In this paper the qualitative analysis methods of planar autonomous systems and numerical simu-lation are used to investigate the peaked wave solutions of CH-r equation. Some explicit expressions of peakedsolitary wav...
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In this paper the qualitative analysis methods of planar autonomous systems and numerical simu-lation are used to investigate the peaked wave solutions of CH-r equation. Some explicit expressions of peakedsolitary wave solutions and peaked periodic wave solutions are obtained, and some of their relationships arerevealed. Why peaked points are generated is discussed.
In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abs...
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In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.
The resonance characteristics of second-sound waves in liquid helium II are analyzed by using standard acoustical techniques. The effects of dissipation, Kapitza resistance and thermal capacity of the heater are asses...
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The resonance characteristics of second-sound waves in liquid helium II are analyzed by using standard acoustical techniques. The effects of dissipation, Kapitza resistance and thermal capacity of the heater are assessed. In typical experimental situations the resonant frequency shift due to these effects is likely to be negligibel. The Q-value of a resonator as usual is dominated by the attenuation coefficient, but the effect of Kapitza resistance could be significant unless a stringent condition on the heater thickness is observed.
This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matri...
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This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are partially known （to a certain accuracy）. This problem aggregates two existing problems： （i） nonnegative matrix factorization where all entries of M are given, and （ii） low-rank matrix completion where non- negativity is not required. By taking the advantages of both nonnegativity and low-rankness, one can generally obtain superior results than those of just using one of the two properties. We propose to solve the non-convex constrained least-squares problem using an algorithm based on tile classical alternating direction augmented Lagrangian method. Preliminary convergence properties of the algorithm and numerical simulation results are presented. Compared to a recent algorithm for nonnegative matrix factorization, the proposed algorithm produces factorizations of similar quality using only about half of the matrix entries. On tasks of recovering incomplete grayscale and hyperspeetral images, the proposed algorithm yields overall better qualities than those produced by two recent matrix-completion algorithms that do not exploit nonnegativity.
An algorithm for the inverse of a general tridiagonal matrix is presented. For a tridiagonal matrix having the Doolittle factorization, an inversion algorithm is established. The algorithm is then generalized to deal ...
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An algorithm for the inverse of a general tridiagonal matrix is presented. For a tridiagonal matrix having the Doolittle factorization, an inversion algorithm is established. The algorithm is then generalized to deal with a general tridiagonal matrix without any restriction. Comparison with other methods is provided, indicating low computational complexity of the proposed algorithm, and its applicability to general tridiagonal matrices.
Invariants of approximate transformation groups are studied. It turns out that the infinitesimal criterion for them is similar to that of Lie's theory. Namely, the problem of invariants of approximate groups reduc...
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Invariants of approximate transformation groups are studied. It turns out that the infinitesimal criterion for them is similar to that of Lie's theory. Namely, the problem of invariants of approximate groups reduces to solving first-order partial differential equations with a small parameter. The problems of solvability, number of independent invariants, and a representation of general approximate invariants are discussed. (C) 1997 Academic Press.
A manufacturing process for glass sheet production is investigated. In the process, molten glass is formed into a continuous sheet which is conveyed on a long train of supporting rollers until it is cool enough to be ...
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A manufacturing process for glass sheet production is investigated. In the process, molten glass is formed into a continuous sheet which is conveyed on a long train of supporting rollers until it is cool enough to be cut into sheets of required length. A mathematical model for the structural behaviour of the sheet in this “roll-out” operation is formulated. In this model the glass is treated as a simple Maxwell elastico-viscous material with temperature-dependent viscosity. The sheet is considered as a continuous beam in horizontal translation over the rollers. computational solutions for the sheet deflection, obtained with the aid of certain analytical results (derived elsewhere), are given for a variety of boundary conditions. These solutions are found to be in good agreement with observed process behaviour.
Interpretation of geophysical data is greatly aided by the combined analysis of data from diverse sources. Probability theory provides a general framework for integrating geophysical data sets. We discuss the applicat...
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Interpretation of geophysical data is greatly aided by the combined analysis of data from diverse sources. Probability theory provides a general framework for integrating geophysical data sets. We discuss the application of joint and conditional probability density functions (PDF) to the detection of anomalies and the prediction and interpolation of gee-variables. Density estimation techniques are discussed and illustrated on a geophysical data set from West Africa consisting of magnetic, elevation, and radiometric data.
Gliomas have the highest mortality rate of all brain *** classifying the glioma risk period can help doctors make reasonable treatment plans and improve patients’survival *** paper proposes a hierarchical multi-scale...
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Gliomas have the highest mortality rate of all brain *** classifying the glioma risk period can help doctors make reasonable treatment plans and improve patients’survival *** paper proposes a hierarchical multi-scale attention feature fusion medical image classification network(HMAC-Net),which effectively combines global features and local *** network framework consists of three parallel layers:The global feature extraction layer,the local feature extraction layer,and the multi-scale feature fusion layer.A linear sparse attention mechanism is designed in the global feature extraction layer to reduce information *** the local feature extraction layer,a bilateral local attention mechanism is introduced to improve the extraction of relevant information between adjacent *** the multi-scale feature fusion layer,a channel fusion block combining convolutional attention mechanism and residual inverse multi-layer perceptron is proposed to prevent gradient disappearance and network degradation and improve feature representation *** double-branch iterative multi-scale classification block is used to improve the classification *** the brain glioma risk grading dataset,the results of the ablation experiment and comparison experiment show that the proposed HMAC-Net has the best performance in both qualitative analysis of heat maps and quantitative analysis of evaluation *** the dataset of skin cancer classification,the generalization experiment results show that the proposed HMAC-Net has a good generalization effect.
Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of ...
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Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping *** resulting iterative schemes have a fast convergence rate to steady-state ***,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local ***,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the *** multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational *** this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational ***,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)*** experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.
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