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91.
Alessio Corti 《Proceedings of the Steklov Institute of Mathematics》2009,264(1):45-47
I propose three equivalent conjectures on the birational geometry of Fano 3-folds. Roughly speaking, they suggest that ergodic,
or chaotic, behaviour does not occur for Fano 3-folds. 相似文献
92.
A group is called extended residually finite (ERF) if every subgroup is closed in the profinite topology. The ERF-property is studied for nilpotent groups, soluble groups, locally finite groups and FC-groups. A complete characterization is given of FC-groups which are ERF. 相似文献
93.
Alessio Figalli Grégoire Loeper 《Calculus of Variations and Partial Differential Equations》2009,35(4):537-550
We prove C
1 regularity of c-convex weak Alexandrov solutions of a Monge–Ampère type equation in dimension two, assuming only a bound from above on the
Monge–Ampère measure. The Monge–Ampère equation involved arises in the optimal transport problem. Our result holds true under
a natural condition on the cost function, namely non-negative cost-sectional curvature, a condition introduced in Ma et al. (Arch Ration Mech Anal 177(2):151–183, 2005), that was shown in Loeper (Acta Math,
to appear) to be necessary for C
1 regularity. Such a condition holds in particular for the case “cost = distance squared” which leads to the usual Monge–Ampère
equation det D
2
u = f. Our result is in some sense optimal, both for the assumptions on the density [thanks to the regularity counterexamples of
Wang (Proc Am Math Soc 123(3):841–845, 1995)] and for the assumptions on the cost-function [thanks to the results of Loeper
(Acta Math, to appear)]. 相似文献
94.
Alessio Moretti 《Logica Universalis》2009,3(1):19-57
Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic
(both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”,
“permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s
“logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic
oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a “deontic hexagon” as being the geometrical
representation of standard deontic logic, whereas Joerden (jointly with Hruschka, in Archiv für Rechtsund Sozialphilosophie
73:1, 1987), McNamara (Mind 105:419, 1996) and Wessels (Die gute Samariterin. Zur Struktur der Supererogation, Walter de Gruyter,
Berlin, 2002) have proposed some new “deontic polygons” for dealing with conservative extensions of standard deontic logic
internalising the concept of “supererogation”. Since 2004 a new formal science of the geometrical oppositions inside logic
has appeared, that is “n-opposition theory”, or “NOT”, which relies on the notion of “logical bi-simplex of dimension m” (m = n − 1). This theory has received a complete mathematical foundation in 2008, and since then several extensions. In this paper,
by using it, we show that in standard deontic logic there are in fact many more oppositional deontic figures than Kalinowski’s
unique “hexagon of norms” (more ones, and more complex ones, geometrically speaking: “deontic squares”, “deontic hexagons”,
“deontic cubes”, . . ., “deontic tetraicosahedra”, . . .): the real geometry of the oppositions between deontic modalities
is composed by the aforementioned structures (squares, hexagons, cubes, . . ., tetraicosahedra and hyper-tetraicosahedra),
whose complete mathematical closure happens in fact to be a “deontic 5-dimensional hyper-tetraicosahedron” (an oppositional
very regular solid).
相似文献
95.
Solomon GC Gagliardi A Pecchia A Frauenheim T Di Carlo A Reimers JR Hush NS 《The Journal of chemical physics》2006,124(9):94704
We present results for a simulated inelastic electron-tunneling spectra (IETS) from calculations using the "gDFTB" code. The geometric and electronic structure is obtained from calculations using a local-basis density-functional scheme, and a nonequilibrium Green's function formalism is employed to deal with the transport aspects of the problem. The calculated spectrum of octanedithiol on gold(111) shows good agreement with experimental results and suggests further details in the assignment of such spectra. We show that some low-energy peaks, unassigned in the experimental spectrum, occur in a region where a number of molecular modes are predicted to be active, suggesting that these modes are the cause of the peaks rather than a matrix signal, as previously postulated. The simulations also reveal the qualitative nature of the processes dominating IETS. It is highly sensitive only to the vibrational motions that occur in the regions of the molecule where there is electron density in the low-voltage conduction channel. This result is illustrated with an examination of the predicted variation of IETS with binding site and alkane chain length. 相似文献
96.
Alessio Figalli Young-Heon Kim Robert J. McCann 《Archive for Rational Mechanics and Analysis》2013,209(3):747-795
Consider transportation of one distribution of mass onto another, chosen to optimize the total expected cost, where cost per unit mass transported from x to y is given by a smooth function c(x, y). If the source density f +(x) is bounded away from zero and infinity in an open region ${U' \subset \mathbf{R}^n}$ , and the target density f ?(y) is bounded away from zero and infinity on its support ${\overline{V} \subset \mathbf{R}^n}$ , which is strongly c-convex with respect to U′, and the transportation cost c satisfies the ${\mathbf{A3}_{\rm w}}$ condition of Trudinger and Wang (Ann Sc Norm Super Pisa Cl Sci 5, 8(1):143–174, 2009), we deduce the local Hölder continuity and injectivity of the optimal map inside U′ (so that the associated potential u belongs to ${C^{1,\alpha}_{loc}(U')}$ ). Here the exponent α > 0 depends only on the dimension and the bounds on the densities, but not on c. Our result provides a crucial step in the low/interior regularity setting: in a sequel (Figalli et al., J Eur Math Soc (JEMS), 1131–1166, 2013), we use it to establish regularity of optimal maps with respect to the Riemannian distance squared on arbitrary products of spheres. Three key tools are introduced in the present paper. Namely, we first find a transformation that under ${\mathbf{A3}_{\rm w}}$ makes c-convex functions level-set convex (as was also obtained independently from us by Liu (Calc Var Partial Diff Eq 34:435–451, 2009)). We then derive new Alexandrov type estimates for the level-set convex c-convex functions, and a topological lemma showing that optimal maps do not mix the interior with the boundary. This topological lemma, which does not require ${\mathbf{A3}_{\rm w}}$ , is needed by Figalli and Loeper (Calc Var Partial Diff Eq 35:537–550, 2009) to conclude the continuity of optimal maps in two dimensions. In higher dimensions, if the densities f ± are Hölder continuous, our result permits continuous differentiability of the map inside U′ (in fact, ${C^{2,\alpha}_{loc}}$ regularity of the associated potential) to be deduced from the work of Liu et al. (Comm Partial Diff Eq 35(1):165–184, 2010). 相似文献
97.
