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1.
We consider the inverse problem of identifying a general source term, which is a function of both time variable and the spatial variable, in a parabolic PDE from the knowledge of boundary measurements of the solution on some portion of the lateral boundary. We transform this inverse problem into a problem of solving a compact linear operator equation. For the regularization of the operator equation with noisy data, we employ the standard Tikhonov regularization, and its finite dimensional realization is done using a discretization procedure involving the space $L^2(0,\tau;L^2(Ω))$. For illustrating the specification of an a priori source condition, we have explicitly obtained the range space of the adjoint of the operator involved in the operator equation.  相似文献   
2.
In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which multiple phases of cell species and other constituents are separated by smooth evolving interfaces. The model involves a mesoscale version of Darcy’s law to capture the flow mechanism in the tissue matrix. Modeling flow and transport processes in the vasculature supplying the healthy and cancerous tissue, one-dimensional (1D) equations are considered. Since the models governing the transport and flow processes are defined together with cell species models on a three-dimensional (3D) domain, we obtain a 3D–1D coupled model.  相似文献   
3.
《中国物理 B》2021,30(6):64216-064216
We theoretically introduce the statistical uncertainty of photon number and phase error to discuss the precision of parameters to be measured based on weak measurements. When the photon counting scheme is used, we discuss the relative accuracy of the system in the presence of phase error by using the orthogonal and nonorthogonal pre-and postselected states, respectively. When using the measurement scheme of pointer shift, we discuss the measurement accuracy in the presence of phase error, pointer resolution, and statistical uncertainty. These results give a guide way to get the smallest relative precision and deepen our understanding about weak measurement.  相似文献   
4.
利用有效场理论研究了纳米管上最近邻弱交换相互作用下spin-1纳米管中Blume-Capel模型的内能、比热和自由能,得到了系统的内能、比热和自由能与最近邻弱交换相互作用和晶场的关系。结果表明:最近邻弱交换相互作用和晶场强度等诸多因素相互竞争,使系统表现出比 = = =1时的BC模型更为复杂的热学性质;系统内能随温度的变化曲线表现出不连续性;比热随温度的变化出现奇异性;高温对自由能的影响更加明显。  相似文献   
5.
Organotin complexes of Schiff bases (derived from the condensation of hydrazides with salicylaldehyde derivatives) were prepared and their characterization was done using several spectroscopic techniques like FTIR, NMR (1H, 13C, and 119Sn) and mass spectrometry. The spectroscopic data of the ligands and their corresponding complexes revealed that the Schiff bases chelated to the tin metal in a tridentate manner through –ONO atoms (oxygen atom of the hydroxyl group of the salicylaldehydic derivatives, the nitrogen atom of azomethine group, and the oxygen atom of enolic group present in the carboxylic acid hydrazides). Around tin atom pentacoordinated geometry was exhibited. The synthesized ligands and their complexes have been assessed for their biological potency (antibacterial, antifungal and antioxidant using Ciprofloxacin, Fluconazole and Ascorbic acid as reference compounds) and few of the compounds showed optimistic activity. The ligands having electron withdrawing group attached showed greater antimicrobial activity as compared to the other ligands. The complexes showed the better activity than the ligands. The general trend followed by the complexes was diphenyl ?> ?dibutyl ?> ?dimethyl substituted complexes. Compound 11 was the most active against microbes. The antioxidant activity increased with electron donating group. The phenyl substituted complexes showed better activity as compared to the dibutyl and dimethyl substituted complexes. Compound 20 was the best antioxidant.  相似文献   
6.
《印度化学会志》2022,99(12):100789
A series of new bis(thiosemicarbazones) have been synthesized from terephthalaldehyde and various thiosemicarbazides. IR, 1H NMR, 13C NMR spectroscopic methods, and elemental analysis were used to characterize the identification of the synthesized compounds. The in vitro antioxidant activity determinations were made using the 1,1-Diphenyl-2-Picryl Hydrazil (DPPH) method. The compounds exhibited very different inhibition activities with the change of groups attached to the bis(thiosemicarbazone) structure. The spectral and electronic properties of the compounds were investigated by DFT calculation. Intramolecular interactions were analyzed by QTAIM and IRI calculations. Intrinsic bond strength index values of the N–H bonds, Fukui indices and the local electron affinities of the compounds were calculated, and the relationships between the compounds and their antioxidant activity properties were investigated. The SET and HAT mechanisms in the reactions of the compounds with DPPH were affected by the concentration of the compounds, and the possible effects of the parameters supporting the dominant characteristics in these reactions were examined using theoretical data.  相似文献   
7.
Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.  相似文献   
8.
We establish the existence of nonnegative weak solutions to nonlinear reaction–diffusion system with cross-diffusion and nonstandard growth conditions subject to the homogeneous Neumann boundary conditions. We assume that the diffusion operators satisfy certain monotonicity condition and nonstandard growth conditions and prove that the existence of weak solutions using Galerkin's approximation technique.  相似文献   
9.
Structures are reported for eight Schiff bases derived from various salicylaldehydes: five are newly synthesized and re‐investigations are reported for three previously reported structures, leading, in each case, to some revision of previous conclusions. In (E)‐N‐(3,4‐dimethylisoxazol‐5‐yl)‐4‐[(2‐hydroxybenzylidene)amino]benzenesulfonamide, C18H17N3O4S, (I), and (E)‐4‐[(5‐bromo‐2‐hydroxy‐3‐methoxybenzylidene)amino]‐N‐(3,4‐dimethylisoxazol‐5‐yl)benzenesulfonamide. C19H18BrN3O5S, (II), the isoxazole rings adopt different orientations relative to the rest of the molecules, despite the additional substituents in (II) being in the aryl ring remote from the isoxazole unit. The molecules of both (E)‐4‐bromo‐2‐[(2‐hydroxyphenylimino)methyl]‐6‐methoxyphenol, C14H12BrNO3, (III), and (E)‐4‐bromo‐2‐methoxy‐6‐[(2‐methoxyphenylimino)methyl]phenol, C15H14BrNO3, (IV), are both effectively planar; while (III) adopts the phenol–imine constitution, (IV) adopts the keto–amine constitution. (E)‐2‐Methoxy‐6‐[(2‐methoxyphenylimino)methyl]phenol, C15H15NO3, (V), which was determined previously using powder X‐ray data assuming the phenol–imine constitution, has now been refined from single‐crystal X‐ray data, confirming the phenol–imine constitution. In (E)‐3‐benzoyl‐2‐[(5‐fluoro‐2‐hydroxybenzylidene)amino]‐4,5,6,7‐tetrahydrobenzo[b]thiophene, C22H18FNO2S, (VI), the fused carbocyclic ring exhibits conformational disorder; both disorder components, having populations of 0.705 (4) and 0.295 (4), adopt half‐chair conformations. The isostructural (E)‐3‐benzoyl‐2‐[(2‐hydroxybenzylidene)amino)]‐4,5,6,7‐tetrahydrobenzo[b]thiophene, C22H19NO2S, (VII), which was originally reported as having a fully ordered structure [Kaur et al. (2014). Acta Cryst. E 70 , o476–o477], has been rerefined using the original data set and found to exhibit the same type of disorder as found in (VI), with disordered populations having occupancies of 0.851 (3) and 0.149 (3). The triclinic polymorph of (E)‐[(2‐hydroxyphenylimino)methyl]phenol, C13H11NO2, (VIII), which crystallizes with Z′ = 2 in the space group P, has been described variously as occurring as the keto–amine tautomer [Maciejewska et al. (1999). J. Phys. Org. Chem. 12 , 875–880] and as the phenol–imine tautomer [Tunç et al. (2009). J. Chem. Crystallogr. 39 , 672–676]. Rerefinement of this structure using one of the original data sets shows that both of the independent molecules exist in the keto–amine form. In the structures of compounds (I), (VI), (VII) and (VIII), hydrogen bonds generate simple chains, while a chain of rings is formed in (V). Sheets are formed by hydrogen bonds in both (II) and (III), while in (IV), the sheet structure is built from aromatic π–π stacking interactions.  相似文献   
10.
Considered as a geophysical fluid, the polluted atmosphere shares the shallow domain characteristics with other natural large-scale fluids such as seas and oceans. This means that its domain is excessively greater horizontally than in the vertical dimension, leading to the classic hydrostatic approximation of the Navier–Stokes equations. In the past there has been proved a convergence theorem for this model with respect to the ocean, without considering pollution effects. The novelty of this present work is to provide a generalization of their result translated to the atmosphere, extending the fluid velocity equations with an additional convection–diffusion equation representing pollutants in the atmosphere.  相似文献   
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