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91.
92.
Let f(t) be an operator monotone function. Then A?B implies f(A)?f(B), but the converse implication is not true. Let A?B be the geometric mean of A,B?0. If A?B, then B−1?A?I; the converse implication is not true either. We will show that if f(λB+I)−1?f(λA+I)?I for all sufficiently small λ>0, then f(λA+I)?f(λB+I) and A?B. Moreover, we extend it to multi-variable matrices means. 相似文献
93.
94.
Mitsuru Sugimoto 《Journal of Functional Analysis》1998,160(2):1
We discuss the problem of boundedness fromLp(Rn) toLp′(Rn) (1/p+1/p′=1, 1?p?2) of operators of the typeM=F−1ei?(ξ)a(ξ) F, which is related to the study of hyperbolic equations with constant coefficients. The boundedness is dependent on a geometrical property ofΣ=?−1(1), and its dependence has been exactly determined in the casesn=2, 1?p?2 andn?3,p=1, 2 (M. Sugimoto,Math. Z.215(1994), 519–531;222(1996), 521–531). This paper is devoted to the unsolved case 1<p<2, and a strange phenomenon is exhibited in the simplest casen=3. 相似文献
95.
In this paper we develop elements of the global calculus of Fourier integral operators in ${{\mathbb R}^n}$ under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev L2 estimates for a class of Fourier integral operators that appears in the analysis of global smoothing problems for dispersive partial differential equations. As an application, we exhibit a new type of weighted estimates for hyperbolic equations, where the decay of data in space is quantitatively translated into the time decay of solutions. 相似文献
96.
Munetaka Takeuchi Yasuo Kameda Yasuhiro Umebayashi Sari Ogawa Takaaki Sonoda Shin-ichi Ishiguro Miho Fujita Mitsuru Sano 《Journal of Molecular Liquids》2009,148(2-3):99-108
Self-diffusion coefficients of Li+ DLi+, PF6− DPF6− and solvent propylene carbonate (PC) DPC in LiPF6−PC solutions were determined at 298 K by the pulse gradient spin echo (PGSE) NMR technique over the salt concentration range of 0.1–3.0 M (M = mol dm– 3). The order of the diffusion coefficients was found to be DLi+ < DPF6− < DPC over the concentration range examined, and they were monotonically decreased with increasing the salt concentration. Haven ratio Λ/ΛNMR, where Λ and ΛNMR represent the ionic conductivity measured electrochemically and that estimated via the Nernst-Einstein equation using the diffusion coefficient, respectively, was evaluated as the measure of the ion–ion interaction in the LiPF6–PC solutions. Though Λ/ΛNMR values for LiPF6-solutions decrease with increasing the salt concentration, they were greater than those for LiBF4–PC solutions over the whole concentration range examined, which indicates that the ion pair formation ability of PF6– ion is weaker than that of the BF4– ion. The smaller value of the ionic conductivity for the highly concentrated LiPF6–PC solution (above 2.0 M) than that of the LiBF4-solutions can be attributed to the more rapidly increased viscosity relative to the LiBF4-solution. Classic molecular dynamics (MD) simulations for the respective LiPF6 and LiBF4-solution of 0.5 and 1.0 M were also carried out based on the effective pair potentials. Diffusion coefficients, ionic conductivity and Haven ratio for these solutions were calculated from MD trajectories, and they qualitatively agree with those evaluated by experiments. Pair correlation functions gLiO(r) (for Li+–O (PC) pair) and gLiPF6(r) (for Li+–PF6– pair) or gLiBF4(r) (for Li+–BF4– pair) revealed that the lithium ion weakly forms the contact ion pairs with PF6–, whilst strongly with BF4–, which supports the present experimental results. Moreover, the simulation results show that both anions in the contact ion pairs predominantly take the monodentate form, which is in contrast to the multidentate coordination predicted by ab initio calculation in gas phase. 相似文献
97.
Tominaga Mai Okajima Mei Yamagishi Mayuko Shinagawa Mitsuru Katsuyama Jun Matsumoto Yoshinori Tomosada Nobuhiro 《Optical Review》2021,28(6):704-715
Optical Review - This paper describes the noise analysis of an electro-optic (EO) sensor system based on experimental and simulation results. We developed a polarization simulator of the EO sensor... 相似文献
98.
Naoki Furutani Tetsuya Takahashi Nobushige Naito Takafumi Maruishi Yuko Yoshimura Chiaki Hasegawa Tetsu Hirosawa Mitsuru Kikuchi 《Entropy (Basel, Switzerland)》2021,23(4)
Recently, measuring the complexity of body movements during sleep has been proven as an objective biomarker of various psychiatric disorders. Although sleep problems are common in children with autism spectrum disorder (ASD) and might exacerbate ASD symptoms, their objectivity as a biomarker remains to be established. Therefore, details of body movement complexity during sleep as estimated by actigraphy were investigated in typically developing (TD) children and in children with ASD. Several complexity analyses were applied to raw and thresholded data of actigraphy from 17 TD children and 17 children with ASD. Determinism, irregularity and unpredictability, and long-range temporal correlation were examined respectively using the false nearest neighbor (FNN) algorithm, information-theoretic analyses, and detrended fluctuation analysis (DFA). Although the FNN algorithm did not reveal determinism in body movements, surrogate analyses identified the influence of nonlinear processes on the irregularity and long-range temporal correlation of body movements. Additionally, the irregularity and unpredictability of body movements measured by expanded sample entropy were significantly lower in ASD than in TD children up to two hours after sleep onset and at approximately six hours after sleep onset. This difference was found especially for the high-irregularity period. Through this study, we characterized details of the complexity of body movements during sleep and demonstrated the group difference of body movement complexity across TD children and children with ASD. Complexity analyses of body movements during sleep have provided valuable insights into sleep profiles. Body movement complexity might be useful as a biomarker for ASD. 相似文献
99.
100.
Oleg N. Ulenikov Eizi Hirota Mitsuru Akiyama S. Alanko M. Koivusaari R. Anttila G. Guelachvili R. N. Tolchenov 《Journal of Molecular Spectroscopy》1996,180(2):423-432
The infrared spectrum of doubly deuterated methane CH2D2has been recorded in the region from 1900 to 2400 cm−1at almost Doppler-limited resolution by using two high-resolution Fourier transform spectrometers. The vibrational bands observed include 2ν4, ν4+ ν7, 2ν7, ν2, ν8, ν4+ ν9, and ν7+ ν9, which were analyzed by taking into account Coriolis and Fermi interactions among them and also those with ν4+ ν5, ν3+ ν7, and ν5+ ν7. Most of the centrifugal distortion constants were constrained to appropriate values, while the vibrational term value and three rotational constants in each of the seven excited states were adjusted along with Coriolis and Fermi interaction parameters by the least-squares analysis of the observed spectrum. The vibration–rotation interaction constants αsthus determined for the ν2and ν8states were combined with those of other fundamental states already published to calculate the equilibrium C–H distance. 相似文献