In this sequel to [3] we try to give a comprehensive account of the “connected components” G00 and G000 as well as the various quotients G/G00, G/G000, G00/G000, for G a group definable in a (saturated) ominimal expansion of a real closed field. Key themes are the structure of G00/G000 and the problem of “exactness” of the G 7→ G00 functor. We prove that the examples produced in [3] are typical...

We consider definably compact groups in an o-minimal expansion of a real closed field. It is known that to each such group G is associated a natural exact sequence 1→ G00 → G → G/G00 → 1 where G00 is the “infinitesimal subgroup” of G and G/G00 is a compact real Lie group. We show that given a connected open subset U of G/G00 there is a canonical isomorphism between the fundamental group of U an...

Article history: Received 7 May 2013 Available online 9 February 2015 JEL classification: D44 D82 G00

The frequency-dependent viscoelastic shear modulus of concentrated suspensions of colloidal hard spheres is shown to be strongly modified as the volume fraction approaches the glass transition. The elastic or storage component, G0, becomes larger than the viscous or loss component, G00. The frequency dependence of G0 develops a plateau while that of G00 develops a minimum. We propose a physical...

We prove that many properties and invariants of definable groups in NIP theories, such as definable amenability, G/G00, etc., are preserved when passing to the theory of the Shelah expansion by externally definable sets, Mext, of a model M . In the light of these results we continue the study of the “definable topological dynamics” of groups in NIP theories. In particular we prove the Ellis gro...

An oscillating capillary rheometer was used to investigate the dynamic viscoelastic and intrinsic viscosity properties of deacetylated xanthan (0.025%), native xanthan (0.025%), guar gum (0.075%), and xanthan–guar mixtures in dilute solutions. Influence of ionic strength on xanthan conformation and interaction with guar gum was elaborated. As the salt concentration increased, a significant (P <...

The κ−Poincare group and its algebra in an arbitrary basis are constructed. The κ−deformation of the Weyl group and its algebra in any dimentions and in the reference frame in which g00 = 0 are discussed.

The consequences of abnormally low lithium abundance in a nearby population II star (which is almost as old as the supposed population III stars) as represented by HE0107-5240 are that standard BBN theory is out of sync with observations. Analysis of the big bang nucleosynthesis may help explain the anomalously low value of lithium abundance in the star HE0107-5240, which by orthodox BBN, shoul...

nervous system disease (GOO-G99) from 2000 to 2005 was analysed in cohort contained manganese exposed male workers (438,693 person years). Also, 2% of Korean men was randomly selected and analysed their hospital admission data. Standardised Admission Ratios (SAR) of nervous disease among manganese exposed workers was estimated reference to Korean men. Results For 6 years, 500 admissions with ne...

We give a commentary on Newelski’s suggestion or conjecture [8] that topological dynamics, in the sense of Ellis [3], applied to the action of a definable group G(M) on its type space SG(M), can explain, account for, or give rise to, the quotient G/G00, at least for suitable groups in NIP theories. We give a positive answer for measure-stable (or fsg) groups in NIP theories. As part of our anal...