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121.
122.
123.
Tanos Elfouhaily Maminirina Joelson Stephan Guignard Donald R. Thompson 《Waves in Random and Complex Media》2003,13(3):165-176
This paper is the third in a series discussing a new approximate bistatic model for electromagnetic scattering from perfectly conducting rough surfaces. Our previous approach supplemented the Kirchhoff model through the addition of new terms involving linear orders in slope and surface elevation differences that arise naturally from a second iteration of the surface current integral equation. This completion of the Kirchhoff was shown to provide the correct first-order small perturbation method (SPM-1) in the general bistatic context. The agreement with SPM-1 was achieved because differences of surface heights are no longer expanded in powers of surface slope. While consistent with SPM, our previous formulation fails to reconverge toward the Kirchhoff model, at some incidence and scattered angles, when the illuminated surface satisfies the high frequency roughness condition. This weakness is also shared with the first-order small slope approximation (SSA-1) which is structurally equivalent to our previous formulation where the polarization is independent of surface roughness. The second-order small slope approximation (SSA-2), which satisfies the SPM-1 and second-order small perturbation method (SPM-2) limits by construction, was shown by Voronovich to converge toward the tangent plane approximation of the Kirchhoff model under high frequency conditions. In the present paper, we show that, in addition to the linear orders in our previous model, one must now include cross-terms between slope and surface elevation to ensure convergence toward both high frequency and small perturbation limits. With the inclusion of these terms, our new formulation becomes comparable to the SSA-2 (second-order kernel) without the need to evaluate all the quadratic order slope and elevations terms. SSA-2 is more complete, however, in the sense that it guarantees convergence toward the second-order Bragg limit (SPM-2) in the fully dielectric case in addition to both SPM-1 and Kirchhoff. Our new generalization is shown to explain correctly extra depolarization in specular conditions to be caused by surface curvature and surface autocorrelation for incoherent and coherent scattering, respectively. This result will have large repercussions on the interpretation of bistatically reflected signals such as those from GPS. 相似文献
124.
The strong and the weak tail dependence coefficients are measures that quantify the probability of conjoint extreme events
of two random variables. Whereas formulas for both tail dependence coefficients exist for the Gaussian and Student t distribution,
only the strong tail dependence coefficient is known for their super-model, the elliptical generalized hyperbolic distribution,
which is extremely popular in finance (see Schmidt 2003). In this work we derive a simple expression for the corresponding weak tail dependence coefficient using the mixture representation
of the elliptical generalized hyperbolic distribution. 相似文献
125.
Stephan?Dahlke Filippo?De Mari Ernesto?De Vito S?ren?H?userEmail author Gabriele?Steidl Gerd?Teschke 《Journal of Geometric Analysis》2016,26(3):1693-1729
Recently, shearlet groups have received much attention in connection with shearlet transforms applied for orientation sensitive image analysis and restoration. The square integrable representations of the shearlet groups provide not only the basis for the shearlet transforms but also for a very natural definition of scales of smoothness spaces, called shearlet coorbit spaces. The aim of this paper is twofold: first we discover isomorphisms between shearlet groups and other well-known groups, namely extended Heisenberg groups and subgroups of the symplectic group. Interestingly, the connected shearlet group with positive dilations has an isomorphic copy in the symplectic group, while this is not true for the full shearlet group with all nonzero dilations. Indeed we prove the general result that there exist, up to adjoint action of the symplectic group, only one embedding of the extended Heisenberg algebra into the Lie algebra of the symplectic group. Having understood the various group isomorphisms it is natural to ask for the relations between coorbit spaces of isomorphic groups with equivalent representations. These connections are examined in the second part of the paper. We describe how isomorphic groups with equivalent representations lead to isomorphic coorbit spaces. In particular we apply this result to square integrable representations of the connected shearlet groups and metaplectic representations of subgroups of the symplectic group. This implies the definition of metaplectic coorbit spaces. Besides the usual full and connected shearlet groups we also deal with Toeplitz shearlet groups. 相似文献
126.
Stephan F. Huckemann 《Annals of the Institute of Statistical Mathematics》2012,64(6):1227-1259
Various concepts of mean shape previously unrelated in the literature are brought into relation. In particular, for non-manifolds, such as Kendall’s 3D shape space, this paper answers the question, for which means one may apply a two-sample test. The answer is positive if intrinsic or Ziezold means are used. The underlying general result of manifold stability of a mean on a shape space, the quotient due to an proper and isometric action of a Lie group on a Riemannian manifold, blends the slice theorem from differential geometry with the statistics of shape. For 3D Procrustes means, however, a counterexample is given. To further elucidate on subtleties of means, for spheres and Kendall’s shape spaces, a first-order relationship between intrinsic, residual/Procrustean and extrinsic/Ziezold means is derived stating that for high concentration the latter approximately divides the (generalized) geodesic segment between the former two by the ratio 1:3. This fact, consequences of coordinate choices for the power of tests and other details, e.g. that extrinsic Schoenberg means may increase dimension are discussed and illustrated by simulations and exemplary datasets. 相似文献
127.
