INVISCID INCOMPRESSIBLE AND COMPRESSIBLE FLOW EQUATIONS UNDER SPACE-TIME TRANSFORMATION

The equations governing incompressible and compressible inviscid flows and written in the physical frame ( t,x,y,z ) are known to be linearly well posed and exhibit elliptic or hyperbolic nature. The linear well posedness is considered here for these equations under a space time transformation ( t,x,y,z)→(τ,ξ,η,ζ ), where the pseudo time τ and the new space coordinate ( ξ,η,ζ ) all depend on ( t,x,y,z ). Such a transformation could be useful for uniformly treating problems in which the flow is fast unsteady somewhere and slow unsteady or steady elsewhere. It is found that the transformation may alter the ellipticity, the hyperbolicty, and even the well posedness of the original equations. In one dimension, the transformed incompressible flow equations become weakly hyperbolic and the compressible ones could degenerate to elliptical equations. In high dimensions there are conditions such that the transformed equations become ill posed.

REAL PALEY-WIENER THEOREMS FOR THE SPACE-TIME FOURIER TRANSFORM

This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.

Reciprocal transformations of the space-time shifted nonlocal short pulse equations

Reciprocal transformations of the space-time shifted nonlocal short pulse equations are elaborated.Covariance of dependent and independent variables involved in the reciprocal transformations is investigated.Exact solutions of the space-time shifted nonlocal short pulse equations are given in terms of double Wronskians.Realness of independent variables involved in the reciprocal transformations is verified.Dynamics of some obtained solutions are illustrated.

Scale Invariant Theory of Gravitation in Einstein-Rosen Space-Time

In this paper, we have studied the perfect fluid distribution in the scale invariant theory of gravitation, when the space-time described by Einstein-Rosen metric with a time dependent gauge function. The cosmological equations for this space-time with gauge function are solved and some physical properties of the model are studied.

Change of Space-Time Structure under Lorentz Transformation

When we study Lorentz transformation in the framework of quantum gauge theory of gravity, we will find that the vacuum gravitational gauge field will be changed under gravitational gauge transformation, which will change the structure of the physical space-time and cause clock dilation effect. The study in this paper provides us with new insights to understand the essential and intrinsic relation between special relativity and general relativity. It provides us with a new way to unify special relativity and general relativity.

基于Contextual Transformer的自动驾驶单目3D目标检测

针对当前单目3D目标检测中存在的漏检和多尺度目标检测效果不佳的问题,提出了一种基于Contextual Transformer的自动驾驶单目3D目标检测算法(CM-RTM3D)。在ResNet-50网络中引入Contextual Transformer(CoT),构建ResNet-Transformer架构以提取特征。设计多尺度空间感知模块(MSP),通过尺度空间响应操作改善浅层特征的丢失情况,嵌入沿水平和竖直两个空间方向的坐标注意力机制(CA),使用softmax函数生成各尺度的重要性软权重。在偏移损失中采用Huber损失函数代替L1损失函数。实验结果表明:在KITTI自动驾驶数据集上,相较于RTM3D算法,该算法在简单、中等、困难三个难度级别下,AP3D分别提升了4.84、3.82、5.36个百分点,APBEV分别提升了4.75、6.26、3.56个百分点。

基于多层次特征融合的Transformer人脸识别方法

卷积神经网络中的卷积操作只能捕获局部信息,而Transformer能保留更多的空间信息且能建立图像的长距离连接.在视觉领域的应用中,Transformer缺乏灵活的图像尺寸及特征尺度适应能力,通过利用层级式网络增强不同尺度建模的灵活性,且引入多尺度特征融合模块丰富特征信息.本文提出了一种基于改进的Swin Transformer人脸模型——Swin Face模型.Swin Face以Swin Transformer为骨干网络,引入多层次特征融合模块,增强了模型对人脸的特征表达能力,并使用联合损失函数优化策略设计人脸识别分类器,实现人脸识别.实验结果表明,与多种人脸识别方法相比,Swin Face模型通过使用分级特征融合网络,在LFW、CALFW、AgeDB-30、CFP数据集上均取得最优的效果,验证了此模型具有良好的泛化性和鲁棒性.

