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871.
S. Morigi 《Journal of Computational and Applied Mathematics》2010,233(5):1277-1287
Surface processing tools based on Partial Differential Equations (PDEs) are useful in a variety of applications in computer graphics, digital animation, computer aided modelling, and computer vision. In this work, we deal with computational issues arising from the discretization of geometric PDE models for the evolution of surfaces, considering both normal and tangential velocities. The evolution of the surface is formulated in a Lagrangian framework. We propose several strategies for tangential velocities, yielding uniform redistribution of mesh points along the evolving family of surfaces, preventing computational instabilities and increasing the mesh regularity. Numerical schemes based on finite co-volume approximation in space will be considered. Finally, we describe how this framework may be employed in applications such as mesh regularization, morphing, and features preserving surface smoothing. 相似文献
872.
Computation of control for a controlled partial differential equation is a di?cult task, especially when the control problem is ill posed. In this paper, we propose a method of computing the regularized control of a diffusion control system using Tikhonov regularization approach when the system is approximately controllable. The method proposed here for choosing regularization parameter guarantees the convergence of the proposed control. 相似文献
873.
874.
We study, for the first time in the literature on the subject, the Cauchy problem for a semilinear fractional elliptic equation. Under an a priori assumption on the solution, we propose the Fourier truncation method for stabilizing the ill-posed problem. A stability estimate of logarithmic type is established. 相似文献
875.
I. Snyman 《Czechoslovak Journal of Physics》2004,54(1):139-142
It has been suggested that the machinery of PT-symmetric quantum mechanics can be utilized to regularize certain singular potentials. In this contribution I point out that different regularizations lead to different results. In a particular model, that of the spiked harmonic oscillator, I use a symmetry inherent in the model to cast some light on this ambiguity. 相似文献
876.
Based on a new regularization-renormalization method, the λφ4 model used in standard model (SM) is studied both perturbatively and nonperturbatively by Gaussian effective potential (GEP).
The invariant property of two mass scales is stressed and the existence of a (Landau) pole is emphasized. Then after coupling
with theSU(2) ×U(1) gauge fields, the Higgs mass in standard model (SM) can be calculated to bem
H≈138 GeV. The critical temperature (T
c
) for restoration of symmetry of Higgs field, the critical energy scale (μmax, the maximum energy scale under which the lower excitation sector of the GEP is valid) and the maximum energy scale (μmax, at which the symmetry of the Higgs field is restored) in the SM areT
c
≈476 GeV, μc≈0.547 × 1015 and μmax≈0.873 × 1015, respectively.
Project supported in part by the National Natural Science Foundation of China. 相似文献
877.
M. Bostan 《Mathematical Methods in the Applied Sciences》2006,29(15):1801-1848
In this work, we study the existence of time periodic weak solution for the N‐dimensional Vlasov–Poisson system with boundary conditions. We start by constructing time periodic solutions with compact support in momentum and bounded electric field for a regularized system. Then, the a priori estimates follow by computations involving the conservation laws of mass, momentum and energy. One of the key point is to impose a geometric hypothesis on the domain: we suppose that its boundary is strictly star‐shaped with respect to some point of the domain. These results apply for both classical or relativistic case and for systems with several species of particles. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
878.
The problem of differentiating spectral data to yield the third and fourth derivatives is converted into one of solving an integral equation of the first kind. This equation is solved by Tikhonov regularization. The method of General Cross Validation is used to guide the choice of the regularization parameter that keeps noise amplification under control. The performance of this route to third and fourth derivative spectra is demonstrated by applying it to a number of published spectra. A computational problem associated with General Cross Validation has been identified. 相似文献
879.
Limitations of the L-curve method in ill-posed problems 总被引:3,自引:0,他引:3
Martin Hanke 《BIT Numerical Mathematics》1996,36(2):287-301
This paper considers the Tikhonov regularization method with the regularization parameter chosen by the so-called L-curve criterion. An infinite dimensional example is constructed for which the selected regularization parameter vanishes too rapidly as the noise to signal ratio in the data goes to zero. As a consequence the computed reconstructions do not converge to the true solution. Numerical examples are given to show that similar phenomena can be observed under more general assumptions in discrete ill-posed problems provided the exact solution of the problem is smooth.This work was partially supported by NATO grant CRG 930044. 相似文献
880.
In this work we determine the normal solution of the finite moment problem in three different Hilbert space settings, both in the absence and in the presence of noisy data. In two cases the normal solution is a polynomial while in the third it is not. However, in each case the normal solution is spanned by orthogonal functions that are obtained by computationally efficient algorithms. A criterion of a posteriori validation, to select that normal solution which minimizes the uniform norm of the recovery error, is also given. The effectiveness of the method is illustrated with a number of test functions, for the most part already proposed in the literature. 相似文献