Finitely fibered Rosenthal compacta and trees

We study some topological properties of trees with the interval topology. In particular, we characterize trees which admit a 2-fibered compactification and we present two examples of trees whose one-point compactifications are Rosenthal compact with certain renorming properties of their spaces of continuous functions.Comment: Small changes, mainly in the introduction and in final remark

The Isomorphism Relation Between Tree-Automatic Structures

An $\omega$-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for $\omega$-tree-automatic structures. We prove first that the isomorphism relation for $\omega$-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n >1) is not determined by the axiomatic system ZFC. Then we prove that the isomorphism problem for $\omega$-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n >1) is neither a $\Sigma_2^1$-set nor a $\Pi_2^1$-set

Universal minimal flows of automorphism groups

We investigate some connections between the Fraïssé theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of countable structures. We show, in particular, that results from the structural Ramsey theory can be quite useful in recognizing the universal minimal flows of this kind of groups. As a result we compute the universal minimal flows of several well known topological groups such as, for example, the automorphism group of the random graph, the automorphism group of the random triangle-free graph, the automorphism group of the ∞-dimensional vector space over a finite field, the automorphism group of the countable atomless Boolean algebra, etc. So we have here a reversal in the traditional relationship between topological dynamics and Ramsey theory: the Ramsey-theoretic results are used in proving theorems of topological dynamics rather than vice versa

A graph which embeds all small graphs on any large set of vertices

For certain cardinals [lambda] and [kappa] a colouring P:[[lambda]]2-->[lambda] is constructed such that if X [epsilon][[lambda]][lambda] and Q:[[kappa]]2-->[lambda], then there is a one-to-one function i:[kappa]-->X such that P(i"A)=Q(A) for every A[epsilon][[kappa]]2. Additional results are obtained.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27309/1/0000330.pd

On the Distribution of Kurepa’s Function

Kurepa’s function and his hypothesis have been investigated by means of numerical simulation. Particular emphasis has been given to the conjecture on its distribution, that should be one of a random uniform distribution, which has been verified for large numbers. A convergence function for the two has been found

Development of a fish cell culture model to investigate the impact of fish oil replacement on lipid peroxidation

Fish oils are rich in omega-3 long-chain polyunsaturated fatty acids (n-3 LC-PUFA), predominantly 20:5n-3 and 22:6n-3, whereas vegetable oils contain abundant C18-PUFA, predominantly 18:3n-3 or 18:2n-6. We hypothesized that replacement of fish oils with vegetable oils would increase the oxidative stability of fish lipids. Here we have used the FHM cell line to test this hypothesis. The FHM cells were readily able to synthesize 20:5n-3 and 24:6n-3 from 18:3n-3 but 22:6n-3 synthesis was negligible. Also, they were readily able to synthesize 20:3n-6 from 18:2n-6 but 20:4n-6 synthesis was negligible. Mitochondrial β-oxidation was greatest for 18:3n-3 and 20:5n-3 and the rates for 16:0, 18:2n-6, 22:6n-3 and 18:1n-9 were significantly lower. Fatty acid incorporation was predominantly into phospholipids (79-97%) with very little incorporation into neutral lipids. Increasing the fatty acid concentration in the growth medium substantially increased the concentrations of 18:3n-3 and 18:2n-6 in the cell phospholipids but this was not the case for 20:5n-3 or 22:6n-3. When they were subjected to oxidative stress, the FHM cells supplemented with either 20:5n-3 or 22:6n-3 (as compared with 18:3n-3 or saturated fatty acids) exhibited significantly higher levels of thiobarbituric reactive substances (TBARS) indicating higher levels of lipid peroxidation. The results are discussed in relation to the effects of fatty acid unsaturation on the oxidative stability of cellular lipids and the implications for sustainable aquaculture