ENTIRE FUNCTIONS REPRESENTED BY LAPLACE-STIELTJES TRANSFORMS CONCERNING THE APPROXIMATION AND GENERALIZED ORDER

The first aim of this paper is to investigate the growth of the entire function defined by the Laplace-Stieltjes transform converges on the whole complex plane.By introducing the concept of generalized order,we obtain two equivalence theorems of Laplace-Stiettjes transforms related to the generalized order,A_(n)^(*)andλ_(n).The second purpose of this paper is to study the problem on the approximation of this Laplace-Stieltjes transform.We also obtain some theorems about the generalized order,the error,and the coefficients of Laplace-Stieltjes transforms,which are generalization and improvement of the previous results.

An integrable generalization of the Fokas–Lenells equation:Darboux transformation, reduction and explicit soliton solutions

Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas–Lenells system is constructed. As a reduction, the N-fold Darboux transformation for the generalized Fokas–Lenells equation is obtained, from which the N-soliton solution in a compact Vandermonde-like determinant form is given. Particularly,the explicit one-and two-soliton solutions are presented and their dynamical behaviors are shown graphically.

The Significance of Generalized Gauge Transformation across Fundamental Interactions

The author of this paper has put forward a unified program of gauge field from the mathematical and physical picture of the principal associated bundles: thinking that our universe may have more fundamental interactions than the four fundamental interactions, and these basic interaction gauge fields are only the projection components to the base manifold, that is our universe, from a unified gauge potential or connection of the principal associated bundle manifold on the base manifold. These components can satisfy the transformation of gauge potential, and can even be transformed from one basic interaction gauge potential to another basic interaction gauge potential, and can be summarized into a unified equation, that is, the generalized gauge Equation (GGE), but the gauge potential or connection on the principal bundle is invariant, corresponding to the invariance of gauge transformation [1]. In this paper, we will continue to discuss this aspect concretely, and specifically construct a spatiotemporal model with the frame bundle as the principal bundle, and the tensor bundle as the associated bundle, so that the four fundamental interactions, especially the electromagnetic interaction and the gravitational interaction, can be reflected in the bottom manifold, that is, the regional distributions in our universe. Furthermore, this paper studies the existence of gauge transformation across basic interactions by establishing a model of gauge transformation of basic interaction field;it is found that the unified expression formula is GGE and the expression relation on the curvature of space-time. Therefore, the author discusses the feasibility of the generalized gauge transformation across the basic electromagnetic interaction and the basic gravitational interaction, and on this basis, specifically determines a method or way to find the generalized gauge transformation, so as to try to realize the last step of the “unification” of the four fundamental interactions in physics, that is, the “unification” of electromagnetism and gravity.

基于Transformer和自适应特征融合的矿井低照度图像亮度提升和细节增强方法

高质量矿井影像为矿山安全生产提供保障,也有利于提高后续图像分析技术的性能。矿井影像受低照度环境的影响,易出现亮度低,照度不均,颜色失真,细节信息丢失严重等问题。针对上述问题,提出一种基于Transformer和自适应特征融合的矿井低照度图像亮度提升和细节增强方法。基于生成对抗思想搭建生成对抗式主体模型框架,使用目标图像域而非单一参考图像驱动判别器监督生成器的训练,实现对低照度图像的充分增强;基于特征表示学习理论搭建特征编码器,将图像解耦为亮度分量和反射分量,避免图像增强过程中亮度与颜色特征相互影响从而导致颜色失真问题;设计CEM-Transformer Encoder通过捕获全局上下文关系和提取局部区域特征,能够充分提升整体图像亮度并消除局部区域照度不均;在反射分量增强过程中,使用结合CEM-Cross-Transformer Encoder的跳跃连接将低级特征与深层网络处特征进行自适应融合,能够有效避免细节特征丢失,并在编码网络中添加ECA-Net,提高浅层网络的特征提取效率。制作矿井低照度图像数据集为矿井低照度图像增强任务提供数据资源。试验显示,在矿井低照度图像数据集和公共数据集中,与5种先进的低照度图像增强算法相比,该算法增强图像的质量指标PSNR、SSIM、VIF平均提高了16.564%,10.998%,16.226%和14.438%,10.888%,14.948%,证明该算法能够有效提升整体图像亮度,消除照度不均,避免颜色失真和细节丢失,实现矿井低照度图像增强。

