This paper belongs to a series of papers devoted the study structure non-wandering set an A-diffeomorphism. We such $ NW(f) for \Omega $-stable diffeomorphism f $, given on closed connected 3-manifold M^3 $. Namely, we prove that if all basic sets in are trivial except attractors, then every non-trivial attractor is either one-dimensional non-orientable or two-dimensional expanding.

Let [n]:={1,2,…,n} and let a k-set denote set of cardinality k. A family sets is union-closed (UC) if the union any two in also family. Frankl’s conjecture states that for nonempty UC F⊆2[n] such F≠{∅}, there exists an element i∈[n] contained at least half F, where 2[n] denotes power on [n]. The 3-sets Morris smallest number distinct (whose n-set) ensure satisfied (in contains them ⌊n/2⌋+1 all ...

We consider a family of inverse limits sequences closed unit intervals with single upper semi-continuous set-valued bonding function whose graph is an arc; the union two line segments in $$[0,1]^2$$ , both which contain origin (0, 0) and have positive slope. One extends to top-boundary other right side boundary $$[0,1]\times [0,1]$$ . show that there large subfamily $$\mathcal F$$ these functio...

In this paper we deal with the following generalized vector quasiequilibrium problem: given a closed convex set K in a normed space X, a subset D in a Hausdorff topological vector space Y , and a closed convex cone C in R. Let Γ : K → 2, Φ : K → 2 be two multifunctions and f : K×D×K → R be a single-valued mapping. Find a point (x̂, ŷ) ∈ K×D such that (x̂, ŷ) ∈ Γ(x̂)× Φ(x̂), and {f(x̂, ŷ, z) : z ∈ Γ(...

For a closed nowhere dense subset C of ∂D a bounded univalent holomorphic function f on D is found such that C equals the cluster set of its fixed points.

Let k be an algebraically closed field of characteristic zero. Denote the projective plane over k by P2 = Proj k[x, y, z]. Let K be the field of rational functions on P2. We view K as the set of all rational functions of the form f/g ∈ k(x, y, z) where f and g are homogeneous forms in k[x, y, z] of the same degree. Since k is algebraically closed, the Brauer group of P2, denoted B(P2), is trivi...

Let C be a nonempty, closed, and convex subset of a real Hilbert space H . Denote the metric projection from x ∈ H onto C by PCx. Let T : C → C be a nonexpansive mapping on C, that is, T : C → C and ‖Tx − Ty‖ ≤ ‖x − y‖, for all x, y ∈ C. We use F T to denote the set of fixed points of T , that is, F T {x ∈ C : x Tx}. Let {T s : s > 0} be a nonexpansive semigroup on a closed convex subset C, tha...

and Applied Analysis 3 Definition 1.4 see 18, 20–23 . 1 The intersection of all fuzzy α-closed resp., semiclosed, preclosed, γ-closed, semi-preclosed, β-closed sets containing a fuzzy set A is called a fuzzy α-closure resp., semiclosure, preclosure, γ-closure, semi-preclosure, β-closure of A. 2 The union of all fuzzy α-open resp., semiopen, preopen, γ-open, semi-preopen, β-open sets contained i...

In the context of semi-abelian categories, several additional conditions have been considered in order to obtain a closer group-like behavior. Among them are locally algebraic cartesian closedness and algebraic coherence. The recent notion of S-protomodular categories, whose main examples are the category of monoids and, more generally, categories of monoids with operations and Jónsson-Tarski v...

One definition of a hyperelliptic curve is a curve C over an algebraically closed field k whose function field K is a degree 2 extension of a purely transcendental extension of k. 1. (a) Show that every hyperelliptic curve is birational to a curve of the form y 2 = f (x) where f ∈ k[x] is a monic squarefree polynomial. (b) Conversely, show that every squarefree f ∈ k[x] gives rise to a hyperell...