基于QR迭代的量子奇异值分解

针对大型矩阵奇异值分解(singular value decomposition,SVD)时使用经典算法时间复杂度较高,以及已有的量子SVD算法要求待分解的矩阵必须具有非稀疏低秩的性质,并且在计算过程中构造任意大小酉矩阵对目前的量子计算机来说实现起来并不容易等问题,提出基于QR迭代的量子SVD。QR迭代使用的是Householder变换,通过量子矩阵乘法运算完成经典矩阵乘法运算过程。实验结果表明,该方法能够得到所求矩阵的奇异值及奇异矩阵,使大型矩阵的SVD具有可行性。

Multi-Scale-Matching neural networks for thin plate bending problem

Physics-informed neural networks are a useful machine learning method for solving differential equations,but encounter challenges in effectively learning thin boundary layers within singular perturbation problems.To resolve this issue,multi-scale-matching neural networks are proposed to solve the singular perturbation problems.Inspired by matched asymptotic expansions,the solution is decomposed into inner solutions for small scales and outer solutions for large scales,corresponding to boundary layers and outer regions,respectively.Moreover,to conform neural networks,we introduce exponential stretched variables in the boundary layers to avoid semiinfinite region problems.Numerical results for the thin plate problem validate the proposed method.

DeepSVDNet:A Deep Learning-Based Approach for Detecting and Classifying Vision-Threatening Diabetic Retinopathy in Retinal Fundus Images

Artificial Intelligence(AI)is being increasingly used for diagnosing Vision-Threatening Diabetic Retinopathy(VTDR),which is a leading cause of visual impairment and blindness worldwide.However,previous automated VTDR detection methods have mainly relied on manual feature extraction and classification,leading to errors.This paper proposes a novel VTDR detection and classification model that combines different models through majority voting.Our proposed methodology involves preprocessing,data augmentation,feature extraction,and classification stages.We use a hybrid convolutional neural network-singular value decomposition(CNN-SVD)model for feature extraction and selection and an improved SVM-RBF with a Decision Tree(DT)and K-Nearest Neighbor(KNN)for classification.We tested our model on the IDRiD dataset and achieved an accuracy of 98.06%,a sensitivity of 83.67%,and a specificity of 100%for DR detection and evaluation tests,respectively.Our proposed approach outperforms baseline techniques and provides a more robust and accurate method for VTDR detection.

Bending strength degradation of a cantilever plate with surface energy due to partial debonding at the clamped boundary

This paper investigates the bending fracture problem of a micro/nanoscale cantilever thin plate with surface energy,where the clamped boundary is partially debonded along the thickness direction.Some fundamental mechanical equations for the bending problem of micro/nanoscale plates are given by the Kirchhoff theory of thin plates,incorporating the Gurtin-Murdoch surface elasticity theory.For two typical cases of constant bending moment and uniform shear force in the debonded segment,the associated problems are reduced to two mixed boundary value problems.By solving the resulting mixed boundary value problems using the Fourier integral transform,a new type of singular integral equation with two Cauchy kernels is obtained for each case,and the exact solutions in terms of the fundamental functions are determined using the PoincareBertrand formula.Asymptotic elastic fields near the debonded tips including the bending moment,effective shear force,and bulk stress components exhibit the oscillatory singularity.The dependence relations among the singular fields,the material constants,and the plate's thickness are analyzed for partially debonded cantilever micro-plates.If surface energy is neglected,these results reduce the bending fracture of a macroscale partially debonded cantilever plate,which has not been previously reported.

THE SUPERCLOSENESS OF THE FINITE ELEMENT METHOD FOR A SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEM ON A BAKHVALOV-TYPE MESH IN 2D

For singularly perturbed convection-diffusion problems,supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,especially in the case of 2D.The difficulties arise from the width of the mesh in the layer adjacent to the transition point,resulting in a suboptimal estimate for convergence.Existing analysis techniques cannot handle these difficulties well.To fill this gap,here a novel interpolation is designed delicately for the smooth part of the solution,bringing about the optimal supercloseness result of almost order 2 under an energy norm for the finite element method.Our theoretical result is uniform in the singular perturbation parameterεand is supported by the numerical experiments.