基于生成对抗Transformer的电力负荷数据异常检测

电力负荷异常数据将给电力系统规划、负荷预测以及用能分析等带来较大的负面影响,因此亟须对负荷数据异常进行检测与识别。首先,针对电力负荷数据异常分类、原因及其特征开展分析。其次,改进传统Transformer编码器结构,采用多头注意力层代替掩码多头注意力层,同时移除前馈网络,以提高模型对负荷时序序列的全局注意力。基于生成对抗网络(generative adversarial networks,GAN)生成器与判别器的博弈结构,提出一种改进的GAN-Transformer模型,以更好地捕捉趋势性特征并加速模型收敛。然后,引入多阶段映射与训练方法,综合焦点分数打分机制,通过分阶段负荷序列重构帮助模型更好地提取负荷数据异常特征。最后,算例分析结果表明,GAN-Transformer模型在负荷数据异常检测精确率、召回率、F_(1)值以及训练时间方面均具有更优的性能,验证了所提方法的有效性和优越性。文中研究工作为基于深度学习进一步实现电力负荷数据异常分类与数据修复提供了有益参考。

基于条件对抗增强的Transformer煤矿微震定位方法

随着人工智能技术的发展以及煤矿微震监测系统的广泛应用,越来越多的深度学习模型被应用到煤矿微震事件震源定位问题的求解上。然而,由于目前的微震数据量小且数据单一不足以训练大且深的神经网络模型,而小且浅的神经网络模型也不足以表征受多方因素影响的微震事件的震源,因而导致了定位模型定位精度低和鲁棒性弱,在实际生产生活中表现较差,严重地阻碍了深度学习模型在微震定位领域上的发展。针对上述问题,提出一种基于条件对抗增强的Transformer煤矿微震定位方法CGAN-Transformer,该方法首先通过一个CGAN架构的网络模型将数据量少且单一的微震数据增强成数据量庞大且具有一定多样性的微震数据;其次,利用Transformer编码器层将微震波形数据转换为特征数据后再利用其注意力机制进一步学习微震波形数据深层次特征和复杂的站间依赖关系,同时也利用高斯分布随机变量抵消了不同地质条件对定位精度的影响;最后,通过引入混合密度输出层获取高斯分布参数,计算最优的震源位置。在智利和辽宁某矿数据集上的实验结果验证了该方法的有效性,结果表明该方法所获得的震中误差与震源误差均优于其他方法,在两个数据集上的定位误差分别降低了38%和12%,达到了提高震源定位精度和定位模型鲁棒性的目的。

ON THE GROWTH OF ZERO ORDER LAPLACE-STIELTJES TRANSFORM CONVERGENT IN THE RIGHT HALF-PLANE

In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between them. Some results similar to Dirichlet series are obtained.

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.

Generalized Demodulation Transform for Bearing Fault Diagnosis Under Nonstationary Conditions and Gear Noise Interferences

It is a challenging issue to detect bearing fault under nonstationary conditions and gear noise interferences. Meanwhile, the application of the traditional methods is limited by their deficiencies in the aspect of computational accuracy and e ciency, or dependence on the tachometer. Hence, a new fault diagnosis strategy is proposed to remove gear interferences and spectrum smearing phenomenon without the tachometer and angular resampling technique. In this method, the instantaneous dominant meshing multiple(IDMM) is firstly extracted from the time-frequency representation(TFR) of the raw signal, which can be used to calculate the phase functions(PF) and the frequency points(FP). Next, the resonance frequency band excited by the faulty bearing is obtained by the band-pass filter. Furthermore, based on the PFs, the generalized demodulation transform(GDT) is applied to the envelope of the filtered signal. Finally, the target bearing is diagnosed by matching the peaks in the spectra of demodulated signals with the theoretical FPs. The analysis results of simulated and experimental signal demonstrate that the proposed method is an e ective and reliable tool for bearing fault diagnosis without the tachometer and the angular resampling.

