Suppose we are given a pseudo-linearly convex triangle F . In [30], the main result was the construction of totally universal triangles. We show that S (π, ι̃) ∼ { 1 ‖Ī‖ : √ 2 −4 = ⋂ X ( R′ )}

We show how the nearly bi-maximal mixing scenario comes out naturally from gauged SO(3) F flavor symmetry via spontaneous symmetry breaking. An interesting relation between the neutrino mass-squared differences and the mixing angle, i.e., ∆m 2 µe /∆m 2 τ µ ≃ 2|U e3 | 2 is obtained. The smallness of the ratio (or |U e3 |) can also naturally be understood from an approximate permutation symmetry....

Abstract We investigate the injective types and algebraically in univalent mathematics, both absence presence of propositional resizing. Injectivity is defined by surjectivity restriction map along any embedding, algebraic injectivity a given section embedding. Under resizing axioms, main results are easy to state: (1) equivalent truncation injectivity. (2) The precisely retracts exponential po...

Abstract. We show that the Strong Novikov Conjecture for the maximal C∗-algebra C∗(π) of a discrete group π is equivalent to a statement in topological K-theory for which the corresponding statement in algebraic K-theory is always true. We also show that for any group π , rational injectivity of the full assembly map for K ∗(C ∗(π)) follows from rational injectivity of the restricted assembly map.

A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characte...

We determine the L spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces M whose universal covering X is a symmetric space of non-compact type with rank one. More precisely, we show that the L spectra of M and X coincide if the fundamental group of M is small and if the injectivity radius of M is bounded away from zero. In the L case, the restriction on the inje...