High-Temperature Phonon-Mediated Superconductivity with T_(c) above 100K in Monolayer Na(BC)_(2) and K(BC)_(2)

Two-dimensional(2D)materials have demonstrated promising prospects owing to their distinctive electronic properties and exceptional mechanical properties.Among them,2D superconductors with T_(c) above the boiling point of liquid nitrogen(77 K)will exhibit tremendous applicable value in the future.Here,we design two 2D superconductors Na(BC)_(2) and K(BC)_(2) with MgB2-like structures,which are theoretically predicted to host T_(c) as high as 99 and 102 K,respectively.The origin of such high T_(c) is ascribed to the presence of both𝜎-bonding bands and van Hove singularity at the Fermi level.Furthermore,T_(c) of Na(BC)_(2) is boosted up to 153K with a biaxial strain of 5%,which sets a new record among 2D superconductors.The predictions of Na(BC)_(2) and K(BC)_(2) open the door to explore 2D high-temperature superconductors and provide a potential future for developing new applications in 2D materials.

Periodic signal extraction of GNSS height time series based on adaptive singular spectrum analysis

Singular spectrum analysis is widely used in geodetic time series analysis.However,when extracting time-varying periodic signals from a large number of Global Navigation Satellite System(GNSS)time series,the selection of appropriate embedding window size and principal components makes this method cumbersome and inefficient.To improve the efficiency and accuracy of singular spectrum analysis,this paper proposes an adaptive singular spectrum analysis method by combining spectrum analysis with a new trace matrix.The running time and correlation analysis indicate that the proposed method can adaptively set the embedding window size to extract the time-varying periodic signals from GNSS time series,and the extraction efficiency of a single time series is six times that of singular spectrum analysis.The method is also accurate and more suitable for time-varying periodic signal analysis of global GNSS sites.

An Initial Perturbation Method for the Multiscale Singular Vector in Global Ensemble Prediction

Ensemble prediction is widely used to represent the uncertainty of single deterministic Numerical Weather Prediction(NWP) caused by errors in initial conditions(ICs). The traditional Singular Vector(SV) initial perturbation method tends only to capture synoptic scale initial uncertainty rather than mesoscale uncertainty in global ensemble prediction. To address this issue, a multiscale SV initial perturbation method based on the China Meteorological Administration Global Ensemble Prediction System(CMA-GEPS) is proposed to quantify multiscale initial uncertainty. The multiscale SV initial perturbation approach entails calculating multiscale SVs at different resolutions with multiple linearized physical processes to capture fast-growing perturbations from mesoscale to synoptic scale in target areas and combining these SVs by using a Gaussian sampling method with amplitude coefficients to generate initial perturbations. Following that, the energy norm,energy spectrum, and structure of multiscale SVs and their impact on GEPS are analyzed based on a batch experiment in different seasons. The results show that the multiscale SV initial perturbations can possess more energy and capture more mesoscale uncertainties than the traditional single-SV method. Meanwhile, multiscale SV initial perturbations can reflect the strongest dynamical instability in target areas. Their performances in global ensemble prediction when compared to single-scale SVs are shown to(i) improve the relationship between the ensemble spread and the root-mean-square error and(ii) provide a better probability forecast skill for atmospheric circulation during the late forecast period and for short-to medium-range precipitation. This study provides scientific evidence and application foundations for the design and development of a multiscale SV initial perturbation method for the GEPS.

Kinematic-mapping-model-guided analysis and optimization of 2-PSS&1-RR circular-rail parallel mechanism for fully steerable phased array antennas

This paper presents a systematic methodology for analyzing and optimizing an innovative antenna mount designed for phased array antennas, implemented through a novel 2-PSS&1-RR circular-rail parallel mechanism. Initially, a comparative motion analysis between the 3D model of the mount and its full-scale prototype is conducted to validate effectiveness. Given the inherent complexity, a kinematic mapping model is established between the mount and the crank-slider linkage, providing a guiding framework for subsequent analysis and optimization. Guided by this model, feasible inverse and forward solutions are derived, enabling precise identification of stiffness singularities. The concept of singularity distance is thus introduced to reflect the structural stiffness of the mount. Subsequently, also guided by the mapping model, a heuristic algorithm incorporating two backtracking procedures is developed to reduce the mount's mass. Additionally, a parametric finite-element model is employed to explore the relation between singularity distance and structural stiffness. The results indicate a significant reduction(about 16%) in the antenna mount's mass through the developed algorithm, while highlighting the singularity distance as an effective stiffness indicator for this type of antenna mount.

