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21.
We study compact perturbations of reflexive algebras with commutative invariant subspace lattices. This leads us to study lattice isomorphisms that are uniform limits of spatially induced mappings and satisfy a compactness condition. We prove that two lattices that are nested or complemented are isomorphic in this way iff their corresponding perturbed algebras are unitary equivalent. While for complemented lattices this relation implies unitary equivalence, we prove that any two continuous nests are equivalent in this way.  相似文献   
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We introduce admissible lattices and Gabor pairs to define discrete versions of wave-front sets with respect to Fourier–Lebesgue and modulation spaces. We prove that these wave-front sets agree with each other and with corresponding wave-front sets of “continuous type”. This implies that the coefficients of a Gabor frame expansion of f are parameter dependent, and describe the wave-front set of f.  相似文献   
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25.
This is the first comprehensive bibliography of Julius Petersen's papers and books, covering not only his mathematical works, but also his contributions to economics, social science, physics and education.  相似文献   
26.
In vivo measurement of metabolite concentrations in the human brain by means of proton-MRS contributes significantly to the clinical evaluation of patients with diseases of the brain. The fully relaxed water signal has been proposed as an internal standard for calibration of the MRS measurements. The major drawbacks are the necesity to make the assumptions that the water concentration in the brain and that all tissue water is MR-visible. A number of in vivo measurements were carried out to estimate the concentration of MR-visible water in the brain of healthy volunteers divided into four age groups: newborn (0–23 days), adolescents (10–15 yr), adults (22–28 yr), and elderly people (60–74 yr). The examinations were carried out using a Siemens Helicon SP 63/84 MR-scanner operating at 1.5 T. Except for the newborn, four regions were studied in each subject using stimulated echo (STEAM) sequences without water suppression. In vitro measurements on a standard phantom were used for calibration. The calculated water concentrations ranged between 35.8 and 39.6 (mean 36.9) mol·[kg wet weight]−1 in the three groups, whereas it was 51.5 mol·[kg wet weight]−1 in the newborn, p<.01. The observed water concentration of neither the four regions nor of the three oldest age groups were significantly different. Comparisons between the water concentrations measured and those expected based on estimation of the content of grey and white matter in the region of interest from T1-weighted images and biochemical data published, suggest that only a small fraction (<5%) of the tissue water may be MR-invisible. The study of healthy volunteers thus shows that errors introduced by using the unsaturated water signal for calibration are less than 10%, which is comparable to expected errors when other calibration procedures are used under similar measurement conditions.  相似文献   
27.
Quasi-isothermal thermogravimetry is a new technique in which the programmed heating of a furnace automatically ceases when the rate of a reaction taking place in a sample, which is indicated by the DTG-signal, exceeds a preset limit. In this way reactions can be studied under nearly isothermal conditions. In this paper the data obtained using this method during oxidation and reduction experiments on nonstoichiometric cerium oxides are compared with the data obtained by conventional isothermal thermogravimetry. The kinetics of the composition changes during isothermal reduction and oxidation of CeO2?x are also analyzed. It appears that, with some reservations, the experimental data are best described by the rate equation for a diffusion-controlled reaction. Finally, both the isothermal and the quasi-isothermal data suggest that the CeO2?x phase region in the phase diagram consists of several subphases, each with a characteristic activation energy for the diffusion-controlled reactions.  相似文献   
28.
Smog chamber/Fourier transform infrared (FTIR) and laser-induced fluorescence (LIF) spectroscopic techniques were used to study the atmospheric degradation of CH3CHF2. The kinetics and products of the Cl(2P(3/2)) (denoted Cl) atom- and the OH radical-initiated oxidation of CH3CHF2 in 700 Torr of air or N2; diluents at 295 +/- 2 K were studied using smog chamber/FTIR techniques. Relative rate methods were used to measure k(Cl + CH3CHF2) = (2.37 +/- 0.31) x 10(-13) and k(OH + CH3CHF2) = (3.08 +/- 0.62) x 10(-14) cm3 molecule(-1) s(-1). Reaction with Cl atoms gives CH3CF2 radicals in a yield of 99.2 +/- 0.1% and CH2CHF2 radicals in a yield of 0.8 +/- 0.1%. Reaction with OH radicals gives CH3CF2 radicals in a yield >75% and CH2CHF2 radicals in a yield <25%. Absolute rate data for the Cl reaction were measured using quantum-state selective LIF detection of Cl(2P(j)) atoms under pseudo-first-order conditions. The rate constant k(Cl + CH3CHF2) was determined to be (2.54 +/- 0.25) x 10(-13) cm3 molecule(-1) s(-1) by the LIF technique, in good agreement with the relative rate results. The removal rate of spin-orbit excited-state Cl(2P(1/2)) (denoted Cl) in collisions with CH3CHF2 was determined to be k(Cl + CH3CHF2) = (2.21 +/- 0.22) x 10(-10) cm3 molecule(-1) s(-1). The atmospheric photooxidation products were examined in the presence and absence of NO(x). In the absence of NO(x)(), the Cl atom-initiated oxidation of CH3CHF2 in air leads to formation of COF2 in a molar yield of 97 +/- 5%. In the presence of NO(x), the observed oxidation products include COF2 and CH3COF. As [NO] increases, the yield of COF2 decreases while the yield of CH3COF increases, reflecting a competition for CH3CF2O radicals. The simplest explanation for the observed dependence of the CH3COF yield on [NO(x)] is that the atmospheric degradation of CH3CF2H proceeds via OH radical attack to give CH3CF2 radicals which add O2 to give CH3CF2O2 radicals. Reaction of CH3CF2O2 radicals with NO gives a substantial fraction of chemically activated alkoxy radicals, [CH3CF2O]. In 1 atm of air, approximately 30% of the alkoxy radicals produced in the CH3CF2O2 + NO reaction possess sufficient internal excitation to undergo "prompt" (rate >10(10) s(-1)) decomposition to give CH3 radicals and COF2. The remaining approximately 70% become thermalized, CH3CF2O, and undergo decomposition more slowly at a rate of approximately 2 x 10(3) s(-1). At high concentrations (>50 mTorr), NO(x) is an efficient scavenger for CH3CF2O radicals leading to the formation of CH3COF and FNO.  相似文献   
29.
A graph G is (k1, k2, …, kt)-saturated if there exists a coloring C of the edges of G in t colors 1, 2, …, t in such a way that there is no monochromatic complete ki-subgraph K of color i, 1 ? i ? t, but the addition of any new edge of color i, joining two nonadjacent vertices in G, with C, creates a monochromatic K of color i, 1 ? i ? t. We determine the maximum and minimum number of edges in such graphs and characterize the unique extremal graphs.  相似文献   
30.
We construct a calculus for generalized SG Fourier integral operators, extending known results to a broader class of symbols of SG type. In particular, we do not require that the phase functions are homogeneous. An essential ingredient in the proofs is a general criterion for asymptotic expansions within the Weyl-Hörmander calculus. We also prove the L2(Rd)-boundedness of the generalized SG Fourier integral operators having regular phase functions and amplitudes uniformly bounded on R2d.  相似文献   
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