Diophantine equations and Fermat's last theorem for multivariate(skew-)polynomials

Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely.The aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate(skew)-polynomials with any characteristic.

Radon CLF:A Novel Approach for Skew Detection Using Radon Transform

In the digital world,a wide range of handwritten and printed documents should be converted to digital format using a variety of tools,including mobile phones and scanners.Unfortunately,this is not an optimal procedure,and the entire document image might be degraded.Imperfect conversion effects due to noise,motion blur,and skew distortion can lead to significant impact on the accuracy and effectiveness of document image segmentation and analysis in Optical Character Recognition(OCR)systems.In Document Image Analysis Systems(DIAS),skew estimation of images is a crucial step.In this paper,a novel,fast,and reliable skew detection algorithm based on the Radon Transform and Curve Length Fitness Function(CLF),so-called Radon CLF,was proposed.The Radon CLF model aims to take advantage of the properties of Radon spaces.The Radon CLF explores the dominating angle more effectively for a 1D signal than it does for a 2D input image due to an innovative fitness function formulation for a projected signal of the Radon space.Several significant performance indicators,including Mean Square Error(MSE),Mean Absolute Error(MAE),Peak Signal-to-Noise Ratio(PSNR),Structural Similarity Measure(SSIM),Accuracy,and run-time,were taken into consideration when assessing the performance of our model.In addition,a new dataset named DSI5000 was constructed to assess the accuracy of the CLF model.Both two-dimensional image signal and the Radon space have been used in our simulations to compare the noise effect.Obtained results show that the proposed method is more effective than other approaches already in use,with an accuracy of roughly 99.87%and a run-time of 0.048(s).The introduced model is far more accurate and timeefficient than current approaches in detecting image skew.

Optimizing Designed Variable Speed Control Moment Gyroscopes with Variable Skew Angle

Large torque can be output by the single gimbal control momentum gyroscope (SGCMG) based on the principle of the gyroscopic precession. However, the singularity is a major obstacle to successfully implement the task of the attitude control. The singularity can be avoided by the additional variable flywheel speed of variable speed control moment gyroscopes (VSCMG). Unfortunately, some kind of singularity cannot be effectively avoided. Consequently, the output toque can be only supported by the reaction torque of the flywheel when the singularity is encountered, and the consume power that is determined by the flywheel speed and reaction torque can be greatly increased when the flywheel spin rate over one thousand revolutions per minute. In this paper, the pyramid configuration with variable skew angle of the VSCMG is considered. A new steering law for the VSCMG with variable skew angle is proposed. The singularity that cannot be avoided by the varying flywheel speed can be effectively avoided with assisting of varying the skew angle. Consequently, the requirement of flywheel torque can be reduced. At last, the optimizing VSCMG with variable skew angle can be cast as a multi-objective function with multi-constraints. The particle swarm optimization method is used to solve the optimizing problem. In summary, the VSCMG with variable skew angle can be redesigned with considering of the singularity avoidance and minimizing system power.

有限精度下Skew Tent映射的抗退化研究

混沌是指确定性动力学系统在初值变化细微的情况下,经过足够多的迭代后表现出来的不可预测性、类随机性的非周期性运动。随着混沌系统在通信工程、密码学、图像加密等方向的应用,有限精度下混沌系统动力学性能退化的问题就随之出现。提高混沌系统有限精度下的动力学性能有多种方法,其中,直接提升应用环境计算精度的代价太大、实际操作性不强。文中从提高混沌系统的抗退化性能方向入手,提出一种利用Lorenz系统对Skew Tent进行参数、输出扰动,从而提高Skew Tent系统的抗退化性能的方法,同时也克服了Skew Tent系统会进入不动点的情况。随后通过对改进后的系统进行初值敏感性、回归映射、自相关性、近似熵测试以及对量化后混沌序列进行NIST测试,结果表明使用该方案改进后的Skew Tent系统具有良好的混沌性,在通信工程、混沌密码算法设计、图像加密等方面有良好的应用前景。

