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.

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。

Recovering implied risk-neutral probability density function using SVR

Using support vector regression （SVR）, a novel non-parametric method for recovering implied risk-neutral probability density function （IRNPDF） is investigated by solving linear operator equations. First, the SVR principle for function approximation is introduced, and an SVR method for solving linear operator equations with knowing some values of the right-hand function and without knowing its form is depicted. Then, the principle for solving the IRNPDF based on SVR and the method for constructing cross-kernel functions are proposed. Finally, an empirical example is given to verify the validity of the method. The results show that the proposed method can overcome the shortcomings of the traditional parametric methods, which have strict restrictions on the option exercise price; meanwhile, it requires less data than other non-parametric methods, and it is a promising method for the recover of IRNPDF.

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.

SKEWNESS FACTOR OF TURBULENT VELOCITY DERIVATIVE

Using nonequilibrium statistical mechanics closure method, it is shown that the skewness factor of the velocity derivative of isotropic turbulence ap- proaches a constant -0.515 when the Reynolds number is very high, which is in agree- ment with the DNS (direct numerical simulation) result of Vincent and Meneguzzi (1991).

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.

Skewness of subsurface ocean temperature in the equatorial Pacific based on assimilated data

The skewness of subsurface temperature anomaly in the equatorial Pacific Ocean shows a significant asymmetry between the east and west. A positive temperature skewness appears in the equatorial eastern Pacific, while the temperature skewness in the western and central Pacific is primarily negative. There is also an asymmetry of the temperature skewness above and below the climatological mean therrnocline in the central and western Pacific. A positive skewness appears below the thermocline, but the skewness is negative above the thermocline. The distinctive vertical asymmetry of the temperature skewness is argued to be attributed to the asymmetric temperature response to upward and downward thermocline displacement in the presence of the observed upper-ocean vertical thermal structure. Because of positive （negative） second derivative of temperature with respect to depth below （above） the thermocline, an upward and a downward shift of the thermocline with equal displacement would lead to a negative temperature skewness above the thermocline but a positive skewness below the thermocline. In the far eastern equatorial Pacific, the thermocline is close to the base of the mixed layer, the shape of the upper-ocean vertical temperature profile cannot be kept. Positive skewness appears in both below the thermocline and above the thermocline in the far eastern basin. Over the central and eastern Pacific, the anomalies of the subsurface waters tend to entrain into the surface mixed layer （by climatological mean upwelling） and then affect the SST. Hence, the positive （negative） subsurface skewness in the far eastern （central） Pacific may favor positive （negative） SST skewness, which is consistent with the observational fact that more La Nina （EI Nino） occur in the central （eastern） Pacific. The present result implies a possible new paradigm for EI Nino and La Nina amplitude asymmetry in the eastern Pacific.

The role of velocity derivative skewness in understanding non-equilibrium turbulence

The turbulence governed by the Navier-Stokes equation is paramount in many physical processes.However,it has been considered as a challenging problem due to its inherent nonlinearity,non-equilibrium,and complexity.Herein,we review the connections between the velocity derivative skewness Sk and the non-equilibrium properties of turbulence.Sk,a reasonable candidate for describing the non-equilibrium turbulence,which varies during the non-equilibrium procedure.A lot of experimental or numerical evidences have shown that the perturbation of energy spectrum,which associated with the excitation of large scales,results in an obvious variation of Sk,and Sk is a negative value in this rapid energy decay process.The variation of positive Sk is closely related to the perturbation of transfer spectrum,and this corresponds to the backward energy transfer process.In addition,the skewness characterizes the production(or reduction)rate of enstrophy due to vortex stretching(or compression).Using the transport equation of turbulent energy dissipation rate and enstrophy,it is possible to establish a theoretical connection between skewness and the non-equilibrium turbulence.It is expected that this work could trigger the rapid advancement of the future studies of non-equilibrium turbulence,and also the improvement of turbulence models.

