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1.
The periodic precipitation pattern formation in gelatinous media is interpreted as a moving boundary problem. The time law,
spacing law and width law are revisited on the basis of the new scenario. The explicit dependence of the geometric structure
on the initial concentrations of the reactants is derived. Matalon—Packter law, which relates the spacing coefficient with
the initial concentrations is reformulated removing many ambiguities and impractical parameters. Experimental results are
discussed to establish the significance of moving boundary concept in the diffusion controlled pattern forming systems 相似文献
2.
Varghese Mathai 《Annals of Global Analysis and Geometry》1992,10(2):103-123
We study topological obstructions to the existence of Riemannian metrics of non-negative scalar curvature on almost spin manifolds using the Dirac operator, the Bochner technique, C
* algebras and von Neumann algebras. We also derive some obstructions in terms of the eta invariants of Atiyah, Patodi and Singer. Next, we prove vanishing theorems for the Atiyah-Milnor genus. Finally, we derive obstructions to the existence of metrics of non-negative scalar curvature along the leaves of a leafwise non-amenable foliation on a spin manifold. 相似文献
3.
4.
Manikandan P Muthukumaran R Thomas KR Varghese B Chandramouli GV Manoharan PT 《Inorganic chemistry》2001,40(10):2378-2389
Copper(II) azide complexes of three tridentate ligands namely 2,6-(3,5-dimethylpyrazol-1-ylmethyl)pyridine (L), 2,6-(pyrazol-1-ylmethyl)pyridine (L'), and dipropylenetriamine (dpt) yield three kinds of complexes with different azide-binding modes. The ligand L forms two end-on-end (mu-1,3) diazido-bridged binuclear complexes, [CuL(mu-N(3))](2)(ClO(4))(2) (1) and [CuL(mu-N(3))(ClO(4))](2).2CH(3)CN (2), and L' forms a perchlorato-bridged quasi-one-dimensional chain complex, [CuL'(N(3))(ClO(4))](n)() (3) with monodentate azide coordination. The ligation of dipropylenetriamine (dpt) gives a end-on (mu-1,1) diazido-bridged binuclear copper complex [Cu(dpt)(mu-N(3))](2)(ClO(4))(2) (4). The crystal and molecular structures of these complexes have been solved. Variable-temperature EPR results of 1 and 2 are identical and indicate the presence of both ferromagnetic and antiferromagnetic interactions within the dimer, the former dominating at low temperatures and the latter at high temperatures. The unusual temperature-dependent magnetic moment and EPR spectra of this dimer reveal the presence of temperature-dependent population of two triplet states, one being caused by antiferromagnetic and the other by ferromagnetic interaction, the former transforming to the latter on cooling. While the interaction of ground spin doublets of the two metal centers gives rise to a ferromagnetic coupling of J(g) = 90.73 cm(-1), the other coupling of J(e) = -185.64 cm(-1) is suggested to be caused by the interaction between an electron in one metal center and an electron from the azide of the other monomer by excitation of a d-electron to the empty ligand orbital. The ferromagnetic state is energetically favored by 104.39 cm(-1). Compound 3 exhibits axial spectra at room temperature and 77 K, and variable-temperature magnetic susceptibility data indicate that the copper centers form a weakly antiferromagnetic one-dimensional chain with J = -0.11 cm(-1). In the case of 4, the unique presence of two nonidentical dimeric units with different bond lengths and bond angles within the unit cell as inferred by crystal structure is proved by single-crystal EPR spectroscopy. 相似文献
5.
Peter Bouwknegt Jarah Evslin Varghese Mathai 《Communications in Mathematical Physics》2015,337(2):909-954
We introduce spherical T-duality, which relates pairs of the form (P, H) consisting of a principal SU(2)-bundle \({P \rightarrow M}\) and a 7-cocycle H on P. Intuitively spherical T-duality exchanges H with the second Chern class c 2(P). Unless \({dim(M) \leq 4}\), not all pairs admit spherical T-duals and the spherical T-duals are not always unique. Nonetheless, we prove that all spherical T-dualities induce a degree-shifting isomorphism on the 7-twisted cohomologies of the bundles and, when \({dim(M) \leq 7}\), also their integral twisted cohomologies and, when \({dim(M) \leq 4}\), even their 7-twisted K-theories. While spherical T-duality does not appear to relate equivalent string theories, it does provide an identification between conserved charges in certain distinct IIB supergravity and string compactifications. 相似文献
6.
