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.

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．

Scale effects on non-cavitation hydrodynamics and noise of highly-skewed propeller in wake flow

Regarding the scale effects on propeller＇s noncavitation hydrodynamics and hydroacoustics, three similar 7bladed highly-skewed propellers in the wake flow are addressed with diameters of 250, 500 and 1 000 mm, respectively. The discrete line-spectrum noise and its standardized spectrum level scaling law, together with the total sound pressure level are analyzed. The non-cavitation noise predictions are completed by both the frequency domain method and the time domain method. As a fluctuated noise source, the time-dependent fluctuated pressure and normal velocity distribution on propeller blades are obtained by the unsteady Reynolds-averaged Navier-Stokes （ URANS ） simulation. Results show that the pressure coefficient distribution of three propellers on the 0.7R section is nearly superposed under the same advance ratio. The periodic thrust fluctuation of three propellers can exactly reflect the tonal components of the axial passing frequency （APF） and the blade passing frequency （BPF）, and the fluctuation enhancement from the small to the middle propeller at the BPF is greater than that from the middle to the big one. By the two noise prediction methods, the increment of the total sound pressure level from the small to the big propeller differs by 2.49 dB. Following the standardized scaling law, the spectrum curves of the middle and big propellers are nearly the same while significantly differing from the small one. The increment of both the line-spectrum level and the total sound pressure increases with the increase in diameter. It is suggested that the model scale of the propeller should be as large as possible in engineering to reduce the prediction error of the empirical scalin~ law and weaken the scale effects.

A Design of Modular Interior Ferrite Magnet Fluxswitching Linear Motor for Track Transport

A novel topology of modular ferrite magnet fluxswitching linear motor(FMFSLM)use for track transport is presented in this paper,which enables more ferrite magnets to be inserted into the primary iron core.The motor has a significant low-cost advantage in long-distance linear drive.The proposed FMFSLM’s structure and working principle were introduced.Further,the thrust force expression of the motor was established.The thrust force components triggering thrust force ripple were investigated,and their expressions can be obtained according to the inductances’Fourier series expressions.Resultantly,the relationship between the harmonics of thrust force and that of self-and mutual inductances was revealed clearly.Based on the relationship,a skewed secondary should be practical to reduce the thrust force ripple.Thus,the effect of employing a skewed secondary to the proposed FMFSLM was investigated,and an optimized skewing span distance was determined.Finite element analysis(FEA)was conducted to validate the exactness of the theoretical analysis.The simulation results indicate that the strategy of suppressing thrust force ripple has a significant effect.Meanwhile,the motor maintains a good efficiency characteristic.The results of the prototype experiment are in good agreement with FEAs,which further verifies the proposed modular interior FMFSLM’s practicability.

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。

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。

Minor Self-conjugate and Skewpositive Semidefinite Solutions to a System of Matrix Equations over Skew Fields

Minor self conjugate (msc) and skewpositive semidefinite (ssd) solutions to the system of matrix equations over skew fields [A mn X nn =A mn ,B sn X nn =O sn ] are considered. Necessary and sufficient conditions for the existence of and the expressions for the msc solutions and the ssd solutions are obtained for the system.

一种校准线延时差异的方法分析

阐述一种在发送端通过自发自收的方式自动校准并行数据不同PIN延时的方法,可以有效提高接收芯片Clock和Data的相位裕度,降低因并行传输信号完整性指标较差,整个系统不稳定而出现花屏,闪屏的现象。

Application of ACP Nonlinear Math in Analyzing Arithmetic and Radiation Transmission Data (Application 1 & 2) [4-21-2024, 820P] (V)

In this study, we explore the application of ACP (asymptotic curve based and proportionality oriented) Alpha Beta (αβ) Nonlinear Math to analyze arithmetic and radiation transmission data. Specifically, we investigate the relationship between two variables. The novel approach involves collecting elementary “y” data and subsequently analyzing the asymptotic cumulative or demulative (opposite of cumulative) Y data. In part I, we examine the connection between the common linear numbers and ideal nonlinear numbers. In part II, we delve into the relationship between X-ray energy and the radiation transmission for various thin film materials. The fundamental physical law asserts that the nonlinear change in continuous variable Y is negatively proportional to the nonlinear change in continuous variable X, expressed mathematically as dα = −Kdβ. Here: dα {Y, Yu, Yb} represents the change in Y, with Yu and Yb denoting the upper and baseline asymptote of Y. dβ {X, Xu, Xb} represents the change in X, with Xu and Xb denoting the upper and baseline asymptote of X. K represents the proportionality constant or rate constant, which varies based on equation arrangement. K is the key inferential factor for describing physical phenomena.

