On the Volume of Unit Tangent Spheres in a Pinsler Manifold

Motivated by some issues which enter into the Gauss-Bonnet-Chern theorem in Finsler geometry, this paper studies the unit tangent sphere (or indicatrix) I_x M at each point x of a Pinsler manifold M. We demonstrate that the volume of I_mM, calculated with respect to a Riemannian metric induced naturally by the Finsler structure, is in general a function of x. This contrasts sharply with the situation in Riemannian geometry. We also express the derivative of such volume function in terms of the second curvature tensor of the Chern connection. In particular, we find that this function is constant on Landsberg spaces (though that constant need not be equal to the value taken by Riemannian manifolds).     

ANALYSIS OF AN INCOMPRESSIBLE RUBBER WEDGE CONTACTING WITH A RIGID NOTCH

I. INTRODUCTION It is well known that rubber materials are much more important in modern society. It is, therefore,not surprising that a sizable number of investigations have been concerned with the rubber materials.Considerable attention has been paid …     

Direct simulation of the motion of neutrally buoyant balls in a three-dimensional Poiseuille flow

In a previous article the authors introduced a Lagrange multiplier based fictitious domain method. Their goal in the present article is to apply a generalization of the above method to: (i) the numerical simulation of the motion of neutrally buoyant particles in a three-dimensional Poiseuille flow; (ii) study – via direct numerical simulations – the migration of neutrally buoyant balls in the tube Poiseuille flow of an incompressible Newtonian viscous fluid. Simulations made with one and several particles show that, as expected, the Segré–Silberberg effect takes place. To cite this article: T.-W. Pan, R. Glowinski, C. R. Mecanique 333 (2005).     

Cantilever beam equilibrium configurations

This article investigates a method for obtaining all equilibrium configurations of a cantilever beam subjected to an end load with a constant angle of inclination. The formulation is based on plane finite-strain beam theory in the elastic domain. An example of a cantilever beam subjected to a horizontal pressure force is discussed in detail.     

Organocatalyzed Asymmetric Conjugate Addition of Heteroaryl and Aryl Trifluoroborates: a Synthetic Strategy for Discoipyrrole D

Bis‐heteroaryl or bis‐aryl stereocenters were formed by an organocatalytic enantioselective conjugate addition using the respective trifluoroborate salts as nucleophiles. Control studies suggested that fluoride dissociation is necessary in the anhydrous conditions. This strategy is applicable to the synthesis of discoipyrrole D, an inhibitor of BR5 fibroblast migration.     

Cyclotetrabenzoin: Facile Synthesis of a Shape‐Persistent Molecular Square and Its Assembly into Hydrogen‐Bonded Nanotubes

Cyanide‐catalyzed benzoin condensation of terephthaldehyde produces a cyclic tetramer, which we propose to name cyclotetrabenzoin. Cyclotetrabenzoin is a square‐shaped macrocycle ornamented with four α‐hydroxyketone functionalities pointing away from the central cavity, the dimensions of which are 6.9×6.9 Å. In the solid state, these functional groups extensively hydrogen bond, resulting in a microporous three‐dimensional organic framework with one‐dimensional nanotube channels. This material exhibits permanent—albeit low‐porosity, with a Langmuir surface area of 52 m² g^?1. Cyclotetrabenzoin’s easy and inexpensive synthesis and purification may inspire the creation of other shape‐persistent macrocycles and porous molecular crystals by benzoin condensation.     

Rigged modules I: Modules over dual operator algebras and the Picard group

In a previous paper we generalized the theory of $W^{?}$-modules to the setting of modules over nonselfadjoint dual operator algebras, obtaining the class of weak^?-rigged modules. At that time we promised a forthcoming paper devoted to other aspects of the theory. We fulfill this promise in the present work and its sequel “Rigged modules II”, giving many new results about weak^?-rigged modules and their tensor products. We also discuss the Picard group of weak* closed subalgebras of a commutative algebra. For example, we compute the weak Picard group of $H^{\infty }(\mathbb{D})$, and prove that for a weak* closed function algebra A, the weak Picard group is a semidirect product of the automorphism group of A, and the subgroup consisting of symmetric equivalence bimodules.