多尺度局部特征和Transformer全局学习融合的发动机剩余寿命预测

飞机发动机剩余寿命(Remaining useful life,RUL)的准确预测对确保其安全性和可靠性至关重要.在基于多传感器检测数据预测时,需解决局部特征提取问题以全面捕捉设备在不同时间尺度下的退化趋势,并需解决时间序列中各元素之间长期依赖性的全局学习问题.因此,提出了结合多尺度局部特征增强单元(Multi-sacle local feature enhancement unit,MSLFU_BLOCK)和Transformer编码器的预测模型,称之为MS_Transformer.MSLFU_BLOCK利用堆叠的因果卷积逐层从时间序列数据中提取多尺度局部信息,同时避免了传统卷积计算中固有的未来数据泄漏问题.随后,Transformer编码器通过其自注意机制进一步捕获时间序列数据中的短期和长期依赖关系.通过将多尺度局部特征增强单元与Transformer编码器相结合,提出的MS_Transformer全面捕捉了时间序列数据中的局部和全局模式.在广泛使用的CMAPSS基准数据集上进行的消融和预测实验验证了模型的合理性和有效性.与13个先进预测模型的比较分析表明,MS_Transformer模型在操作条件更复杂的FD002和FD004数据集上的RMSE和Score指标优于其他模型,同时在四个数据集上的平均性能最优.该研究为发动机剩余寿命预测提供了更为可靠的解决方案.

基于边缘辅助和多尺度Transformer的无参考屏幕内容图像质量评估

与从现实场景中拍摄的自然图像不同,屏幕内容图像是一种合成图像,通常由计算机生成的文本、图形和动画等各种多媒体形式组合而成.现有评估方法通常未能充分考虑图像边缘结构信息和全局上下文信息对屏幕内容图像质量感知的影响.为解决上述问题,本文提出一种基于边缘辅助和多尺度Transformer的无参考屏幕内容图像质量评估模型.首先,使用高斯拉普拉斯算子构造由失真屏幕内容图像高频信息组成的边缘结构图,然后通过卷积神经网络(Convolutional Neural Network,CNN)对输入的失真屏幕内容图像和相应的边缘结构图进行多尺度的特征提取与融合,以图像的边缘结构信息为模型训练提供额外的信息增益.此外,本文进一步构建了基于Transformer的多尺度特征编码模块,从而在CNN获得的局部特征基础上更好地建模不同尺度图像和边缘特征的全局上下文信息.实验结果表明,本文提出的方法在指标上优于其他现有的无参考和全参考屏幕内容图像质量评估方法,能够取得更高的主客观视觉感知一致性.

Generalized canonical transformation for second-order Birkhoffian systems on time scales

The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems.In this paper,the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied,which extends the canonical transformation theory of Hamilton canonical equations.First,the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second,based on this condition,six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given.Also,the relationships between new variables and old variables for each of these cases are derived.In the end,an example is given to show the application of the results.

结合沙漏注意力与渐进式混合Transformer的图像分类方法

Transformer在图像分类任务中具有广泛应用,但在小数据集分类任务中,Transformer受到数据量较少、模型参数量过大等因素的影响,导致分类精度低、收敛速度缓慢。本文提出了一种融合沙漏注意力的渐进式混合Transformer模型。首先,通过下-上采样的沙漏自注意力建模全局特征关系,利用上采样补充下采样操作丢失的信息,同时采用可学习温度参数和负对角掩码锐化注意力的分数分布,避免因层数过多产生过度平滑的现象;其次,设计渐进式下采样模块获得细粒度多尺度特征图,有效捕获低维特征信息;最后,使用混合架构,在顶层阶段使用设计的沙漏注意力,底层阶段使用池化层替代注意力模块,并引入带有深度卷积的层归一化,增加网络局部性。所提方法在T-ImageNet、CIFAR10、CIFAR100、SVHN数据集上进行实验,分类精度可以达到97.42%,计算量和参数量分别为3.41G和25M。实验结果表明,与对比算法相比,该方法的分类精度有明显提升,计算量和参数量有明显降低,提高了Transformer模型在小数据集上的性能表现。

Multiple Time Scale Analysis of River Runoff Using Wavelet Transform for Dagujia River Basin, Yantai, China

