Group-theoretical investigation of the tunneling splitting patterns of enolic acetylacetone

Extensive experimental and theoretical studies for enolic acetylacetone have been presented in the literature, but studies of the tunneling splitting patterns are still lacking. In this work we adopt the C_s symmetry equilibrium structure and apply a group-theoretical formalism to study the tunneling splitting pattern of the ground vibrational level of enolic acetylacetone. Enolic acetylacetone has three large-amplitude motions, one intramolecular hydrogen transfer and two methyl torsions. Therefore, the C_s structure of enolic acetylacetone has 18 (3 × 3 × 2) equivalent equilibrium molecular frameworks, nine (3 × 3) of them are from the two methyl torsions, and two are from the intramolecular hydrogen transfer. Tunneling motions among the 18 equivalent molecular frameworks split the ground vibrational level into eight sublevels: A₁, A₄, E₁, E₂, E₃, E₄, G(1) and G(2). In enolic acetylacetone the intramolecular hydrogen transfer induces a rearrangement of the CC, CO single and double bonds, and then triggers two additional 60° internal rotations, one in each of the two methyl groups attached to the hydrogen-bonded malonaldehyde ring. This interaction further complicates the tunneling splitting patterns and increases the difficulty of spectral analysis. In this work the influence of the intramolecular hydrogen transfer on the energy order of the eight sublevels is determined by a group-theoretical formalism.     

On finitely generated module whose first nonzero fitting ideal is maximal

Let R be a Noetherian ring and M be a finitely generated R-module. Let I(M) be the first nonzero Fitting ideal of M. The main result of this paper asserts that when I(M) = Q is a regular maximal ideal of R, then M?R∕Q⊕P, for some projective R-module P of constant rank if and only if T(M)?QM. As a consequence, it is shown that if M is an Artinian R-module and I(M) = Q is a regular maximal ideal of R, then M?R∕Q.     

波形钢腹板箱梁的约束扭转剪应力分析

基于周边不变形理论,结合闭口薄壁杆件约束扭转的计算分析,研究了波形钢腹板箱梁在约束扭转时混凝土悬臂板上扭转剪应力的分布,并进行了计算.通过对悬臂板在约束扭转中剪力流计算公式的推导,进一步阐述了其自由扭转剪应力及翘曲扭转剪应力的分布,指出了相关文献在这部分计算中存在的问题.通过一个简支波形钢腹板组合箱梁算例,将该文方法计算结果与ANSYS有限元计算结果进行比较.结果表明:在波形钢腹板箱梁截面中,主要由波形钢腹板承受扭转剪应力,其次是混凝土底板,底板剪应力最大值发生在底板中心处,其数值近似等于腹板剪应力的一半,而混凝土顶板和悬臂部分的扭转剪应力很小;该文计算的扭转剪应力结果在总体上符合有限元得到的扭转剪应力分布规律,在悬臂自由端为0,随着离开悬臂自由端距离的增大,扭转剪应力逐渐增大并达到峰值.     

Twisted analytic torsion

We review the Reidemeister, Ray-Singer’s analytic torsion and the Cheeger-Mller theorem. We describe the analytic torsion of the de Rham complex twisted by a flux form introduced by the current authors and recall its properties. We define a new twisted analytic torsion for the complex of invariant differential forms on the total space of a principal circle bundle twisted by an invariant flux form. We show that when the dimension is even, such a torsion is invariant under certain deformation of the metric and the flux form. Under T-duality which exchanges the topology of the bundle and the flux form and the radius of the circular fiber with its inverse, the twisted torsion of invariant forms are inverse to each other for any dimension.     

