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71.
Eero Hyry 《Transactions of the American Mathematical Society》1999,351(6):2213-2232
Let be a multigraded ring defined over a local ring . This paper deals with the question how the Cohen-Macaulay property of is related to that of its diagonal subring . In the bigraded case we are able to give necessary and sufficient conditions for the Cohen-Macaulayness of . If are ideals of positive height, we can then compare the Cohen-Macaulay property of the multi-Rees algebra with the Cohen-Macaulay property of the usual Rees algebra . We also obtain a bound for the joint reduction numbers of two -primary ideals in the case the corresponding multi-Rees algebra is Cohen-Macaulay.
72.
The structure of the subspaces having the Dunford-Pettis property (DPP) is studied, where is the space of all compact operators on and . The following conditions are shown to be equivalent: (i) M has the DPP, (ii) M is isomorphic to a subspace of (iii) the sets and are relatively compact for all and . The equivalence between (i) and (iii) was recently proven in the case of arbitrary Hilbert spaces by Brown and ülger. It
is also shown that (i) and (ii) are equivalent for subspaces . This result is optimal in the sense that for there is a DPP-subspace that fails to be isomorphic to a subspace of .
Received January 9, 1998; in final form October 1, 1998 相似文献
73.
74.
Eero Hyry 《manuscripta mathematica》1999,98(3):377-390
Let A be a normal local ring which is essentially finite type over a field of characteristic zero. Let I⊂A be an ideal such that the Rees algebra R
A
(I) is Cohen–Macaulay and normal. In this paper we address the question: “When does R
A
(I) have rational singularities?” In particular, we study the connection between rational singularities of R
A
(I) and the adjoint ideals of the powers I
n
(n∋ℕ).
Received: 25 May 1998 / Revised version: 20 August 1998 相似文献
75.
Katja Heise Gwendoline Delepierre Alistair W. T. King Mauri A. Kostiainen Justin Zoppe Christoph Weder Eero Kontturi 《Angewandte Chemie (International ed. in English)》2021,60(1):66-87
Native plant cellulose has an intrinsic supramolecular structure. Consequently, it can be isolated as nanocellulose species, which can be utilized as building blocks for renewable nanomaterials. The structure of cellulose also permits its end‐wise modification, i.e., chemical reactions exclusively on one end of a cellulose chain or a nanocellulose particle. The premises for end‐wise modification have been known for decades. Nevertheless, different approaches for the reactions have emerged only recently, because of formidable synthetic and analytical challenges associated with the issue, including the adverse reactivity of the cellulose reducing end and the low abundance of newly introduced functionalities. This Review gives a full account of the scientific underpinnings and challenges related to end‐wise modification of cellulose nanocrystals. Furthermore, we present how the chemical modification of cellulose nanocrystal ends may be applied to directed assembly, resulting in numerous possibilities for the construction of new materials, such as responsive liquid crystal templates and composites with tailored interactions. 相似文献
76.
In this article we investigate when a complete ideal in a two-dimensional regular local ring is a multiplier ideal of some ideal with an integral multiplying parameter. In particular, we show that this question is closely connected to the Gorenstein property of the blowup along the ideal.Dedicated to Prof. Kei-ichi Watanabe on the occasion of his 60th birthday. 相似文献
77.
Kiviniemi T Hulkko E Kiljunen T Pettersson M 《The journal of physical chemistry. A》2008,112(23):5025-5027
The structure and properties of a 1:1 iodine-benzene complex isolated in an inert krypton matrix at low temperature have been studied with infrared and resonance Raman spectroscopy and with MP2 calculations. The structure of the ground-state complex is found to be unsymmetric, and the I-I vibrational frequency is found to be red-shifted by 3.94 cm(-1) upon complexation. The experimental data agree well with computational results, leading to the conclusion that the I2-Bz complex structure is not axial but of above-bond type, identically with other halogen-benzene complexes. 相似文献
78.
Ruuska H Arola E Kortelainen T Rantala TT Kannus K Valkealahti S 《The Journal of chemical physics》2011,134(13):134904
Influence of acrylic acid grafting of isotactic polypropylene on the dielectric properties of the polymer is investigated using density functional theory (DFT) calculations, both in the molecular modeling and three-dimensional (3D) bulk periodic system frameworks. In our molecular modeling calculations, polarizability volume, and polarizability volume per mass which reflects the permittivity of the polymer, as well as the HOMO-LUMO gap, one of the important measures indicating the electrical breakdown voltage strength, were examined for oligomers with various chain lengths and carboxyl mixture ratios. When a polypropylene oligomer is grafted with carboxyl groups (cf. acrylic acid), our calculations show that the increase of the polarizability volume α' of the oligomer is proportional to the increase of its mass m, while the ratio α'/m decreases from the value of a pure polymer when increasing the mixture ratio. The decreasing ratio of α'/m under carboxyl grafting indicates that the material permittivity might also decrease if the mass density of the material remains constant. Furthermore, our calculations show that the HOMO-LUMO gap energy decreases by only about 15% in grafting, but this decrease seems to be independent on the mixture ratio of carboxyl. This indicates that by doping polymers with additives better dielectric properties can be tailored. Finally, using the first-principles molecular DFT results for polarizability volume per mass in connection with the classical Clausius-Mossotti relation, we have estimated static permittivity for acrylic acid grafted polypropylene, assuming the structural density keeping constant under grafting. The computed permittivity values are in a qualitative agreement with the recent experiments, showing increasing tendency of the permittivity as a function of the grafting composition. In order to validate our molecular DFT based approach, we have also carried out extensive three-dimensional bulk periodic first-principles total-energy calculations in the frameworks of the density functional theory and density functional perturbation theory (DFPT) for crystalline acrylic acid grafted polypropylene. Interestingly, the computed electronic and dielectric properties behave very similarly between the simplified molecular DFT modeling and the more realistic 3D bulk periodic DFPT method. In particular, the static permittivity values [ε(r)(0)] from the molecular DFT-Clausius-Mossotti modeling are in excellent agreement with the high-frequency dielectric constant values (ε(∞)) from the DFPT method. This obviously implies that the chain-to-chain interaction to dielectric and electronic properties of acrylic acid polypropylene, to a first approximation, can be neglected, therefore justifying the usage of molecular DFT modeling in our calculations. 相似文献
79.
80.
Pekka J. Nieminen Eero Saksman 《Journal of Mathematical Analysis and Applications》2004,298(2):501-522
Let φ and ψ be analytic self-maps of the unit disc, and denote by Cφ and Cψ the induced composition operators. The compactness and weak compactness of the difference T=Cφ−Cψ are studied on Hp spaces of the unit disc and Lp spaces of the unit circle. It is shown that the compactness of T on Hp is independent of p∈[1,∞). The compactness of T on L1 and M (the space of complex measures) is characterized, and examples of φ and ψ are constructed such that T is compact on H1 but non-compact on L1. Other given results deal with L∞, weakly compact counterparts of the previous results, and a conjecture of J.E. Shapiro. 相似文献