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991.
W.H. Enright 《Numerical Algorithms》2002,31(1-4):125-137
In the last decade it has become standard for students and researchers to be introduced to state-of-the-art numerical software through a problem solving environment (PSE) rather than through the use of scientific libraries callable from a high level language such as Fortran or C. In this paper we will identify the constraints and implications that this imposes on the ODE software we investigate and develop. In particular, the way a numerical solution is displayed and viewed by a user dictates that new measures of performance and quality must be adopted. We will use the MATLAB environment and ODE software for initial value problems, boundary value problems and delay problems to illustrate the issues that arise and the progress that has been made. One of the major implications is the expectation that accurate approximations at off-mesh points must be provided. Traditional numerical methods for ODEs have produced approximations to the underlying solution on an associated discrete, adaptively chosen mesh. In recent years it has become common for the ODE software to also deliver approximations at off-mesh values of the independent variable. Such a feature can be extremely valuable in applications and leads to new measures of quality and performance which are more meaningful to users and more consistently interpreted and implemented in contemporary ODE software. Numerical examples of the robust and reliable behaviour of such software will be presented and the cost/reliability trade-offs that arise will be quantified. 相似文献
992.
Nakao Hayashi Pavel I. Naumkin Yasuko Yamazaki 《Proceedings of the American Mathematical Society》2002,130(3):779-789
We consider the derivative nonlinear Schrödinger equations
where the coefficient satisfies the time growth condition
is a sufficiently small constant and the nonlinear interaction term consists of cubic nonlinearities of derivative type
where and . We suppose that the initial data satifsfy the exponential decay conditions. Then we prove the sharp decay estimate , for all , where . Furthermore we show that for there exist the usual scattering states, when and the modified scattering states, when
where the coefficient satisfies the time growth condition
is a sufficiently small constant and the nonlinear interaction term consists of cubic nonlinearities of derivative type
where and . We suppose that the initial data satifsfy the exponential decay conditions. Then we prove the sharp decay estimate , for all , where . Furthermore we show that for there exist the usual scattering states, when and the modified scattering states, when
993.
Yanheng Ding 《Proceedings of the American Mathematical Society》2002,130(3):689-696
We establish existence and multiplicity of solutions to a class of nonlinear Schrödinger equations with, e.g., ``atomic' Hamiltonians, via critical point theory.
994.
Tero Kilpelä inen Xiao Zhong 《Proceedings of the American Mathematical Society》2002,130(6):1681-1688
We show that sets of Hausdorff measure zero are removable for -Hölder continuous solutions to quasilinear elliptic equations similar to the -Laplacian. The result is optimal. We also treat larger sets in terms of a growth condition. In particular, our results apply to quasiregular mappings.
995.
In this paper, we first consider a delay difference equation of neutral type of the form:
Δ(y
n
+ py
n−k
+ q
n
y
n−l
= 0 for n∈ℤ+(0) (1*)
and give a different condition from that of Yu and Wang (Funkcial Ekvac, 1994, 37(2): 241–248) to guarantee that every non-oscillatory solution of (1*) with p = 1 tends to zero as n→∞. Moreover, we consider a delay reaction-diffusion difference equation of neutral type of the form:
Δ1(u
n,m
+ pu
n−k,m
) + q
n,m
u
n−l,m
= a
2Δ2
2
u
n
+1,
m−1
for (n,m) ∈ℤ+ (0) ×Ω, (2*)
study various cases of p in the neutral term and obtain that if p≥−1 then every non-oscillatory solution of (2*) tends uniformly in m∈Ω to zero as n→∞; if p = −1 then every solution of (2*) oscillates and if p < −1 then every non-oscillatory solution of (2*) goes uniformly in m∈Ω to infinity or minus infinity as n→∞ under some hypotheses.
Received July 14, 1999, Revised August 10, 2000, Accepted September 30, 2000 相似文献
996.
Richard L. Liboff 《International Journal of Theoretical Physics》2002,41(10):1957-1970
Three problems related to the spherical quantum billiard in
are considered. In the first, a compact form of the hyperspherical equations leads to their complex contracted representation. Employing these contracted equations, a proof is given of Courant's nodal-symmetry intersection theorem for diagonal eigenstates of spherical-like quantum billiards in
. The second topic addresses the first-excited-state theorem for the spherical quantum billiard in
. Wavefunctions for this system are given by the product form, (
)Z
q+()Y
(n)
, where is dimensionless displacement,
is angular-momentum number, qis an integer function of dimension, Z() is either a spherical Bessel function (nodd) or a Bessel function of the first kind (neven) and represents (n– 1) independent angular components. Generalized spherical harmonics are written
. It is found that the first excited state (i.e., the second eigenstate of the Laplacian) for the spherical quantum billiard in
is n-fold degenerate and a first excited state for this quantum billiard exists which contains a nodal bisecting hypersurface of mirror symmetry. These findings establish the first-excited-state theorem for the spherical quantum billiard in
. In a third study, an expression is derived for the dimension of the th irreducible representation (irrep) of the rotation group O(n) in
by enumerating independent degenerate product eigenstates of the Laplacian. 相似文献
997.
S. Esposito 《International Journal of Theoretical Physics》2002,41(12):2417-2426
We present a method for reducing the order of ordinary differential equations satisfying a given scaling relation (Majorana scale-invariant equations). We also develop a variant of this method, aimed to reduce the degree of nonlinearity of the lower order equation. Some applications of these methods are carried out and, in particular, we show that second-order Emden–Fowler equations can be transformed into first-order Abel equations. The work presented here is a generalization of a method used by Majorana in order to solve the Thomas–Fermi equation. 相似文献
998.
999.
Structure and Photoelectric Characteristics of Functional Polymers and of Compositions Based on Them 总被引:1,自引:0,他引:1
The electronic processes in disordered organic solids were analyzed, classified, and summarized. They include the photogeneration of charge pairs, electron transport, geminal and bimolecular recombination, and the capture of charge carriers in local electronic states. General criteria were formulated for the targeted search for and the creation of new prospective polymers and their compositions with organic pigments and related compounds having specific photoelectric characteristics for electrographic and holographic media, photoelectric converters, and electroluminescent and photorefractive devices. 相似文献
1000.
The solubility of siderite (FeCO3) at 25°C under constant CO2 partial pressure [p(CO2)] was determined in NaCl solutions as a function of ionic strength. The dissolution of FeCO3(s) for the reaction
has been determined as a function of pH = – log[H+]. From these values we have determined the equilibrium constant for the stoichiometric solubility to FeCO3(s) in NaCl
These values have been fitted to the equation
with a standard error of s = 0.15. The extrapolated value of log(K
o
sp) – 10.9 in water is in good agreement with data in the literature (– 10.8 to – 11.2) determined in solutions of different composition and ionic strength.The measured values of the activity coefficient, T(Fe2+) T(CO3
2–), have been used to estimate the stability constant for the formation of the FeCO3 ion pair, K*(FeCO3). The values of K*(FeCO3) have been fitted to the equation (s = 0.09)
The value of log[K
o(FeCO3)] in water found in this study (6.3 ± 0.2) is slightly higher than the value found from extrapolations in 1.0 m NaClO4 solutions (5.9 ± 0.2). These differences are related to the model used to determine the activity coefficients of the Fe(II) and carbonate species in the two solutions. 相似文献