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.

Nonadditive Skew(Anti-)commuting Maps on Operator Algebras

In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obtain the concrete characterizations of all nonadditive skew(anti-)commuting maps on some operator algebras.

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.

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。

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.

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.

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.

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.

The effect of different intensity measures and earthquake directions on the seismic assessment of skewed highway bridges

In this study the probable seismic behavior of skewed bridges with continuous decks under earthquake excitations from different directions is investigated. A 45° skewed bridge is studied. A suite of 20 records is used to perform an Incremental Dynamic Analysis （IDA） for fragility curves. Four different earthquake directions have been considered： -45°, 0°, 22.5, 45°. A sensitivity analysis on different spectral intensity measures is presented; efficiency and practicality of different intensity measures have been studied. The fragility curves obtained indicate that the critical direction for skewed bridges is the skew direction as well as the longitudinal direction. The study shows the importance of finding the most critical earthquake in understanding and predicting the behavior of skewed bridges.

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.

SKEWED SYMMETRY DETECTION OF QUADRIC SURFACE SOLIDS UNDER ORTHOGRAPHIC PROJECTION

The skewed symmetry detection plays an improtant role in three-dimensional（3-D） reconstruction. The skewed symmetry depicts a real symmetry viewed from some unknown viewing directions. And the skewed symmetry detection can decrease the geometric constrains and the complexity of 3-D reconstruction. The detection technique for the quadric curve ellipse proposed by Sugimoto is improved to further cover quadric curves including hyperbola and parabola. With the parametric detection, the 3-D quadric curve projection matching is automatical- ly accomplished. Finally, the skewed symmetry surface of the quadric surface solid is obtained. Several examples are used to verify the feasibility of the algorithm and satisfying results can be obtained.

Genomic Instability in Cancer I: DNA-Repair Triggering Primitive Hereditary 4n-Skewed, Amitotic Division-System, the Culprit in EMT/MET/Metaplasia Cancer-Concepts

The objective was to gain proof of genome damage-repair induced mitotic slippage process (MSP) to 4n-diplochromosome skewed division-system, earlier suggested to have “cancer-deciding” consequences. Our damage-model showed two succeeding phases: molecular mutations for initiation of fitness-gained cells, and large chromosomal changes to aneuploidy from inherited DNA-breakage-repair inaccuracies. The mutations were gained while DNA-repair and DNA-replication, co-existed in the route to tetraploidy, a phenomenon also expressed for some existing unicellular organisms. These organisms also showed genome reductive, amitotic, meioticlike division, and was the origin of human genome conserved, self-inflicted 90° reorientation of the 4n nucleus relative to the cytoskeleton axis. In the in vitro DNA-damage model, this remarkable 4n-event deciding “flat-upright” cell-growth characteristics showed several consequences, for example, cancer-important, E-cadherin-β-catenin cell-to-cell adherence destruction, which gave diploid progeny cells, mobility freedom from cell contact inhibition, likely in renewal tissues. This 4n-skewed division-system with inheritance in progeny cells for repeat occurrences as mentioned for flat-up-right growth patterns is similar to claimed concepts of metaplasia-EMT/MET embryogenesis events in cancer evolution. A scrutiny of this literature, proof-wise invalidated this embryological concept by tetraploid 8C cells occurring in MET events and, was noted for small cell occurrence, i.e., diploidy from 4n-8C reductive division, an also event for tumor relapse cells, derived from genome damaging therapy agents. Pre-cancer hyperplasia reported MSP, cadherincatenin destruction and 90° perpendicularity to basal cell membrane. The DNA-damage-repair model can weed-out therapy-agents triggering 4n-skewed division. Cancer-control, beginning-information, is likely from mutational identity of the 4n derived fitness-gained cells.

A numerical study for boundary layer current and sheet flow transport induced by a skewed asymmetric wave

An analytical model with essential parameters given by a two-phase numerical model is utilized to study the net boundary layer current and sediment transport under skewed asymmetric oscillatory sheet flows. The analytical model is the first instantaneous type model that can consider phase-lag and asymmetric boundary layer development. The two-phase model supplies the essential phase-lead, instantaneous erosion depth and boundary layer development for the analytical model to enhance the understanding of velocity skewness and acceleration skewness in sediment flux and transport rate. The sediment transport difference between onshore and offshore stages caused by velocity skewness or acceleration skewness is shown to illustrate the determination of net sediment transport by the analytical model. In previous studies about sediment transport in skewed asymmetric sheet flows, the generation of net sediment transport is mainly concluded to the phase-lag effect.However, the phase-lag effect is shown important but not enough for the net sediment transport, while the skewed asymmetric boundary layer development generated net boundary layer current and mobile bed effect are key important in the transport process.

Influence of active constrained layer damping on the coupled vibration response of functionally graded magneto-electro-elastic plates with skewed edges

This article makes the first attempt in assessing the influence of active constrained layer damping(ACLD)treatment towards precise control of frequency responses of functionally graded skew-magneto-electroelastic(FGSMEE)plates by employing finite element methods.The materials are functionally graded across the thickness of the plate in terms of modest power-law distributions.The principal equations of motion of FGSMEE are derived via Hamilton’s principle and solved using condensation technique.The effect of ACLD patches are modelled by following the complex modulus approach(CMA).Additionally,distinctive emphasis is laid to evaluate the influence of geometrical skewness on the attenuation capabilities of the plate.The accuracy of the current analysis is corroborated with comparison of previous researches of similar kind.Additionally,a complete parametric study is directed to understand the combined impacts of various factors like coupling fields,patch location,fiber orientation of piezoelectric patch in association with skew angle and power-law index.

Hydrodynamic Efficiency Improvement of the High Skew Propeller for the Underwater Vehicle Under Surface and Submerged Conditions

An algorithm based on the Boundary Element Method(BEM)is presented for designing the High Skew Propeller(HSP)used in an Underwater Vehicle(UV).Since UVs operate under two different kinds of working conditions(i.e.surface and submerged conditions),the design of such a propeller is an unwieldy task.This is mainly due to the fact that the resistance forces as well as the vessel efficiency under these conditions are significantly different.Therefore,some factors are necessary for the design of the opti-mum propeller to utilize the power under the mentioned conditions.The design objectives of the optimum propeller are to obtain the highest possible thrust and efficiency with the minimum torque.For the current UV,the main dimensions of the propeller are pre-dicted based on the given required thrust and the defined operating conditions.These dimensions(number of blades,pitch,diameter,expanded area ratio,thickness and camber)are determined through iterative procedure.Because the propeller operates at the stern of the UV where the inflow velocity to the propeller is non-uniform,a 5-blade HSP is preferred for running the UV.Finally,the propel-ler is designed based on the numerical calculations to acquire the improved hydrodynamic efficiency.

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。

Prediction of Skewed Bridge Behaviors with Arbitrary Boundary Conditions—— Theoretical Approach and Its Design Application

In this paper, we report on an analytical solution for beam-type skewed highway bridges subjected to truck loading. To confirm the analysis derivation and the solution obtained, the moment and shear responses to the design truck load are acquired using the analytical method for a number of typical US highway bridges and compared with those from numerical finite element method （FEM） analysis. In addition, the lateral distribution factors for moment and shear used in routine design are investigated based on comparison of the analytical approach and FEM. The analytical solution is shown in good agreement with the FEM result. Furthermore, the relevant provisions in the American Association of State Highway Transportation Officials＇ （AASHTO＇s） LRFD Bridge Design Specifications are also discussed here for comparison, particularly with respect to design application. It is observed that the design code specified load distribution factor may not predict well, especially for shear and/or severe skew.

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。