Weak WT_2-class of differential forms and weakly A-harmonic tensors

In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of weakly A-harmonic tensors due to B. Stroffolini.

Some new integral inequalities for conjugate A-harmonic tensors

A new kind of weight-Ar^λ3 （λ1, λ2, Ω）-weight is used to prove the local and global integral inequalities for conjugate A-harmonic tensors, which can be regarded as generalizations of the classical results. Some applications of the above results to quasiregular mappings are given.

三维稳态Q-tensor液晶流系统各向异性的Liouville型定理

考虑速度分量的各向异性进行能量估计,得到三维稳态Q-tensor液晶流系统的Liouville型定理,即若u∈L^(q)(R^(3))∩˙H^(1)(R^(3)),u_(i)∈L xi q/q−2 L s xei(R×R^(2))(i=1,2,3),且Q∈H^(2)(R^(3)),其中2/q+1/s≥1/2,1≤s≤∞,2<q<∞,则该稳态系统只有平凡解.这个结论推广了已有的结果.

Euler Product Expressions of Absolute Tensor Products of Dirichlet L-Functions

In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.

Fault Diagnosis Scheme for Railway Switch Machine Using Multi-Sensor Fusion Tensor Machine

Railway switch machine is essential for maintaining the safety and punctuality of train operations.A data-driven fault diagnosis scheme for railway switch machine using tensor machine and multi-representation monitoring data is developed herein.Unlike existing methods,this approach takes into account the spatial information of the time series monitoring data,aligning with the domain expertise of on-site manual monitoring.Besides,a multi-sensor fusion tensor machine is designed to improve single signal data’s limitations in insufficient information.First,one-dimensional signal data is preprocessed and transformed into two-dimensional images.Afterward,the fusion feature tensor is created by utilizing the images of the three-phase current and employing the CANDE-COMP/PARAFAC(CP)decomposition method.Then,the tensor learning-based model is built using the extracted fusion feature tensor.The developed fault diagnosis scheme is valid with the field three-phase current dataset.The experiment indicates an enhanced performance of the developed fault diagnosis scheme over the current approach,particularly in terms of recall,precision,and F1-score.

Stress tensor determination by modified hydraulic tests on pre-existing fractures:Method and stress constraints

The hydraulic testing of pre-existing fractures(HTPF)is one of the most promising in situ stress measurement methods,particularly for three-dimensional stress tensor determination.However,the stress tensor determination based on the HTPF method requires at least six tests or a minimum of 14-15 tests(under different conditions)for reliable results.In this study,we modified the HTPF method by considering the shear stress on each pre-existing fracture,which increased the number of equations for the stress tensor determination and decreased the number of tests required.Different shear stresses were attributed to different fractures by random sampling;therefore,the stress tensors were obtained by searching for the optimal solution using the least squares criterion based on the Monte Carlo method.Thereafter,we constrained the stress tensor based on the tensile strength criterion,compressive strength criterion,and vertical stress constraints.The inverted stress tensors were presented and analyzed based on the tensorial nature of the stress using the Euclidean mean stress tensor.Two stress-measurement campaigns in Weifang(Shandong Province,China)and Mercantour road tunnel(France)were implemented to highlight the validity and efficiency of the modified HTPF(M-HTPF)method.The results showed that the M-HTPF method can be applied for stress tensor inversion using only three to four tests on pre-existing fractures,neglecting the stress gradient.The inversion results were confined to relatively small distribution dispersions and were significantly reliable and stable due to the shear stresses on the fractures and the stress constraints employed.The M-HTPF method is highly feasible and efficient for complete stress tensor determination in a single borehole.

Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model

We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger(SSH)model with long-range hopping terms.By computing the quantum geometry tensor,we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons,and we obtain the phase diagram of the model marked by the first Chern number.Furthermore,we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone.However,some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric,which leads to ill-defined non-integer topological Euler numbers.Nevertheless,the non-integer"Euler number"provides valuable insights and an upper bound for the absolute values of the Chern numbers.

