Ray-Singer type theorem for the refined analytic torsion

We show that the refined analytic torsion is a holomorphic section of the determinant line bundle over the space of complex representations of the fundamental group of a closed oriented odd-dimensional manifold. Further, we calculate the ratio of the refined analytic torsion and the Farber-Turaev combinatorial torsion. As an application, we establish a formula relating the eta-invariant and the phase of the Farber-Turaev torsion, which extends a theorem of Farber and earlier results of ours. This formula allows to study the spectral flow using methods of combinatorial topology.     

Mayberry-Murasugi's formula for links in homology 3-spheres

We prove the Mayberry-Murasugi formula for links in homology 3-spheres, which was proved before only for links in the 3-sphere. Our proof uses Franz-Reidemeister torsions.

     

Rotational spectra, conformational structures, and dipole moments of thiodiglycol by jet-cooled FTMW and ab initio calculations

The rotational spectra of three low-energy conformers of thiodiglycol (TDG) (HOCH₂CH₂SCH₂CH₂OH) have been measured in a molecular beam using a pulsed-nozzle Fourier-transform microwave spectrometer. To determine the likely conformational structures with ab initio approach, conformational structures of 2-(ethylthio)ethanol (HOEES) (CH₃CH₂SCH₂CH₂OH) were used as starting points together with the consideration of possible intramolecular hydrogen bonding in TDG. Three lower-energy conformers have been found for TDG at the MP2=Full/6311G** level and ab initio results agree nicely with experimentally determined rotational constants. In addition, Stark measurements were performed for two of the three conformers for dipole moment determinations, adding to our confidence of the conformational structure matches between experimental observations and ab initio calculations. Of the three lower-energy conformers, one displays a compact folded-like structure with strong hydrogen bonding between the two hydroxyl groups and the central sulfide atom. Two other conformers have relatively open chain-like structures with hydrogen bonding between each of the hydroxyl groups to the central sulfur atom, of which one has pure b-type dipole moment according to the ab initio results.     

摩擦离合器的数学模型及其算例

用力学分析的方法 ,建立了摩擦离合器的数学模型 ,求出了摩擦离合器中扭力弹簧的圈数 ,其计算值与实际值基本一致 .该模型对摩擦离合器的设计有一定的参考价值 .     

Interacting Spin 0 Fields with Torsion via Duffin-Kemmer-Petiau Theory

Here we study the behaviour of the spin 0 sector of the DKP field in spaces with torsion. First we show that in a Riemann-Cartan manifold the DKP field presents an interaction with torsion when minimal coupling is performed, contrary to the behaviour of the KG field, a result that breaks the usual equivalence between the DKP and the KG fields.Next we analyse the case of the Teleparallel Equivalent of General Relativity (Weitzenböck manifold), showing that in this case there is a perfect agreement between KG and DKP fields. The origins of both results are also discussed.On leave from     

Elliptic cross section without warping under torsion

The object of this paper is the pure torsion of the nonhomogeneous anisotropic elastic beam. The results of Saint-Venant’s theory of uniform torsion are used to prove a nonwarping property of elliptic cylinders.     

Dependence of the rate constants on the treatment of internal rotation modes: the reaction OH + CH3SH --> CH3S + H2O as an example

The title reaction has been used as an example to test the importance of using a hindered rotor treatment instead of a harmonic oscillator model for calculating vibrational partition functions corresponding to low-frequency internal rotation modes. First, a normal-mode analysis according to the Ayala and Schlegel's algorithm has been used to identify the internal rotation modes of methanethiol and the transition state structure. Then, after calculation of the energy barrier for each internal rotation, the corresponding hindered rotor partition functions have been calculated following the CW scheme of Chuang and Truhlar. The results show that the anharmonic treatment produces a rather modest improvement of the rate constants at room temperature or below.     

Gravity and CP violation

The non-conservation of CP symmetry in the decay of neutralK mesons was discovered almost three decades ago. The origin of this unique phenomenon is still not well understood. There have been attempts to link it with energy splitting of theK and in the earth's gravitational field. In this essay we examine these attempts critically. A more natural way in which a gravitational field can couple asymmetrically to the system is through torsion, which coupling to isospin can, in addition to parity violation, also give rise to a C violation. The magnitude of this effect is estimated in the vicinity of a kaon and found to give a CP-violating parameter of the right value. Moreover, it is predicted that the CP violating parameter for the new system is much smaller 10^–6. Implications for baryogenesis in the early universe is also studied. In this paper we work not with the Newtonian gravitational constantG but with a torsion coupling constant, which is energy-dependent and can be related to the Fermi weak interaction constant.     

Network dimensionality and ligand flexibility in lanthanide terephthalate hydrates

Various lanthanide open framework materials incorporating the terephthalate (TP) entity were prepared using hydrothermal synthesis methods at a moderate temperature of 170 °C. The compounds Nd₂(TP)₃(H₂O)₄(1), Er₂(TP)₃(H₂O)₄(2), Yb₂(TP)₃(H₂O)₂(3), Yb₂(TP)₃(H₂O)₆(4), and Yb₂(TP)₃(H₂O)₈·2H₂O (5), were characterized by single crystal structural analysis and FT-IR spectroscopy. While compounds 1 and 2 have been reported before on the basis of powder X-ray diffraction, the structural characterization of any ytterbium terephthalate species is unprecedented. Compounds 1-5 crystallize in triclinic settings with space group P-1. The compounds are compared with their previously reported Er and Tb-counterparts and the reduction of the dimensionality of the resulting networks from 3D over 2D to 1D with increasing level of hydration is discussed. Compounds 1, 2, and 3 with the lowest water content assemble in three-dimensional network lattices. Compounds 4 and 5, however, form 2D layered systems and 1D rod like chains, respectively, which are held together by hydrogen bonds originating from coordinating H₂O. The crystal lattices of the 3D networks experience higher levels of tension as can be seen by increasing out-of-plane torsion with regard to the terephthalate carboxylate groups. Moreover, there seems to be a correlation between the level of strain on the aromatic ligands and the reduction of the number of carboxylate oxygen atoms that are part of the coordination polyhedra.     

轴对称弹性体扭转问题的无网格自然邻接点Petrov-Galerkin法

本文将无网格自然邻接点Petrov-Galerkin 法应用于轴对称弹性体扭转问题的求解．无网格自然邻接点Petrov-Galerkin 法采用自然邻接点插值构造试函数，并且采用三角形线性单元的形函数作为加权残值法的加权函数．自然邻接点插值构造的试函数满足Kronecker delta 函数性质，因此本质边界条件的施加十分方便．由于几何形状和边界条件的轴对称特点，原来的空间问题简化为二维问题求解，因此计算时只需要横截面上离散节点的信息．数值算例结果表明，所提出的方法对求解轴对称弹性体扭转问题是行之有效的．