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.     

Theoretical study of magnetic properties of ammonia molecule in nonuniform magnetic field

The interaction Hamiltonian within the Bloch gauge for the potentials of the electromagnetic field has been used to define magnetic multipole moment operators and operators for the magnetic field of electrons acting on the nuclei of a molecule in the presence of nonhomogeneous external magnetic field. Perturbation theory has been applied to evaluate the induced electronic moments and magnetic field at the nuclei. Multipole magnetic susceptibility and nuclear magnetic shielding tensors have been introduced to describe the contributions arising in nonuniform fields, and their origin dependence has been analyzed. Extended numerical tests on the ammonia molecule in a static, nonuniform magnetic field have been carried out, using the random-phase approximation within the framework of accurate Hartree-Fock zero-order wavefunctions, and allowing for both angular momentum and torque formalisms in the calculation of paramagnetic contributions.     

Improvement of the performance of facilitated transport membrane process through nonuniformity

Facilitated transport process has attracted much attention because high selectivity and high permeability may be achieved. However, most research on facilitated transport process is concerned only with uniform membranes. In this paper, a model predicting the gas separation performance of a hollow-fiber module with facilitated transport membrane is developed. The influence of feed rate, operation pressure, and permeant-feed flow pattern on the module performance are analyzed and the effect of the nonuniform distribution of reaction equilibrium constant is examined. The calculated results show that the nonuniform active distribution may cause an improved module performance. Because of the passive transport characteristics of the facilitated transport process, the mass transfer driving force across the membrane has a great influence on the improvement of the module performance through a facilitated transport effect.     

Nonuniform sampling and maximum entropy reconstruction applied to the accurate measurement of residual dipolar couplings

Residual dipolar couplings (RDC) provide important global restraints for accurate structure determination by NMR. We show that nonuniform sampling in combination with maximum entropy reconstruction (MaxEnt) is a promising strategy for accelerating and potentially enhancing the acquisition of RDC spectra. Using MaxEnt-processed spectra of nonuniformly sampled data sets that are reduced up to one fifth relative to uniform sampling, accurate 13C'-13Calpha RDCs can be obtained that agree with an RMS of 0.67 Hz with those derived from uniformly sampled, Fourier transformed spectra. While confirming that frequency errors in MaxEnt spectra are very slight, an unexpected class of systematic errors was found to occur in the 6th significant figure of 13C' chemical shifts of doublets obtained by MaxEnt reconstruction. We show that this error stems from slight line shape perturbations and predict it should be encountered in other nonlinear spectral estimation algorithms. In the case of MaxEnt reconstruction, the error can easily be rendered systematic by straightforward optimization of MaxEnt reconstruction parameters and self-cancels in obtaining RDCs from nonuniformly sampled, MaxEnt reconstructed spectra.     

Cosmological constant from quarks and torsion

We present a simple and natural way to derive the observed small, positive cosmological constant from the gravitational interaction of condensing fermions. In the Riemann‐Cartan spacetime, torsion gives rise to the axial–axial vector four‐fermion interaction term in the Dirac Lagrangian for spinor fields. We show that this nonlinear term acts like a cosmological constant if these fields have a nonzero vacuum expectation value. For quark fields in QCD, such a torsion‐induced cosmological constant is positive and its energy scale is only about 8 times larger than the observed value. Adding leptons to this picture could lower this scale to the observed value.     

Pseudoinstantons in Metric-Affine Field Theory

In abstract Yang–Mills theory the standard instanton construction relies on the Hodge star having real eigenvalues which makes it inapplicable in the Lorentzian case. We show that for the affine connection an instanton-type construction can be carried out in the Lorentzian setting. The Lorentzian analogue of an instanton is a spacetime whose connection is metric compatible and Riemann curvature irreducible (pseudoinstanton). We suggest a metric-affine action which is a natural generalization of the Yang–Mills action and for which pseudoinstantons are stationary points. We show that a spacetime with a Ricci flat Levi-Civita connection is a pseudoinstanton, so the vacuum Einstein equation is a special case of our theory. We also find another pseudoinstanton which is a wave of torsion in Minkowski space. Analysis of the latter solution indicates the possibility of using it as a model for the neutrino.     

Ab initio calculations on peptide-derived oxazoles and thiazoles: Improved molecular mechanics parameters for the AMBER* force field

Ab initio calculations at the RHF/6-31G* and MP2/6- 31G*//RHF/6-31G* levels of theory are performed for 2-methyl-4-carboxamido-oxazoles and -thiazoles, including rotational profiles for the ring-carboxamide bond, which showed the expected conjugation and hydrogen bonding effects. On the basis of these data, newly optimised stretch, bend and torsional parameters for the AMBER* force field are derived, along with CHELPG-fitted partial atomic charges.     

Cyclic torsion of elliptic curves

Let be an elliptic curve over a number field such that
and let denote the number of roots of unity in . Ross proposed a question: Is isogenous over to an elliptic curve such that is cyclic of order dividing ? A counter-example of this question is given. We show that is isogenous to such that . In case has complex multiplication and , we obtain certain criteria whether or not is isogenous to such that .

     

格序群的扭自由根式格

证明了发下结果；格序群的扭自由根式全体构成一个完备格县这个格满足并无限分配律，所有主扭自由根式构成这个格的一个理想。     

Selectivity of complex heterogeneous catalytic reactions over energetically nonuniform surfaces

The selectivity in parallel and consecutive heterogeneous catalytic reactions over nonuniform surfaces has been analyzed within the framework of the surface electron gas model. Equations for the selectivity are derived in the case of slow adsorption (no rate-limiting steps). Conditions when the nonuniform character of real catalytic surfaces should be taken into account in modeling of the selectivity behavior are discussed.