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1.
We construct a diffeomorphism of T3 admitting any finite or countable number of physical measures with intermingled basins. The examples are partially hyperbolic with splitting TT3 = E cs E u and can be made volume hyperbolic and topologically mixing.  相似文献   
2.
Hydride abstraction from diarylamines with the trityl ion is explored in an attempt to generate a stable diarylnitrenium ion, Ar2N+. Sequential H-atom abstraction reactions ensue. The first H-atom abstraction leads to intensely colored aminium radical cations, Ar2NH.+, some of which are quite stable. However, most undergo a second H-atom abstraction leading to ammonium ions, Ar2NH2+. In the absence of a ready source of H-atoms, a unique self-abstraction reaction occurs when Ar=Me5C6, leading to a novel iminium radical cation, Ar=N.+Ar, which decays via a second self H-atom abstraction reaction to give a stable iminium ion, Ar=N+HAr. These products differ substantially from those derived via photochemically produced diarylnitrenium ions.  相似文献   
3.
An efficient and general approach for the synthesis of amphiphilic 1,2-amino alcohols is reported. The use of N-benzyl protecting groups is essential for obtaining good yields when opening a long-chain terminal epoxide with an amine.  相似文献   
4.
We consider an inverse source problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. The inverse source problem, with an arbitrary source term on the right-hand side of the wave equation, is not uniquely solvable. Here we formulate conditions on the source term that allow us to show uniqueness and that provide a reasonable model for the application of interest. We assume that the source term is supported on a finite set of times and that the support in space moves with subsonic velocity. Moreover, we assume that the spatial part of the source is singular on a hypersurface, an application being a seismic rupture along a fault plane. Given data collected over time on a detection surface that encloses the spatial projection of the support of the source, we show how to recover the times and locations of sources microlocally and then reconstruct the smooth part of the source assuming that it is the same at each source location.  相似文献   
5.
We consider an inverse problem for a Lorentzian spacetime (Mg), and show that time measurements, that is, the knowledge of the Lorentzian time separation function on a submanifold \(\Sigma \subset M\) determine the \(C^\infty \)-jet of the metric in the Fermi coordinates associated to \(\Sigma \). We use this result to study the global determination of the spacetime (Mg) when it has a real-analytic structure or is stationary and satisfies the Einstein-scalar field equations. In addition to this, we require that (Mg) is geodesically complete modulo scalar curvature singularities. The results are Lorentzian counterparts of extensively studied inverse problems in Riemannian geometry—the determination of the jet of the metric and the boundary rigidity problem. We give also counterexamples in cases when the assumptions are not valid, and discuss inverse problems in general relativity.  相似文献   
6.
According to high level calculations, the upper part of the previously published FT-ICR lithium cation basicity (LiCB at 373 K) scale appeared to be biased by a systematic downward shift. The purpose of this work was to determine the source of this systematic difference. New experimental LiCB values at 373 K have been measured for 31 ligands by proton-transfer equilibrium techniques, ranging from tetrahydrofuran (137.2 kJ mol?1) to 1,2-dimethoxyethane (202.7 kJ mol?1). The relative basicities (ΔLiCB) were included in a single self-consistent ladder anchored to the absolute LiCB value of pyridine (146.7 kJ mol?1). This new LiCB scale exhibits a good agreement with theoretical values obtained at G2(MP2) level. By means of kinetic modeling, it was also shown that equilibrium measurements can be performed in spite of the formation of Li+ bound dimers. The key feature for achieving accurate equilibrium measurements is the ion trapping time. The potential causes of discrepancies between the new data and previous experimental measurements were analyzed. It was concluded that the disagreement essentially finds its origin in the estimation of temperature and the calibration of Cook’s kinetic method. Graphical Abstract
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7.
We have changed the amino acid set of the genetic code of Escherichia coli by evolving cultures capable of growing on the synthetic noncanonical amino acid L ‐β‐(thieno[3,2‐b]pyrrolyl)alanine ([3,2]Tpa) as a sole surrogate for the canonical amino acid L ‐tryptophan (Trp). A long‐term cultivation experiment in defined synthetic media resulted in the evolution of cells capable of surviving Trp→[3,2]Tpa substitutions in their proteomes in response to the 20 899 TGG codons of the E. coli W3110 genome. These evolved bacteria with new‐to‐nature amino acid composition showed robust growth in the complete absence of Trp. Our experimental results illustrate an approach for the evolution of synthetic cells with alternative biochemical building blocks.  相似文献   
8.
We prove an Itô–Tanaka formula and existence of pathwise stochastic integrals for a wide class of Gaussian processes. Motivated by financial applications, we define the stochastic integrals as forward-type pathwise integrals introduced by Föllmer and as pathwise generalized Lebesgue–Stieltjes integrals introduced by Zähle. As an application, we illustrate the importance of the Itô–Tanaka formula for pricing and hedging of financial derivatives.  相似文献   
9.
We show that by cutting off the vertices and then the edges of neighborly cubical polytopes, one obtains simple 4-dimensional polytopes with n vertices such that all separators of the graph have size at least Ω(n/log3/2 n). This disproves a conjecture by Kalai from 1991/2004.  相似文献   
10.
Four oil shale samples with different amounts of organic and mineral matter were analysed through non-isothermal thermogravimetric analysis using a heating rate of 50 °C min?1 in nitrogen. The goal of the paper is to study the supposed catalytic effect of the indigenous and removed minerals. The samples contained 30, 49, 70 and 90% of organic matter, respectively. X-ray diffraction analysis was used to identify the minerals in the samples. Thermal analysis experiments were carried out up to temperatures of 850 °C in pyrolysis conditions. The mass loss data were used to study the variations in the conversion profiles of the organic matter depending on the content of the mineral matter. The obtained data and the comparison of the sample composition show that the effect of the mineral matter amount on the course of the pyrolysis processes is insignificant.  相似文献   
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