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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.
设计、合成了3种新型席夫碱Zn2+荧光探针:水杨醛缩三羟甲基氨基甲烷(L1)、5-氯水杨醛缩三羟甲基氨基甲烷(L2)和4-甲氧基水杨醛缩三羟甲基氨基甲烷(L3),并用1H NMR、13C NMR、元素分析和HRMS进行了表征。光谱分析实验结果表明,相比于探针L1和L3,探针L2对Zn2+具有更好的选择性和灵敏度,检出限为11.96 nmol·L-1,远低于国标GB5749—2006规定的饮水中Zn2+的限量值1.0 mg·L-1(约15 μmol·L-1)。在0~10 μmol·L-1范围内,探针L2的荧光强度与Zn2+浓度可呈良好的线性关系。同时,配合物[Zn (C11H13ClNO4)2](L2-Zn2+)的单晶结构和Job曲线证实探针L2与Zn2+以物质的量之比2∶1配位。另外,探针L2能够对实际水样中的Zn2+进行有效检测。  相似文献   
6.
In this paper, a novel Zn(II) and Co(II) Schiff base complexes were synthesized by template method via refluxing 2,3-Naphthalenedicarboxaldehyde, Metal(II) chloride (Metal = Zn or Co), and L-phenylalanine. ZnO and Co3O4 nanoparticles were synthesized by thermal decomposition of Zn(II) and Co(II) complexes, respectively. The products were characterized using different instruments such as CHN, Conductivity, FT-IR, XRD, HR-TEM, and UV–Vis spectrophotometer. The experimental results of elemental analysis for Zn(II) and Co(II) complexes, agree with the calculated results, indicating that the Zn(II) and Co(II) complexes have 1:1 ligand/metal ratios. The molar conductance of the Zn(II) and Co(II) complexes, is less than 5 Ω?1cm?1mol?1, confirming the non-electrolytic nature of the synthesized complexes. The average crystallite diameter of the ZnO and Co3O4 samples is 39.64 and 30.38 nm, respectively. The optical energy gap of the ZnO and Co3O4 samples are 2.75 and 3.25 eV, respectively. Methylene blue dye was utilized to examine the photocatalytic properties of the synthesized nanoparticles using UV irradiations in the absence and presence of hydrogen peroxide. The % degradation of the methylene blue dye in the presence of hydrogen peroxide using ZnO and Co3O4 samples after 40 min is 94.55 and 98.98, respectively. Six pathogenic microbes were utilized to examine the antimicrobial properties of the synthesized Schiff base complexes and their nanoparticles: Staphylococcus aureus, Escherichia coli, Pseudomonas aeruginosa, Streptococcus species, Aspergillus species, and Candida species. Zn(II) and Co(II) complexes display inhibition towards all the studied microbes. Besides, ZnO and Co3O4 nanoparticles exhibit less inhibition towards Staphylococcus aureus, Escherichia coli, Pseudomonas aeruginosa, and Streptococcus species. Moreover, ZnO and Co3O4 nanoparticles have no activity towards Aspergillus and Candida species.  相似文献   
7.
A new methodology for the synthesis of 2,2-disubstituted 2H-chromenes was developed by utilizing the [1,2]-phospha-Brook rearrangement under Brønsted base catalysis. Phosphazene P2-tBu efficiently catalyzed the addition reaction of 4H-chromen-4-ols containing a diethoxyphosphoryl group with α,β-unsaturated ketones, which involved the catalytic generation of a carbanion through the [1,2]-phospha-Brook rearrangement and subsequent conjugate addition at the 2-position to afford adducts possessing an alkenylphosphate moiety in a highly diastereoselective manner. Further transformation of the adducts based on a nickel-catalyzed cross-coupling reaction with arylzinc reagents provided densely functionalized 2,2-disubstituted 2H-chromenes.  相似文献   
8.
The consumption of non-essential aluminum ion (Al3+) at higher concentration from biotic and abiotic sources can cause serious adverse effects to the human body. Therefore, there is bourgeoning need of developing facile analytical methods for the on-site and real-time monitoring of Al3+ concentration in various environmental and biological samples. The chromo-fluorogenic based sensors have been widely developed in the recent years to detect and monitor Al3+ ion. Among the various types of developed chemical sensors, the Schiff bases proved to have several advantages due to their facile synthesis with high yield, fascinating coordination behavior and easy structural modification. This review was narrated to compile the Schiff bases introduced recently for the sensing of Al3+ in various environmental and biological samples. The designing of sensor, sensing mechanisms and other analytical novelties of the developed sensors are discussed.  相似文献   
9.
Synthesis and characterization of 4-{(E)-[(5-bromo-2-hydroxyphenyl)methylidene]amino}-N-carbamimidoylbenzene-1-sulfonamide(SA) and its composites with graphene(SA-GF) were performed. Compound SA and SA-GF were characterized by FTIR and 1H NMR. The GF dispersion in the composites was analyzed by means of scanning electron microscopy(SEM) for morphology. Thermal properties of SA and nanocomposites were investigated using differential thermal analysis(DTA) and thermogravimetric analysis(TGA). The optimum electrical conductivity of the new sulfonamide-based Schiff base was determined to be 1.78×10–5 S/cm at a frequency of 9923 Hz, an applied voltage of –19 V, a mass fraction of 9.38% for graphene loading using a central composite design in the response surface methodology. The significance of the selected parameters(frequency, voltage and GF amount) in the model was determined by the analysis of variance(ANOVA). The results showed that frequency and graphene loading represent important model terms and have considerable effects on the conductivity of SA.  相似文献   
10.
Zhengran Wang 《中国物理 B》2022,31(4):48202-048202
Excited-state double proton transfer (ESDPT) in the 1-[(2-hydroxy-3-methoxy-benzylidene)-hydrazonomethyl]-naphthalen-2-ol (HYDRAVH2) ligand was studied by the density functional theory and time-dependent density functional theory method. The analysis of frontier molecular orbitals, infrared spectra, and non-covalent interactions have cross-validated that the asymmetric structure has an influence on the proton transfer, which makes the proton transfer ability of the two hydrogen protons different. The potential energy surfaces in both S0 and S1 states were scanned with varying O-H bond lengths. The results of potential energy surface analysis adequately proved that the HYDRAVH2 can undergo the ESDPT process in the S1 state and the double proton transfer process is a stepwise proton transfer mechanism. Our work can pave the way towards the design and synthesis of new molecules.  相似文献   
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