We consider words over the alphabet [k] = {1, 2, . . . , k}, k ?? 2. For a fixed nonnegative integer p, a p-succession in a word w 1 w 2 . . . w n consists of two consecutive letters of the form (w i , w i ?+ p), i = 1, 2, . . . , n ? 1. We analyze words with respect to a given number of contained p-successions. First we find the mean and variance of the number of p-successions. We then determine the distribution of the number of p-successions in words of length n as n (and possibly k) tends to infinity; a simple instance of a phase transition (Gaussian-Poisson-degenerate) is encountered. Finally, we also investigate successions in compositions of integers. 相似文献
128.
Hongxin Wang Anthony T. Young Jinghua Guo Stephen P. Cramer Stephan Friedrich Artur Braun Weiwei Gu 《Journal of synchrotron radiation》2013,20(4):614-619
X‐ray absorption and scattering spectroscopies involving the 3d transition‐metal K‐ and L‐edges have a long history in studying inorganic and bioinorganic molecules. However, there have been very few studies using the M‐edges, which are below 100 eV. Synchrotron‐based X‐ray sources can have higher energy resolution at M‐edges. M‐edge X‐ray absorption spectroscopy (XAS) and resonant inelastic X‐ray scattering (RIXS) could therefore provide complementary information to K‐ and L‐edge spectroscopies. In this study, M2,3‐edge XAS on several Co, Ni and Cu complexes are measured and their spectral information, such as chemical shifts and covalency effects, are analyzed and discussed. In addition, M2,3‐edge RIXS on NiO, NiF2 and two other covalent complexes have been performed and different d–d transition patterns have been observed. Although still preliminary, this work on 3d metal complexes demonstrates the potential to use M‐edge XAS and RIXS on more complicated 3d metal complexes in the future. The potential for using high‐sensitivity and high‐resolution superconducting tunnel junction X‐ray detectors below 100 eV is also illustrated and discussed. 相似文献
129.
Frank Stephan 《Archive for Mathematical Logic》2001,40(7):489-513
One-sided classifiers are computable devices which read the characteristic function of a set and output a sequence of guesses
which converges to 1 iff the set on the input belongs to the gven class. Such a classifier istwo-sided if the sequence of
its output in addition converges to 0 on setsnot belonging to the class. The present work obtains the below mentionedresults
for one-sided classes (= Σ0
2 classes) with respect to four areas: Turing complexity, 1-reductions, index sets and measure.
There are one-sided classes which are not two-sided. This can have two reasons: (1) the class has only high Turing complexity.
Then there are some oracles which allow to construct noncomputale two-sided classifiers. (2) The class is difficult because
of some topological constraints and then there are also no nonrecursive two-sided classifiers. For case (1), several results
are obtainedto localize the Turing complexity of certain types of one-sided classes.
The concepts of 1-reduction, 1-completeness and simple sets is transferred to one-sided classes: There are 1-complete classes
and simple classes, but no class is at the same time 1-complete nd simple.
The one-sided classes have a natural numbering. Most of the common index sets relative to this numbering have the high complexity
Π1
1: the index set of the class {0,1}∞, the index set of the equality problem and the index set of all two-sided classes. On the other side the index set of the
empty class has complexity Π0
2; Π0
2 and Σ0
2 are the least complexities any nontrivial index set can have.
Lusin showed that any one-sided class is measurable. Concerning the effectiveness of this measure, it is shown that a one-sided
class has recursive measure 0 if it has measure 0, but that thre are one-sided classes having measure 1 without having measure
1 effectively. The measure of a two-sided class can be computed in the limit.
Received: 2 December 1999 / Revised version: 28 February 2000 / Published online: 15 June 2001 相似文献
130.
Lordi V Gambin V Friedrich S Funk T Takizawa T Uno K Harris JS 《Physical review letters》2003,90(14):145505
Ga(1-x)In(x)N(y)As(1-y) is a promising material system for the fabrication of inexpensive "last-mile" optoelectronic components. However, details of its atomic arrangement and the relationship to observed optical properties is not fully known. Particularly, a blueshift of emission wavelength is observed after annealing. In this work, we use x-ray absorption fine structure to study the chemical environment around N atoms in the material before and after annealing. We find that as-grown molecular beam epitaxy material consists of a nearly random distribution of atoms, while postannealed material shows segregation of In toward N. Ab initio simulations show that this short-range ordering creates a more thermodynamically stable alloy and is responsible for blueshifting the emission. 相似文献