunctions into a number of subdomains. The envelope functions in subdomains are expanded by various efficient basis functions and then patched by the BenDaniel-Duke boundary conditions to preserve exponential order of accuracy. Importantly, the consideration to choose the basis functions depends on the oscillatory characteristics of envelope functions. Three kinds of basis functions including prolate spheroidal wave functions, Chebyshev polynomials, and Laguerre-Gaussian functions are used according to the mathematical features in this work. In addition, the determinations of optimum values of scaling factor in Laguerre-Gaussian functions and bandwidth parameter in prolate spheroidal wave functions are also discussed in detail. Several quantum well examples are simulated to validate the effectiveness of the present scheme. The relative errors of energy levels achieve the order of 10⁻¹² requiring merely a few grid points.     

Classification of gene functions using support vector machine for time-course gene expression data

Since most biological systems are developmental and dynamic, time-course gene expression profiles provide an important characterization of gene functions. Assigning functions for genes with unknown functions based on time-course gene expressions is an important task in functional genomics. Recently, various methods have been proposed for the classification of gene functions based on time-course gene expression data. In this paper, we consider the classification of gene functions from functional data analysis viewpoint, where a functional support vector machine is adopted. The functional support vector machine can model temporal effects of time-course gene expression data by incorporating the coefficients as well as the basis matrix obtained from a finite expansion of gene expressions on a set of basis functions. We apply the functional support vector machine to both real microarray and simulated data. Our results indicate that the functional support vector machine is effective in discriminating gene functions of time-course gene expressions with predefined functions. The method also provides valuable functional information about interactions between genes and allows the assignment of new functions to genes with unknown functions.     

Dirichlet multiplication and easily-generated function analysis

Following sine-cosine functions, sawtooth wave, square wave, triangular wave, and trapezoidal wave become new easily-generated periodic functions. Can a signal be considered to be a superposition of easily-generated functions with different frequencies? In order to answer this question, we generalize Fourier analysis to easily-generated function analysis including easily-generated functions series, easily-generated function transformation, and discrete transformation for easily-generated functions. The results in this paper make it possible to represent a signal by use of easily-generated functions. A lot of techniques based on sine-cosine functions can be translated into techniques based on easily-generated functions. Because Dirichlet multiplication in number theory plays a basic role in easily-generated function analysis, we briefly introduce this concept and present a related formula. The main contents of this paper include Dirichlet multiplication and a related formula, relations between basic waveforms in electronics, easily-generated function series, easily-generated function transformation, discrete transformation for easily-generated functions, and techniques of easily-generated function analysis.     

Closure Properties of Real Number Classes under CBV Functions

CBV functions are computable real functions of bounded variation. In this paper we investigate the basic properties of CBV functions. We are especially interested in the question of whether a real number class is closed under CBV functions. The real number classes considered here include the classes of computable (EC), semi-computable (SC), weakly computable (WC), divergence bounded computable (DBC) and recursively approximable (RA) real numbers. We show that the classes EC, RA and DBC are closed under CBV functions but SC and WC are not. Furthermore, WC$ is not even closed under computable monotone functions and, finally, the image sets of $\wc$ under computable monotone functions and CBV functions are different.     

Creep in Thin Magnetic Films†

In this paper a method of testing and realization of two-realizable threshold functions have been suggested. It is shown that the two–realizable functions may be factored into three different forms, (i) sum of or (ii) product of or (iii) ‘ sum–of–product ’ of threshold functions. Since threshold functions are unate functions, a method of decomposition of Boolean functions into unate functions in the above three forms is suggested. The concept of minimal unate function and the cover table of the given Boolean function und its complement is utilized to obtain the above three factored forms.