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We give a classification of affine rotational surfaces in affine 3-space with vanishing affine Gauss-Kronecker curvature. Non-degenerated surfaces in three dimensional affine space with affine rotational symmetry have been studied...
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We give a classification of affine rotational surfaces in affine 3-space with vanishing affine Gauss-Kronecker curvature. Non-degenerated surfaces in three dimensional affine space with affine rotational symmetry have been studied by a number of authors (I.C. Lee. [3], P. Lehebel [4], P.A. Schirokow [10], B. Su [12], W. Süss [13]). In the present paper we study these surfaces with the additional property of vanishing affine Gauss-Kronecker curvature, that means the determinant of the affine shape operator is zero. We give a complete classification of these surfaces, which are the affine analogues to the cylinders and cones of rotation in euclidean geometry. These surfaces are examples of surfaces with diagonalizable rank one (affine) shape operator (cf. B. Opozda [8] and B. Opozda, T. Sasaki [7]). The affine normal images are curves.
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We investigate the problem of recognizing a generalization of surfaces of revolution appearing in the field of affine differential geometry, namely affine rotation surfaces. By using some notions from affine differential geometry,...
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We investigate the problem of recognizing a generalization of surfaces of revolution appearing in the field of affine differential geometry, namely affine rotation surfaces. By using some notions from affine differential geometry, we determine how to detect whether or not a given implicit algebraic surface is an affine rotation surface. These results generalize some previous results of the authors on surfaces of revolution. As a by-product, we also provide an algorithm to detect whether or not an algebraic surface is an affine sphere, a generalization of Euclidean spheres of interest not only in geometry, but also in other fields.
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摘要 :
We give a classification of affine rotational surfaces in affine 3-space with vanishing affine Gauss-Kronecker curvature. Non-degenerated surfaces in three dimensional affine space with affine rotational symmetry have been studied...
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We give a classification of affine rotational surfaces in affine 3-space with vanishing affine Gauss-Kronecker curvature. Non-degenerated surfaces in three dimensional affine space with affine rotational symmetry have been studied by a number of authors (I.C. Lee. [3], P. Lehebel [4], P.A. Schirokow [10], B. Su [12], W. Süss [13]). In the present paper we study these surfaces with the additional property of vanishing affine Gauss-Kronecker curvature, that means the determinant of the affine shape operator is zero. We give a complete classification of these surfaces, which are the affine analogues to the cylinders and cones of rotation in euclidean geometry. These surfaces are examples of surfaces with diagonalizable rank one (affine) shape operator (cf. B. Opozda [8] and B. Opozda, T. Sasaki [7]). The affine normal images are curves.
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In this paper, we classify affine rotation surfaces of elliptic type in Affine 3- space satisfying some algebraic equations regarding the coordinate functions and the Laplacian operators in relation to the first and the second aff...
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In this paper, we classify affine rotation surfaces of elliptic type in Affine 3- space satisfying some algebraic equations regarding the coordinate functions and the Laplacian operators in relation to the first and the second affine fundamental forms of affine rotation surfaces of elliptic type. We also give explicit forms of these surfaces.
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We characterize centroaffine surfaces of cohomogeneity one which have vanishing Tchebychev vector fields. Moreover, we classify centroaffine minimal surfaces of cohomogeneity one which have centroaffine metrics of constant curvature.
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V-ATPases are ubiquitous proton-transporting ATPases of eukaryotic and prokaryotic membranes that utilize energy from ATP hydrolysis. The hydrophilic catalytic part called V(1)ATPase is composed of a ringshaped hexametric A(3)B(3)...
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V-ATPases are ubiquitous proton-transporting ATPases of eukaryotic and prokaryotic membranes that utilize energy from ATP hydrolysis. The hydrophilic catalytic part called V(1)ATPase is composed of a ringshaped hexametric A(3)B(3) complex and a central DF shaft. We previously proposed a rotation mechanism of the Enterococcus hirae V(1)ATPase based on the crystal structures of the V-1 and A(3)B(3) complexes. However, the driving force that induces the conformational changes of A(3)B(3) and rotation of the DF shaft remains unclear. In this study, we investigated the binding affinity changes between subunits of V(1)ATPase by surface plasmon resonance analysis. The binding of ATP to subunit A was found to considerably increase the affinity between the A and B subunits, and thereby ATP binding contributes to forming the A(1)B(1) tight conformation. Furthermore, the DF shaft bound to the reconstituted A(1)B(1) complex with high affinity, suggesting that the tight A(1)B(1) complex is a major binding unit of the shaft in the A(3)B(3) ring complex. Based on these results, we propose that rotation of the V-1-ATPase is driven by affinity changes between each subunit via thermal fluctuations. (C) 2020 Elsevier Inc. All rights reserved.
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The nature and concentrations of the local environments in a series of deuterated jarosite (nominally AFe(3)(SO4)(2)(OD)(6) with A = K, Na, and D3O) samples with different levels of iron and cation vacancies have been determined b...
