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941.
Summary We study a model equation describing the temporal evolution of nonlinear finite-amplitude waves on a density front in a rotating
fluid. The linear spectrum includes an unstable interval where exponential growth of the amplitude is expected. It is shown
that the length scale of the waves in the nonlinear situation is determined by the linear instabilities; the effect of the
nonlinearities is to limit the amplitude's growth, leaving the wavelength unchanged. When linearly stable waves are prescribed
as initial data, a short interval of rapid decrease in amplitude is encountered first, followed by a transfer of energy to
the unstable part of the spectrum, where the fastest growing mode starts to dominate. A localized disturbance is broken up
into its Fourier components, the linearly unstable modes grow at the expense of all other modes, and final amplitudes are
determined by the nonlinear term. Periodic evolution of linearly unstable waves in the nonlinear situation is also observed.
Based on the numerical results, the existence of low-order chaos in the partial differential equation governing weakly nonlinear
wave evolution is conjectured. 相似文献
942.
Symplectic scheme-shooting method (SSSM) is applied to solve the energy eigenvalues of anharmonic oscillators characterized by the potentials V(x)=λx4 and V(x)=(1/2)x2+λx2α with α=2,3,4 and doubly anharmonic oscillators characterized by the potentials V(x)=(1/2)x2+λ1x4+λ2x6, and a high order symplectic scheme tailored to the "time"-dependent Hamiltonian function is presented. The numerical results illustrate that the energy eigenvalues of anharmonic oscillators with the symplectic scheme-shooting method are in good agreement with the numerical accurate ones obtained from the non-perturbative method by using an appropriately scaled basis for the expansion of each eigenfunction; and the energy eigenvalues of doubly anharmonic oscillators with the sympolectic scheme-shooting method are in good agreement with the exact ones and are better than the results obtained from the four-term asymptotic series. Therefore, the symplectic scheme-shooting method, which is very simple and is easy to grasp, is a good numerical algorithm. 相似文献
943.
944.
David T. Gay 《Transactions of the American Mathematical Society》2002,354(3):1027-1047
A standard convexity condition on the boundary of a symplectic manifold involves an induced positive contact form (and contact structure) on the boundary; the corresponding concavity condition involves an induced negative contact form. We present two methods of symplectically attaching -handles to convex boundaries of symplectic -manifolds along links transverse to the induced contact structures. One method results in concave boundaries and depends on a fibration of the link complement over ; in this case the handles can be attached with any framing larger than a lower bound determined by the fibration. The other method results in a weaker convexity condition on the new boundary (sufficient to imply tightness of the new contact structure), and in this case the handles can be attached with any framing less than a certain upper bound. These methods supplement methods developed by Weinstein and Eliashberg for attaching symplectic -handles along Legendrian knots.
945.
On stable numerical differentiation 总被引:6,自引:0,他引:6
A new approach to the construction of finite-difference methods is presented. It is shown how the multi-point differentiators can generate regularizing algorithms with a stepsize being a regularization parameter. The explicitly computable estimation constants are given. Also an iteratively regularized scheme for solving the numerical differentiation problem in the form of Volterra integral equation is developed.
946.
Marek Andrzej Kojdecki 《BIT Numerical Mathematics》2001,41(5):1059-1068
Tikhonov regularization is one of the most popular methods for solving linear operator equations of the first kind Au = f with bounded operator, which are ill-posed in general (Fredholm's integral equation of the first kind is a typical example). For problems with inexact data (both the operator and the right-hand side) the rate of convergence of regularized solutions to the generalised solution u
+ (i.e.the minimal-norm least-squares solution) can be estimated under the condition that this solution has the source form: u
+ im(A*A). It is well known that for Tikhonov regularization the highest-possible worst-case convergence rates increase with only for some values of , in general not greater than one. This phenomenon is called the saturation of convergence rate. In this article the analysis of this property of the method with a criterion of a priori regularization parameter choice is presented and illustrated by examples constructed for equations with compact operators.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
947.