A Protection Method of VSC-HVDC Cables Based on Generalized S-Transform

Generalized S-transform is a time-frequency analysis method which has higher resolution than S-transform. It can precisely extract the time-amplitude characteristics of different frequency components in the signal. In this paper, a novel protection method for VSC-HVDC (Voltage source converter based high voltage DC) based on Generalized S-transform is proposed. Firstly, extracting frequency component of fault current by Generalized S-transform and using mutation point of high frequency to determine the fault time. Secondly, using the zero-frequency component of fault current to eliminate disturbances. Finally, the polarity of sudden change currents in the two terminals is employed to discriminate the internal and external faults. Simulations in PSCAD/EMTDC and MATLAB show that the proposed method can distinguish faults accurately and effectively.

Brain Functional Network Generation Using Distribution-Regularized Adversarial Graph Autoencoder with Transformer for Dementia Diagnosis

The topological connectivity information derived from the brain functional network can bring new insights for diagnosing and analyzing dementia disorders.The brain functional network is suitable to bridge the correlation between abnormal connectivities and dementia disorders.However,it is challenging to access considerable amounts of brain functional network data,which hinders the widespread application of data-driven models in dementia diagnosis.In this study,a novel distribution-regularized adversarial graph auto-Encoder(DAGAE)with transformer is proposed to generate new fake brain functional networks to augment the brain functional network dataset,improving the dementia diagnosis accuracy of data-driven models.Specifically,the label distribution is estimated to regularize the latent space learned by the graph encoder,which canmake the learning process stable and the learned representation robust.Also,the transformer generator is devised to map the node representations into node-to-node connections by exploring the long-term dependence of highly-correlated distant brain regions.The typical topological properties and discriminative features can be preserved entirely.Furthermore,the generated brain functional networks improve the prediction performance using different classifiers,which can be applied to analyze other cognitive diseases.Attempts on the Alzheimer’s Disease Neuroimaging Initiative(ADNI)dataset demonstrate that the proposed model can generate good brain functional networks.The classification results show adding generated data can achieve the best accuracy value of 85.33%,sensitivity value of 84.00%,specificity value of 86.67%.The proposed model also achieves superior performance compared with other related augmentedmodels.Overall,the proposedmodel effectively improves cognitive disease diagnosis by generating diverse brain functional networks.

On the Approximation of an Analytic Function Represented by Laplace-Stieltjes Transformation

In the present paper,we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in terms of the rate of decrease of E;（F,β） where E;（F,β） is the error in approximating of the function F（s） by definite integral polynomials in the half plane Res≤β<α.

基于Swin Transformer生成对抗网络的图像生成算法

针对图像生成算法中生成对抗网络训练效率低且不稳定的问题,本文提出了一种改进生成对抗网络的图像生成算法(STGAN),该算法首先在判别器中引入Swin Transformer机制,来增强网络的判别能力;其次改进了生成器,使用自注意力代替卷积神经并且加入谱范数规范化,来达到平衡生成器和判别器的效果;最后使用Wasserstein距离作为损失函数,以提高网络的训练稳定性.实验数据表明,在CelebA和LSUN两种不同数据集上STGAN比自注意力生成对抗网络所生成图像的FID值分别降低了2.5266和5.4476,IS值分别提高了0.0941和0.0343.从实验结果可以看出,STGAN模型生成的图片具有非常高的自然度和逼真度,有效地提升了生成图像的质量和真实性.

Symmetry Transformations and Exact Solutions of a Generalized Hyperelastic Rod Equation

In this paper,a nonlinear wave equation with variable coefficients is studied,interestingly,this equation can be used to describe the travelling waves propagating along the circular rod composed of a general compressible hyperelastic material with variable cross-sections and variable material densities.With the aid of Lou’s direct method1,the nonlinear wave equation with variable coefficients is reduced and two sets of symmetry transformations and exact solutions of the nonlinear wave equation are obtained.The corresponding numerical examples of exact solutions are presented by using different coefficients.Particularly,while the variable coefficients are taken as some special constants,the nonlinear wave equation with variable coefficients reduces to the one with constant coefficients,which can be used to describe the propagation of the travelling waves in general cylindrical rods composed of generally hyperelastic materials.Using the same method to solve the nonlinear wave equation,the validity and rationality of this method are verified.

