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991.
Finitary Markov processes are described in G. Morvai and B. Weiss, Prediction for discrete time series, Probability Theory and Related Fields 132 (2005), 1–12. The transition functions of finitary Markov processes are residually locally constant g-functions that can be extended by continuity to their maximal domain of definition. The study of their associated symbolic
dynamics leads one to the D-shifts as introduced in W. Krieger, On g-functions for subshifts, Institute of Mathematical Statistics Lecture Notes-Monograph Series, Vol. 48, Dynamics & Stochastics, arXiv:math.DS/0608259,
(2006), 306–316, We study the phenomena that can arise in residually locally constant and locally constant maximally defined
g-functions on D-shifts, Markov shifts and synchronizing systems with respect to future measures and g-measures 相似文献
992.
We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and “double-free” left modules (that is, free modules over a free algebra). We first give Chibrikov’s Composition-Diamond lemma for modules and then we show that Kang-Lee’s Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra sl 2, the Verma module over a Kac-Moody algebra, the Verma module over the Lie algebra of coefficients of a free conformal algebra, and a universal enveloping module for a Sabinin algebra. As applications, we also obtain linear bases for the above modules. 相似文献
993.
We consider the median regression with a LASSO-type penalty term for variable selection. With the fixed number of variables
in regression model, a two-stage method is proposed for simultaneous estimation and variable selection where the degree of
penalty is adaptively chosen. A Bayesian information criterion type approach is proposed and used to obtain a data-driven
procedure which is proved to automatically select asymptotically optimal tuning parameters. It is shown that the resultant
estimator achieves the so-called oracle property. The combination of the median regression and LASSO penalty is computationally
easy to implement via the standard linear programming. A random perturbation scheme can be made use of to get simple estimator
of the standard error. Simulation studies are conducted to assess the finite-sample performance of the proposed method. We
illustrate the methodology with a real example. 相似文献
994.
Branko Sarić 《Czechoslovak Mathematical Journal》2010,60(4):1043-1048
Let [a, b] be an interval in ℝ Rand let F be a real valued function defined at the endpoints of [a, b] and with a certain number of discontinuities within [a, b]. Assuming F to be differentiable on a set [a, b] | E to the derivative f, where E is a subset of [a, b] at whose points F can take values ±∞ or not be defined at all, we adopt the convention that F and f are equal to 0 at all points of E and show that KH-vt ∝
a
b
f = F(b) − F(a), where KH-vt denotes the total value of the Kurzweil-Henstock integral. The paper ends with a few examples that illustrate the theory. 相似文献
995.
Ivan Feshchenko Danylo Radchenko Lev Radzivilovsky Maksym Tantsiura 《Geometriae Dedicata》2010,145(1):159-168
Consider the set of all lengths of sides of an N-dimensional parallelepiped. If this set has no more than k elements, the parallelepiped will be called a bar (the definition of a bar depends on k). We prove that a parallelepiped can be dissected into a finite number of bars if and only if the lengths of its sides span
a linear space of dimension at most k over
\mathbb Q{{\mathbb Q}} . This extends and generalizes a well-known theorem of Max Dehn about the splitting of rectangles into squares. Several other
results about dissections of parallelepipeds are obtained. 相似文献
996.
We propose new robust classification algorithms for planar and spatial curves subjected to affine transformations. Our motivation comes from the problems in computer image recognition. To each planar or spatial curve, we assign a planar signature curve. Curves, equivalent under an affine transformation, have the same signature. The signatures are based on integral invariants, which are significantly less sensitive to small perturbations of curves and noise than classically known differential invariants. Affine invariants are derived in terms of Euclidean invariants. We present two types of signatures: the global and the local signature. Both signatures are independent of curve parameterization. The global signature depends on a choice of the initial point and, therefore, cannot be used for local comparison. The local signature, albeit being slightly more sensitive to noise, is independent of the choice of the initial point and can be used to solve local equivalence problem. An experiment that illustrates robustness of the proposed signatures is presented. 相似文献
997.
Energy Decay for the Strongly Damped Nonlinear Beam Equation and Its Applications in Moving Boundary
We study the existence and energy decay of solutions for the strongly damped nonlinear beam equation. We apply a method based
on Nakao method to show that the solution decays exponentially, and to obtain precise estimates of the constants in the estimates.
Finally, we discuss its applications in moving boundary. 相似文献
998.
We consider a risk minimization problem in a continuous-time Markovian regime-switching financial model modulated by a continuous-time,
observable and finite-state Markov chain whose states represent different market regimes. We adopt a particular form of convex
risk measure, which includes the entropic risk measure as a particular case, as a measure of risk. The risk-minimization problem
is formulated as a Markovian regime-switching version of a two-player, zero-sum stochastic differential game. One important
feature of our model is to allow the flexibility of controlling both the diffusion process representing the financial risk
and the Markov chain representing macro-economic risk. This is novel and interesting from both the perspectives of stochastic
differential game and stochastic control. A verification theorem for the Hamilton-Jacobi-Bellman (HJB) solution of the game
is provided and some particular cases are discussed. 相似文献
999.
Cristina Fernández-Córdoba Jaume Pujol Mercè Villanueva 《Designs, Codes and Cryptography》2010,56(1):43-59
A code C{{\mathcal C}} is
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C{{\mathcal C}} by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary linear code). The corresponding binary codes of
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-additive codes under an extended Gray map are called
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes. In this paper, the invariants for
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes, the rank and dimension of the kernel, are studied. Specifically, given the algebraic parameters of
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes, the possible values of these two invariants, giving lower and upper bounds, are established. For each possible
rank r between these bounds, the construction of a
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code with rank r is given. Equivalently, for each possible dimension of the kernel k, the construction of a
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code with dimension of the kernel k is given. Finally, the bounds on the rank, once the kernel dimension is fixed, are established and the construction of a
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code for each possible pair (r, k) is given. 相似文献
1000.
Given two arbitrary functions f (0), f (1) on the boundary of the unit disk D in \({\mathbb R}^2\), it is shown that there exists a second order uniformly elliptic operator L and a function v in L p , with L p second derivatives (1?p?2 ), satisfying Lv?=?0 a.e. in D and with v?=?f (0) and \(\frac{ \partial v}{\partial n} = f^{(1)}\) on \(\partial{D}\). A similar extension property was proved in Cavazzoni (2003) for any pair of functions f (0), f (1) that are analytic; a result is obtained under weaker regularity assumptions, e.g. with \(\frac{\partial f^{(0)}}{\partial \theta}\) and f (1) Hölder continuous with exponent \(\eta > \frac{1}{2}\). 相似文献