Implementing and evaluating an automatic centroid moment tensor procedure for the Indonesia region and surrounding areas

The purpose of this research was to suggest an applicable procedure for computing the centroid moment tensor(CMT)automatically and in real time from earthquakes that occur in Indonesia and the surrounding areas.Gisola software was used to estimate the CMT solution by selecting the velocity model that best suited the local and regional geological conditions in Indonesia and the surrounding areas.The data used in this study were earthquakes with magnitudes of 5.4 to 8.0.High-quality,real-time broadband seismographic data were provided by the International Federation of Digital Seismograph Networks Web Services(FDSNWS)and the European Integrated Data Archive(EIDA)Federation in Indonesia and the surrounding areas.Furthermore,the inversion process and filter adjustment were carried out on the seismographic data to obtain good CMT solutions.The CMT solutions from Gisola provided good-quality solutions,in which all earthquake data had A-level quality(high quality,with good variant reduction).The Gisola CMT solution was justified with the Global CMT(GCMT)solution by using the Kagan angle value,with an average of approximately 11.2°.This result suggested that the CMT solution generated from Gisola was trustworthy and reliable.The Gisola CMT solution was typically available within approximately 15 minutes after an earthquake occurred.Once it met the quality requirement,it was automatically published on the internet.The catalog of local and regional earthquake records obtained through this technology holds great promise for improving the current understanding of regional seismic activity and ongoing tectonic processes.The accurate and real-time CMT solution generated by implementing the Gisola algorithm consisted of moment tensors and moment magnitudes,which provided invaluable insights into earthquakes occurring in Indonesia and the surrounding areas.

A Novel Tensor Decomposition-Based Efficient Detector for Low-Altitude Aerial Objects With Knowledge Distillation Scheme

Unmanned aerial vehicles(UAVs) have gained significant attention in practical applications, especially the low-altitude aerial(LAA) object detection imposes stringent requirements on recognition accuracy and computational resources. In this paper, the LAA images-oriented tensor decomposition and knowledge distillation-based network(TDKD-Net) is proposed,where the TT-format TD(tensor decomposition) and equalweighted response-based KD(knowledge distillation) methods are designed to minimize redundant parameters while ensuring comparable performance. Moreover, some robust network structures are developed, including the small object detection head and the dual-domain attention mechanism, which enable the model to leverage the learned knowledge from small-scale targets and selectively focus on salient features. Considering the imbalance of bounding box regression samples and the inaccuracy of regression geometric factors, the focal and efficient IoU(intersection of union) loss with optimal transport assignment(F-EIoU-OTA)mechanism is proposed to improve the detection accuracy. The proposed TDKD-Net is comprehensively evaluated through extensive experiments, and the results have demonstrated the effectiveness and superiority of the developed methods in comparison to other advanced detection algorithms, which also present high generalization and strong robustness. As a resource-efficient precise network, the complex detection of small and occluded LAA objects is also well addressed by TDKD-Net, which provides useful insights on handling imbalanced issues and realizing domain adaptation.

Least Squares One-Class Support Tensor Machine

One-class classification problem has become a popular problem in many fields, with a wide range of applications in anomaly detection, fault diagnosis, and face recognition. We investigate the one-class classification problem for second-order tensor data. Traditional vector-based one-class classification methods such as one-class support vector machine (OCSVM) and least squares one-class support vector machine (LSOCSVM) have limitations when tensor is used as input data, so we propose a new tensor one-class classification method, LSOCSTM, which directly uses tensor as input data. On one hand, using tensor as input data not only enables to classify tensor data, but also for vector data, classifying it after high dimensionalizing it into tensor still improves the classification accuracy and overcomes the over-fitting problem. On the other hand, different from one-class support tensor machine (OCSTM), we use squared loss instead of the original loss function so that we solve a series of linear equations instead of quadratic programming problems. Therefore, we use the distance to the hyperplane as a metric for classification, and the proposed method is more accurate and faster compared to existing methods. The experimental results show the high efficiency of the proposed method compared with several state-of-the-art methods.

