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51.
Peter Somora 《Mathematica Slovaca》2008,58(4):439-454
A second order nonlinear differential equation with homogeneous Dirichlet boundary conditions is considered. An explicit expression
for the root functions for an autonomous nonlinear boundary value problem is obtained using the results of the paper [SOMORA,
P.: The lower bound of the number of solutions for the second order nonlinear boundary value problem via the root functions method, Math. Slovaca 57 (2007), 141–156]. Other assumptions are supposed to prove the monotonicity of root functions and to get the exact number
of solutions. The existence of infinitely many solutions of the boundary value problem with strong nonlinearity is obtained
by the root function method as well.
The paper was supported by the Grant VEGA No. 2/7140/27, Bratislava. 相似文献
52.
给出一种计算方程重根及重数的迭代算法,分别具有平方收敛和线性收敛.(i)迭代:x_(n+1)=x_n-f x_n (f'(x_n))/((f'(x_n))~2-(f(x_n)f~n(x_n)),m_n=((f'(x_n)))~2/((f'(x_n))~2-f(xn_)f″(x_n)),n=0,1,2,…,重数m≈mn;(ii)加速迭代:x_(n+1)=x_n-(f~((m-1))(x_n))/(f(~m)(x_n)). 相似文献
53.
A test of the independence of two sets of variables is developed to have high power against a special family of dependence. In this each set of variables has the structure of a single factor model and the dependence is solely via the correlation γ between the underlying latent variables. This is a model with only one nonzero canonical correlation. It is shown that a test based on the maximum likelihood estimate of γ is appreciably more powerful than that based on r1, the largest sample canonical correlation. If, however, the model is used, not just as a family of alternatives but as the basis for interpretation, and if substantial cross-correlation is present then the procedure is essentially equivalent to the use of r1. 相似文献
54.
当归特征组分的识别与定量对比 总被引:3,自引:1,他引:2
将高效液相色谱模式 /二极管阵列检测与自编紫外光谱库管理软件结合 ,用液相色谱 /紫外光谱以及特征参数研究同种当归多个特征组分的识别及快速定量对比。色谱 /光谱及其特征参数共同表达同种当归 2 3个特征组分 ;探讨定量对比的关键技术 ;定量比较两个同种当归相同组分的浓度差异。多指标表达当归特征组分 ,可用于它们的识别 ;定量手段的建立 ,可对比当归特征组分定量结果的差异性。不用化学对照品 ,便能识别和定量比较当归样品中的多组分。方法简便易行、快速 ,结果的代表性强、重现性良好。 相似文献
55.
A problem very often arising in applications is presented: finding the minimal root of an equation with the objective function being multiextremal and nondifferentiable. Applications from the field of electronic measurements are given. Three methods based on global optimization ideas are introduced for solving this problem. The first one uses an a priori estimate of the global Lipschitz constant. The second method adaptively estimates the global Lipschitz constant. The third algorithm adaptively estimates local Lipschitz constants during the search. All the methods either find the minimal root or determine the global minimizers (in the case when the equation under consideration has no roots). Sufficient convergence conditions of the new methods to the desired solution are established. Numerical results including wide experiments with test functions, stability study, and a real-life applied problem are also presented. 相似文献
56.
Martin Lorenz 《Algebras and Representation Theory》2001,4(3):293-304
Let G be a finite group acting by automorphism on a lattice A, and hence on the group algebra S=k[A]. The algebra of G-invariants in S is called an algebra of multiplicative invariants. We present an explicit version of a result of Farkas stating that multiplicative invariants of finite reflection groups are semigroup algebras. 相似文献
57.
58.
Marianna A. Shubov 《Mathematische Nachrichten》2014,287(13):1497-1523
The paper is the second in a set of two papers, which are devoted to a unified approach to the problem of completeness of the generalized eigenvectors (the root vectors) for a specific class of linear non‐selfadjoint unbounded matrix differential operators. The list of the problems for which such operators are the dynamics generators includes the following: (a) initial boundary‐value problem (IBVP) for a non‐homogeneous string with both distributed and boundary damping; (b) IBVP for small vibrations of an ideal filament with a one‐parameter family of dissipative boundary conditions at one end and with a heavy load at the other end; this filament problem is treated for two cases of the boundary parameter: non‐singular and singular; (c) IBVP for a three‐dimensional damped wave equation with spherically symmetric coefficients and both distributed and boundary damping; (d) IBVP for a system of two coupled hyperbolic equations constituting a Timoshenko beam model with variable coefficients and boundary damping; (e) IBVP for a coupled Euler‐Bernoulli and Timoshenko beam model with boundary energy dissipation (the model known in engineering literature as bending‐torsion vibration model); (f) IBVP for two coupled Timoshenko beams model, which is currently accepted as an appropriate model describing vibrational behavior of a longer double‐walled carbon nanotube. Problems have been discussed in the first paper of the aforementioned set. Problems are discussed in the present paper. 相似文献
59.
In this paper, we consider the problem where λ is a spectral parameter; q(x) ∈ L1(0,1) is complex‐valued function; αs, s = 1,2,3, are arbitrary complex constants that satisfy α2 = α1 + α3 and σ = 0,1. The boundary conditions of this problem are regular, but not strongly regular. Asymptotic formulae for eigenvalues and eigenfunctions of the considered boundary value problem are established. It is proved that all the eigenvalues, except for finite number, are simple and the system of root functions of this spectral problem forms a basis in the space Lp(0,1), 1 < p < ∞ , when ; moreover, this basis is unconditional for p = 2. We note that the considered problem was previously investigated in the condition of α2 ≠ α1 + α3. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
60.