Justification of the kinematic assumptions for thin-walled rods with shallow profile

In this Note we present a justification of the kinematic assumptions for thin-walled rods with shallow profile. These assumptions are fundamental to writing the one-dimensional equilibrium equations for such structures. The obtained kinematics are different from the Vlassov case, which is only valid for strongly curved profiles. They are also different from the that classically used in shell theory. The justification given in this Note is based on an asymptotic approach. To cite this article: L. Grillet et al., C. R. Mecanique 333 (2005).     

The commutative cohomology of nilmonoids,revisited

Semigroup Forum - A nilmonoid is a nilsemigroup N with an identity element adjoined. New properties of the canonical presentation of N yield a more precise characterization of 2-cocycles,...     

Coset extensions of <Emphasis Type=”Italic”>S</Emphasis>-sets

Summary Three weak variants of compactness which lie strictly between compactness and quasicompactness, are introduced. Their basic properties are studied. The interplay with mapping and their direct and inverse preservation under mappings are investigated. In the process three decompositions of compactness are observed.     

Microstructure development in concentrated suspensions in a spinning ball rheometer

The spinning ball rheometer has been proposed as a method to measure the microstructure effect on the bulk rheological properties of concentrated suspensions. Recent experiments have shown that the measured extra torque on the spinning ball decreases as the radius of the spinning ball becomes comparable to the size of the suspended particle. We have performed a series of three‐dimensional boundary element calculations of the rheometer geometry to probe the microstructure effects that contribute to that apparent slip. We present a series of quasi‐static results based on random initial configurations as well as fully three‐dimensional transient calculations, both of which are compared to the available experimental data. For the two cases, the apparent viscosity decreased as the size of the spinning ball decreased relative to the suspended particle. Comparison of the quasi‐static and transient simulations indicates that the microstructure development is critical even at short times. In the transient calculations, the viscosity was observed to increase substantially relative to the torque based on the random initial configuration. Published in 2005 by John Wiley & Sons, Ltd.     

The number of commutative semigroups of order N

An explicit upper bound is given for the number of commutative semigroups withn elements.     

Subdirect decompositions of finitely generated commutative semigroups

All finitely generated commutative semigroups which do not have proper finite subdirect decompositions are determined. This yields subdirect decompositions of finitely generated commutative semigroups and some idea of their structure.     

Computing Finite Semigroups, I: The First Row

New precedence results are obtained for finite, not necessarily commutative semigroups, which are used to further sharpen existing algorithms for the computation of finite semigroups. The results in this first part describe the first row of the multiplication table in detail and provide a numerical profile with which it can be compared to other rows.     

Subdirect decompositions of finite commutative semigroups

The Ponizovskîi decomposition of a finite commutative semigroup yields all shortest elementary subdirect decompositions of that semigroup.