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131.
We derive two expansions of the Randles–Sevcik function
: an asymptotic expansion of
for x and its Taylor expansion at any x
0
. These expansions are accompanied by error bounds for the remainder at any order of the approximation. 相似文献
132.
Aydin ?zgi 《Applied mathematics and computation》2009,213(2):426-431
Approximation on an unbounded interval is studied in this work by means of a newly-defined two-parameter polynomial operator based on Chlodowsky polynomials. The operator’s properties including convergence rate are investigated using the weighted modulus of continuity. An example is given to illustrate the effect of the parameters. Some basic results are presented. 相似文献
133.
134.
J. J. Mačys 《Lithuanian Mathematical Journal》2008,48(4):401-404
An elementary proof of the irrationality of the number e is well known, while this is not the case with the number π or even,
e.g., e7. In this note, simple and quite transparent proofs of the irrationality of the number π and rational degrees of e, as well
as some other values of elementary functions, are proposed.
The research was partially supported by the Lithuanian State Science and Studies Foundation (grant No T-25/08). 相似文献
135.
In this work an iteration one-step method to integrate systems of nonlinear ordinary differential equations with initial values is presented 相似文献
136.
Taylor级数与Fourier级数是两类非常重要的函数项级数,二者在发展与应用背景、展开条件、收敛性和展开的唯一性等方面不尽相同,本文对此作了一些总结与探讨。 相似文献
137.
Didier Bresch Benoît Desjardins Marguerite Gisclon Rémy Sart 《Annali dell'Universita di Ferrara》2008,54(1):11-36
This paper presents the study of surface tension effects in compressible mixtures in the framework of diffuse interface models.
In the first part, we describe results previously obtained on the so-called compressible Korteweg and shallow water models
and we present nonlinear stability using energy estimates and a new entropy equality recently discovered. These diffuse interface
models also allow to take account of capillarity effects in turbulent mixtures and plasma flows subject to Rayleigh–Taylor
instabilities. The aim of the last part is to study the influence of surface tension on this instability phenomena. More precisely
we look at the expression of the growth rate under a small perturbation of wave number k. We prove that for an appropriate choice of the capillary number σ in terms on the surface tension coefficient T
s
(that means particular pressure laws), we find the same expression as for the two incompressible fluids model with surface
tension coefficient on a sharp interface studied for instance by Chandrasekhar (Hydrodynamic and hydromagnetic stability.
Dover Publications, Inc. New York, 1981).
The first author would like to thank the CEA/DAM (Bruyères le Chatel, France) for its financial support through the contract
no. 4600052302/P6H28. He is also partially supported by the IDOPT project in Grenoble and the “ACI jeunes chercheurs 2004”
du ministère de la Recherche “études mathématiques de paramétrisations en océanographie”. 相似文献
138.
In this paper, we numerically studied the late-time evolutional mechanism of three-dimensional (3D) single-mode immiscible Rayleigh–Taylor instability (RTI) by using an improved lattice Boltzmann multiphase method implemented on graphics processing units. The influences of extensive dimensionless Reynolds numbers and Atwood numbers on phase interfacial dynamics, spike and bubble growth were investigated in details. The longtime numerical experiments indicate that the development of 3D singlemode RTI with a high Reynolds number can be summarized into four different stages: linear growth stage, saturated velocity growth stage, reacceleration stage and turbulent mixing stage. A series of complex interfacial structures with large topological changes can be observed at the turbulent mixing stage, which always preserve the symmetries with respect to the middle axis for a low Atwood number, and the lines of symmetry within spike and bubble are broken as the Atwood number is increased. Five statistical methods for computing the spike and bubble growth rates were then analyzed to reveal the growth law of 3D single-mode RTI in turbulent mixing stage. It is found that the spike late-time growth rate shows an overall increase with the Atwood number, while the bubble growth rate experiences a slight decrease with the Atwood number at first and then basically maintains a steady value of around 0.1. When the Reynolds number decreases, the later stages cannot be reached gradually and the evolution of phase interface presents a laminar flow state. 相似文献
139.
We study non-skewselfadjoint representations of a finite dimensional real Lie algebra . To this end we embed a non-skewselfadjoint representation of into a more complicated structure, that we call a -operator vessel and that is associated to an overdetermined linear conservative input/state/output system on the corresponding simply connected Lie group . We develop the frequency domain theory of the system in terms of representations of , and introduce the joint characteristic function of a -operator vessel which is the analogue of the classical notion of the characteristic function of a single non-selfadjoint operator. As the first non-commutative example, we apply the theory to the Lie algebra of the group, the group of affine transformations of the line. 相似文献
140.
In this note we estimate the lower bound of the average number of real zeros of a random algebraic polynomials when the random coefficients are standard normal random variables 相似文献