Ample thoughts

International audienceNon-n-ampleness as defined by Pillay and Evans is preserved under analysability. Generalizing this to a more general notion of Sigma-ampleness, we obtain an immediate proof for all simple theories of CHatzidakis weak Canonical Base Property (CBP) for types of finite SU-rank. This is then applied to the special case of groups

On Variants of CM-triviality

We introduce a generalization of CM-triviality relative to a fixed invariant collection of partial types, in analogy to the Canonical Base Property defined by Pillay, Ziegler and Chatzidakis which generalizes one-basedness. We show that, under this condition, a stable field is internal to the family, and a group of finite Lascar rank has a normal nilpotent subgroup such that the quotient is almost internal to the family

On the canonical base property

We give an example of a finite rank, in fact aleph-1 categorical theory where the CBP (canonical base property) does not hold. We include a "group-like" example. We also prove, in a finite Morley rank context, if all definable Galois groups are "rigid" then the theory has the CBP (in a strong sense).Comment: 15 page

Elimination of Hyperimaginaries and Stable Independence in simple CM-trivial theories

International audienceIn a simple CM-trivial theory every hyperimaginary is interbounded with a sequence of finitary hyperimaginaries. Moreover, such a theory eliminates hyperimaginaries whenever it eliminates finitary hyperimaginaries. In a supersimple CM-trivial theory, the independence relation is stable

Biofouling : a means of aquatic species transfer

Ships carry seawater in their ballast tanks when they are not fully loaded with cargo, in order to maintain adequate trim, draught and stability, adjust list and limit stresses on the hull. It is now well documented that the water pumped into the ship contains aquatic organisms – which can also sink to the sediments at the bottom of tanks – and that these organisms are thereby transferred from the port of origin to the destination. But it is seldom mentioned that aquatic organisms are also found on the outside of ships, attached on their hulls and appendages, as a result of a very dynamic process called ‘biofouling’.https://commons.wmu.se/nsbwo/1002/thumbnail.jp

Plus ultra

International audienceWe define a reasonably well-behaved class of ultraimaginaries, i.e.\ classes modulo invariant equivalence relations, called {\em tame}, and establish some basic simplicity-theoretic facts. We also show feeble elimination of supersimple ultraimaginaries: If $e$ is an ultraimaginary definable over a tuple $a$ with $SU(a)<\omega^{\alpha+1}$, then $e$ is eliminable up to rank $<\omega^\alpha$. Finally, we prove some uniform versions of the weak canonical base property

TEACHER’S WORKLOAD INTENSIFICATION: A QUALITATIVE CASE STUDY OF ITS IMPLICATIONS ON TEACHING QUALITY

Educative process relies on the active interrelation of teacher, student, and learning environment. But it is the teacher who has the control over the two elements and professionally exposed to different challenges including workload intensification. Such educational problem has become one of the major foci of educational researchers since the last half of the 20th century due to the evolution of teaching-learning and education in general. This paper was approached using Apple’s original thesis of workload intensification and the three refinements formulated by Ballet &amp; Kelchtermans, namely: there are multiple sources of intensification, the intensification impact is mediated, and the intensification impact is differentiated. The study aims to better understand the nature of intensification and its underlying impact on the teaching quality of a teacher in qualitative terms

Exact results of one-dimensional repulsive Hubbard model

We present analytical results of fundamental properties of one-dimensional (1D) Hubbard model with a repulsive interaction, ranging from fractional excitations to universal thermodynamics, interaction-driven criticality, correlation functions, Contact susceptibilities and quantum cooling. Using the exact solutions of the Bethe Ansatz equations of the Hubbard model, we first rigorously calculate the gapless spin and charge excitations, exhibiting exotic features of fractionalized spinons and holons. Based on the analysis on the fractional charge and spin excitations, the spin-incoherent Luttinger liquid with only the charge propagation mode is elucidated by the asymptotic of the two-point correlation functions with the help of the conformal field theory. Near quadruple critical point, we then further analytically obtain the thermodynamical properties, dimensionless ratios and scaling functions near quantum phase transitions in terms of chemical potential, magnetic field and interaction. In particular, we determine additivity rules of spin and charge susceptibilities, and derive explicit forms of thermodynamics of spin-incoherent Luttinger liquid. Finally, in order to capture deeper insight into the Mott insulator and interaction driven criticality, we further study the double occupancy and its associated Contact and Contact susceptibilities through which an adiabatic cooling scheme upon the quantum criticality is introduced.Comment: slight changes, 50 pages +18 figures, new analytical result