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931.
This is a continuation of the article(Comm.Partial Differential Equations 26(2001)965).In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational force,fixed boundary condition,a general pressure and the density-dependent viscosity coefficient when the viscous gas connects to vacuum state with a jump in density.Precisely,the viscosity coefficient μ is proportional to ρ^θ and 0〈θ〈1/2,where ρ is the density,and the pressure P=P(ρ)is a general pressure.The global existence and the uniqueness of weak solution are proved. 相似文献
932.
Abstract. In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier—Stokes equation in bounded
and unbounded domains. These solutions are stochastic analogs of the classical Lions—Prodi solutions to the deterministic
Navier—Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability
space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions
to the Navier—Stokes martingale problem where the probability space is also obtained as a part of the solution. 相似文献
933.
We consider the approximation of trigonometric operator functions that arise in the numerical solution of wave equations by
trigonometric integrators. It is well known that Krylov subspace methods for matrix functions without exponential decay show
superlinear convergence behavior if the number of steps is larger than the norm of the operator. Thus, Krylov approximations
may fail to converge for unbounded operators. In this paper, we propose and analyze a rational Krylov subspace method which
converges not only for finite element or finite difference approximations to differential operators but even for abstract,
unbounded operators. In contrast to standard Krylov methods, the convergence will be independent of the norm of the operator
and thus of its spatial discretization. We will discuss efficient implementations for finite element discretizations and illustrate
our analysis with numerical experiments.
AMS subject classification (2000) 65F10, 65L60, 65M60, 65N22 相似文献
934.
Jeffrey Goldstein 《Nonlinear dynamics, psychology, and life sciences》2001,5(3):197-204
This article examines recent attempts to gain insight into philosophical paradoxes through using NDS models employing iterated difference equations and resulting phase portraits and escape time diagrams. The temporal nature of such models is contrasted with an alternative approach based on the a-temporal and non-dynamical construct of a lattice. Finally, there is a discussion of how such strategies for understanding paradox transcend the realm of empirical research and enter territory in the philosophy of mathematics. 相似文献
935.
Karem B. Ben Mahmoud 《Numerical Methods for Partial Differential Equations》2009,25(4):802-809
In this article, a new set of polynomials is proposed as a new tool for solving bivaried partial differential equation related with some appropriated applied physics problems. A concrete formulation of canonical expressions, with respect to more common boundary conditions, is yielded out of the recently established Boubaker polynomials. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
936.
Hideaki Matsunaga 《Proceedings of the American Mathematical Society》2008,136(12):4305-4312
For a linear delay differential system with two coefficients and one delay, we establish some necessary and sufficient conditions on the asymptotic stability of the zero solution, which are composed of delay-dependent and delay-independent stability criteria. On the former criterion, the range of the delay is explicitly given.
937.
Nenad Ujevi? 《Applied mathematics and computation》2009,212(1):273-274
In abstract of the paper [A. Rafiq, A note on “A family of methods for solving nonlinear equations”, Appl. Math. Comput. 195 (2008) 819-821] we can find the following sentences. We cite: Ujevi? et al. introduced a family of methods for solving nonlinear equations. However the main Algorithm 1 put forward by Ujevi? et al. (p. 7) is wrong. This is the main aim of this note. We also point out some major bugs in the results of Ujevi? et al. - the end of the citation. Here it is shown that all of the mentioned assertions are not true. In other words, the Algorithm 1 is correct (up to an obvious misprint, which is not mentioned in the above paper) and there are no major bugs in the paper by Ujevi? et al. In fact, these observations, which will be given in this note, show that the main aim of the paper by Rafiq is wrong. 相似文献
938.
I. G. Mamedov 《Computational Mathematics and Mathematical Physics》2009,49(1):93-104
The Cauchy problem for a fourth-order pseudoparabolic equation describing liquid filtration problems in fissured media, moisture transfer in soil, etc., is studied. Under certain summability and boundedness conditions imposed on the coefficients, the operator of this problem and its adjoint operator are proved to be homeomorphism between certain pairs of Banach spaces. Introduced under the same conditions, the concept of a θ-fundamental solution is introduced, which naturally generalizes the concept of the Riemann function to the equations with discontinuous coefficients; the new concept makes it possible to find an integral form of the solution to a nonhomogeneous problem. 相似文献
939.
We present a theory which allows us to justify the existence theorems and derive majorant estimates for solutions of the Cauchy problem for a countable system of partial differential equations. Our results also allow to estimate the maximum existence interval for a solution. 相似文献
940.
In the mathematical modeling of population growth, and in particular of bacterial growth, parameters are either measured directly or determined by curve fitting. These parameters have large variability that depends on the experimental method and its inherent error, on differences in the actual population sample size used, as well as other factors that are difficult to account for. In this work the parameters that appear in the Monod kinetics growth model are considered random variables with specified distributions. A stochastic spectral representation of the parameters is used, together with the polynomial chaos method, to obtain a system of differential equations, which is integrated numerically to obtain the evolution of the mean and higher-order moments with respect to time. 相似文献