A Statistical Power Comparison of the Kolmogorov-Smirnov Two-Sample Test and the Wald Wolfowitz Test in Terms of Fixed Skewness and Fixed Kurtosis in Large Sample Sizes

In this study, the statistical powers of Kolmogorov-Smimov two-sample （KS-2） and Wald Wolfowitz （WW） tests, non-parametric tests used in testing data from two independent samples, have been compared in terms of fixed skewness and fixed kurtosis by means of Monte Carlo simulation. This comparison has been made when the ratio of variance is two as well as with equal and different sample sizes for large sample volumes. The sample used in the study is： （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 25）, （50, 50）, （50, 75）, （50, 100）, （75, 25）, （75, 50）, （75, 75）, （75, 100）, （100, 25）, （100, 50）, （100, 75）, and （100, 100）. According to the results of the study, it has been observed that the statistical power of both tests decreases when the coefficient of kurtosis is held fixed and the coefficient of skewness is reduced while it increases when the coefficient of skewness is held fixed and the coefficient of kurtosis is reduced. When the ratio of skewness is reduced in the case of fixed kurtosis, the WW test is stronger in sample volumes （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 75）, and （50, 100） while KS-2 test is stronger in other sample volumes. When the ratio of kurtosis is reduced in the case of fixed skewness, the statistical power of WW test is stronger in volume samples （25, 25）, （25, 75）, （25, 100）, and （75, 25） while KS-2 test is stronger in other sample volumes.

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。

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.

河道斜交桥梁壅水及流场特性分析

圆端桥墩是平原河道内一种常见的桥墩型式,为探究斜交圆端桥墩不同布置方式引起的壅水特性和水流流态变化,建立三维数值模型,采用SIMPLE算法耦合k-ε紊流模型求解N-S方程组,应用VOF法追踪自由液面,分析了单个桥墩壅水特性、绕流流场和升阻力系数随斜交角度变化的规律。研究结果表明:下游墩前壅水高度最大,壅水长度最长,上游墩前冲高值最大;水流绕流经过上游桥墩后偏向下游桥墩侧,桥墩垂直桥轴线布置方式绕流形成的壅水叠加效应更明显;斜交桥梁布置采取圆端桥墩时,桥墩顺水流布置,可有效减小阻水宽度与壅水高度,弱化流场结构变化。

面向负载均衡的动态均衡分区策略

针对MapReduce计算框架处理倾斜数据集时造成Reduce端出现负载不均衡现象,提出一种动态均衡分区策略。在mapper阶段提出基于分治法的数据切分原则处理任务传入的数据组;结合最佳适应算法思想设计动态分配原则逐步将切分后的数据块均衡分配到预分区链表中;根据分区索引分配到各Reduce节点上实现负载均衡。实验结果显示,动态均衡分区策略与两个基准模型相比任务执行时长平均降低了7.7%,表明动态均衡分区策略更好地解决了数据倾斜问题,降低了任务执行时间,验证了模型的有效性。

HINTS联合血清IL-6诊断孤立性眩晕患者脑梗死的价值研究

目的 探讨头脉冲-眼震-眼偏斜(HINTS)联合血清IL-6诊断孤立性眩晕患者脑梗死的价值。方法 回顾性选择2022年6月至2023年10月青岛市第八人民医院收治的91例孤立性眩晕患者,根据临床评估及颅脑MRI检查结果分为脑梗死组23例和周围性眩晕组68例。比较两组患者的一般资料、实验室检查结果;所有患者入院即行HINTS床旁检查,根据HINTS检查结果初步诊断为脑梗死或周围性眩晕,与临床评估及颅脑MRI检查作出的诊断进行比较。采用多因素logistic回归分析影响孤立性眩晕患者脑梗死的危险因素。采用ROC曲线评估HINTS、血清IL-6及HINTS联合血清IL-6对孤立性眩晕患者脑梗死的诊断效能。结果 脑梗死组吸烟、糖尿病、高血压、椎基底动脉狭窄患者占比及FPG、血清IL-6水平均高于周围性眩晕组(均P<0.05)。多因素logistic回归分析显示高血清IL-6水平(OR=1.445,95%CI:1.016~2.054)是孤立性眩晕患者脑梗死的危险因素(P<0.05)。HINTS对孤立性眩晕患者脑梗死的诊断灵敏度为0.826(95%CI:0.612~0.951),特异度为0.868(95%CI:0.764~0.938),阳性预测值为0.679(95%CI:0.528~0.800),阴性预测值为0.937(95%CI:0.858~0.973),准确度为0.857(95%CI:0.768~0.922)。ROC曲线分析结果显示HINTS、血清IL-6、HINTS联合血清IL-6诊断孤立性眩晕患者脑梗死的灵敏度分别为0.826、0.696、0.826,特异度分别为0.868、0.735、0.897,AUC分别为0.847、0.751、0.919。结论 HINTS联合血清IL-6对孤立性眩晕患者脑梗死有较高的诊断效能。

