We propose a new approach to superrigidity phenomena and implement it for lattice representations and measurable cocycles with Homeo+(S ) as the target group. We are motivated by Ghys’ theorem stating that any representation ̺ : Γ → Homeo+(S ) of an irreducible lattice Γ in a semi-simple real Lie group G of higher rank, either has a finite orbit or, up to a semi-conjugacy, extends to G which act...

In this paper, we have established an intimate connection between near-nings and linear automata, and obtain the following results: 1) For a near-ring N there exists a linear GSA S with   N N  S iff (a) is abelian, (b) N has an identity 1, (c) There is some such that is generated by {1,d}; 2) Let  , N  : h   d d N  0 N  S S be a GSAepimorphism. Then there exists a near-ring epimorphism...

We investigate if every quasi-minimal group is abelian, and give a positive answer for a quasi-minimal pure group having a ∅-definable partial order with uncountable chains. We also relate two properties of a complete theory in a countable language: the existence of a quasi-minimal model and the existence of a strongly regular type. As a consequence we derive the equivalence of conjectures on c...

Let k be a field of arbitrary characteristic. Suppose that f1, . . . , fn are polynomials in k[t] and di = deg(fi). We prove that, if gcd of d1, . . . , dn is 1, then k(f1, . . . , fn) = f(t), or equivalently, the morphism ψ = (f1, . . . , fn) : Ak → A n k is proper and birational onto its image. By combining this result with the epimorphism theorem of Abhyankar and Moh, we prove that, if f and...

Let G be a quasi simply reducible group, and let V be a representation of G over the complex numbers C. In this thesis, we introduce the twisted 6j-symbols over G which have their origin to Wigner’s 6j-symbols over the group SU(2) to study the structure constants of the subrepresentation semiring SG(End(V )), and we study the representation theory of a quasi simply reducible group G laying emph...

We propose a new approach to superrigidity phenomena and implement it for lattice representations and measurable cocycles with Homeo+(S ) as the target group. We are motivated by Ghys’ theorem stating that any representation ̺ : Γ → Homeo+(S ) of an irreducible lattice Γ in a semi-simple real Lie group G of higher rank, either has a finite orbit or, up to a semi-conjugacy, extends to G which act...

Although originally devised to define the higher algebraic K-theory of rings [ 1, 7, 161, the plus-construction has quickly established its usefulness in such diverse areas as stable homotopy theory [ 15 J, bordism of manifolds [lo], and the study of knot complements [ 141. Recall (from, e.g., 11 ] h w ose notation we foHow) that the plusconstruction qx : X --, X+ is a pointed cofibration which...

The preservative qualities of individual ionic compounds impacting the infectivity T4 virions were elucidated. immersed in quasi-pure solutions prior to adsorption process, and plaque forming unit (pfu) values these measured following conventional method. In neutral solutions, minimum optimum concentrations corresponded with results obtained from multi-ionic media/buffers. acid alkali phages sh...

A quasi-particle model is presented which describes QCD lattice results for the 0, 2 and 4 quark-flavor equation of state. The results are mapped to finite baryo-chemical potentials. As an application of the model we make a prediction of deconfined matter with appropriate inclusion of strange quarks and consider pure quark stars.