Based on monthly river runoff and meteorological data, a method of Morlet wavelet transform was used to analyze the multiple time scale characteristics of river runoff in the Dagujia River Basin, Yantai City, Shandong Province. The results showed that the total annual river runoffin the Dagujia River Basin decreased significantly from 1966 to 2004, and the rate of decrease was 48× 10^6ma/10yr, which was higher than the mean value of most rivers in China. Multiple time scale characteristics existed, which accounted for different aspects of the changes in annual river runoff, and the major periods of the runofftime series were identified as about 28 years, 14 years and 4 years with decreasing levels of fluctuation. The river runoff evolution process was controlled by changes in precipitation to a certain extent, but it was also greatly influenced by human activities. Also, for different time periods and scales, the impacts of climate changes and human activities on annual river runoff evolution occurred at the same time. Changes in the annual river runoffwere mainly associated with climate change before the 1980s and with human activities after 1981.

多尺度融合卷积的轻量化Transformer无人机地物识别模型

Transformer模型性能优越,但其巨大的参数量不适合资源受限的无人机遥感任务。为此,提出一种用于无人机遥感图像的多尺度融合卷积的轻量化Transformer模型,通过设计三种优化策略来提高精度以及减少参数量。首先,设计了一种轻量级多尺度融合卷积方法,补充Transformer丢失的块内空间信息,从而有效提取多尺度上的粗、细粒度特征表示。其次,设计了多尺度缩减键值序列的方式,优化Transformer中的自注意力计算。最后,设计了轻量级的MLP解码器,进一步减少模型参数量。在Vaihingen和Potsdam数据集上与一些主流模型进行了对比实验,结果表明,所提模型的F 1值和交并比均有所提升。同时,在Potsdam数据集上准确度提升0.29%,参数量比双分支网络STransFuse减少18%。

混合U型网络与Transformer的图像去模糊

针对现有去模糊方法不能有效地恢复图像精细细节的问题,提出了一种混合U型网络与Transformer的图像去模糊方法。首先,使用一个多尺度特征提取模块提取图像的浅层特征信息。然后,通过一个含逐级特征增强模块的层级嵌套U型子网络,在保留图像细节信息的同时获取图像深层特征信息。再次,构建了一个局部-全局残差细化模块,通过卷积神经网络和SwinTransformer之间的信息交互充分提取全局和局部信息,并实现特征信息的进一步细化。最后,使用一个1×1卷积层进行特征重建。所提方法在GoPro数据集上的实验结果显示,图像的峰值信噪比和结构相似度均值分别为32.92和0.964,均优于其他对比方法。实验结果表明,所提方法可以有效地去除模糊,重建出具有丰富细节的潜在清晰图像。

LES prediction of space-time correlations in turbulent shear flows

We compare the space-time correlations calculated from direct numerical simulation （DNS） and large-eddy simulation （LES） of turbulent channel flows. It is found from the comparisons that the LES with an eddy-viscosity subgrid scale （SGS） model over-predicts the space-time corre- lations than the DNS. The overpredictions are further quantified by the integral scales of directional correlations and convection velocities. A physical argument for the overpre- diction is provided that the eddy-viscosity SGS model alone does not includes the backscatter effects although it correctly represents the energy dissipations of SGS motions. This argument is confirmed by the recently developed elliptic model for space-time correlations in turbulent shear flows. It suggests that enstrophy is crucial to the LES prediction of spacetime correlations. The random forcing models and stochastic SGS models are proposed to overcome the overpredictions on space-time correlations.

结合Swin Transformer的多尺度遥感图像变化检测研究

由于地物信息的复杂性及变化检测数据的多元性,遥感图像特征提取的充分性和有效性难以得到保证,导致变化检测方法获取的检测结果可靠性较低。虽然卷积神经网络(CNN)凭借有效提取语义特征的优势,被广泛应用于遥感领域的变化检测之中,但卷积操作固有的局部性导致感受野受限,无法捕获时空上的全局信息以至于特征空间对中远距离依赖关系的建模受限。为捕获远距离的语义依赖,提取深层全局语义特征,设计了一种基于Swin Transformer的多尺度特征融合网络SwinChangeNet。首先,SwinChangeNet采用孪生的多级Swin Transformer特征编码器进行远距离上下文建模;其次,编码器中引入特征差异提取模块,计算不同尺度下变化前后的多级特征差异,再通过自适应融合层将多尺度特征图进行融合;最后,引入残差连接和通道注意力机制对融合后的特征信息进行解码,从而生成完整准确的变化图。在CDD和CD_Data_GZ 2个公开数据集上分别与7种经典和前沿变化检测方法进行比较,CDD数据集中本文模型的性能最优,相比于性能第二的模型,F1分数提高了1.11%,精确率提高了2.38%。CD_Data_GZ数据集中本文模型的性能最优,相比于性能第二的模型,F1分数、精确率和召回率分别提高了4.78%,4.32%,4.09%,提升幅度较大。对比实验结果证明了该模型具有更好的检测效果。在消融实验中也证实了模型中各个改进模块的稳定性和有效性。本文模型针对遥感图像变化检测任务,引入了Swin Transformer结构,使网络可以对遥感图像的局部特征和全局特征进行更有效地编码,让检测结果更加准确,同时保证网络在地物要素种类繁多的数据集上容易收敛。

