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101.
We propose a method for solving the (2+1)-dimensional Kadomtsev-Petviashvili equation with negative dispersion (KP-II) using the second and third members of the disipative version of the AKNS hierarchy. We show that dissipative solitons (dissipatons) of those members yield the planar solitons of the KP-II. From the Hirota bilinear form of the SL(2, ℝ) AKNS flows, we formulate a new bilinear representation for the KP-II, by which we construct one- and two-soliton solutions and study the resonance character of their mutual interactions. Using our bilinear form, for the first time, we create a four-virtual-soliton resonance solution of the KP-II, and we show that it can be obtained as a reduction of a four-soliton solution in the Hirota-Satsuma bilinear form for the KP-II.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 1, pp. 162–170, July, 2005. 相似文献
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104.
Spiral wave chimeras in populations of oscillators coupled to a slowly varying diffusive environment
Chimera states are firstly discovered in nonlocally coupled oscillator systems. Such a nonlocal coupling arises typically as oscillators are coupled via an external environment whose characteristic time scale τ is so small (i.e., τ → 0) that it could be eliminated adiabatically. Nevertheless, whether the chimera states still exist in the opposite situation (i.e., τ ≫ 1) is unknown. Here, by coupling large populations of Stuart−Landau oscillators to a diffusive environment, we demonstrate that spiral wave chimeras do exist in this oscillator-environment coupling system even when τ is very large. Various transitions such as from spiral wave chimeras to spiral waves or unstable spiral wave chimeras as functions of the system parameters are explored. A physical picture for explaining the formation of spiral wave chimeras is also provided. The existence of spiral wave chimeras is further confirmed in ensembles of FitzHugh−Nagumo oscillators with the similar oscillator-environment coupling mechanism. Our results provide an affirmative answer to the observation of spiral wave chimeras in populations of oscillators mediated via a slowly changing environment and give important hints to generate chimera patterns in both laboratory and realistic chemical or biological systems. 相似文献
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106.
Under normal conditions, blood coagulation provides an effective protective mechanism preventing bleeding in case of vessel damage. Details of its functioning are of particular importance since any blood coagulation disorders lead to severe physiological aggravations. Multiple experimental and computational studies demonstrate the thrombin concentration distribution to determine the spatio-temporal dynamics of clot formation. Propagating from the injury site with constant speed, thrombin concentration profile can be modeled with a traveling wave solution of the system of partial differential equations describing main reactions of the coagulation cascade. In the current study, we derive conditions on the existence and stability of such solutions and provide an analytic approach of their wave speed estimation. 相似文献
107.
G. I. Shishkin 《Computational Mathematics and Mathematical Physics》2007,47(5):797-828
In a rectangle, the Dirichlet problem for a system of two singularly perturbed elliptic reaction-diffusion equations is considered. The higher order derivatives of the ith equation are multiplied by the perturbation parameter ? i 2 (i = 1, 2). The parameters ?i take arbitrary values in the half-open interval (0, 1]. When the vector parameter ? = (?1, ?2) vanishes, the system of elliptic equations degenerates into a system of algebraic equations. When the components ?1 and (or) ?2 tend to zero, a double boundary layer with the characteristic width ?1 and ?2 appears in the vicinity of the boundary. Using the grid refinement technique and the classical finite difference approximations of the boundary value problem, special difference schemes that converge ?-uniformly at the rate of O(N ?2ln2 N) are constructed, where N = min N s, N s + 1 is the number of mesh points on the axis x s. 相似文献
108.
SHUICHIROU IKE 《The Journal of mathematical sociology》2013,37(3):137-155
Although we generally tend to conceive that fertility decline has been caused by the alterations of socioeconomic conditions, fertility decline in the 19th century in Europe was a reaction-diffusion process independent of them (e.g., see Coale, 1967, 1973; Becker, 1978, 1981). Once we postulate a reaction-diffusion process for this phenomenon, we can estimate the velocity of a progressive wave of diffusion. By means of the estimated velocity, we can estimate where a singularity of fertility decline was and when it appeared. The singularity existed in a French district Aquitaine basin. From Lot-et-Garonne in Aquitaine, the reaction-diffusion of fertility decline began to diffuse to all Europe maintaining relative independence of socioeconomic conditions. 相似文献
109.
This paper deals with the numerical approximation of the solution of 1D parabolic singularly perturbed problems of reaction-diffusion type. The numerical method combines the standard implicit Euler method on a uniform mesh to discretize in time and a HODIE compact fourth order finite difference scheme to discretize in space, which is defined on a priori special meshes condensing the grid points in the boundary layer regions. The method is uniformly convergent having first order in time and almost fourth order in space. The analysis of the uniform convergence is made in two steps, splitting the contribution to the error from the time and the space discretization. Although this idea has been previously used to prove the uniform convergence for parabolic singularly perturbed problems, here the proof is based on a new study of the asymptotic behavior of the exact solution of the semidiscrete problems obtained after the time discretization by using the Euler method. Some numerical results are given corroborating in practice the theoretical results. 相似文献
110.
周凤燕 《数学的实践与认识》2012,42(3):168-179
研究了一类反应扩散广义时滞细胞神经网络在噪声干扰下的指数稳定性.利用Ito公式,Holder不等式,M矩阵性质和微分不等式技巧,给出了系统均值指数稳定的充分条件,并且判断方法简单易操作.最后给出了主要定理的两个应用实例,表明结论的有效性. 相似文献