Let T̄ 3 s be arbitrary. Every student is aware that every field is Artinian and injective. We show that Erdős’s conjecture is true in the context of Eisenstein manifolds. We wish to extend the results of [19] to homeomorphisms. Hence in future work, we plan to address questions of maximality as well as invertibility.

An optimal algorithm is described for solving the deconvolution problem of the form ku := ∫ t 0 k(t − s)u(s)ds = f(t) given the noisy data fδ, ||f − fδ|| ≤ δ. The idea of the method consists of the representation k = A(I+S), where S is a compact operator, I + S is injective, I is the identity operator, A is not boundedly invertible, and an optimal regularizer is constructed for A. The optimal r...

Alternate proof. Using a bit of differential topology (or a more geometric construction along the lines of Hatcher § 4.1 Exercise 15), consider the degree of a smooth map f : S → S. Since every homotopy class [f ] contains a smooth representative, and all such maps have the same degree (i.e. degree is a homotopy invariant), this defines a function deg : πn(S )→ Z. One readily shows that deg is ...

Peano’s Axioms. N is a set with the following properties. (1) N has a distinguished element which we call ‘1’. (2) There exists a distinguished set map σ : N→ N. (3) σ is one-to-one (injective). (4) There does not exist an element n ∈ N such that σ(n) = 1. (So, in particular σ is not surjective). (5) (Principle of Induction) Let S ⊂ N such that a) 1 ∈ S and b) if n ∈ S, then σ(n) ∈ S. Then S = ...

Many applications require computational systems to respond to queries by a particular deadline. Failure to meet the deadlines may render the returned solution useless. Moreover, the deadlines of such time-critical applications are often uncertain at system design time. Anytime algorithms have been suggested to cope with these challenges by trading the quality of the solutions for the reactivene...

If for any maximal right ideal P of B and a ∈ N(B) ,aB/ aP is almost N-injective, then ring said to be generalized N-injective. In this article, we present some significant findings that are known N-injective rings demonstrate they hold rings. At the same time, study case in which every S.S.Right B-module

Minimality ranks in the style of Deissler are one way of measuring the structural complexity of minimal extensions of first-order structures. In particular, positive Deissler rank measures the complexity of the injective envelope of a module as an extension of that module. In this paper we solve a problem of the second author by showing that certain injective envelopes have the maximum possible...

We find the injective hulls of partially ordered monoids in the category whose objects are po-monoids and submultiplicative order-preserving functions. These injective hulls are with respect to a special class of monics called “embeddings”. We show as well that the injective objects with respect to these embeddings are precisely the quantales.

Let A be an artin algebra, Gélinas has introduced interesting upper bound for the finitistic dimension fin-pro of A, namely delooping level del A. We assert that fin-proA=delA any Nakayama algebra This yields also a new proof and its opposite are equal, as shown recently by Sen. If S is simple module, let e(S) minimum projective injective envelope (one these numbers to finite); e?(S) cover. The...