Alessio Boldrin Steffen Foss Hansen Anders Baun Nanna Isabella Bloch Hartmann Thomas Fruergaard Astrup 《Journal of nanoparticle research》2014,16(6):1-19
Information related to the potential environmental exposure of engineered nanomaterials (ENMs) in the solid waste management phase is extremely scarce. In this paper, we define nanowaste as separately collected or collectable waste materials which are or contain ENMs, and we present a five-step framework for the systematic assessment of ENM exposure during nanowaste management. The framework includes deriving EOL nanoproducts and evaluating the physicochemical properties of the nanostructure, matrix properties and nanowaste treatment processes as well as transformation processes and environment releases, eventually leading to a final assessment of potential ENM exposure. The proposed framework was applied to three selected nanoproducts: nanosilver polyester textile, nanoTiO2 sunscreen lotion and carbon nanotube tennis racquets. We found that the potential global environmental exposure of ENMs associated with these three products was an estimated 0.5–143 Mg/year, which can also be characterised qualitatively as medium, medium, low, respectively. Specific challenges remain and should be subject to further research: (1) analytical techniques for the characterisation of nanowaste and its transformation during waste treatment processes, (2) mechanisms for the release of ENMs, (3) the quantification of nanowaste amounts at the regional scale, (4) a definition of acceptable limit values for exposure to ENMs from nanowaste and (5) the reporting of nanowaste generation data. 相似文献
98.
We consider a set of macroscopic (classical) degrees of freedom coupled to an arbitrary many-particle Hamiltonian system, quantum or classical. These degrees of freedom can represent positions of objects in space, their angles, shape distortions, magnetization, currents and so on. Expanding their dynamics near the adiabatic limit we find the emergent Newton’s second law (force is equal to the mass times acceleration) with an extra dissipative term. In systems with broken time reversal symmetry there is an additional Coriolis type force proportional to the Berry curvature. We give the microscopic definition of the mass tensor. The mass tensor is related to the non-equal time correlation functions in equilibrium and describes the dressing of the slow degree of freedom by virtual excitations in the system. In the classical (high-temperature) limit the mass tensor is given by the product of the inverse temperature and the Fubini–Study metric tensor determining the natural distance between the eigenstates of the Hamiltonian. For free particles this result reduces to the conventional definition of mass. This finding shows that any mass, at least in the classical limit, emerges from the distortions of the Hilbert space highlighting deep connections between any motion (not necessarily in space) and geometry. We illustrate our findings with four simple examples. 相似文献
99.
A Terenzi C Ducani V Blanco L Zerzankova AF Westendorf C Peinador JM Quintela PJ Bednarski G Barone MJ Hannon 《Chemistry (Weinheim an der Bergstrasse, Germany)》2012,18(35):10983-10990
The interaction with native DNA of a 2,7-diazapyrenium-based ligand 1 and its Pt(II) rectangular metallacycle 2 is explored through circular and linear dichroism and fluorescence spectroscopies. The metal-free ligand 1 binds through intercalation, with a binding constant of approximately 5×10(5) M(-1) , whereas the metallacycle 2 binds and bends the DNA with a binding constant of 7×10(6) M(-1) . PCR assays show that metallo-supramolecular box 2 interferes with DNA transactions in vitro whereas the intercalator 1 does not. The metallacycle is active against four human cancer cell lines, with IC(50) values ranging between 3.1 and 19.2?μM and shows similar levels of efficacy, but a different spectrum of activity, to cisplatin. 相似文献
100.
Spectroscopic techniques both in steady-state (in absorption and emission) and pulsed (absorption of excited states with femtosecond resolution) conditions were used to study the complexation process between six molecules belonging to the tetracycline family and Mg(2+); in the case of TC the study was extended to the metal ions Ca(2+) and Cu(2+). The study was carried out in aqueous solution at various pH values, where one acid-base form of the substrate prevails over the others. The processing of experimental results, performed by means of Singular Value Decomposition and Global Analysis methods, allowed us to evaluate the extent of interaction through the association constants, to identify the number of equilibria present in solution and the stoichiometry (1:1 or 1:2) of the tetracycline:metal ion complex, and to define the spectral and photophysical properties of the latter (in terms of fluorescence quantum yields, lifetimes and rate constants). In fact, the (allowed) radiative decay process is a minor root for the lowest excited state of the complexes which mainly decay to the ground state by internal conversion. Details of the complexation sites are proposed for the various protonated forms of tetracyclines, and for the various cations in the case of TC. In particular, the molecular structure seems to affect significantly the dynamics of interaction when the upper peripheral region of tetracycline is rich in additional hydroxyl groups. Moreover, the state of protonation of the substrate produces changes in the order of the complexation sites, whose affinity for the cation increases significantly when they are negatively charged owing to the loss of protons. Magnesium and calcium (hard cations) give similar interactions, at least in acid solution, while copper(ii) (borderline cation) binds more efficiently on different sites, thus forming complexes with different properties. 相似文献