1 This paper grew out of an observation that some new stable structures discovered in the 1990' as counterexamples to well-known conjectures in pure model theory might be related to non-commutative geometry. The general meaning of the conjectures was that " very good " , or more technically, very stable structures must be in a certain way reducible to algebraic geometry over algebraically close...

We give two slight generalizations of results of Poizat about elementary theories of groups obtained by free constructions. The firstone concerns generic types and the non-superstability of such groups in many cases. The second-one concerns the connectedness of most free products of groups without amalgamation. First-order theories of free products of groups have been recently investigated in [...

We consider an L-Wasserstein type distance ρ on the configuration space ΓX over a Riemannian manifold X, and we prove that ρ-Lipschitz functions are contained in a Dirichlet space associated with a measure on ΓX satisfying certain natural assumptions. These assumptions are in particular fulfilled by the classical Poisson measures and by a large class of tempered grandcanonical Gibbs measures wi...

It is known that the Pak-Stanley labeling of the Shi hyperplane arrangement provides a bijection between the regions of the arrangement and parking functions. For any graph G, we define the G-semiorder arrangement and show that the Pak-Stanley labeling of its regions produces all G-parking functions. In his study of Kazhdan-Lusztig cells of the affine Weyl group of typeAn−1, [10], J.-Y. Shi int...

We demonstrate that the dynamics toward and within the Feigenbaum attractor combine to form a q -deformed statistical-mechanical construction. The rate at which ensemble trajectories converge to the attractor (and to the repellor) is described by a q entropy obtained from a partition function generated by summing distances between neighboring positions of the attractor. The values of the q indi...

Assume T is superstable, Φ(x) is a formula over ∅, Q = Φ(M∗) is countable and KQ = {M : M is countable and Φ(M) = Q}. We investigate models in KQ assuming KQ has the prime model property. We prove some corollaries on the number of models inKQ. We show an example of an ω-stable T and Q with KQ having exactly 3 models. First we fix the general set-up. Throughout, T is a countable complete theory ...

We observe simple links between preorders, semi-groups, rings and categories (and between equivalence relations, groups, elds and groupoids), which are in nitely de nable in an arbitrary structure, and apply these observations to small structures. Recall that a structure is small if it has countably many pure n-types for each integer n. A category de ned by a pure n-type in a small structure is...

and Applied Analysis 3 for x, y, z ∈ A. A Banach non-Archimedean ternary algebra is a normed non-Archimedean ternary algebra such that the normed non-Archimedean vector space with norm ‖ · ‖ is complete. The ternary algebras have been studied in nineteenth century. Their structures appeared more or less naturally in various domains of mathematical physics and data processing. The discovery of t...

Intervention of the inflammation cascade with tumor necrosis factor-a (TNF-a) monoclonal antibodies or receptors represents a major approach in clinical immunotherapy against inflammatory diseases, which however, often suffers from high cost, autoimmunity to antibodies, and various side effects. siRNA-mediated RNA interference (RNAi) has recently emerged as a potent modality in regulating gene ...

We show that the two complementary parts of the dynamics associated to the Feigenbaum attractor, inside and towards the attractor, form together a q-deformed statisticalmechanical structure. A time-dependent partition function produced by summing distances between neighboring positions of the attractor leads to a q-entropy that measures the ratio of ensemble trajectories still away at a given t...