Complex-variable distribution theory for Laplace and z transforms

The author proposes a generalisation of the theory of generalised functions, also known as the theory of distributions, by extending the theory to include generalised functions of a complex variable, both in the complex plane associated with continuous-time functions and that with discrete-time functions. The generalisation provides, among others, mathematical justifications of the properties of recently introduced generalised Dirac-delta impulses, using the principles of distribution theory. Properties of generalised functions of a complex variable are explored both in the Laplace domain associated with continuous-time functions and the z domain associated with discrete-time functions. Shifting of distributions, scaling, derivation, convolution with distributions and convolution with ordinary functions are evaluated in Laplace and z domains. Three-dimensional generalisations of sequences leading to generalised impulses, and of test functions in Laplace and z domains are presented. New expanded Laplace and z transforms are obtained using the proposed generalisation.     

Amplitude- and Time-Limited Functions With Minimum Out-of-Band Energy

The theory of time-limited functions with minimum out-of-band energy is extended to apply to functions whose amplitude is held constant and hence, are limited to phase modulation. In the absence of the amplitude constraint, the desired functions are prolate spheroidal functions of time, of order zero, with time-bandwidth product as a parameter. With the amplitude constraint, the desired functions can be expressed in terms of sums of even-order prolate spheroidal functions. An algorithm suitable for computations of the amplitude constrained functions is derived.     

高非线性度的平衡相关免疫函数

首先分别给出了Bent函数和不重复齐次k次函数的非线性度、平衡性和相关免疫性;其次,深入研究了这两类函数在非线性组合函数构造中的应用;最后,以这两类函数为基础构造出了具有较高非线性度的平衡相关免疫函数。     

Plateaued函数的密码学性质

Plateaued函数是包含Bent函数和部分Bent函数的更大函数类,是一类密码学性质优良的密码函数,在非线性组合函数的设计中有重要的应用。该文以Walsh谱和自相关系数为工具,从密码函数的角度证明了r阶Plateaued函数的全体线性结构构成的子空间维数的上界为n-r,且等号成立当且仅当f(x)为部分Bent函数,同时还给出了Plateaued函数的其他一些密码学性质。     

布尔函数的对偶性和线性点

本文主要讨论了部分自对偶和部分反自对偶函数、部分线性函数以及具有线性点的函数的性质。     

Raised cosine function for image restoration

In this paper, a new set of raised cosine functions is proposed. These functions have all the useful properties of the spline functions with the additional advantage of continuous infinite derivatives as against only a finite number of derivatives in case of the spline functions. Because of this property they exhibit a smoother behaviour. The property of smoothness, coupled with convolution, makes the raised cosine functions readily applicable to the image restoragtion problem, where the degradation is through a shift invariant blurring function. The results confirm the superior behaviour of these functions in comparison to spline functions.     

部分Bent函数的构造

部分Bent函数是一类具有若干优良密码学性质的函数,在流密码和分组密码的设计中有着重要的作用.文中以Walsh谱和自相关函数为工具,通过级联Bent函数的方法,构造出一类部分Bent函数,该函数是平衡的且具有高非线性度,同时给出了该函数的其它一些密码学性质.     

对称布尔函数的扩展代数免疫度

构造具有最优代数免疫度的布尔函数在流密码中有重要作用,基于布尔函数的单变量多项式表示,构造了一类达到最大扩展代数免疫度的布尔函数。以前的一些函数是这类函数的特例。利用对称布尔函数的基本性质,分析了具有最大代数免疫度的对称布尔函数的扩展代数免疫度。得出结论：共有 个达到最大扩展代数免疫度的 （ 是偶数）元对称布尔函数。     

三类Semi-Bent函数的构造

Semi-bent函数是一种具有高非线性度的布尔函数,它们在密码和通信领域中都有重要的应用价值.本文构造了三类由迹函数表示的semi-bent函数.证明了当限制某些参数的取值范围时,这些新构造函数的semi-bent性与Kloosterman和密切相关.并且证明了每一类新构造的含有n个变元的semi-bent函数,都存...     

Construction and count of multi-output rotation symmetric resilient functions with 8 input variables

The value ranges of the number of output variables were determined respectively under the existence of multi-output rotation symmetric balanced functions and resilient functions with 2^rinput variables.Based on the equivalence between the resilient functions and large sets of orthogonal arrays,some results on the construction and count of multi-output rotation symmetric balanced functions with 8 input variables were presented according to the different dimensions of output vectors,and construction and count of multi-output rotation symmetric 1-resilient functions with 8 input variables were also studied.Besides,constructions of multi-output rotation symmetric resilient functions are transformed into the problem of solving a system of equations.     

