The local multiplier C*-algebra Mloc(A) of any C*-algebra A can be ∗-isomorphicly embedded into the injective envelope I(A) of A in such a way that the canonical embeddings of A into both these C*-algebras are identified. If A is commutative then Mloc(A) ≡ I(A). The injective envelopes of A and Mloc(A) always coincide, and every higher order local multiplier C*-algebra of A is contained in the ...

Trapezoid maps are a kind of continuous and piecewise linear maps with a flat top. By the conjugacy relationship, we present a complete classification for four families of trapezoid maps. Firstly, using an extension method, we construct all homeomorphic solutions of conjugacy equation φ ◦ f = g ◦ φ for some non-monotone continuous maps f and g. Secondly, using an iterative construction method a...

We analyze the signature type of a cascade of periodic orbits associated to period doubling renormalizable maps of the two dimensional disk. The signature is a sequence of rational numbers which describes how periodic orbits turn each other and is invariant by topological conjugacies that preserve orientation. We prove that in the class of area contracting maps the signature cannot be a monoton...

The contribution of this paper is a framework for relating butterfly-shaped hysteresis maps to simple (single-loop) hysteresis maps, which are typically easier to model and more amenable to control design. In particular, a unimodal mapping is used to transform simple loops to butterfly loops. For the practically important class of piecewise monotone hysteresis maps, we provide conditions for pr...

Fixed point results for a self-map satisfying locally contractive conditions on a closed ball in an ordered 0-complete quasi-partial metric space have been established. Instead of monotone mapping, the notion of dominated mappings is applied. We have used weaker metric, weaker contractive conditions, and weaker restrictions to obtain unique fixed points. An example is given which shows that how...

We study the uniqueness of weak solutions for Dirichlet problems with variable exponent and non-standard growth conditions. First, we provide two uniqueness results under ellipticity type hypotheses. Next, we provide a uniqueness result when the operator driving the problem is in the form of the divergence of a monotone map. Finally, we derive a fourth uniqueness result under homogeneity type h...

We show that Reed-Muller codes achieve capacity under maximum a posteriori bit decoding for transmission over the binary erasure channel for all rates 0 < R < 1. The proof is generic and applies to other codes with sufficient amount of symmetry as well. The main idea is to combine the following observations: (i) monotone functions experience a sharp threshold behavior, (ii) the extrinsic inform...

We consider concave continuous-kernel games characterized by monotonicity properties and propose discounted mirror descent type dynamics. introduce two classes of dynamics whereby the associated map is constructed based on a strongly convex or Legendre regularizer. Depending regularizer, we show that these new can converge asymptotically in with merely monotone (negative) pseudogradient. Furthe...

We present an elementary proof that, for a multivalued map φ : R R with nonempty connected values and monotone margins, the existence of a periodic orbit of any order k > 1 implies the existence of periodic orbits of all orders. This generalizes a very recent result of this type in terms of scalar ordinary differential equations without uniqueness, due to F. Obersnel and P. Omari, obtained by m...

This paper is about certain linear subspaces of Banach SN spaces (that is to say Banach spaces which have a symmetric nonexpansive linear map into their dual spaces). We apply our results to monotone linear subspaces of the product of a Banach space and its dual. In this paper, we establish several new results and also give improved proofs of some known ones in both the general and the special ...