Locally conformally Hermitian-flat manifolds

We introduce the notion of a locally conformally Hermitian-flat manifold and derive a necessary and sufficient condition for a Hermitian manifold to be locally conformally Hermitian-flat. In addition, we construct a family of examples.     

间隔不变性与相对论拉格朗日力学

文章证明由时空和速度间隔不变性可以导出相对论哈密顿和拉格朗日力学，由此说明哈密顿或拉格朗日为洛仑兹不变量是时空和速度间隔不变性的必然结果。     

Bimodule Deformations, Picard Groups and Contravariant Connections

We study deformations of invertible bimodules and the behavior of Picard groups under deformation quantization. While K ₀-groups are known to be stable under formal deformations of algebras, Picard groups may change drastically. We identify the semiclassical limit of bimodule deformations as contravariant connections and study the associated deformation quantization problem. Our main focus is on formal deformation quantization of Poisson manifolds by star products.     

On extensions of the domain invariance theorem

If f maps continuously a compact subset X of Rⁿ into Rⁿ and x is a point whose distance from the boundary ∂X is greater than double diameter of the fibres of the points in f(∂X) then f(x) is in the interior of f(X). This theorem extends some results due to Borsuk and Sitnikov.     

Galois theory for comatrix corings: Descent theory, Morita theory, Frobenius and separability properties

El Kaoutit and Gómez-Torrecillas introduced comatrix corings, generalizing Sweedler's canonical coring, and proved a new version of the Faithfully Flat Descent Theorem. They also introduced Galois corings as corings isomorphic to a comatrix coring. In this paper, we further investigate this theory. We prove a new version of the Joyal-Tierney Descent Theorem, and generalize the Galois Coring Structure Theorem. We associate a Morita context to a coring with a fixed comodule, and relate it to Galois-type properties of the coring. An affineness criterion is proved in the situation where the coring is coseparable. Further properties of the Morita context are studied in the situation where the coring is (co)Frobenius.

     

Proof of perturbative gauge invariance for tree diagrams to all orders

It is proved that classical BRS‐invariance of the Lagrangian implies perturbative gauge invariance for tree diagrams to all orders. The proof applies in particular to the Einstein Hilbert Lagrangian of gravity.     

非完整力学系统Raitzin正则方程的形式不变性

研究非完整力学系统Raitzin正则方程的形式不变性。建立系统的Raitzin正则方程。给出在无限小变换下系统形式不变性的定义和判据。得到系统的守恒量与形式不变性之间的关系并举例说明结果的应用。     

Duality in algebra and topology

We apply ideas from commutative algebra, and Morita theory to algebraic topology using ring spectra. This allows us to prove new duality results in algebra and topology, and to view (1) Poincaré duality for manifolds, (2) Gorenstein duality for commutative rings, (3) Benson–Carlson duality for cohomology rings of finite groups, (4) Poincaré duality for groups and (5) Gross–Hopkins duality in chromatic stable homotopy theory as examples of a single phenomenon.     

A lattice gas model for thermohydrodynamics

The lattice gas model is extended to include a temperature variable in order to study thermohydrodynamics, the combination of fluid dynamics and heat transfer. The compressible Navier-Stokes equations are derived using a Chapman-Enskog expansion. Heat conduction and convection problems are investigated, including Bénard convection. It is shown that the usual rescaling procedure can be avoided by controlling the temperature.     

Solution of Müller's paradox of frame dependence in mixtures of polymeric liquid crystals

Recently, there appeared in this journal a short review article by Müller ((2002), 14: 227–229), in which it was argued that the internal energy of a reacting mixture of liquid crystals should not be an objective quantity (i.e., a quantity independent of the referential frame). Such a paradoxical conclusion has revealed the urging necessity for a better comprehension of the interactions taking place in structured mixtures, specially when referred to non-inertial observers. This work shows that Müller's paradox is avoided when all inertial effects are carefully accounted for. Further, it predicts interesting phenomena without analogue in reacting mixtures of structureless fluids: internal inertial effects, produced by a combination of mass exchanges (e.g. by chemical reactions or phase changes) with the extra degrees of freedom posed by the microstructure. Such effects clarify the reasons why inertial forces and couples acting on a mixture do not always coincide with the sum of the inertial forces and couples exerted upon its individual constituents. The present conclusions establish a reinterpretation of some fundamental concepts of continuum mechanics and thermodynamics, including a deeper understanding of the manner in which total energy and momenta are conserved in complex media. Received: July 25, 2002 / Published online: February 17, 2003 Communicated by Kolumban Hutter, Darmstadt e-mail: faria@mechanik.tu-darmstadt.de