*-诣零McCoy环

研究了具有对合映射*-诣零McCoy环的性质,给出了一批*-诣零McCoy环例子,并讨论了其扩张和*-斜多项式环的*-诣零McCoy性,证明了(1)设*-环R满足nil(R[x])=nil(R)[x],则环R是*-诣零McCoy环当且仅当环R[x]是*-诣零McCoy环;(2)设R[x;*]是*-斜多项式环,如果R是*-可逆环,则R[x;*]是*-诣零McCoy环。

多轴平稳非高斯随机振动试验控制方法

多轴向平稳非高斯随机振动控制试验能够对指定响应信号的时、频域特征进行同时控制。提出了一种快速生成具有指定功率谱密度、斜度和峭度的平稳非高斯随机振动信号的方法。通过频率采样方法将目标功率谱密度设计成滤波器,利用非线性变换方法获取非高斯随机信号,再将此信号经过设计的滤波器以获得满足要求的非高斯随机信号。该方法简单、快速并克服了传统非线性变换方法的缺点。进一步将此方法应用于三轴向平稳非高斯随机振动试验中,给出了三轴向非高斯随机振动控制的闭环均衡步骤,此方法能够同时对信号的功率谱自谱、相干系数、相位差以及斜度和峭度进行解耦控制。进行了三轴向平稳非高斯随机振动控制试验,三个方向上加速度信号的功率谱密度、斜度和峭度控制效果均令人满意,满足工程应用要求。

一例Xq22.3q27.3缺失患者的遗传学分析

目的:对1例无相关特异表型的Turner综合征患者进行遗传学分析,为临床医生识别女性X染色体偏倚失活提供参考。方法:采集1例原发不孕3年的女性及其丈夫和父母的外周静脉血,行染色体核型分析、女方染色体拷贝数变异(CNVs)检测,并进行遗传学分析。结果:原发不孕患者外周血染色体核型为46,X,del(X)(q22.3),其父母及丈夫染色体核型结果均正常。患者CNVs结果提示X染色体q22.3-q27.3缺失40.62Mb,为致病性改变。患者缺失的X染色体失活偏倚比例为98:2,为X染色体极度失活偏倚。结论:临床医生应考虑到女性患者存在X染色体偏倚失活的可能,尽早发现染色体异常患者,以避免生育风险及出生缺陷的发生。

基于改进CoF的红外与可见光图像融合

为了使红外与可见光图像融合能够保留图像边缘信息和背景信息,提出改进共现滤波算法。首先分析共现滤波效果取决于滤波尺度标准差、图像内容;接着基于像素强度偏斜度和基于像素能量对滤波尺度优化,自适应确定像素对距离阈值提高了滤波的速度;最后NSST算法对图像的低、高频子带使用不同融合方法,低频子带图像的融合使用Delaunay插值计算、最大对称环绕显著性方法,高频子带图像的融合使用修正拉普拉斯和方法。实验仿真表明,本文算法融合结果边缘细节部分更丰富,没有伪影出现,主观视觉和客观指标上均具有明显的优势。