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。

Global Calibration Method of Multi-sensor Vision System Using Skew Laser Lines

Multi-sensor vision system plays an important role in the 3D measurement of large objects.However,due to the widely distribution of sensors,the problem of lacking common fields of view（FOV） arises frequently,which makes the global calibration of the vision system quite difficult.The primary existing solution relies on large-scale surveying equipments,which is ponderous and inconvenient for field calibrations.In this paper,a global calibration method of multi-sensor vision system is proposed and investigated.The proposed method utilizes pairs of skew laser lines,which are generated by a group of laser pointers,as the calibration objects.Each pair of skew laser lines provides a unique coordinate system in space which can be reconstructed in certain vision sensor＇s coordinates by using a planar pattern.Then the geometries of sensors are computed under rigid transformation constrains by taking coordinates of each skew lines pair as the intermediary.The method is applied on both visual cameras with synthetic data and a real two-camera vision system;results show the validity and good performance.The prime contribution of this paper is taking skew laser lines as the global calibration objects,which makes the method simple and flexible.The method need no expensive equipments and can be used in large-scale calibration.

Performance-based seismic assessment of skewed bridges with and without considering soil-foundation interaction effects for various site classes

The seismic behavior of skewed bridges has not been well studied compared to straight bridges. Skewed bridges have shown extensive damage, especially due to deck rotation, shear keys failure, abutment unseating and column- bent drift. This research, therefore, aims to study the behavior of skewed and straight highway overpass bridges both with and without taking into account the effects of Soil-Structure Interaction （SSI） due to near-fault ground motions. Due to several sources of uncertainty associated with the ground motions, soil and structure, a probabilistic approach is needed. Thus, a probabilistic methodology similar to the one developed by the Pacific Earthquake Engineering Research Center （PEER） has been utilized to assess the probability of damage due to various levels of shaking using appropriate intensity measures with minimum dispersions. The probabilistic analyses were performed for various bridge configurations and site conditions, including sand ranging from loose to dense and clay ranging from soft to stiff, in order to evaluate the effects. The results proved a considerable susceptibility of skewed bridges to deck rotation and shear keys displacement. It was also found that SSI had a decreasing effect on the damage probability for various demands compared to the fixed-base model without including SSI. However, deck rotation for all types of the soil and also abutment unseating for very loose sand and soft clay showed an increase in damage probability compared to the fixed-base model. The damage probability for various demands has also been found to decrease with an increase of soil strength for both sandy and clayey sites. With respect to the variations in the skew angle, an increase in skew angle has had an increasing effect on the amplitude of the seismic response for various demands. Deck rotation has been very sensitive to the increase in the skew angle; therefore, as the skew angle increased, the deck rotation responded accordingly. Furthermore, abutment unseating showed an increasing trend due to an increase in skew angle for both fixed-base and SSI models.

Maximal and total skew information for a two-qubit system using nonlinear interaction models

Maximal and total skew information is studied. For symmetric pure states of two-qubit, they are closely related to the linear entropy, the concurrence, and the spin squeezing parameter. For a two-qubit system implemented in three nonlinear interaction models with an external field, we give the exact state vectors and the expectation value （Sz） at any time t. Based on （Sz）2, we give the maximal and the total skew information and a condition in which the maximal and the total skew information can reach 1 and 2, respectively.

