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21.
Ralph deLaubenfels 《Semigroup Forum》1990,41(1):83-95
LetA be a linear operator on a Banach space. We consider when the following holds. (*)u′(t,x)=A(u(t,x)) (t≥0),u(0,x)=x, has a unique solution, for allx in the domain ofA
n+1
.
We discuss the relationship between (*), integrated semigroups, and C-semigroups. We use this to obtain new results about
integrated semigroups and the abstract Cauchy problem.
We give several examples where (*) may be easily shown using C-semigroups. Many of these examples may not be done directly
using integrated semigroups. 相似文献
22.
Ralph Kummetz 《Applied Categorical Structures》2003,11(1):3-25
This paper investigates function spaces of structures consisting of a partially ordered set together with some directed family of projections.More precisely, given a fixed directed index set (I,), we consider triples (D,,(p
i
)
iI
) with (D,) a poset and (p
i
)
iI
a monotone net of projections of D. We call them (I,)-pop's (posets with projections). Our main purpose is to study structure preserving maps between (I,)-pop's. Such homomorphisms respect both order and projections.Any (I,)-pop is known to induce a uniformity and thus a topology. The set of all homomorphisms between two (I,)-pop's turns out to form an (I,)-pop itself. We show that its uniformity is the uniformity of uniform convergence. This enables us to prove that properties such as completeness and compactness transfer to function pop's.Concerning categorical properties of (I,)-pop's, we will see that we are in a lucky situation from a computer scientist's point of view: we obtain Cartesian closed categories. Moreover, by a D
-construction we get (I,)-pop's that are isomorphic to their own exponent. This yields new models for the untyped -calculus. 相似文献
23.
Ralph Chill 《Journal of Functional Analysis》2003,201(2):572-601
We prove a general version of the ?ojasiewicz-Simon inequality, and we show how to apply the abstract result to study energy functionals E of the form
24.
25.
Lorraine R. Gardiner Ralph E. Steuer 《The Journal of the Operational Research Society》1994,45(12):1456-1466
It has previously been shown that nine of the most prominent procedures of interactive multiple objective programming can be considered as special cases of a common procedure called the unified algorithm. In this paper, we show how four additional procedures can be similarly included in the unified approach. Also, the paper presents a procedure-switching matrix that depicts the possibilities for switching from one procedure to another, one iteration to the next, in the unified algorithm if so directed by a user. 相似文献
26.
Ralph McKenzie 《Algebra Universalis》1987,24(3):224-250
In this paper it is proved that a variety generated by a finite algebraic system with finitely many operations is finitely axiomatizable, provided that the variety is congruence modular and residually small. This result is an extension to congruence modular varieties of a well known theorem for congruence distributive varieties, due to K. A. Baker. Also, under somewhat less restrictive hypotheses, (which are satisfied by finite groups and rings) it is proved that a finite algebraic system belongs to a finitely axiomatizable locally finite variety.Research supported by National Science Foundation Grant No. DMS-8302295.Presented by George Gratzer. 相似文献
27.
Ralph Weissleder David D. Stark Guillermo Elizondo Peter F. Hahn Carolyn Compton Sanjay Saini Jack Wittenberg Joseph T. Ferrucci 《Magnetic resonance imaging》1988,6(6):675-681
Thirteen patients with biopsy proven hepatic lymphoma (2 Hodgkin, 11 Non-Hodgkin) and a control group of 15 patients with hepatic metastases were analyzed quantitatively and qualitatively by MRI. Focal hepatic lymphoma was most reliably detected (eight of eight patients) and appeared hypointense relative to liver on T1 weighted (CNR − 7.4 ± 2.3) and hyperintense on T2 weighted (CNR + 8.4 ± 2.9) images. The mean T1 and T2 relaxation times of focal hepatic lymphoma (T1 = 832 ± 234 msec, T2 = 84 ± 16 ms) differed significantly from adjacent non-tumorous liver (T1 = 420 ± 121 ms, T2 = 51 ± 9 ms; p < 0.05), however CNR values and relaxation times were similar to those of hepatic metastases. Diffuse hepatic lymphoma (microscopic periportal infiltration) was undetectable by MRI in three patients by either morphologic features or quantitative criteria. A mixed pattern of hepatic lymphoma (focal lesions and diffuse infiltration) showed focal areas of slightly decreased signal intensity on T1 weighted images (CNR = −1.7 ± 0.4) while T2 weighted images revealed multiple regions of focal hyperintensity (CNR = +13.3 ± 8.4) superimposed on a diffusely hyperintense liver. Our experience demonstrates that either T1 or T2 weighted techniques are useful in detecting focal and that T2 weighted techniques are useful in detecting mixed hepatic lymphoma. Conventional image derived relaxation time measurements and quantitative parameters were of no additional diagnostic value. 相似文献
28.