Geochemical Anomalies Identified by Multifractal Modeling: Implications for Mineral Exploration in the Ziyoutun Cu-Au District, Jilin Province, China

The Ziyoutun Cu-Au district is located in the Jizhong–Yanbian Metallogenic Belt and possesses excellent prospects. However, the thick regolith and complex tectonic settings present challenges in terms of detecting and decomposition of weak geochemical anomalies. To address this challenge, we initially conducted a comprehensive analysis of 1:10,000-scale soil geochemical data. This analysis included multivariate statistical techniques, such as correlation analysis, R-mode cluster analysis, Q–Q plots and factor analysis. Subsequently, we decomposed the geochemical anomalies, identifying weak anomalies using spectrum-area modeling and local singularity analysis. The results indicate that the assemblage of Au-Cu-Bi-As-Sb represents the mineralization at Ziyoutun. In comparison to conventional methods, spectrumarea modeling and local singularity analysis outperform in terms of identification of anomalies. Ultimately, we considered four specific target areas(AP01, AP02, AP03 and AP04) for future exploration, based on geochemical anomalies and favorable geological factors. Within AP01 and AP02, the geochemical anomalies suggest potential mineralization at depth, whereas in AP03 and AP04 the surface anomalies require additional geological investigation. Consequently, we recommend conducting drilling, following more extensive surface fieldwork, at the first two targets and verifying surface anomalies in the last two targets. We anticipate these findings will significantly enhance future exploration in Ziyoutun.

SOME PROPERTIES OF THE INTEGRATION OPERATORS ON THE SPACES F(p,q,s)

We study the closed range property and the strict singularity of integration operators acting on the spaces F(p,pα-2,s).We completely characterize the closed range property of the Volterra companion operator I_(g)on F(p,pα-2,s),which generalizes the existing results and answers a question raised in[A.Anderson,Integral Equations Operator Theory,69(2011),no.1,87-99].For the Volterra operator J_(g),we show that,for 0<α≤1,J_(g)never has a closed range on F(p,pα-2,s).We then prove that the notions of compactness,weak compactness and strict singularity coincide in the case of J_(g)acting on F(p,p-2,s).

A reweighted damped singular spectrum analysis method for robust seismic noise suppression

(Multichannel)Singular spectrum analysis is considered as one of the most effective methods for seismic incoherent noise suppression.It utilizes the low-rank feature of seismic signal and regards the noise suppression as a low-rank reconstruction problem.However,in some cases the seismic geophones receive some erratic disturbances and the amplitudes are dramatically larger than other receivers.The presence of this kind of noise,called erratic noise,makes singular spectrum analysis(SSA)reconstruction unstable and has undesirable effects on the final results.We robustify the low-rank reconstruction of seismic data by a reweighted damped SSA(RD-SSA)method.It incorporates the damped SSA,an improved version of SSA,into a reweighted framework.The damping operator is used to weaken the artificial disturbance introduced by the low-rank projection of both erratic and random noise.The central idea of the RD-SSA method is to iteratively approximate the observed data with the quadratic norm for the first iteration and the Tukeys bisquare norm for the rest iterations.The RD-SSA method can suppress seismic incoherent noise and keep the reconstruction process robust to the erratic disturbance.The feasibility of RD-SSA is validated via both synthetic and field data examples.

Indentation behavior of a semi-infinite piezoelectric semiconductor under a rigid flat-ended cylindrical indenter

This paper theoretically studies the axisymmetric frictionless indentation of a transversely isotropic piezoelectric semiconductor(PSC)half-space subject to a rigid flatended cylindrical indenter.The contact area and other surface of the PSC half-space are assumed to be electrically insulating.By the Hankel integral transformation,the problem is reduced to the Fredholm integral equation of the second kind.This equation is solved numerically to obtain the indentation behaviors of the PSC half-space,mainly including the indentation force-depth relation and the electric potential-depth relation.The results show that the effect of the semiconductor property on the indentation responses is limited within a certain range of variation of the steady carrier concentration.The dependence of indentation behavior on material properties is also analyzed by two different kinds of PSCs.Finite element simulations are conducted to verify the results calculated by the integral equation technique,and good agreement is demonstrated.

