Split-hom together structure is a new heavy load rack structure, and its reliability needs to be verified. Through analyzing multimodal hom-connection principle from the perspective of bionics and contact mechanics, the article puts forward three kinds of hom-connection methods and establishes the finite element model and mathematical model of the rack. Afterwards, the finite element model and ...

We start by showing that (1) is injective. Take an u ∈ Hom (A,B)⊗ Zl that maps to zero in HomΓ (Tl(A), Tl(B)). Write u = ∑∞ j=0 l uj , uj ∈ Hom(A,B), and [u]n for ∑n j=0 l uj . Note that since Hom (A,B) is a Z-module [u]n is in Hom (A,B). Now (since u maps to zero) [u]n is the zero morphism A[l ] → B[l], so it kills the ltorsion. As it is well known, this implies the existence of a certain ψn ∈...

In this paper we will try to introduce a good smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should has.

When G is a connected compact Lie group, and π is a closed surface group, then Hom(π,G)/G contains an open dense Out(π)-invariant subset which is a smooth symplectic manifold. This symplectic structure is Out(π)-invariant and therefore defines an invariant measure μ, which has finite volume. The corresponding unitary representation of Out(π) on L(Hom(π,G)/G, μ) contains no finite-dimensional su...

A connection-like objects, termed hom-connections are defined in the realm of non-commutative geometry. The definition is based on the use of homomorphisms rather than tensor products. It is shown that hom-connections arise naturally from (strong) connections in non-commutative principal bundles. The induction procedure of hom-connections via a map of differential graded algebras or a different...

A class of non-associative and non-coassociative generalizations of cobraided bialgebras, called cobraided Hom-bialgebras, is introduced. The non-(co)associativity in a cobraided Hom-bialgebra is controlled by a twisting map. Several methods for constructing cobraided Hombialgebras are given. In particular, Hom-type generalizations of FRT quantum groups, including quantum matrices and related q...

Hom-dendriform algebras are twisted analogs of dendriform and splittings hom-associative algebras. In this paper, we define a cohomology deformations for hom-dendriform We relate to the Hochschild-type cohomol

Following [SW2] we consider a knot group G, its commutator subgroup K = [G,G], a finite group Σ and the space Hom(K,Σ) of all representations ρ : K → Σ, endowed with the weak topology. We choose a meridian x ∈ G of the knot and consider the homeomorphism σx of Hom(K,Σ) onto itself: σxρ(a) = ρ(xax) ∀a ∈ K, ρ ∈ Hom(K,Σ). As proven in [SW1], the dynamical system (Hom(K,Σ), σx) is a shift of finite...