Asymmetric transfer hydrogenations of β-N-substituted enamino esters with ammonia borane

Optically active β-amino acids and their derivatives are very useful building blocks in synthetic and medicinal chemistry. The catalytic asymmetric reduction of β-enamino esters is one of the most efficient approaches for their synthesis. Ammonia borane with low molecular weight, high hydrogen capacity, and good stability, is an ideal hydrogen source for the transfer hydrogenation. However, only a few successful examples have been reported for the asymmetric reduction with ammonia borane. In this work, an asymmetric metal-free transfer hydrogenation of β-N-substituted enamino esters with ammoinia borane was successfully realized by using a frustrated Lewis pair of Piers’ borane and (S)-tert-butylsulfinamide as a chiral catalyst. A variety of β-amino acid derivatives were obtained in 51–90% yields with up to 91% ee.     

Six-dimensional heavenly equation. Dressing scheme and the hierarchy

We consider six-dimensional heavenly equation as a reduction in the framework of general six-dimensional linearly degenerate dispersionless hierarchy. We characterise the reduction in terms of wave functions, introduce generating relation, Lax–Sato equations and develop the dressing scheme for the reduced hierarchy. Using the dressing scheme, we construct a class of solutions for six-dimensional heavenly equation in terms of implicit functions.     

A 9× 9 Matrix Representation of Birman-Wenzl-Murakami Algebra and Berry Phase in Yang-Baxter System

We present a 9×9 S-matrix and E-matrix. A representation of specialized Birman-Wenzl-Murakami algebra is obtained. Starting from the given braid group representation S-matrix, we obtain the trigonometric solution of Yang-Baxter equation. A unitary matrix \breve{R}(x,φ₁,φ₂) is generated via theYang-Baxterization approach. Then we construct a Yang-BaxterHamiltonian through the unitary matrix \breve{R}(x,φ₁,φ₂). Berry phase of this Yang-Baxter system is investigated in detail.     

Elliptic Quantum Groups and Ruijsenaars Models

We construct symmetric and exterior powers of the vector representation of the elliptic quantum groupsE _Τ,η(slN). The corresponding transfer matrices give rise to various integrable difference equations which could be solved in principle by the nested Bethe ansatz method. In special cases we recover the Ruijsenaars systems of commuting difference operators.     

中国的中药微量元素研究Ⅳ.微量元素:汇通传统中药理论与现代科学理论的桥梁

中国中药微量元素研究表明,中药微量元素化学性质及含量水平是决定中药阴阳性的重要因素.综述了传统中药理论与现代科学理论对应关系以及中药阴阳性与微量元素量化关系的研究结果.     

Hierarchical Spherical Model from a Geometric Point of View

A continuous version of the hierarchical spherical model at dimension d=4 is investigated. Two limit distributions of the block spin variable X ^γ , normalized with exponents γ=d+2 and γ=d at and above the critical temperature, are established. These results are proven by solving certain evolution equations corresponding to the renormalization group (RG) transformation of the O(N) hierarchical spin model of block size L ^d in the limit L ↓1 and N→∞. Starting far away from the stationary Gaussian fixed point the trajectories of these dynamical system pass through two different regimes with distinguishable crossover behavior. An interpretation of this trajectories is given by the geometric theory of functions which describe precisely the motion of the Lee–Yang zeroes. The large-N limit of RG transformation with L ^d fixed equal to 2, at the criticality, has recently been investigated in both weak and strong (coupling) regimes by Watanabe (J. Stat. Phys. 115:1669–1713, 2004) . Although our analysis deals only with N=∞ case, it complements various aspects of that work. D.H.U. Marchetti partially supported by CNPq and FAPESP. W.R.P. Conti supported by FAPESP under grant 05/57416-8.     

Cosmological Parameters from Planck Data in SU(2)CMB,Their Local ΛCDM Values,and the Modified Photon Boltzmann Equation

A review of the spatially flat cosmological model SU(2)_CMB, minimally induced by the postulate that the cosmic microwave background (CMB) is subject to an SU(2) rather than a U(1) gauge principle, is given. Cosmological parameter values, which are determined from the Planck CMB power spectra at small angular scales, are compared to their values in spatially flat ΛCDM from both local and global extractions. As a global model SU(2)_CMB leans toward local ΛCDM cosmology and is in tension with some global ΛCDM parameter values. Spectral antiscreening / screening effects in SU(2)_CMB radiance are presented within the Rayleigh– Jeans regime in dependence on temperature and frequency. Such radiance anomalies can cause CMB large-angle anomalies. Therefore, it is pointed out how SU(2)_CMB modifies the Boltzmann equation  for the perturbations of the photon phase space distribution at low redshift and why this requires to the solve the ℓ-hierarchy on a comoving momentum grid (q-grid) for all z.     

Lee–Yang zeros in the Rydberg atoms

Lee–Yang (LY) zeros play a fundamental role in the formulation of statistical physics in terms of (grand) partition functions, and assume theoretical significance for the phenomenon of phase transitions. In this paper, motivated by recent progress in cold Rydberg atom experiments, we explore the LY zeros in classical Rydberg blockade models. We find that the distribution of zeros of partition functions for these models in one dimension (1d) can be obtained analytically. We prove that all the LY zeros are real and negative for such models with arbitrary blockade radii. Therefore, no phase transitions happen in 1d classical Rydberg chains. We investigate how the zeros redistribute as one interpolates between different blockade radii. We also discuss possible experimental measurements of these zeros.