改良Transformer模型应用于乳腺结节超声报告自主生成的可行性研究

目的将改良Transformer模型应用于乳腺结节超声报告自主生成,并对其可行性进行初步探讨。方法收集832例乳腺结节患者(共1284个结节)的超声图像构建BND数据集,引入一种改良Transformer模型对BND数据集进行智能分析,生成相应文本报告,并与Ensemble Model、SSD、R-FCN模型进行比较;同时引入LGK数据集,将改良Transformer模型与TieNet、Kerp、VTI、RNCM模型进行比较。采用BLEU评分评估各模型的性能。结果在BND数据集中,改良模型的BLEU-1、BLEU-2、BLEU-3及BLEU-4评分分别为0.547、0.474、0.352、0.282,均高于Ensemble Model、SSD、R-FCN模型。在LGK数据集中,改良Transformer模型的BLEU-1、BLEU-2、BLEU-3及BLEU-4评分分别为0.579、0.391、0.288、0.152。结论改良Transformer模型能够快速识别乳腺结节并自主生成标准报告,与Ensemble Model、SSD、R-FCN模型相比,获得了良好的BLEU评分,同时该模型在LGK数据集中BLEU评分也较高,表明改良Transformer模型具有较高的文本泛化性能。

GENERALIZED WAVELETS AND INVERSION OF THE RADON TRANSFORM ON THE LAGUERRE HYPERGROUP

Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.

基于Transformer和GAN的对抗样本生成算法

对抗攻击与防御是计算机安全领域的一个热门研究方向。针对现有基于梯度的对抗样本生成方法可视质量差、基于优化的方法生成效率低的问题,提出基于Transformer和生成对抗网络(GAN)的对抗样本生成算法Trans-GAN。首先利用Transformer强大的视觉表征能力,将其作为重构网络,用于接收干净图像并生成攻击噪声;其次将Transformer重构网络作为生成器,与基于深度卷积网络的鉴别器相结合组成GAN网络架构,提高生成图像的真实性并保证训练的稳定性,同时提出改进的注意力机制Targeted Self-Attention,在训练网络时引入目标标签作为先验知识,指导网络模型学习生成具有特定攻击目标的对抗扰动;最后利用跳转连接将对抗噪声施加在干净样本上,形成对抗样本,攻击目标分类网络。实验结果表明:Trans-GAN算法针对MNIST数据集中2种模型的攻击成功率都达到99.9%以上,针对CIFAR10数据集中2种模型的攻击成功率分别达到96.36%和98.47%,优于目前先进的基于生成式的对抗样本生成方法;相比快速梯度符号法和投影梯度下降法,Trans-GAN算法生成的对抗噪声扰动量更小,形成的对抗样本更加自然,满足人类视觉不易分辨的要求。

基于孪生Transformer的双时相遥感影像变化检测方法

针对卷积神经网络无法充分利用全局上下文信息的问题,提出了基于孪生transformer结构的双时相遥感影像变化检测方法。首先,利用swin transformer网络提取双时相遥感影像的抽象特征,并将不同尺度的特征嵌入到特征金字塔网络中输出变化检测结果;然后,为了使变化检测结果形态更接近真实标记,在训练过程中采用对抗训练方法,即引入判别器来判断变化检测结果是由模型预测得到还是人工标记得到,从而使模型预测结果更加接近真实标记。在LEVIR-CD和SYSU-CD两个变化检测数据集上的实验表明,所提出的方法能够有效提高变化检测精度。

Mutual transformations between the P–Q, Q–P, and generalized Weyl ordering of operators

Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok （p, q） with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, - 1,0, respectively, we find the mutual transformations between 6 （p - P） （q - Q）, （q - Q） 3 （p - P）, and （p, q）, which are, respectively, the integration kernels of the P-Q, Q-P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The - and - ordered forms of （p, q） are also derived, which helps us to put the operators into their - and - ordering, respectively.

Certain Integral Transforms of Generalized k-Bessel Function

The objective of this note is to provide some(potentially useful) integral transforms(for example, Euler, Laplace, Whittaker etc.) associated with the generalized k-Bessel function defined by Saiful and Nisar [3]. We have also discussed some other transforms as special cases of our main results.