Teresa Regińska 《BIT Numerical Mathematics》2001,41(5):1101-1110
The sideways heat equation is considered in terms of the ill-posed operator equation Au = g, g R(A) L
2(), with a given noisy right hand side. For a reconstruction of the solution from indirect data the dual least square method generated by the family of Meyer wavelet subspaces is applied. An explicit relation between the truncation level of the wavelet expansion and the data error bound is found under which convergence results including error estimation are obtained. Next, a certain simple nonlinear modification of the method based on local refinements of the wavelet expansion of the noisy data is investigated. Moreover, it is shown that an accuracy of the solution reconstruction can be improved by adding some sufficiently large coefficients on the level higher than that indicated by the convergence theorem.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
948.
Aluffi-Pentini F. Castrignanò T. Maponi P. Parisi V. Zirilli F. 《Journal of Optimization Theory and Applications》1999,103(1):45-64
Let n, m be positive integers; we consider m×n real linear systems. We define regularized solutions of a linear system as the minimizers of an optimization problem. The objective function of this optimization problem can be seen as the Tikhonov functional when the p-norm is considered instead of the Euclidean norm. The cases p=1 and p= are studied. This analysis is used to restore defocused synthetic images and real images with encouraging results. 相似文献
949.
Michaela Vancliff 《Algebras and Representation Theory》1999,2(3):269-285
A family of flat deformations of a commutative polynomial ring S on n generators is considered, where each deformation B is a twist of S by a semisimple, linear automorphism of
n–1, such that a Poisson bracket is induced on S. We show that if the symplectic leaves associated with this Poisson structure are algebraic, then they are the orbits of an algebraic group G determined by the Poisson bracket. In this case, we prove that if is 'generic enough', then there is a natural one-to-one correspondence between the primitive ideals of B and the symplectic leaves if and only if has a representative in GL(
n
) which belongs to G. As an example, the results are applied to the coordinate ring
of quantum 2 × 2 matrices which is not a twist of a polynomial ring, although it is a flat deformation of one; if q is not a root of unity, then there is a bijection between the primitive ideals of
and the symplectic leaves. 相似文献
950.
Explicit evaluation of the following parameters has been carried out in the extraU (1) superstring inspired model: (i) As Mz2 varies from 555 GeV to 620 GeV and (m
t) CDF = 175.6 ± 5.7 GeV (Table 1): (a) SNew varies from -0.100 ± 0.089 to -0.130 ± 0.090, (b) TNew varies from -0.098 ± 0.097 to -0.129 ± 0.098, (c) UNew varies from -0.229 ± 0.177 to -0.253 ± 0.206, (d) Τz varies from 2.487 ± 0.027 to 2.486 ± 0.027, (e) ALR varies from 0.0125 ± 0.0003 to 0.0126 ± 0.0003, (f) A
FB
b
remains constant at 0.0080 ± 0.0007. Almost identical values are obtained for (m
t)D0 = 169 GeV (see table 2). (ii) Triple gauge boson vertices (TGV) contributions: AsMz
2 varies from 555 GeV to 620 GeV and (m
t) CDF = 175.6 ±5.7 GeV. (a)√s = 500 GeV, asymptotic case:
varies from -0.301 to -0.179;
varies from -0.622 to -0.379;
varies from +0.0061 to 0.0056;
varies from -3.691 to -2.186.
varies from +0.270 to +0.118;
varies from +0.552 to 0.238;
varies from +0.0004 to +0.0002;
remains constant at -0.110. (b)√s = 700 GeV, asymptotic case:
varies from -0.297 to -0.176;
varies from -0.609 to -0.370;
varies from -0.0082 to -0.0078;
varies from -3.680 to -2.171.√s = 700 GeV, nonasymptotic case:
varies from -0.173 to -0.299;
varies from-0.343 to -0.591;
varies from -0.005 to -0.011;
remains constant at -0.110.
The pattern of form factors values for√s = 1000, 1200 GeV is almost identical to that of√s= 700 GeV. Further the values of the form factors for (m
t)D0 (=169 GeV) follow identical pattern as that of (m
t) CDF form factors values (see tables 5, 6, 9, 10).
We conclude that the values of all the form factors with the exception of these of
,
are comparable or larger than theS, T values and therefore the TGV contributions are important while deciding the use of extraU (1) model for doing physics beyond standard model. 相似文献