where are closed differential forms and 2kn. Our main results (the case k=n having been handled by Moser [J. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965) 286–294] and Dacorogna and Moser [B. Dacorogna, J. Moser, On a partial differential equation involving the Jacobian determinant, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990) 1–26]) are that
– when n is even and k=2, under some natural non-degeneracy condition, we can prove the existence of such diffeomorphism satisfying Dirichlet data on the boundary of a bounded open set and the natural Hölder regularity; at the same time we get Darboux theorem with optimal regularity;
– we are also able to handle the degenerate cases when k=2 (in particular when n is odd), k=n−1 and some cases where 3kn−2.

Résumé

Nous montrons l'existence d'un difféomorphisme satisfaisant
φ*(g)=f
sont des formes différentielles fermées et 2kn. Nos résultats principaux (le cas k=n a été discuté notamment dans Moser [J. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965) 286–294] et Dacorogna et Moser [B. Dacorogna, J. Moser, On a partial differential equation involving the Jacobian determinant, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990) 1–26]) sont les suivants.
– Si n est pair, k=2 et sous des conditions naturelles de non dégénérescence, nous montrons l'existence et la régularité dans les espaces de Hölder d'un tel difféomorphisme satisfaisant de plus une condition de Dirichlet. On obtient aussi le théorème de Darboux avec la régularité optimale.
– Par ailleurs quand k=2 et n est impair ou k=n−1, ainsi que quelques cas particuliers où 3kn−2, nous montrons l'existence locale d'un tel difféomorphisme satisfaisant, en outre, des conditions de Cauchy.
Keywords: Darboux theorem; Symplectic forms; Pullback; Hölder regularity  相似文献   
140.
Favorable pendant-amino metal chelation in VX nerve agent model systems     
Bandyopadhyay I  Kim MJ  Lee YS  Churchill DG 《The journal of physical chemistry. A》2006,110(10):3655-3661
We have performed DFT computational studies [B3LYP, 6-31+G] to obtain metal ion coordination isomers of VX-Me [MeP(O)(OMe)(SCH2CH2NMe2)], a model of two of the most lethal nerve agents: VX [MeP(O)(OEt)(SCH2CH2N(iPr)2)] and Russian-VX [MeP(O)(OCH2CHMe2)(SCH2CH2N(Et)2)]. Our calculations involved geometry optimizations of the neutral VX-Me model as well as complexes with H+, Li+, Na+, K+, Be2+, Mg2+, and Ca2+ that yielded 2-8 different stable chelation modes for each ion that involved mainly mono- and bidentate binding. Importantly, our studies revealed that the [O(P),N] bidentate binding mode, long thought to be the active mode in differentiating the hydrolytic path of VX from other nerve agents, was the most stable for all ions studied here. Binding energy depended mainly on ionic size as well as charge, with binding energies ranging from 364 kcal mol(-1) for Be2+ to 33 kcal mol(-1) for K+. Furthermore, calculated NMR shifts for VX-Me correlate to experimental values of VX.  相似文献   
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131.
The dynamics of water near the polar headgroups of surfactants in a monolayer adsorbed at the air/water interface is likely to play a decisive role in determining the physical behavior of such organized assemblies. We have carried out an atomistic molecular dynamics (MD) simulation of a monolayer of the anionic surfactant sodium bis(2-ethyl-1-hexyl) sulfosuccinate (aerosol-OT or AOT) adsorbed at the air/water interface. The simulation is performed at room temperature with a surface coverage of that at the critical micelle concentration (78 Angstrom(2)/molecule). Detailed analyses of the lifetime dynamics of surfactant-water (SW) and water-water (WW) hydrogen bonds at the interface have been carried out. The nonexponential hydrogen bond lifetime correlation functions have been analyzed by using the formalism of Luzar and Chandler, which allowed identification of the bound states at the interface and quantification of the dynamic equilibrium between bound and quasi-free water molecules, in terms of time-dependent relaxation rates. It is observed that the water molecules present in the first hydration layer form strong hydrogen bonds with the surfactant headgroups and hence have longer lifetimes. Importantly, it is found that the overall relaxation of the SW hydrogen bonds is faster for those water molecules which form two hydrogen bonds with the surfactant headgroups than those forming one such hydrogen bond. Equally interestingly, it is further noticed that water molecules beyond the first hydration layer form weaker hydrogen bonds than pure bulk water.  相似文献   
132.
A cryptand with six secondary amino groups has been derivatized by reacting with acid chlorides of different chain lengths (C(7), C(10) and C(18)) to get three cryptand based hexa-tailed neutral amphiphiles (L(1)-L(3)). The cavity of the cryptand head group accommodates two Cu(II) ion giving another set of three amphiphiles. These amphiphiles and its copper complexes can aggregate spontaneously as giant vesicular microcapsules in 10% ethanolic water medium. In all cases vesicles formed are mostly unilamellar in nature. Vesicular microcapsules prepared from L(1)-L(3) can encapsulate hydrophilic dye 5(6)-carboxyfluorescein (CF). Stability of microcapsules, CF encapsulation efficiencies and release rates were dependent on the hydrophobic chain length of the amphiphiles. Results show the permeability of the L(2) and L(3) bilayer is lower than that of phosphatidylcholine vesicles and the loading capacity is approximately 3 times greater. Microcapsules have been characterized by optical microscopy, freeze fracture scanning electron microscopy and confocal fluorescence microscopy.  相似文献   
133.
