可调激活函数递进提升输出维的选参方法

针对一类变参数 Sigmoid可调激活函数构成三层前向神经网络 ,分析其可调激活函数中参数所表示意义 ;给出了递进提升输出向量空间维数的可调变参数激活函数中参数选取的方法 ,解决了隐含神经元采用相同激活函数限制了神经网络逼近能力这一问题 .其目的给人们在采用变参数可调激活函数神经网络解决问题时 ,如何选取激活函数中的参数提供了一种数学依据和方法 .     

纵横步进编织规律的数学描述及其证明

对于纵横编织步进编织中的步长选取规律用精确的数学语言描述 ,并给出其严格的数学证明 ,为进一步设计和实现纵横编织技术提供了理论基础 .     

铸造锌铝合金稀土变质机制的电子理论研究

根据分子动力学理论建立了液态锌铝合金ZA27的模型，结合计算机编程构造出了ZA27合金相与液相共存时的原子结构模型，利用Reeursion方法计算了稀土固溶于晶粒内和富集于晶界前沿时的电子结构。由此得出：稀土处于相界区比在晶内更稳定，从而解释了稀土在相内溶解度很小，结晶时富集于相界前沿液体中的事实；稀土处于液态和晶态的结构能差相对于铝较大，解释了稀土在晶界前的富集使晶枝产生熔断、游离、增殖的观点。原子间的键级积分计算也表明，稀土处于晶界前沿液体中与铝相比不容易结晶到晶体表面，起到阻碍晶粒长大，细化晶粒的作用，这就从电子层次解释了稀土的变质机制。     

Riemann‐Hilbert problem and matrix discrete Painlevé II systems

Matrix Szeg? biorthogonal polynomials for quasi‐definite matrices of Hölder continuous weights are studied. A Riemann‐Hilbert problem is uniquely solved in terms of the matrix Szeg? polynomials and its Cauchy transforms. The Riemann‐Hilbert problem is given as an appropriate framework for the discussion of the Szeg? matrix and the associated Szeg? recursion relations for the matrix orthogonal polynomials and its Cauchy transforms. Pearson‐type differential systems characterizing the matrix of weights are studied. These are linear systems of ordinary differential equations that are required to have trivial monodromy. Linear ordinary differential equations for the matrix Szeg? polynomials and its Cauchy transforms are derived. It is shown how these Pearson systems lead to nonlinear difference equations for the Verblunsky matrices and two examples, of Fuchsian and non‐Fuchsian type, are considered. For both cases, a new matrix version of the discrete Painlevé II equation for the Verblunsky matrices is found. Reductions of these matrix discrete Painlevé II systems presenting locality are discussed.     

PANSYSTEMS METHODOLOGY AND CONSTRUCTION OF MAGIC SQUARES

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A variety of (3 + 1)‐dimensional Burgers equations derived by using the Burgers recursion operator

A new variety of (3 + 1)‐dimensional Burgers equations is presented. The recursion operator of the Burgers equation is employed to establish these higher‐dimensional integrable models. A generalized dispersion relation and a generalized form for the one kink solutions is developed. The new equations generate distinct solitons structures and distinct dispersion relations as well. Copyright © 2014 John Wiley & Sons, Ltd.     

Ordinal machines and admissible recursion theory

We generalize standard Turing machines, which work in time ω on a tape of length ω, to α-machines with time α and tape length α, for α some limit ordinal. We show that this provides a simple machine model adequate for classical admissible recursion theory as developed by G. Sacks and his school. For α an admissible ordinal, the basic notions of α-recursive or α-recursively enumerable are equivalent to being computable or computably enumerable by an α-machine, respectively. We emphasize the algorithmic approach to admissible recursion theory by indicating how the proof of the Sacks–Simpson theorem, i.e., the solution of Post’s problem in α-recursion theory, could be based on α-machines, without involving constructibility theory.     

A foundation for real recursive function theory

The class of recursive functions over the reals, denoted by , was introduced by Cristopher Moore in his seminal paper written in 1995. Since then many subsequent investigations brought new results: the class was put in relation with the class of functions generated by the General Purpose Analogue Computer of Claude Shannon; classical digital computation was embedded in several ways into the new model of computation; restrictions of were proved to represent different classes of recursive functions, e.g., recursive, primitive recursive and elementary functions, and structures such as the Ritchie and the Grzergorczyk hierarchies.The class of real recursive functions was then stratified in a natural way, and and the analytic hierarchy were recently recognised as two faces of the same mathematical concept.In this new article, we bring a strong foundational support to the Real Recursive Function Theory, rooted in Mathematical Analysis, in a way that the reader can easily recognise both its intrinsic mathematical beauty and its extreme simplicity. The new paradigm is now robust and smooth enough to be taught. To achieve such a result some concepts had to change and some new results were added.