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51.
52.
The classification of the equilibrium shapes that a self-gravitating fluid can take in a Riemannian manifold is a classical problem in Mathematical Physics. In this paper it is proved that the equilibrium shapes are isoparametric submanifolds. Some geometric properties of them are also obtained, e.g. classification and existence for some Riemannian spaces and relationship with the isoperimetric problem and the group of isometries of the manifold. Our approach to the problem is geometrical and allows to study the equilibrium shapes on general Riemannian spaces.  相似文献   
53.
In this paper we axiomatize some constructions and results due to Cayley and Hilbert. We define the concept of -process for an arbitrary affine algebraic monoid with zero and unit group . In our situation we show how to produce from the process and for a linear rational representation of a number of elements of the ring of -invariants that is large enough to guarantee its finite generation. Moreover, using complete reducibility, we give an explicit construction of all -processes for reductive monoids.

  相似文献   

54.
The complexation of metal cations into a host–guest situation is particularly well exemplified by [2.2.2]paracyclophane and AgI, which leads to a strong cation–π interaction with a specific face of the host molecule. Through this study we sought a deeper understanding of the effects the metal center has on the NMR spectroscopic properties of the prototypical organic host, generating theoretical reasons for the observed experimental results with an aim to determine the role of the cation–π interaction in a host–guest scenario. From an analysis of certain components of the induced magnetic field and the 13C NMR shielding tensor under its own principal axis system (PAS), the local and overall magnetic behavior can be clearly described. Interestingly, the magnetic response of such a complex exhibits a large axis-dependent behavior, which leads to an overall shielding effect for the coordinating carbon atoms and a deshielding effect for the respective uncoordinated counterparts, evidence that complements previous experimental results. This proposed approach can be useful to gain further insight into the local and overall variation of NMR shifts for host–guest pairs involving both inorganic and organic hosts.  相似文献   
55.
A numerical investigation was conducted to analyze the unsteady laminar flow field and heat transfer characteristics in a plane channel with two square bars mounted side by side to the approaching flow. A finite volume technique is applied with a fine grid and time resolution. The transverse separation distance between the bars (G/d) is varied from 0 to 5, whereas the bar height to channel height is d/H=1/8, and the channel length is L=5H. Different flow regimes develop in the channel due the interaction between the two mounted square bars, steady flow, flow with vortex shedding synchronization either in phase or in anti-phase, or biased flow with low frequency modulation of vortex shedding are found. Results show that the pressure drop increase and heat transfer enhancement are strongly dependent of the transverse separation distance of the bars and the channel Reynolds number.  相似文献   
56.
Benchmark, full-dimensional calculations on the ground and excited vibrational states for the tetra-, and penta-atomic weakly bound He(2,3)ICl complexes are reported. The representation of the potential energy surfaces includes three-body HeICl potentials parameterized to coupled-cluster singles, doubles, and perturbative triples ab initio data. These terms are important in accurately describing the interactions of such highly floppy systems. The corresponding 6D/9D computations are performed with the multi-configuration time dependent Hartree method, using natural potential fits, and a mode combination scheme to optimize the computational effort in the improved relaxation calculations. For these complexes several low-lying vibrational states are computed, and their binding energies and radial/angular probability density distributions are obtained. We found various isomers which are assigned to different structural models related with combinations of the triatomic isomers, like linear, T-shaped, and antilinear ones. Comparison of these results with recent experimental data is presented, and the quantitative deviations found with respect to the experiment are discussed.  相似文献   
57.
A simple and accurate group contribution method to estimate the heat capacity of ionic liquids is presented. The method considers groups previously defined for a successful method used to estimate critical properties of ionic liquids. Additionally a structural parameter known as mass connectivity index recently defined by the authors has been incorporated to define the model equation. To better define the values of the groups, heat capacity data at 298 K for 126 organic substances were used with the 469 heat capacity data for 32 ionic liquids. The results were compared with experimental data and with values reported by other available estimation methods. Results show that the new group contribution method gives low deviations and can be used with confidence in thermodynamic and engineering calculations.  相似文献   
58.
Three MIL-100 (Fe) samples differing in average crystal size (from 60-70 to >400 nm) have been synthesized by microwave heating using three HF/Fe(3+) ratios. Oxidation of diphenylmethane with tert-butylhydroperoxide (TBHP) and thiophenol with oxygen are catalyzed by three MIL-100 (Fe) samples with similar reaction rates regardless of its average particle size. In contrast, the activity of the three MIL-100 (Fe) samples for the oxidation of bulky triphenylmethane by TBHP largely depends on the average crystal size of the sample: the smaller the average particle size, the larger the initial reaction rate of triphenylmethane oxidation. These results show that diffusion limitation takes place on MOF catalysis depending on the substrate size and provides indirect evidence that these reactions take place inside the intracrystalline space of the porous catalysts.  相似文献   
59.
The ultrafast relaxation of jet-cooled aniline was followed by time-resolved ionization, after excitation in the 294-234 interval. The studied range of energy covers the absorption of the two bright ππ? excitations, S(1) and S(3), and the almost dark S(2) (πσ?) state. The employed probe wavelengths permit to identify different ultrafast time constants related with the coupling of the involved electronic surfaces. A τ(1) = 165 ± 30 fs lifetime is attributed to dynamics along the S(2) (πσ?) repulsive surface. Other relaxation channels as the S(1)→S(0) and S(3)→S(1) internal conversion are also identified and characterized. The work provides a general view of the photophysics of aniline, particularly regarding the role of the πσ? state. This state appears as minor dissipation process due to the ineffective coupling with the bright S(1) and S(3) states, being the S(1)→S(0) internal conversion the main non-radiative process in the full studied energy range. Additionally, the influence of the off-resonance adiabatic excitation of higher energy electronic states, particularly S(3), is also observed and discussed.  相似文献   
60.
Relativistic density functional calculations were carried out on several nickel toroid mercaptides of the general formula [Ni(μ-SR)(2)](n), with the aim to characterize and analyze their stability and magnetic response properties, in order to gain more insights into their stabilization and size-dependent behavior. The Ni-ligand interaction has been studied by means projected density of states and energy decomposition analysis, which denotes its stabilizing character. The graphical representation of the response to an external magnetic field is applied for the very first time taking into account the spin-orbit term. This map allows one to clearly characterize the magnetic behavior inside and in the closeness of the toroid structure showing the prescence of paratropic ring currents inside the Ni(n) ring, and by contrast, diatropic currents confined in each Ni(2)S(2) motif denoting an aromatic behavior (in terms of magnetic criteria). The calculated data suggests that the Ni(2)S(2) moiety can be regarded as a stable constructing block, which can afford several toroid structures of different nuclearities in agreement with that reported in the experimental literature. In addition, the effects of the relativistic treatment over the magnetic response properties on these lighter compounds are denoted by comparing nonrelativistic, scalar relativistic, and scalar plus spin-orbit relativistic treatments, showing their acting, although nonpronunced, role.  相似文献   
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