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1.
On Regularization of a Source Identification Problem in a Parabolic PDE and its Finite Dimensional Analysis 下载免费PDF全文
Subhankar Mondal & M. Thamban Nair 《偏微分方程(英文版)》2021,34(3):240-257
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.
Hacer Bilgin Ellidokuzoğlu & Serkan Demiriz 《分析论及其应用》2021,37(4):557-571
Başar and Braha [1], introduced the sequence spaces $\breve{\ell}_\infty$, $\breve{c}$ and $\breve{c}_0$ of Euler-Cesáro bounded, convergent and null difference sequences and studied their some properties. Then, in [2], we introduced the sequence spaces ${[\ell_\infty]}_{e.r}, {[c]}_{e.r}$ and ${[c_0]}_{e.r}$ of Euler-Riesz bounded, convergent and null difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. The main purpose of this study is to introduce the sequence space ${[\ell_p]}_{e.r}$ of Euler-Riesz $p-$absolutely convergent series, where $1 \leq p <\infty$, difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. Furthermore, the inclusion $\ell_p\subset{[\ell_p]}_{e.r}$ hold, the basis of the sequence space ${[\ell_p]}_{e.r}$ is constructed and $\alpha-$, $\beta-$ and $\gamma-$duals of the space are determined. Finally, the classes of matrix transformations from the ${[\ell_p]}_{e.r}$ Euler-Riesz difference sequence space to the spaces $\ell_\infty, c$ and $c_0$ are characterized. We devote the final section of the paper to examine some geometric properties of the space ${[\ell_p]}_{e.r}$. 相似文献
3.
Presenting the devices invented by Toepler, Holtz, Wimshurst, and Wommelsdorf, the history of the influence machines, the progress made, and the remaining deficits are discussed. The theoretical considerations published in the literature lack generalizable statements on the efficiency. Based on R. W. Pohl's model (1927), an elementary analysis is made, with the result that the upper limit of the theoretically achievable efficiency of influence machines is only 50%. 相似文献
4.
上转换发光是一种将长波长的激发光转化为短波长发射的反斯托克斯发光现象,三线态-三线态湮灭上转换(TTA-UC)能够在较低密度能量下被激发,且上转换量子产率高,因此获得研究者们广泛关注。关于敏化剂分子结构与上转换发光性能相关性的研究一直是TTA-UC研究领域的重要热点,选择两种代表性的卟啉钯光敏剂[PdOEP-八乙基卟啉钯(Ⅱ)和PdBrTPP-四溴苯基卟啉钯(Ⅱ)]与蒽衍生物9,10-(4-羟甲基)苯基蒽p-DHMPA发光剂组合上转换体系作为研究模型,通过一系列合成工作获得材料分子后,进一步比较两种敏化剂的光谱性质与体系最终上转换性能之间关系。通过细致研究敏化剂和发光剂的荧光发射和寿命等光谱性质对敏化剂系间窜越,三线态-三线态能量转移及三线态-三线态湮灭等能量传递过程的影响后,发现在532 nm处的摩尔吸光系数PdBrTPP (10.8 cm-1·mmol-1)大于PdOEP (3.0 cm-1·mmol-1);三线态寿命PdBrTPP (173.13 μs)大于PdOEP (109.21 μs)。但与p-DHMPA配对时光敏剂与发光剂的三线态能级差ΔETT,PdOEP (0.140 eV)却高于PdBrTPP (0.062 eV),通过Stern-Volmer方程得到Stern-Volmer猝灭常数KSV和双分子猝灭常数kq值也是PdOEP略高,最终表现出上转换阈值PdOEP/p-DHMPA (22.40 mW·cm-2)小于PdBrTPP/p-DHMPA (29.78 mW·cm-2),上转换发光效率ΦUC,PdOEP/p-DHMPA (28.3%)大于PdBrTPP/p-DHMPA (26.8%)。因此,卟啉钯敏化剂的构效对三重态湮灭上转换发光效率影响最为重要的决定因素是敏化剂三线态高低。对于不同的敏化剂,在分子主体结构、摩尔吸光系数与三线态寿命等光谱参数差别不大的情况下,敏化剂的三线态能级越高,就将会具有更大的上转换发光效率。然而如果以总上转换能力指标来评价,PdBrTPP的共轭结构能够提升其在激发波长处吸收更多光子的能力,具有比PdOEP更高的摩尔吸光系数,造成其总上转换能力η比PdOEP高3.4倍。因此从上转换总效能指标来评价,通过敏化剂分子设计调控其在激发光波长处的摩尔吸光系数也不失为一种简单易行的方法。 相似文献
5.
