When the boundary of the curve complex is connected any quasi-isometry is bounded distance from a simplicial automorphism. As a consequence, when the boundary is connected the quasi-isometry type of the curve complex determines the homeomorphism type of the surface.

In this paper , the completion of t^ω-approach spaces, isometric in space and equivalent sequences are defined. Every normed can be embedded Banach is proved, χ ̃ an isometry ψ from onto subspace F which dense introduced, as well as, shown uniquely up to isometry. addition, what mentioned above, some essential definitions, examples, important theorems included illustrate our work.

In this paper, it is proved that every s-sparse vector x ∈ R can be exactly recovered from the measurement vector z = Ax ∈ R via some `-minimization with 0 < q ≤ 1, as soon as each s-sparse vector x ∈ R is uniquely determined by the measurement z. Moreover it is shown that the exponent q in the `-minimization can be so chosen to be about 0.6796× (1− δ2s(A)), where δ2s(A) is the restricted isome...

We prove a finite-dimensional covariant Stinespring theorem for compact quantum groups. Let G be group, and let T:= Rep(G) the rigid C*-tensor category of continuous unitary representations G. Mod(T) C*-2-category cofinite semisimple finitely decomposable T-module categories. show that G-C*-algebras can identified with equivalence classes 1-morphisms out object T in Mod(T). For X: -> M1, Y: M2,...

This book presents the construction of finitely “twisted” Laplace operators whose spectrum determines covering equivalence two Riemannian manifolds.