关于Focal Loss的Tensor Train多项式分类器

在模式分类领域,多项式分类器因其复杂决策边界能力而得到广泛研究。利用TensorTrain分解形式来表示多项式分类器,可有效克服维数灾难。针对多项式分类器在训练过程中遇到的训练集分布不平衡问题,文章使用FocalLoss重塑了标准交叉损失,以降低分配给易分类样本的损失的权重,并在被广泛使用的图像分类数据集MNIST上验证了分类器的有效性。

OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS UNDER THE NATURAL GROWTH CONDITION:THE METHOD OF A-HARMONIC APPROXIMATION

In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. And directly establish the optimal Holder exponent for the derivative of a weak solution.

ON VERY WEAK SOLUTIONS OF A-HARMONICEQUATION WITH VERY WEAK BOUNDARYVALUES

In this paper,the following result is given by using Hodge decomposition: There exists r(0) = r(0)(n,p,a,b), such that if u is an element of W-loc(1,r)(Omega) is a very weak solution of (1.1),with C max{1,p - 1} < r < p and u is an element of W-0(1,r)(Omega;partial derivativeOmega\E) where E subset of partial derivativeOmega is a closed set and small in an appropriate capacity sense, then u = 0, a.e. in Omega provided that r(0) < r < p.

Verification of neutron-induced fission product yields evaluated by a tensor decompsition model in transport-burnup simulations

Neutron-induced fission is an important research object in basic science.Moreover,its product yield data are an indispensable nuclear data basis in nuclear engineering and technology.The fission yield tensor decomposition(FYTD)model has been developed and used to evaluate the independent fission product yield.In general,fission yield data are verified by the direct comparison of experimental and evaluated data.However,such direct comparison cannot reflect the impact of the evaluated data on application scenarios,such as reactor transport-burnup simulation.Therefore,this study applies the evaluated fission yield data in transport-burnup simulation to verify their accuracy and possibility of application.Herein,the evaluated yield data of235U and239Pu are applied in the transport-burnup simulation of a pressurized water reactor(PWR)and sodium-cooled fast reactor(SFR)for verification.During the reactor operation stage,the errors in pin-cell reactivity caused by the evaluated fission yield do not exceed 500 and 200 pcm for the PWR and SFR,respectively.The errors in decay heat and135Xe and149Sm concentrations during the short-term shutdown of the PWR are all less than 1%;the errors in decay heat and activity of the spent fuel of the PWR and SFR during the temporary storage stage are all less than 2%.For the PWR,the errors in important nuclide concentrations in spent fuel,such as90Sr,137Cs,85Kr,and99Tc,are all less than 6%,and a larger error of 37%is observed on129I.For the SFR,the concentration errors of ten important nuclides in spent fuel are all less than 16%.A comparison of various aspects reveals that the transport-burnup simulation results using the FYTD model evaluation have little difference compared with the reference results using ENDF/B-Ⅷ.0 data.This proves that the evaluation of the FYTD model may have application value in reactor physical analysis.

Analysis of rockburst mechanism and warning based on microseismic moment tensors and dynamic Bayesian networks

One of the major factors inhibiting the construction of deep underground projects is the risk posed by rockbursts.A study was conducted on the access tunnel of the Shuangjiangkou hydropower station to determine the evolutionary mechanism of microfractures within the surrounding rock mass during rockburst development and develop a rockburst warning model.The study area was chosen through the combination of field studies with an analysis of the spatial and temporal distribution of microseismic(MS)events.The moment tensor inversion method was adopted to study rockburst mechanism,and a dynamic Bayesian network(DBN)was applied to investigating the sensitivity of MS source parameters for rockburst warnings.A MS multivariable rockburst warning model was proposed and validated using two case studies.The results indicate that fractures in the surrounding rock mass during the development of strain-structure rockbursts initially show shear failure and are then followed by tensile failure.The effectiveness of the DBN-based rockburst warning model was demonstrated using self-validation and K-fold cross-validation.Moment magnitude and source radius are the most sensitive factors based on an investigation of the influence on the parent and child nodes in the model,which can serve as important standards for rockburst warnings.The proposed rockburst warning model was found to be effective when applied to two actual projects.

