We prove that every asymptotic cone of a mapping class group has a bi-Lipschitz equivariant embedding into a product of real trees, with image a median subspace. We deduce several applications of this, one of which is that a group with Kazhdan’s property (T) can only have finitely many pairwise non-conjugate homomorphisms into a mapping class group.

and Applied Analysis 3 Example 8. LetX = Z = R, Y = R, and E = F = [0, +∞) ⊂ X and let G,C : E → 2, e : E → Y define as G (u) = {(U, V) : U − u ≤ V ≤ u − U, 0 ≤ U ≤ u} , ∀u ∈ F, C (x) = {(U, V) : 0 ≤ V ≤ ( 3 2 + x)U,U ≥ 0} , ∀x ∈ E, e (x) = (1, 1) , ∀x ∈ E, (7) respectively. We can see that ξ G (x, u) = (1 + (2/(1 + 2x)))u. Definition 9. LetD ⊂ Y be a cone,H : F → 2, and ς : F → R. ς is calledm...

The growth cone, which is a unique structure with high motility that forms at the tips of extending axons and dendrites, is crucial to neuronal network formation. Axonal growth of the mammalian CNS is most likely achieved by the complicated coordination of cytoskeletal rearrangement and vesicular trafficking via many proteins. Before recent advances, no methods to identify numerous proteins exi...

The optimality conditions of a nonlinear second-order cone program can be reformulated as a nonsmooth system of equations using a projection mapping. This allows the application of nonsmooth Newton methods for the solution of the nonlinear second-order cone program. Conditions for the local quadratic convergence of these nonsmooth Newton methods are investigated. Related conditions are also giv...

The optimality conditions of a nonlinear second-order cone program can be reformulated as a nonsmooth system of equations using a projection mapping. This allows the application of nonsmooth Newton methods for the solution of the nonlinear second-order cone program. Conditions for the local quadratic convergence of these nonsmooth Newton methods are investigated. Related conditions are also giv...

Sub-millimeter emission lines are important tracers of the cold gas and ionized environments galaxies targets for future line intensity mapping surveys. Physics-based simulations that predict multiple arising from different phases interstellar medium crucial constraining global physical conditions with upcoming LIM observations. In this work we present a general framework creating multitracer m...

Abstract In this manuscript, we investigate the existence and uniqueness of a common fixed point for self-mappings defined on quasi-cone metric space over divisible Banach algebra via an auxiliary mapping ϕ .

Let P be cone Banach space E, A, K are two mappings in P, A accretive, K s k-set contraction, then fixed point index defined for mapping -A+K, some fixed point theorems are also deduced.