On a reduction of the generalized Darboux–Halphen system

The equations for the general Darboux–Halphen system obtained as a reduction of the self-dual Yang–Mills can be transformed to a third-order system which resembles the classical Darboux–Halphen system with a common additive terms. It is shown that the transformed system can be further reduced to a constrained non-autonomous, non-homogeneous dynamical system. This dynamical system becomes homogeneous for the classical Darboux–Halphen case, and was studied in the context of self-dual Einstein's equations for Bianchi IX metrics. A Lax pair and Hamiltonian for this reduced system is derived and the solutions for the system are prescribed in terms of hypergeometric functions.     

A Static Solution of Yang-Mills Equation on Anti-de Sitter Space

Since product metric on AdS space has played a very important role in Lorentz version of AdS/CFT correspondence, the Yang Mills equation on AdS space with this metric is considered and a static solution is obtained in this paper, which helps to understand the AdS/CFT correspondence of Yang Mills fields.     

Infrared safe observables in super Yang–Mills theory

The infrared structure of MHV gluon amplitudes in planar limit for super Yang–Mills theory is considered in the next-to-leading order of PT. Explicit cancellation of the infrared divergencies in properly defined cross-sections is demonstrated. The remaining finite parts for some inclusive differential cross-sections in planar limit are calculated analytically. In general, contrary to the virtual corrections, they do not reveal any simple structure.     

Thermal photon dispersion law and modified black‐body spectra

Based on the postulate that photon propagation is governed by an SU(2) gauge principle we numerically compute the one‐loop dispersion for thermalized photon propagation on the radiatively induced mass shell. Formerly, the dispersion was addressed by assuming p² = 0. While this approximation turns out to be excellent for temperatures ≤ 2 T_CMB the exact result exhibits a much faster (power‐like) shrinking of the gap in the black‐body spectral intensity with rising temperature. Our previous statements on anomalous large‐angle CMB temperature‐temperature correlations, obtained in the approximation p² = 0, remain valid.     

A new form of liquid matter: Quantum droplets

This brief review summarizes recent theoretical and experimental results which predict and establish the existence of quantum droplets (QDs), i.e., robust two- and three-dimensional (2D and 3D) selftrapped states in Bose–Einstein condensates (BECs), which are stabilized by effective self-repulsion induced by quantum fluctuations around the mean-field (MF) states [alias the Lee–Huang–Yang (LHY) effect]. The basic models are presented, taking special care of the dimension crossover, 2D→3D. Recently reported experimental results, which exhibit stable 3D and quasi-2D QDs in binary BECs, with the inter-component attraction slightly exceeding the MF self-repulsion in each component, and in single-component condensates of atoms carrying permanent magnetic moments, are presented in some detail. The summary of theoretical results is focused, chiefly, on 3D and quasi-2D QDs with embedded vorticity, as the possibility to stabilize such states is a remarkable prediction. Stable vortex states are presented both for QDs in free space, and for singular but physically relevant 2D modes pulled to the center by the inverse-square potential, with the quantum collapse suppressed by the LHY effect.     

Quantum Mechanics on Manifolds

In this paper, we investigate the relationships between quantum mechanics and the theory of partial differential equations. We closely follow the De Broglie and Schrödinger picture. Namely, we consider the well-known wave-particle duality as a relation between solutions of partial differential equations, describing waves, and singularities of solutions, that is particles. Our analysis of these relations shows that the necessary ingredients of any quantum mechanical picture are two connections. The first one is a connection in the tangent bundle of the configuration manifold and the second one is a connection in the trivial linear bundle.We also consider mechanical systems equipped with an inner structure and show that quantization of these systems requires a linear connection in the corresponding vector bundle.These are gravity and electromagnetic fields, or Yang–Mills fields if the configuration space is the Minkowski space. In the case of general mechanical systems, they should be considered as natural generalizations of these fields.Explicit formulas for quantizations of some mechanical systems and the corresponding star-products are given.     

电感耦合等离子体质谱法(ICP-MS)测定养生堂维生素C中的无机元素

用HNO3-HClO4混酸溶解养生堂维生素C片,用电感耦合等离子体质谱法测定其中的无机元素,实验表明养生堂维C中Fe,Na,Ca,Mg,K,Zn和Cu的含量较为丰富。方法灵敏可靠,测量相对标准偏差3.3%,回收率在99.5%~103.6%,实验结果为探讨养生堂维生素C对人体的保健作用提供了参考数据。     

杨辉三角矩阵(英文)

杨辉三角矩阵的性质吸引许多研究者．本文进一步研究杨辉矩阵,获得一些颇为有趣的性质     

Remark on Relations Between Different Non-integrable Phases

There are three non-integrable phases in literatures: Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the definitions and relations between these three non-integrable phases.     

汉阳陵东阙门出土蓝紫色颜料的科学分析

鉴于微区X射线衍射(micro-XRD)技术的微区、微量、原位、无损等优势,尝试将其与超景深显微法,扫描电镜能谱(SEM-EDX)和显微激光拉曼(MLRM)技术相结合,对汉阳陵东阙门出土的蓝紫色颜料样块进行显微观察和无损分析鉴定,结果证实该蓝紫色颜料的成分为中国紫(BaCuSi₂O₆),并伴有黄铅矿(Pb₂[SO₄]O)和重晶石(BaSO₄)。中国紫这类人工合成硅酸铜钡系化合物颜料在西汉帝陵遗址中的发现,反映了紫色在当时具有崇高的社会等级地位,而其在东阙门的出土也进一步表示了西汉帝陵在设计、装饰方面深受五行思想的影响。另外黄铅矿和重晶石的发现可推测当时合成中国紫颜料时所使用的钡源是重晶石,黄铅矿以铅盐添加物在合成中国紫时作为助熔剂和催化剂,从化学史的角度反映了当时合成技术的成熟。