Full wave analysis of microstrip floating line structures bywavelet expansion method

A full wave analysis of microstrip floating line structures by wavelet expansion method is presented. The surface integral equation developed from a dyadic Green's function is solved by Galerkin's method, with the integral kernel and the unknown current expanded in terms of orthogonal wavelets. Using the orthonormal wavelets (and scaling functions) with compact support as basis functions and weighting functions, the integral equation is converted into a set of linear algebraic equations, with the matrices nearly diagonal or block-diagonal due to the localization, orthogonality, and cancellation properties of the orthogonal wavelets. Limitations inherited in the traditional orthogonal basis systems are released: The problem-dependent normal modes have been replaced by the problem-independent wavelets, preserving the orthogonality; the trade-off between orthogonality and continuity (e.g. subsectional basis functions including pulse functions, roof-top functions, piecewise sinusoidal functions, etc.) is well balanced by the orthogonal wavelets. Numerical results are compared with measurements and previous published data with good agreement     

On the use of differential equations of nonentire order to generateentire domain basis functions with edge singularity

Entire domain analytical basis functions with edge singularity are a very useful tool for analysing planar transmission lines and planar rectangular or circular circuits in a moment method solution. Analytical basis functions are limited to separable geometry. In this paper we introduce new entire domain basis functions including edge singularity at the edges of a domain with arbitrary shape. These basis functions are derived from a differential equation of nonentire order which includes a fractional derivative. The one dimensional case is considered first. In the two dimensional case the basis functions are constructed numerically using the boundary element method and the Galerkin method. The basis functions are applied in a moment method solution to analyse a shielded microstrip. The current and the electric field are calculated and compared with the results obtained by analytical basis functions     

Introduction to Bridge Functions

In this paper, a bridge function system is introduced, where bridge functions make up a three-valued function system, only taking the values +1, -1, and 0, and they are orthogonal. It is constructed with the concepts of sequence shift and sequence copying. The notation, waveforms, and recursive relation of the bridge functions are given. Walsh functions are a special case of the bridge functions. Block pulses are another special case. The bridge functions connect the Walsh functions and the block pulse functions. The bridge functions have the property of modulo 2 sum.     

Analytic Expressions of Two Discrete Hermite–Gauss Signals

This brief presents the analytical expressions for the discrete zeroth-and first-order Hermite-Gauss functions, which are normally obtained by numerical methods. These two ldquoGaussian-typerdquo functions have the following interesting properties. (a) They have simple analytic forms (form of a product) when the lengths of the functions satisfy certain conditions. (b) They are the eigenvectors of discrete Fourier transforms (DFTs). The zero points of the functions and their respective DFTs are all located on the real axis. These discrete functions are compared with the continuous zeroth and first Hermite Gaussians. They resemble very well to the continuous functions, and the coincidence of the shapes with the continuous cases is remarkable.     

高非线性度多输出布尔函数的构造

本文主要讨论了构造具有高非线性度多输出布尔函数的方法.对于输入变量个数少于输出变量个数的多输出布尔函数,我们给出了存在非零非线性度的充分必要条件及具体的构造方法.我们还利用一类特殊的多输出bent函数构造出具有非常高非线性度的无偏多输出函数.     

Higher order interpolatory vector bases for computationalelectromagnetics

Low-order vector basis functions compatible with the Nedelec (1980) representations are widely used for electromagnetic field problems. Higher-order functions are receiving wider application, but their development is hampered by the complex procedures used to generate them and lack of a consistent notation for both elements and bases. In this paper, fully interpolatory higher order vector basis functions of the Nedelec type are defined in a unified and consistent manner for the most common element shapes. It is shown that these functions can be obtained as the product of zeroth-order Nedelec representations and interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties of the vector functions are discussed, and expressions for the vector functions of arbitrary polynomial order are presented. Sample numerical results confirm the faster convergence of the higher order functions     

Can threshold networks be trained directly?

Neural networks with threshold activation functions are highly desirable because of the ease of hardware implementation. However, the popular gradient-based learning algorithms cannot be directly used to train these networks as the threshold functions are nondifferentiable. Methods available in the literature mainly focus on approximating the threshold activation functions by using sigmoid functions. In this paper, we show theoretically that the recently developed extreme learning machine (ELM) algorithm can be used to train the neural networks with threshold functions directly instead of approximating them with sigmoid functions. Experimental results based on real-world benchmark regression problems demonstrate that the generalization performance obtained by ELM is better than other algorithms used in threshold networks. Also, the ELM method does not need control variables (manually tuned parameters) and is much faster.     

几类密码函数的线性结构研究

线性结构是度量密码函数安全性的一个重要指标。本文基于线性分组码理论，分析了文献[1～4]所构造的密码函数的线性结构，并指出这些函数均具有线性结构，且其线性结构集和构造这些函数所运用的线性分组码的对偶码有关。这就说明了文献[1～4]的密码函数本质上是密码学意义下的弱函数。     

Correlation Immune Functions with Controllable Nonlinearity

In this paper, we consider the relationship between nonlinearity and correlation immunity of Boolean functions. In particular, we discuss the nonlinearity of correlation immune functions suggested by P. Camion et al. For the analysis of such functions, we present a simple method of generating the same set of functions, which makes it possible to construct correlation immune functions with controllable correlation immunity and nonlinearity. Also, we find a bound for the correlation immunity of functions having maximal nonlinearity.