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1.
J. A. Rush 《Geometriae Dedicata》1994,53(2):217-221
It has long been known that the admissibility of a lattice with respect to a symmetric convex bodyB is equivalent to being a packing lattice for 1/2B. This fact is the basis of the interplay between the classical theory of the arithmetic minima of positive definite quadratic forms, on the one hand, and the dense lattice packing of spheres inR
n
, on the other.We give an indexed set of bounds
L
(B) a
j
, where 0 j n/2, on the lattice packing density ofB. The casej=0 reduces to the aforementioned long-known fact, andj=1 was proved by Elkies, Odlyzko, and Rush, and was used to obtain record high packing densities for various superballs. The new cases make possible the use of smaller primes in the construction of these dense packings.Supported by National Science Foundation grant DMS-9103233. 相似文献
2.
The rate constants at which oxidizing and reducing radicals react with the dinuclear iron(III) complex Fe2O(ttha)2− were measured in neutral aqueous solution. The rate constants for reduction of the complex by ·CO2.− CH3.CHOH and O2.− were found to be comparable with rate constants previously measured in mononuclear iron(III) polyaminocarboxylate systems. Fe2O(ttha)2− reacts slowly with O2.− (k8 = (1.2 ± 0.2) × 104 dm3 mol−1 s−1) and, hence, is a relatively poor catalyst for the dismutation of superoxide radical. The hydrated electron reduces the complex at a diffusion-controlled rate in a process which consumes one proton: eaq− + Fe2O(ttha)2− → Fe2III,IIO(ttha)3− The reduction by carbon-centered radicals produces a (III,II) mixed-valence complex with an absorption spectrum different from that of the Fe2(II,III) species produced from reduction by the hydrated electron. The oxidizing radicals .OH and ·CO3− appear to act as reductants of the complex via ligand oxidation rather than by oxidation of the Fe2IIIO core to Fe2III,IVO. In the former case ligand attack appears to occur mainly at the methylene carbon of a glycinate group. The decarboxylation product, CO2, was detected by its aquation reaction in the presence of a pH sensitive dye, bromthymol blue. 相似文献
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4.
Verdal N Udovic TJ Rush JJ Stavila V Wu H Zhou W Jenkins T 《The Journal of chemical physics》2011,135(9):094501
Low-temperature neutron scattering spectra of diammonium dodecahydro-closo-dodecaborate [(NH(4))(2)B(12)H(12)] reveal two NH(4)(+) rotational tunneling peaks (e.g., 18.5 μeV and 37 μeV at 4 K), consistent with the tetrahedral symmetry and environment of the cations. The tunneling peaks persist between 4 K and 40 K. An estimate was made for the tunnel splitting of the first NH(4)(+) librational state from a fit of the observed ground-state tunnel splitting as a function of temperature. At temperatures of 50 K-70 K, classical neutron quasi-elastic scattering appears to dominate the spectra and is attributed to NH(4)(+) cation jump reorientation about the four C(3) axes defined by the N-H bonds. A reorientational activation energy of 8.1 ± 0.6 meV (0.79 ± 0.06 kJ/mol) is determined from the behavior of the quasi-elastic linewidths in this temperature regime. This activation energy is in accord with a change in NH(4)(+) dynamical behavior above 70 K. A low-temperature inelastic neutron scattering feature at 7.8 meV is assigned to a NH(4)(+) librational mode. At increased temperatures, this feature drops in intensity, having shifted entirely to higher energies by 200 K, suggesting the onset of quasi-free NH(4)(+) rotation. This is consistent with neutron-diffraction-based model refinements, which derive very large thermal ellipsoids for the ammonium-ion hydrogen atoms at room temperature in the direction of reorientation. 相似文献
5.
Batch extraction and polymerization of indole and 3-methylindole (skatole) with acidic cation exchange resins functioned as pseudo first-order reactions. Activation energies of 3.4 and 5.7 keal/mole indicated greater steric hindrance to skatole polymerization, as would be expected from 2,2′ bonding of skatole compared to 3,2′ bonding for indole. Linear polymerization occurred, although a heterocyclic ring opened at the trimer stage of poly(indole). 2-Methylindole did not polymerize. General acid-base catalysis caused unreproducible partial depolytnerization when the polymers were extracted from resin beads. Thus, compounds chromatographically separated probably were of lower degree of polymerization than were the polymers formed in the resin matrix. 相似文献
6.
David E. Rush 《Proceedings of the American Mathematical Society》2000,128(10):2879-2884
Let be a commutative ring, let be an indeterminate, and let . There has been much recent work concerned with determining the Dedekind-Mertens number =min , especially on determining when = . In this note we introduce a universal Dedekind-Mertens number , which takes into account the fact that deg() + for any ring containing as a subring, and show that behaves more predictably than .
7.
Skripov AV Mushnikov NV Terent'ev PB Gaviko VS Udovic TJ Rush JJ 《J Phys Condens Matter》2011,23(40):405402
The vibrational spectrum of hydrogen and the parameters of H jump motion in the rhombohedral Th(2)Zn(17)-type compound Ce(2)Fe(17)H(5) have been studied by means of inelastic and quasielastic neutron scattering. It is found that hydrogen atoms occupying interstitial Ce(2)Fe(2) sites participate in the fast localized jump motion over the hexagons formed by these tetrahedral sites. The H jump rate τ(-1) of this localized motion is found to change from 3.9 × 10(9) s(-1) at T = 140 K to 4.9 × 10(11) s(-1) at T = 350 K, and the temperature dependence of τ(-1) in the range 140-350 K is well described by the Arrhenius law with the activation energy of 103±3 meV. Our results suggest that the hydrogen jump rate in Th(2)Zn(17)-type compounds strongly increases with decreasing nearest-neighbor distance between the tetrahedral sites within the hexagons. Since each such hexagon in Ce(2)Fe(17)H(5) is populated by two hydrogen atoms, the jump motions of H atoms on the same hexagon should be correlated. 相似文献
8.
L. J. Ratliff Jr. D. E. Rush Jr. 《Transactions of the American Mathematical Society》2000,352(4):1647-1674
The main theorem characterizes, in terms of bracket powers, analytic spread one ideals in local rings. Specifically, let be regular nonunits in a local (Noetherian) ring and assume that , the integral closure of , where . Then the main result shows that for all but finitely many units in that are non-congruent modulo and for all large integers and it holds that for and not divisible by , where is the -th bracket power of . And, conversely, if there exist positive integers , , and such that has a basis such that , then has analytic spread one.
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