Scale transform algorithm used in FMCW SAR data processing

The frequency-modulated continuous-wave （FMCW） synthetic aperture radar （SAR） is a light-weight, cost-effective, high-resolution imaging radar, which is suitable for a small flight platform. The signal model is derived for FMCW SAR used in unmanned aerial vehicles （UAV） reconnaissance and remote sensing. An appropriate algorithm is proposed. The algorithm performs the range cell migration correction （RCMC） for continuous nonchirped raw data using the energy invariance of the scaling of a signal in the scale domain. The azimuth processing is based on step transform without geometric resampling operation. The complete derivation of the algorithm is presented. The algorithm performance is shown by simulation results.

High-order perturbed corrections with scaling transformation

The performance of the so-called superconvergent quantum perturbation theory （Wenhua Hal et al2000 Phys. Rev. A 61 052105） is investigated for the case of the ground-state energy of the helium-like ions. The scaling transformation τ → τ/Z applied to the Hamiltonian of a two-electron atomic ion with a nuclear charge Z （in atomic units）. Using the improved Rayleigh-SchrSdinger perturbation theory based on the integral equation to helium-like ions in the ground states and treating the electron correlations as perturbations, we have performed a third-order perturbation calculation and obtained the second-order corrected wavefunctions consisting of a few terms and third-order energy corrections. We find that third-order and higher-order energy corrections are improved with decreasing nuclear charge. This result means that the former is quadratically integrable and the latter is physically meaningful. The improved quantum perturbation theory fits the higher-order perturbation case. This work shows that it is a development on the quantum perturbation problem of helium-like systems.

LNG-Transformer:基于多尺度信息交互的图像分类网络

鉴于Transformer的Self-Attention机制具有优秀的表征能力,许多研究者提出了基于Self-Attention机制的图像处理模型,并取得了巨大成功。然而,基于Self-Attention的传统图像分类网络无法兼顾全局信息和计算复杂度,限制了Self-Attention的广泛应用。文中提出了一种有效的、可扩展的注意力模块Local Neighbor Global Self-Attention(LNG-SA),该模块在任意时期都能进行局部信息、邻居信息和全局信息的交互。通过重复级联LNG-SA模块,设计了一个全新的网络,称为LNG-Transformer。该网络整体采用层次化结构,具有优秀的灵活性,其计算复杂度与图像分辨率呈线性关系。LNG-SA模块的特性使得LNG-Transformer即使在早期的高分辨率阶段,也可以进行局部信息、邻居信息和全局信息的交互,从而带来更高的效率、更强的学习能力。实验结果表明,LNG-Transformer在图像分类任务中具有良好的性能。

SIMPLIFIED SCALING TRANSFORMATION FOR THE NUMERICAL SIMULATION OF MEMS DEVICES WITH THIN FILM STRUCTURES

Thin film is a widely used structure in the present microelectromechanical systems （MEMS） and plays a vital role in many functional devices. However, the great size difference between the film＇s thickness and its planar dimensions makes it difficult to study the thin film performance numerically. In this work, a scaling transformation was presented to make the different dimensional sizes equivalent, and thereby, to improve the grid quality considerably. Two numerical experiments were studied to validate the present scaling transformation method. The numerical results indicated that the largest grid size difference can be decreased to one to two orders of magnitude by using the present scaling transformation, and the memory required by the numerical simulation, i.e., the total grid number, could be reduced by about two to three orders of magnitude, while the numerical accuracies with and without this scaling transformation were nearly the same.