Chien-physics-informed neural networks for solving singularly perturbed boundary-layer problems

A physics-informed neural network(PINN)is a powerful tool for solving differential equations in solid and fluid mechanics.However,it suffers from singularly perturbed boundary-layer problems in which there exist sharp changes caused by a small perturbation parameter multiplying the highest-order derivatives.In this paper,we introduce Chien's composite expansion method into PINNs,and propose a novel architecture for the PINNs,namely,the Chien-PINN(C-PINN)method.This novel PINN method is validated by singularly perturbed differential equations,and successfully solves the wellknown thin plate bending problems.In particular,no cumbersome matching conditions are needed for the C-PINN method,compared with the previous studies based on matched asymptotic expansions.

THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

This paper is mainly about the spectral properties of a class of Jacobi operators(H_(c,b)u)(n)=c_(n)u(n+1)+c_(n-1)u(n-1)+b_(n)u(n),.where∣c_(n)−1∣=O(n^(−α))and b_(n)=O(n^(−1)).We will show that,forα≥1,the singular continuous spectrum of the operator is empty.

Adaptive Optimal Output Regulation of Interconnected Singularly Perturbed Systems With Application to Power Systems

This article studies the adaptive optimal output regulation problem for a class of interconnected singularly perturbed systems(SPSs) with unknown dynamics based on reinforcement learning(RL).Taking into account the slow and fast characteristics among system states,the interconnected SPS is decomposed into the slow time-scale dynamics and the fast timescale dynamics through singular perturbation theory.For the fast time-scale dynamics with interconnections,we devise a decentralized optimal control strategy by selecting appropriate weight matrices in the cost function.For the slow time-scale dynamics with unknown system parameters,an off-policy RL algorithm with convergence guarantee is given to learn the optimal control strategy in terms of measurement data.By combining the slow and fast controllers,we establish the composite decentralized adaptive optimal output regulator,and rigorously analyze the stability and optimality of the closed-loop system.The proposed decomposition design not only bypasses the numerical stiffness but also alleviates the high-dimensionality.The efficacy of the proposed methodology is validated by a load-frequency control application of a two-area power system.

An improved wind quality control for the China-France Oceanography Satellite (CFOSAT) scatterometer

Quality control(QC)is an essential procedure in scatterometer wind retrieval,which is used to distinguish good-quality data from poor-quality wind vector cells(WVCs)for the sake of wind applications.The current wind processor of the China-France Oceanography Satellite(CFOSAT)scatterometer(CSCAT)adopts a maximum likelihood estimator(MLE)-based QC method to filter WVCs affected by geophysical noise,such as rainfall and wind variability.As the first Ku-band rotating fan-beam scatterometer,CSCAT can acquire up to 16 observations over a single WVC,giving abundant information with diverse incidence/azimuth angles,as such its MLE statistical characteristics may be different from the previous scatterometers.In this study,several QC indicators,including MLE,its spatially averaged value(MLE_(m)),and the singularity exponents(SE),are analyzed using the collocated Global Precipitation Mission rainfall data as well as buoy data,to compare their sensitivity to rainfall and wind quality.The results show that wind error characteristics of CSCAT under different QC methods are similar to those of other Ku-band scatterometers,i.e.,SE is more suitable than other parameters for the wind QC at outer-swath and nadir regions,while MLE_(m) is the best QC indicator for the sweet region WVCs.Specifically,SE is much more favorable than others at high wind speeds.By combining different indicators,an improved QC method is developed for CSCAT.The validation with the collocated buoy data shows that it accepts more WVCs,and in turn,improves the quality control of CSCAT wind data.

Wavelet Multi-Resolution Interpolation Galerkin Method for Linear Singularly Perturbed Boundary Value Problems

In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.

A SINGULAR DIRICHLET PROBLEM FOR THE MONGE-AMPÈRE TYPE EQUATION

We consider the singular Dirichlet problem for the Monge-Ampère type equation■=0,whereΩis a strictly convex and bounded smooth domain in■is positive and strictly decreasing in(0,∞)with■is positive inΩ.We obtain the existence,nonexistence and global asymptotic behavior of the convex solution to such a problem for more general b and g.Our approach is based on the Karamata regular variation theory and the construction of suitable sub-and super-solutions.

具有奇异势和一般非线性的伪抛物方程解的局部存在性和爆破

In this paper,a semilinear pseudo-parabolic equation with a general nonlin-earity and singular potential is considered.We prove the local existence of solution by Galerkin method and contraction mapping theorem.Moreover,we prove the blow-up of solution and estimate the upper bound of the blow-up time for J(u0)≤0.Finally,we prove the finite time blow-up and estimate the upper bound of blow-up time for J(u0)>0.