MAPS PRESERVING STRONG SKEW LIE PRODUCT ON FACTOR VON NEUMANN ALGEBRAS

Let A be a factor von Neumann algebra and Ф be a nonlinear surjective map from A onto itself. We prove that, if Ф satisfies that Ф（A）Ф（B） - Ф（B）Ф（A）＊ -- AB - BA＊ for all A, B ∈ A, then there exist a linear bijective map ψA →A satisfying ψ（A）ψ（B） - ψ（B）ψ（A）＊ = AB - BA＊ for A, B ∈ A and a real functional h on A with h（0） -= 0 such that Ф（A） = ψ（A） ＋ h（A）I for every A ∈ A. In particular, if .4 is a type I factor, then, Ф（A） = cA ＋ h（A）I for every A ∈ .4, where c = ±1.

Mobile bed thickness in skewed asymmetric oscillatory sheet flows

A new instantaneous mobile bed thickness model is presented for sediment transport in skewed asymmetric oscillatory sheet flows. The proposed model includes a basic bed load part and a suspended load part related to the Shields parameter, and takes into account the effects of mass conservation, phase-lag, and asymmetric boundary layer development, which are important in skewed asymmetric flows but usually absent in classical models. The proposed model is validated by erosion depth and sheet flow layer thickness data in both steady and unsteady flows, and applied to a new instantaneous sediment transport rate formula. With higher accuracy than classical empirical models in steady flows, the new formula can also be used for instantaneous sediment transport rate prediction in skewed asymmetric oscillatory sheet flows.

一种FPGA芯片时钟SKEW的测试方法

随着FPGA规模的扩大和工作频率的提高,时钟Skew成为FPGA越来越重要的性能指标,而如何精确测试芯片中的时钟Skew也就显得尤为重要.对此以JFPGA-YX2芯片为例,介绍一种可以精确测量FPGA时钟Skew的测试方法.将芯片内部的时钟资源通过配置逻辑配置成一系列的环形振荡器,每个振荡器的振荡频率由该振荡器所包含路径的延时决定.对这些振荡器的测量频率值进行运算处理即可获得精确的时钟Skew.

Seismic response of skewed RC box-girder bridges

It is critical to ensure the functionality of highway bridges after earthquakes to provide access to important facilities. Since the 1971 San Fernando earthquake, there has been a better understanding of the seismic performance of bridges. Nonetheless, there are no detailed guidelines addressing the performance of skewed highway bridges. Several parameters affect the response of skewed highway bridges under both service and seismic loads which makes their behavior complex. Therefore, there is a need for more research to study the effect of skew angle and other related factors on the performance of highway bridges. This paper examines the seismic performance of a three-span continuous concrete box girder bridge with skew angles from 0 to 60 degrees, analytically. Finite element （FE） and simplified beam-stick （BS） models of the bridge were developed using SAP2000. Different types of analysis were considered on both models such as： nonlinear static pushover, and linear and nonlinear time history analyses. A comparison was conducted between FE and BS, different skew angles, abutment support conditions, and time history and pushover analysis. It is shown that the BS model has the capability to capture the coupling due to skew and the significant modes for moderate skew angles. Boundary conditions and pushover load profile are determined to have a major effect on pushover analysis. Pushover analysis may be used to predict the maximum deformation and hinge formation adequately.

Improving MapReduce Performance by Balancing Skewed Loads

MapReduce has emerged as a popular computing model used in datacenters to process large amount of datasets.In the map phase,hash partitioning is employed to distribute data that sharing the same key across data center-scale cluster nodes.However,we observe that this approach can lead to uneven data distribution,which can result in skewed loads among reduce tasks,thus hamper performance of MapReduce systems.Moreover,worker nodes in MapReduce systems may differ in computing capability due to(1) multiple generations of hardware in non-virtualized data centers,or(2) co-location of virtual machines in virtualized data centers.The heterogeneity among cluster nodes exacerbates the negative effects of uneven data distribution.To improve MapReduce performance in heterogeneous clusters,we propose a novel load balancing approach in the reduce phase.This approach consists of two components:(1) performance prediction for reducers that run on heterogeneous nodes based on support vector machines models,and(2) heterogeneity-aware partitioning(HAP),which balances skewed data for reduce tasks.We implement this approach as a plug-in in current MapReduce system.Experimental results demonstrate that our proposed approach distributes work evenly among reduce tasks,and improves MapReduce performance with little overhead.