J.D. Petke Gerald M. Maggiora Lester L. Shipman Ralph E. Christoffersen 《Journal of Molecular Spectroscopy》1978,73(2):311-331
Ab initio configuration interaction wavefunctions and energies are reported for the ground state and many low-lying singlet and triplet states of magnesium chlorin and chlorin, and are employed in an analysis of the electronic absorption spectra of these systems.In chlorin, the calculated visible spectrum consists of two states, the lower energy, y-polarized state exhibiting moderate absorption intensity in contrast to the very weak absorption of the higher energy x-polarized state. The configurational composition of both states is well described by the four-orbital model. Five states are responsible for the Soret band envelope. A moderately intense y-state lies under the low energy edge of the band envelope, while two x-polarized states of moderate and strong intensity, respectively, are responsible for the band maximum. The final two states lie at the high energy edge of the Soret band and introduce a measure of asymmetry into the band envelope. Two states of very weak oscillator strength are also found in this region of the spectrum. All the Soret states are of complex configurational composition, and several of the higher lying states contain contributions from doubly excited configurations.The calculated visible spectrum of magnesium chlorin also consists of two states, with the weakly absorbing x-polarized state lying approximately 200 cm?1 lower in energy than the moderately intense y-polarized state. The configurational composition of both states is well described by the four-orbital model. Four states constitute the bulk of the intensity in the Soret band envelope. In distinction to chlorin, the moderately intense state at the low energy edge of the band envelope is x-polarized. Two intense states of y- and x-polarization, respectively, constitute the band maximum region, and a single x-polarized state of moderately strong intensity can be assigned to the high energy shoulder of the band envelope. Two other weakly absorbing states are also found in this region, along with another weakly absorbing state of mixed in-plane and out-of-plane polarization. No clearly defined states are observed. As was the case for chlorin, all the Soret states are of complex configurational composition, and some of the higher energy states contain significant contributions from doubly excited configurations.Chlorin and magnesium chlorin both possess three states which lie below S1 and a single which lies slightly above S2. All four of the low-lying states in each molecule are well described by the four-orbital model, with T1 being essentially a single configuration in each case. The remainder of the states are clustered in the same energetic region as the comparable Soret states, with comparably complex configurational compositions.Dipole moments and charge distributions for low-lying singlet and triplet states are also reported, and are used to rationalize chemical reactivity characteristics. 相似文献
29.
A 2(2J + 1)-component relativistic Hamiltonian H that describes free particles of mass m and spin J is said to be linear if it has the form , where , h is a numerical factor, and g commutes with x and p. All such Hamiltonians are found, provided that the metric is either the unit matrix or ?3 and provided that the theory is invariant under the discrete symmetries. If the operator Γ in the generator of Lorentz boosts is required to be local, there are only two possibilities; either Γ = 0, which generalizes the Dirac spin- theory, or , which generalizes the Sakata-Taketani spin-0 and spin-1 theories. The relationship to linear manifestly covariant equations and its significance is discussed. 相似文献
30.
Characteristics of the adsorption of nitrogen on the (110) plane of tungsten were determined by thermal desorption and work function measurements. The low temperature γ-N2 state desorbs with first order kinetics and an activation energy of 6 kcal mole?1. The absence of isotope mixing between 14N2 and 15N2 demonstrates γ-N2 is adsorbed molecularly. Monolayer coverage shows a decrease of 0.19 eV in work function. A Topping model plot indicates the layer is immobile at 123 K. 相似文献