A new numerical method is proposed to solve the Boltzmann equation. A frame is set up by using a discrete velocity approximation in the infinite velocity space, but by considering only those distribution function points which are not too small. The distribution function points may occur anywhere in the infinite discrete velocity space and are not constrained to a pre-specified region. A fourth-order finite difference is used for the convection terms. A Monte Carlo-like method is applied to the discrete velocity model of the collision integral. The effort of the method is proportional to the number of discrete points. Numerical examples are given for the full Boltzmann equation and results for some benchmark problems are compared with analytical or prior solutions. 相似文献
7.
Gerig A Chen Q Zagzebski J Varghese T 《The Journal of the Acoustical Society of America》2004,116(3):1832-1841
Ultrasonic scatterer size estimates generally have large variances due to the inherent noise of spectral estimates used to calculate size. Compounding partially correlated size estimates associated with the same tissue, but produced with data acquired from different angles of incidence, is an effective way to reduce the variance without making dramatic sacrifices in spatial resolution. This work derives theoretical approximations for the correlation between these size estimates, and the coherence between their associated spectral estimates, as functions of ultrasonic system parameters. A Gaussian spatial autocorrelation function is assumed to adequately model scatterer shape. Both approximations compare favorably with simulation results, which consider validation near the focus. Utilization of the correlation/coherence expressions for statistical analysis and optimization is discussed. Approximations, such as the invariance of phase and amplitude terms with angle, are made to obtain closed-form solutions to the derived spectral coherence near the focus and permit analytical optimization analysis. Results indicate that recommended parameter adjustments for performance improvement generally depend upon whether, for the system under consideration, the primary source of change in total coherence with rotation is phase term variation due to the change in the relative position of scattering sites, or field amplitude term variation due to beam movement. 相似文献
8.
Varghese Anto P. Nair Shantikumar Santhanagopalan Dhamodaran 《Journal of Solid State Electrochemistry》2019,23(2):513-518
Journal of Solid State Electrochemistry - Here, we report reactive DC-sputter deposited Co3O4 thin films as a promising and stable Li-ion battery anode. Thin films were deposited on stainless steel... 相似文献
9.
Varghese Mathai 《Geometriae Dedicata》2003,99(1):1-15
We outline a twisted analogue of the Mishchenko–Kasparov approach to prove the Novikov conjecture on the homotopy invariance of the higher signatures. Using our approach, we give a new and simple proof of the homotopy invariance of the higher signatures associated to all cohomology classes of the classifying space that belong to the subring of the cohomology ring of the classifying space that is generated by cohomology classes of degree less than or equal to 2, a result that was first established by Connes and Gromov and Moscovici using other methods. A key new ingredient is the construction of a tautological C*
r
(, )-bundle and connection, which can be used to construct a C*
r
(, )-index that lies in the Grothendieck group of C*
r
(, ), where is a multiplier on the discrete group corresponding to a degree 2 cohomology class. We also utilise a main result of Hilsum and Skandalis to establish our theorem. 相似文献
10.
Surface modification of cetyltrimethylammonium bromide-capped gold nanorods to make molecular probes
Yu C Varghese L Irudayaraj J 《Langmuir : the ACS journal of surfaces and colloids》2007,23(17):9114-9119
A chemical procedure to replace the cetyltrimethylammonium bromide (CTAB) cap on gold nanorods (GNRs) fabricated through seed-mediated growth with organothiol compounds [3-animo-5-mercapto-1,2,4-triazole (AMTAZ) and 11-mercaptoundecaonic acid (MUDA)] was developed to reduce the cytotoxity of GNRs and facilitate further biofunctionalization. Compared to phosphatidylcholine (PC) modification, our procedure yields stable GNRs that are biocompatible and suitable for whole-cell studies. The PC-, AMTAZ-, and MUDA-activated GNRs all showed low cytotoxicity. By choosing different organothiols, net positive or negative charges could be created on the nanorod surface, for different applications. Gold nanorod molecular probes (GNrMPs) were fabricated by subsequent attachment of antibodies to the activated GNRs and were used to visualize and detect cell surface biomarkers in normal and transformed human breast epithelial cells, demonstrating the potential of developing novel biosensors using gold nanorods. The sensitivity of GNrMPs made from organothiol-activated GNRs is considerably higher than that of CTAB/PC-activated GNRs, demonstrating that the protocol reported here is favored in developing molecular probes using GNRs. 相似文献