GPU-acceleration 3D rotated-staggered-grid solutions to microseismic anisotropic wave equation with moment tensor implementation

To improve the accuracy of microseismic inversion,seismic anisotropy and moment tensor source should be carefully considered in the forward modelling stage.In this study,3D microseismic anisotropy wave forward modelling with a moment tensor source was proposed.The modelling was carried out based on a rotated-staggered-grid(RSG)scheme.In contrast to staggered-grids,the RSG scheme defines the velocity components and densities at the same grid,as do the stress components and elastic parameters.Therefore,the elastic moduli do not need to be interpolated.In addition,the detailed formulation and implementation of moment-tensor source loaded on the RSG was presented by equating the source to the stress increments.Meanwhile,the RSG-based 3D wave equation forward modelling was performed in parallel using compute unified device architecture(CUDA)programming on a graphics processing unit(GPU)to improve its efficiency.Numerical simulations including homogeneous and anisotropic models were carried out using the method proposed in this paper,and compared with other methods to prove the reliability of this method.Furthermore,the high efficiency of the proposed approach was evaluated.The results show that the computational efficiency of proposed method can be improved by about two orders of magnitude compared with traditional central processing unit(CPU)computing methods.It could not only help the analysis of microseismic full wavefield records,but also provide support for passive source inversion,including location and focal mechanism inversion,and velocities inversion.

PARTIAL REGULARITY FOR STATIONARY NAVIER-STOKES SYSTEMS BY THE METHOD OF A-HARMONIC APPROXIMATION

In this article,we prove a regularity result for weak solutions away from singular set of stationary Navier-Stokes systems with subquadratic growth under controllable growth condition.The proof is based on the A-harmonic approximation technique.In this article,we extend the result of Shuhong Chen and Zhong Tan[7]and Giaquinta and Modica[18]to the stationary Navier-Stokes system with subquadratic growth.

REGULARITY FOR VERY WEAK SOLUTIONS TO A-HARMONIC EQUATION

In this paper, the following result is given by using Hodge decomposition and weak reverse Holder inequality： For every r1 with P-（2^n＋1 100^n^2 p（2^3＋n/（P-1）＋1）b/a）^-1〈r1〈p,there exists the exponent r2 = r2（n, r1,p） 〉 p, such that for every very weak solution u∈W^1r1,loc（Ω） to A-harmonic equation, u also belongs to W^1r2,loc（Ω） . In particular, u is the weak solution to A-harmonic equation in the usual sense.

Popularity Prediction of Social Media Post Using Tensor Factorization

The traditional method of doing business has been disrupted by socialmedia. In order to develop the enterprise, it is essential to forecast the level ofinteraction that a new post would receive from social media users. It is possiblefor the user’s interest in any one social media post to be impacted by external factors or to dwindle as a result of changes in his behaviour. The popularity detectionstrategies that are user-based or population-based are unable to keep up with theseshifts, which leads to inaccurate forecasts. This work makes a prediction abouthow popular the post will be and addresses any anomalies caused by factors outside of the study. A novel improved PARAFAC (A-PARAFAC) method that istensor factorization-based has been presented in order to cope with the user criteria that will be used in the future to rate any project. We consolidated the information on the historically popular content, and we accelerated the computation bychoosing the top contents that were most like each other. The tensor is factorisedwith the application of the Adam optimization. It has been modified such that thebias is now included in the gradient function of A-PARAFAC, and the value ofthe bias is updated after each iteration. The prediction accuracy is improved by32.25% with this strategy compared to other state of the art methods.

Extremum Principle for Very Weak Solutions of A-Harmonic Equation with Weight

Extremum principle for very weak solutions of A-harmonic equation div A(x,▽u)=0 is obtained, where the operator A:Ω × Rn→Rnsatisfies some coercivity and controllable growth conditions with Mucken-houpt weight.