Atomistic molecular dynamics simulations of a fully hydrated liquid crystalline lamellar phase of a dimyrystoylphosphatidylcholine lipid bilayer containing ethanol at 1:1 composition as well as of the pure lamellar phase of the bilayer have been performed. Detailed analyses have been carried out to investigate the effects of ethanol, if any, on the lifetime dynamics of lipid-water and water-water hydrogen bonds in the hydration layer of the lipid headgroups. The nonexponential hydrogen bond lifetime correlation functions have been analyzed by using the formalism of Luzar and Chandler, which allowed the identification of the bound states at the bilayer interface and the quantification of the dynamic equilibrium between the bound and the free water molecules, in terms of time-dependent relaxation rates. The calculations show that the overall relaxation of phosphate-water hydrogen bonds is faster in the presence of ethanol. Studies of the residence time and the number fluctuation of the hydration layer water molecules reveal that the presence of ethanol molecules decreases the rigidity of the lipid hydration layer.  相似文献   
134.
The neutron dose is estimated by linear energy transfer (LET) spectrometry method for two reactions, viz. 1H+9Be and 1H+12C at 20 MeV proton energy using CR-39 track detectors. The LET spectrum is generated from the major, minor radii of each track and thickness of removed surface from each side of the detector due to chemical etching. Microdosimetric distributions of absorbed dose and dose equivalents are obtained from the LET spectrum. The absorbed dose and dose equivalent per incident proton obtained from the LET spectra are found to be about 12.5 and 8 times higher in 1H+9Be reaction than 1H+12C reaction.  相似文献   
135.
In recent years multi-spectral device is steadily growing popularity. Multi-spectral antireflection coating effective in visible region for sighting system, laser wavelength for ranging and MWIR region for thermal system can use common objective/receiver optics highly useful for state of art thermal instrumentation. In this paper, design and fabrication of antireflection coating simultaneously effective in visible region (450–650 nm), Eye safe laser wave length (1540 nm) and MWIR region (3.6–4.9 μm) has been reported. Comprehensive search method of design was used and the number of layers in the design was optimised with lowest evaluated merit function studied with respect to various layers. Finally eight-layer design stack was established using hafnium oxide as high index layer and silicon-di-oxide as low index coating material combination. The multilayer stack had been fabricated by using electron beam gun evaporation system in Symphony 9 vacuum coating unit. During layer deposition the substrate was irradiated with End-Hall ion gun. The evaporation was carried out in presence of oxygen and layer thicknesses were measured with crystal monitor. The result achieved for the antireflection coating was 85% average transmission from 450 to 650 nm in visible region, 95% transmission at 1540 nm and 96% average transmission from 3.6 to 4.9 μm in MWIR region.  相似文献   
136.
The radiation induced graft copolymerization of acrylamide onto jute fibers was studied following preirradiation of jute in air using a60Co source of γ-radiation and subsequent polymerization of acrylamide in a limited aqueous system under nitrogen at 607°C. An increase of the time of preirradiation (at a fixed dose rate) increased the percent grafting measurably and the grafting efficiency marginall Grafting effects showed further improvement on addition of Fe2+ or Co2+ ions to the system prior to the polymerization step. Increasing the concentration of Fe2+ or Co2+ ion led to an increase in the grafting parameters with a leveling off effect in the higher concentration range, however. An increase in the polymer (jute) content for a fixed monomer content produced a significant increase in the efficiency of grafting, while % grafting followed a slowly decreasing trend.  相似文献   
137.
5Cr-0.5Mo steel having initial bainitic microstructure has been aged at 600 °C for 5000 h and subjected to creep at 600 °C/60 MPa. At different lengths of time the tests were interrupted for magnetic measurement using magnetic Barkhausen emissions (MBE) and magnetic hysteresis loop (MHL) techniques. Composition, morphology and distribution of carbides were studied using scanning electron microscopy (SEM). Magnetic softness was observed in the material up to 1600 h of ageing due to the decrease in pinning density for the coarsening of carbides by accumulation of large number of finer carbides. At higher ageing periods the demagnetizing field offered by the large massive carbides causes magnetic hardening. During creep test since the material has been normalized at 50 h of creep test also the structural change in creep test is accelerated, the magnetic softening for the interstitial carbon migration to the grain boundary and stress relaxation has removed in such early periods of ageing. When the carbides started coarsening the number density of the carbides decreased and inter-carbide distance increased which enhances the magnetic softening in the material in the secondary stage of creep. Formation of massive carbides and micro voids at the late tertiary stage of creep offers demagnetizing field causes magnetic hardening before failure of the material.  相似文献   
138.
High catalytic proficiencies observed for the native and promiscuous reaction of the Pseudomonas aeruginosa arylsulfatase (PAS; the picture shows transition states of the two substrates with corresponding binding constants Ktx) suggest that the trade‐off between high activity and tight specificity can be substantially relaxed.

  相似文献   

139.
We discuss the existence of a diffeomorphism such that
φ*(g)=f
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