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The nature and concentrations of the local environments in a series of deuterated jarosite (nominally AFe(3)(SO4)(2)(OD)(6) with A = K, Na, and D3O) samples with different levels of iron and cation vacancies have been determined by H-2 MAS NMR spectroscopy at ambient temperatures. Three different local deuteron environments, Fe2OD, FeOD2, and D2O/D3O+, can be separated based on their very different Fermi contact shifts of delta approximate to 237, 70, and 0 ppm, respectively. The FeOD2 group arises from the charge, compensation of the Fe3+ vacancies, allowing the concentrations of the vacancies to be readily determined. Analysis of the 2 H quadrupole interaction indicates that the FeOD2 groups are mobile, undergoing rapid 180 degrees flips on the NMR time scale; the D2O/D3O+ species (located on the A sites) undergo close to isotropic motion, whereas the Fe20D groups are rigid and are hydrogen-bonded to nearby sulfate 0 atoms, with a (Fe)OD-O(S) distance of 2.79(4) angstrom. No evidence for the intrinsic protonation reaction Fe2OH + H3O+ -> Fe2OH2 + H2O is found in the hydronium jarosite, suggesting that this mechanism is not the cause of the anomalous magnetic behavior of this material. The results illustrate that 2 H MAS NMR spectroscopy is an excellent probe of the local environments and defects, on the atomic/molecular level, providing information that is complementary to diffraction techniques and that will help to rationalize the magnetic properties of these materials.
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An overview is given of the possibilities and limitations of secondary ion mass spectrometry as an analytical tool in the investigation of near-perfect, i.e. almost atomically-sharp, dopant and impurity distributions. The operatin...
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An overview is given of the possibilities and limitations of secondary ion mass spectrometry as an analytical tool in the investigation of near-perfect, i.e. almost atomically-sharp, dopant and impurity distributions. The operating principles of the technique and the various quantification schemes are briefly presented. The most elaborate discussion pertains to the factors that determine the attainable depth resolution and what can be done to improve things, both from an experimental and from a theoretical point of view. Emphasis is placed on semiconductors and other brittle target materials, but the implications for metals are indicated. [References: 165]
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An analysis of O(P-3) reaction mechanisms and kinetics with CH3OOH and CH3CH2OOH has been examined. Potential energy diagrams for the named reactions have been evaluated at the W1 and CCSD(T)/aug-cc-pVTZ// MP2/aug-cc-pVTZ levels o...
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An analysis of O(P-3) reaction mechanisms and kinetics with CH3OOH and CH3CH2OOH has been examined. Potential energy diagrams for the named reactions have been evaluated at the W1 and CCSD(T)/aug-cc-pVTZ// MP2/aug-cc-pVTZ levels of theory. For the two reactions, a total of seven abstraction channels have been described. The reaction enthalpies and standard reaction Gibbs free energy are calculated at the W1 level. The kinetic study is conducted within the temperature range of 210-350 K using transition state theory (TST), TST with Wigner correction (TST/W), and TST with zero curvature tunneling (TST/ZCT). The rate coefficients were also calculated using canonical variational transition state theory (CVT), CVT with zero curvature tunneling (CVT/ZCT), and CVT with small curvature tunneling (CVT/SCT). Branching ratios have been computed using the CVT/SCT rate coefficients. Hydrogen abstraction from the hydroxyl group is identified as a significant pathway in both reactions.
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The rotationally resolved infrared spectrum of the Na+-H-2 cation complex is recorded in the H-H stretch region (4067-4118 cm(-1)) by monitoring the production of Na+ photofragments. Altogether 42 lines are identified, 40 of which...
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The rotationally resolved infrared spectrum of the Na+-H-2 cation complex is recorded in the H-H stretch region (4067-4118 cm(-1)) by monitoring the production of Na+ photofragments. Altogether 42 lines are identified, 40 of which are assigned to K-a=1-1 transitions (associated with complexes containing ortho-H-2) and two tentatively assigned to K-a=0-0 transitions (associated with complexes containing para-H-2). The K-a=1-1 subband lines were fitted using a Watson A-reduced Hamiltonian, yielding effective spectroscopic constants. The band origin is estimated as 4094.6 cm(-1), a shift of -66.6 cm(-1) with respect to the Q(1)(0) transition of the free H-2 molecule. The results demonstrate that Na+-H-2 has a T-shaped equilibrium configuration with the Na+ ion attached to a slightly perturbed H-2 molecule but that large-amplitude vibrational motions significantly influence the rotational constants derived from the asymmetric rigid rotor analysis. The vibrationally averaged intermolecular separation in the ground vibrational state is estimated as 2.493 A, increasing slightly (by 0.002 A) when the H-2 subunit is vibrationally excited. A new three-dimensional potential energy surface is developed to describe the Na+-H-2 complex. Ab initio points calculated using the CCSD(T) method and aug-cc-pVQZ basis set augmented by bond functions are fitted using a reproducing kernel Hilbert space method [Ho , J. Chem. Phys. 104, 2584 (1996)] to give an analytical representation of the potential energy surface. Ensuing variational calculations of the rovibrational energy levels demonstrate that the potential energy surface correctly predicts the frequency of the nu(HH) transition (to within 2.9 cm(-1)) and the dissociation energies [842 cm(-1) for Na+-H-2(para) and 888 cm(-1) for Na+-H-2(ortho)]. The B and C rotational constants are slightly underestimated (by 1.7%), while the vibrationally averaged intermolecular separation is overestimated by 0.02 A.
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