Large Amplitude Motions of Pyruvic Acid (CH3-CO-COOH)

Torsional and rotational spectroscopic properties of pyruvic acid are determined using highly correlated ab initio methods and combining two different theoretical approaches: Second order perturbation theory and a variational procedure in three-dimensions. Four equilibrium geometries of pyruvic acid, Tc, Tt, Ct, and CC, outcome from a search with CCSD(T)-F12. All of them can be classified in the C_s point group. The variational calculations are performed considering the three internal rotation modes responsible for the non-rigidity as independent coordinates. More than 50 torsional energy levels (including torsional subcomponents) are localized in the 406–986 cm⁻¹ region and represent excitations of the ν₂₄ (skeletal torsion) and the ν₂₃ (methyl torsion) modes. The third independent variable, the OH torsion, interacts strongly with ν₂₃. The A₁/E splitting of the ground vibrational state has been evaluated to be 0.024 cm⁻¹ as it was expected given the high of the methyl torsional barrier (338 cm⁻¹). A very good agreement with respect to previous experimental data concerning fundamental frequencies (ν^CAL − ν^EXP ~ 1 cm⁻¹), and rotational parameters (B₀^CAL − B₀^EXP < 5 MHz), is obtained.     

Boyle’s conjecture and perfect localizations

ABSTRACT

In this article we study the behavior of left QI-rings under perfect localizations. We show that a perfect localization of a left QI-ring is a left QI-ring. We prove that Boyle’s conjecture is true for left QI-rings with finite Gabriel dimension such that every hereditary torsion theory in the Gabriel filtration is perfect. As corollary, we get that Boyle’s conjecture is true for left QI-rings which satisfy the restricted left socle condition, a result proved by Faith in [6 Faith, C. (1976). On hereditary rings and Boyle’s conjecture. Arch. Math. 27(1):113–119.[Crossref] , [Google Scholar]].     

一种新的计算Timoshenko梁截面剪切系数的方法

Timoshenko梁理论中考虑了截面剪切变形的影响,推导了一种新的计算剪切系数的方法,首先采用悬臂梁纯弯曲变形条件下截面剪应力分布的精确解,基于能量原理得到了各种梁截面剪切系数新的表达式,然后推导了弯扭耦合变形条件下截面剪应力分布的精确解,进一步获得了该条件下截面的剪切系数.结果表明,悬臂梁端面作用力偏离截面的弯曲中心将使剪切系数变小,通过与Cowper计算结果的对比发现结果偏小,其原因是Cowper没有考虑与外力垂直的剪应力的影响,因此新的计算结果更优越.     

A comparison of the von Mises and Hencky equivalent strains for use in simple shear experiments

The von Mises equivalent strain increment is derived for the case of large strain simple shear (torsion testing). This is used, in conjunction with the von Mises yield surface, to define the von Mises equivalent stress as well as the incremental work per unit volume. Integration of the equivalent strain increment leads to the definition of the von Mises equivalent strain for torsion. The Hencky equivalent strain increment is derived from the Hencky strain defined as the logarithm of the semi major and minor axes of the strain ellipse. This is then used, via the incremental work, to derive the ‘Hencky equivalent stress’. In the Onaka approach, the numerical values of the principal strain increments were integrated without taking into account the continuous rotation of the strain ellipse. This invalid operation leads to an expression for the equivalent strain increment that cannot be applied to the large strains considered by Onaka. Using the correct increments of the Hencky strain, it is shown that the shear strain increments turn negative and consequently, the incremental work becomes negative when the shear is large.     

High-pressure torsion applied to nickel single crystals

Nickel single crystals with different crystallographic orientations were deformed by high-pressure torsion. Special attention is devoted to examining the evolution of the micro-texture and microstructure. The initial crystal orientation was found to have a significant effect on the mechanical hardening and evolution of micro-texture at low and medium equivalent strains, whereas at very high strains no effect of the initial orientation was observed and the behaviour was very similar to a polycrystal. The evolution of micro-texture is in good qualitative agreement with the full constrained Taylor model. At very high equivalent strains the initial crystal orientation has no influence on micro-texture. At such strains, the hardening, the refinement of the structure and the texture reaches a saturation. The final micro-texture is explained by the change from one preferred crystallographic orientation to another.