一种新型Skew Tent映射的混沌混合优化算法

针对已有的混沌优化算法几乎都是利用Logistic映射作为混沌序列发生器,而该混沌序列的概率密度函数呈两头多、中间少的切比雪夫型的分布性质,不利于搜索的效率和能力,为此,首先构造一种新型混沌映射序列发生器—Skew Tent映射并结合迭代优化特点加以改进,然后分析了它的混沌特性．其次,将改进的混沌映射与Alopex启发算法相结合,充分发挥Alopex算法的快速搜索能力和混沌优化全局寻优的特性,提出一种混沌混合优化算法,提高了算法的收敛速度和有效搜索全局最优解．最后,仿真算例验证了该算法的有效性和Skew Tent混沌映射的应用前景．

改进分段Skew Tent映射及其在扩频通信中应用

混沌序列用作扩频系统扩频码,具有码元丰富、保密性好等优点。针对传统Skew Tent映射所产生随机序列的混沌特性较弱,特别是其随机性、相关性等指标较差等不足,将Skew Tent映射进行分段对偶扩展获得一种改进分段Skew Tent映射构造方法,并将其所产生的随机序列用于构造扩频通信系统的扩频码。通过扩频通信系统仿真测试验证了改进分段Skew Tent映射相比Skew Tent映射具有更加良好的混沌特性,以及所产生随机序列作为扩频系统地址码在降低系统的误码率方面有了较大的改善。改进分段Skew Tent映射作为加密算法用于图像通信系统中,有效提高了图像信息的传输质量和安全性。混沌映射进行分段对偶扩展是一种行之有效的改进方法,混沌特性更好的迭代映射更利于扩频通信在军民领域的广泛应用。

一类半环的skew-环同余的刻画

利用半环的满的、自共轭的闭的理想给出了加法是正则半群的半环上的skew-环同余的一种刻画.类似于环中理想和同余的对应关系理论,给出了加法正则半环的skwe-环同余和一类特殊理想的一一对应关系;另外,借助于半环的一个逆序给出了skew-环同余类的一种表示.

基于Skewed-t分布的FIGARCH模型与VaR的度量

金融资产收益率序列的波动具有典型的尖峰厚尾和非对称性特征,描述这种特性需以合适的概率分布函数为基础.因此,寻求更好的概率分布函数对风险度量、VaR的计算有着十分重要的意义.有鉴于此引入Skewed-t分布度量VaR,并比较分析了RiskMetrics及FIGARCH类模型度量VaR值的准确程度,本文同时分析了多头头寸和空头头寸情况下的VaR.结果表明,在两种头寸情况下,Skewed-t分布在空头和多头情形对资产厚尾特性以及非对称性的拟合效果均要比正态分布好;在两种头寸中不同的置信水平下,FIAGARCH(CHUNG)模型预测的VaR值改进了使用传统模型的精确性,高估或低估风险的程度较轻.

A parametric bootstrap approach for one-way classification model with skew-normal random effects

In this paper,several properties of one-way classification model with skew-normal random effects are obtained,such as moment generating function,density function and noncentral skew chi-square distribution,etc.Based on the EM algorithm,we discuss the maximum likelihood(ML)estimation of unknown parameters.For testing problem of fixed effect,a parametric bootstrap(PB)approach is developed.Finally,some simulation results on the Type I error rates and powers of the PB approach are obtained,which show that the PB approach provides satisfactory performances on the Type I error rates and powers,even for small samples.For illustration,our main results are applied to a real data problem.

A skew–normal mixture of joint location, scale and skewness models

Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this paper, we propose and study a novel class of models： a skew-normal mixture of joint location, scale and skewness models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population. The issues of maximum likelihood estimation are addressed. In particular, an Expectation-Maximization （EM） algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments. Results from the analysis of a real data set from the Body Mass Index （BMI） data are presented.

一类上三角矩阵环的Skew Armendariz性质

设α是环R的一个自同态.若R是-αrigid环,则R上的上三角矩阵环的子环Wn既是-α-skew Armendariz环又是Armendariz环.