6.
近几年,钙钛矿/硅异质结叠层太阳电池发展迅速,效率已经从13.7%提升到29.1%.由于叠层电池器件的制作工艺复杂,而叠层太阳电池中的光学损失对转换效率的影响很大,所以通过光学模拟进而获得高效电池至关重要.本文首先从商业软件和自建模型两方面概述了光学模拟的方法,接着从反射损失和寄生吸收两方面针对光学模拟研究进展进行了总结和分析,最后指出了叠层电池光学模拟过程中需要注意的问题.钙钛矿/硅异质结叠层太阳电池的转换效率极限最高可达40%,具备很大的提升空间,结合模拟工作的研究,叠层电池的发展将会取得更大的进步. 相似文献
7.
In this paper, we develop a simplified hybrid weighted essentially non-oscillatory (WENO) method combined with the modified ghost fluid method (MGFM)
[31] to simulate the compressible two-medium flow problems. The MGFM can turn
the two-medium flow problems into two single-medium cases by defining the ghost
fluids state in terms of the predicted the interface state, which makes the material
interface “invisible”. For the single medium flow case, we adapt between the linear
upwind scheme and the WENO scheme automatically by identifying the regions of
the extreme points for the reconstruction polynomial as same as the hybrid WENO
scheme [55]. Instead of calculating their exact locations, we only need to know the
regions of the extreme points based on the zero point existence theorem, which is
simpler for implementation and saves computation time. Meanwhile, it still keeps
the robustness and has high efficiency. Extensive numerical results for both one
and two dimensional two-medium flow problems are performed to demonstrate the
good performances of the proposed method. 相似文献
8.
采用时域有限差分(FDTD)法研究Au纳米颗粒@碳球(AuNPs@CS)复合结构的光吸收控制。发现Au纳米颗粒@碳球复合结构中Au颗粒的位置可以控制复合结构光吸收。模型计算中选取两粒Au纳米颗粒以最佳深度(0 nm)嵌入碳球表面。当两粒Au颗粒球心与碳球球心夹角为22.5°和45°时,复合结构光吸收较单一碳球光吸收明显增强;当夹角为315°、270°、180°、90°时,光吸收增量逐渐减小;当夹角为337.5°时,光吸收量低于单一碳球。这一结果主要归因于Au纳米颗粒位置变化可引起表面等离子体光强度和光散射方向的变化。改变碳球表面Au纳米颗粒的数量和位置,可以进一步调节AuNPs@CS复合结构的光吸收。 相似文献
9.
With the emergence of wireless networks, cooperation for secrecy is recognized as an attractive way to establish secure communications. Departing from cryptographic techniques, secrecy can be provided by exploiting the wireless channel characteristics; that is, some error-correcting codes besides reliability have been shown to achieve information-theoretic security. In this paper, we propose a polar-coding-based technique for the primitive relay wiretap channel and show that this technique is suitable to provide information-theoretic security. Specifically, we integrate at the relay an additional functionality, which allows it to smartly decide whether it will cooperate or not based on the decoding detector result. In the case of cooperation, the relay operates in a decode-and-forward mode and assists the communication by transmitting a complementary message to the destination in order to correctly decode the initial source’s message. Otherwise, the communication is completed with direct transmission from source to the destination. Finally, we first prove that the proposed encoding scheme achieves weak secrecy, then, in order to overcome the obstacle of misaligned bits, we implement a double-chaining construction, which achieves strong secrecy. 相似文献
10.