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101.
In this paper,the quaternion matrix equations XF-AX=BY and XF-A=BY are investigated.For convenience,they were called generalized Sylvesterquaternion matrix equation and generalized Sylvester-j-conjugate quaternion matrix equation,which include the Sylvester matrix equation and Lyapunov matrix equation as special cases.By applying of Kronecker map and complex representation of a quaternion matrix,the sufficient conditions to compute the solution can be given and the expressions of the explicit solutions to the above two quaternion matrix equations XF-AX=BY and XF-A=BY are also obtained.By the established expressions,it is easy to compute the solution of the quaternion matrix equation in the above two forms.In addition,two practical algorithms for these two quaternion matrix equations are give.One is complex representation matrix method and the other is a direct algorithm by the given expression.Furthermore,two illustrative examples are proposed to show the efficiency of the given method. 相似文献
102.
给出指数2情形下阶数为2l_1~(r1)l_1~(r2)的高斯和的显式计算公式.证明方法直接利用Stickelberger理想分解定理,进而结果独立于其他指数2情形高斯和的结果而成立. 相似文献
103.
Zhang S 《Journal of computational chemistry》2012,33(5):517-526
A popular method for predicting pK(a) values for organic molecules in aqueous solution is to establish empirical linear least-squares fits between calculated deprotonation energies and known experimental pK(a) values. In virtually all such calculations, the empirically observed slope of the pK(a) vs. ΔE fit is significantly less than the theoretical value, 1/(2.303RT) (which is 0.73 mol/kcal at room temperature). In our own continuum solvation calculations (Zhang et al., J Phys Chem A 2010, 114, 432), the empirical slope for carboxylic acids was only 0.23 mol/kcal, despite the excellent fit to the experimental pK(a) values. There has been much speculation about the reason for this phenomenon. Although the ΔE - pK(a) relation neglects entropic effects, these are expected to largely cancel. The most likely cause for the strange behavior of the fitted slope is explicit solute-solvent (water) interactions, especially involving the ions, which cannot be described accurately by continuum solvation models. We used our previously developed pK(a) protocol (OLYP/6-311+G(d,p)//3-21G(d) with the COSMO solvation model) to investigate the effect of adding one or two explicit water molecules to the system. The slopes for organic acids (especially carboxylic acids) are much closer to the theoretical value when explicit water molecules are added to both the neutral molecule and the anion. However, explicit water molecules have almost no effect on the slopes for organic bases. Adding explicit water molecules to the ions only produces intermediate results. Unfortunately, linear fits involving explicit water molecules have much larger errors than with continuum solvation models alone and are also much more expensive. Consequently, they are not suitable for large-scale pK(a) calculations. The results compared with literature values showed that our predicted pK(a) s are more accurate. 相似文献
104.
In this paper,by means of similarity transfomations,we obtain explicit solutions to the cubic-quintic nonlinear Schrdinger equation with varying coefficients,which involve four free functions of space.Four types of free functions are chosen to exhibit the corresponding nonlinear wave propagations. 相似文献
105.
Implicit and explicit integration in the solution of the absolute nodal coordinate differential/algebraic equations 总被引:1,自引:0,他引:1
This investigation is concerned with the use of an implicit integration method with adjustable numerical damping properties
in the simulation of flexible multibody systems. The flexible bodies in the system are modeled using the finite element absolute nodal coordinate formulation (ANCF), which can be used in the simulation of large deformations and rotations of flexible bodies. This formulation, when
used with the general continuum mechanics theory, leads to displacement modes, such as Poisson modes, that couple the cross section deformations, and bending and extension of structural elements such as beams. While these
modes can be significant in the case of large deformations, and they have no significant effect on the CPU time for very flexible
bodies; in the case of thin and stiff structures, the ANCF coupled deformation modes can be associated with very high frequencies that can be a source of numerical problems when explicit integration methods
are used. The implicit integration method used in this investigation is the Hilber–Hughes–Taylor method applied in the context of Index 3 differential-algebraic equations (HHT-I3). The results obtained using this integration method are compared with the results obtained using an explicit Adams-predictor-corrector method, which has no adjustable numerical damping. Numerical examples that include bodies with different degrees of flexibility
are solved in order to examine the performance of the HHT-I3 implicit integration method when the finite element absolute
nodal coordinate formulation is used. The results obtained in this study show that for very flexible structures there is no
significant difference in accuracy and CPU time between the solutions obtained using the implicit and explicit integrators.
As the stiffness increases, the effect of some ANCF coupled deformation modes becomes more significant, leading to a stiff
system of equations. The resulting high frequencies are filtered out when the HHT-I3 integrator is used due to its numerical
damping properties. The results of this study also show that the CPU time associated with the HHT-I3 integrator does not change
significantly when the stiffness of the bodies increases, while in the case of the explicit Adams method the CPU time increases
exponentially. The fundamental differences between the solution procedures used with the implicit and explicit integrations
are also discussed in this paper. 相似文献
106.
WANG Ling DONG Zhong-Zhou LIU Xi-Qiang 《理论物理通讯》2008,49(1):1-8
By applying a direct symmetry method, we get the symmetry of the asymmetric Nizhnik-Novikov-Veselov equation (ANNV). Taking the special case, we have a finite-dimensional symmetry. By using the equivalent vector of the symmetry, we construct an eight-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, we reduce the ANNV equation and obtain some solutions to the reduced equations. Furthermore, we find some new explicit solutions of the ANNV equation. At last, we give the conservation laws of the ANNV equation. 相似文献
107.
Solving (2+1)-dimensional sine-Poisson equation by a modified variable separated ordinary differential equation method 下载免费PDF全文
By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ordinary differential equation method is presented for solving the (2+1)-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the (2+1)-dimensional sine-Poisson equation are derived in a simple manner by this technique. 相似文献
108.
109.
K.T. Joseph A.S. Vasudeva Murthy 《NoDEA : Nonlinear Differential Equations and Applications》2001,8(2):173-193
In this paper we study a system of nonlinear partial differential equations which we write as a Burgers equation for matrix
and use the Hopf-Cole transformation to linearize it. Using this method we solve initial value problem and initial boundary
value problems for some systems of parabolic partial differential equations. Also we study an initial value problem for a
system of nonlinear partial differential equations of first order which does not have solution in the standard distribution
sense and construct an explicit solution in the algebra of generalized functions of Colombeau.
Received November 1999 相似文献
110.
In this paper we present the development of a generator of hybrid explicit methods for the numerical solution of the Schrödinger equation. The methods are of algebraic order ten. The coefficients of the generator are calculated appropriately. 相似文献