基于Skewness纹理的北京城市化区域提取

北京地区部分农作物和城市化区域的光谱属性接近,仅仅利用光谱信息无法有效地提取北京的城市化区域。提出了利用Skewness纹理区分农作物和城市化区域,结合光谱和高程信息可以有效提取城市化区域。经过大量的样本检验表明,引入Skewness特征能够大幅度提高分类精度。

Joint modelling of location and scale parameters of the skew-normal distribution

Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.

农产品期货价格波动特征分析——基于Beta-skew-t-EGARCH模型的实证分析

根据2008~2019年国内大豆、玉米、棉花、豆粕和白糖期货合约日收盘价格数据,通过建立基于Beta-skew-t-EGARCH模型研究了农产品期货价格波动规律,实证研究结果表明:农产品期货合约价格波动具有较强的持续性和聚集性且呈现出杠杆效应,并且在履约期前后价格剧烈波动。以玉米为例,从供求关系和物价指数2个方面分析了波动成因以及影响程度。从供给层面角度来看,种植面积的上升从源头推动了玉米产量的上涨,从而稳定了玉米价格;从需求层面角度来看,人口总数和人均GDP的增加扩大了玉米的需求量,促使了玉米价格持续上涨。因此,建议我国保持农产品种植面积的平稳,稳定农产品供给,同时,还要提高农产品价格市场监测和预警能力,并积极优化期货交易主体结构。

投资组合行业配置的动态VaR研究——基于时变Copula-GJR-Skewed-t模型

用时变Copula-GJR-Skewed-t模型研究了深证22个行业分类指数中任意两个投资组合的动态VaR,并与静态VaR比较。实证结果表明,时变t-Copula函数在众多Copula函数中对行业投资组合的拟合效果最优,给出了模型估计出的VaR最大和最小的5对行业组合,不同行业组合的动态VaR在股市周期各阶段关系相对稳定,同一行业组合的动态VaR和静态VaR关系相对稳定,且略高于静态VaR。

摩擦市场条件下的Mean-Variance-Skewness模型

在投资组合选择模型中考虑了资产收益率分布中正的偏度水平,并通过引入一些市场摩擦因素建立了摩擦市场条件下的Mean-Variance-Skewness模型.提出了一个新的遗传算法加速其搜索收敛过程,解决了该模型的计算复杂性问题.在该模型框架内对交易费用和税收等市场摩擦因素进行了敏感性分析.研究证明资产收益率分布的偏度水平是与投资者的决策相关的,市场摩擦因素对投资者的决策行为也有直接的影响.因此,考虑摩擦市场条件下基于正偏度水平偏好的最优投资组合模型对投资者有很强的实践指导价值.

拟正则半环上的skew-环同余

利用半环的满的、自共轭的闭理想给出了加法半群是拟正则半群的半环上的skew-环同余的一种刻画.类似于环中理想和同余对应关系,给出了拟正则半环上的skew-环同余和一类特殊理想的一一对应关系.

关于弱α-skew Armendariz环和α-rigid环

研究了弱-αskew Armendariz环、-αrigid环、α-SC环以及半交换环的关系.设α是环R的一个自同态,nil(R)是R的理想,如果R是α-SC环,那么R是弱-αskew Armendariz环.

The Alpha-Beta-Gamma Skew Normal Distribution and Its Application

In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become its special cases. The statistical properties of the new distribution are studied in detail, its moment generating function, skewness coefficient, kurtosis coefficient, Fisher information matrix, maximum likelihood estimators are derived. Moreover, a random simulation study is carried out for test the performance of the estimators, the simulation results show that with the increase of sample size, the mean value of maximum likelihood estimators tends to the true value. The new distribution family provides a better fit compared with other known skew distributions through the analysis of a real data set.

同步电路设计中CLOCK SKEW的分析

Clock skew是数字集成电路设计中一个重要的因素。本文比较了在同步电路设计中 0 clock skew和非 0clock skew时钟分布对电路性能的影响 ,分析了通过调整时钟树中 CL OCK SKEW来改善电路性能的方法 ,从而说明非 0 clock skew时钟分布是如何提高同步电路运行的最大时钟频率的。