As is well known, an irreducible nonnegative matrix possesses a uniquely determined Perron vector. As the main result of this paper we give a description of the set of Perron vectors of all the matrices contained in an irreducible nonnegative interval matrix A. This result is then applied to show that there exists a subset A∗ of A parameterized by n parameters (instead of n2 ones in the descrip...

The main result is that, for any projective compact analytic subset Y of dimension q > 0 in a reduced complex space X , there is a neighborhood Ω of Y such that, for any covering space Υ: X̂ → X in which Ŷ ≡ Υ(Y ) has no noncompact connected analytic subsets of pure dimension q with only compact irreducible components, there exists a C∞ exhaustion function φ on X̂ which is strongly q-convex on Ω̂ ...

Using an invariant of Cuntz, we classify reducible shifts of nite type with two irre-ducible components up to ow equivalence. 0. Introduction Let A be an n n matrix over the non-negative integers Z +. Form a directed graph G A with n vertices and A(i; j) edges from vertex i to vertex j. Let E be the set of all edges of G A endowed with the discrete topology. Then the product space E Z is a comp...

An analytic hypersurface of M is a subset V ⊂ M such that for each point x ∈ V there exists an open set Ux ⊂ M containing x and a holomorphic function fx defined on Ux such that V ⊂ Ux is the zero-set of fx. Such an fx is called a local defining function for V near x. The quotient of any two local defining functions around x is a non-vanishing holomorphic function around x. An analytic hypersur...

Let Q denote the rationals, P the irrationals, C the Cantor set and L the space C {p} (where p e C). Let / : X —> Y be a perfect continuous surjection. We show: (1) If X G { Q , P, QxP} , or if / is irreducible and Xe{C, L}, then Y is homeomorphic to X if Y is zero-dimensional. (2) If X G {P, C, L} and / is irreducible, then there is a dense subset S of Y such that / | /*~[S] is a homeomorphism...

A stick figure $X\subset \mathbb{P}^r$ is a nodal curve whose irreducible components are lines. For fixed integers $r\ge 3$, $s\ge 2$ and $d$ we study the maximal arithmetic genus of connected (or any reduced curve) such that $\deg (X)=d$ $h^0(\mathcal{I}_X(s-1))=0$. We consider Halphen's problem obtaining all genera below one.

STUDY DESIGN This study analyzed the natural course of cervical spine involvement in rheumatoid arthritis by serial radiographs. OBJECTIVES The purpose was to determine the pattern of progression of cervical spine lesions in rheumatoid arthritis and predictors for the extent of progression. SUMMARY OF BACKGROUND DATA Subluxation frequently occurs as a result of rheumatoid involvement of the...

• A uniform approach to d -spaces, sober spaces and well-filtered is provided. The theory of (super) H-sober established. If H has property M, then the function space super equipped with topology pointwise convergence H-sober. a T 0 X iff its Smyth power P S ( ) category all reflective in Top . if M. In this paper, we provide spaces, develop general framework for dealing these spaces. concepts ...

We prove an induction step that can be used to show that in certain cases the removal of finitely many points from a product space produces an irreducible space. For example, we show that whenever γ is less than אω, removing finitely many points from the product of γ many first countable compact spaces gives an irreducible space. This result answers questions asked privately by Alexander Arhang...

Let L̃ ≥ א0 be arbitrary. In [20], it is shown that C = ξ̂. We show that −1 < 0. Recent developments in symbolic combinatorics [20] have raised the question of whether there exists an anti-universally ultra-geometric subset. Is it possible to examine Fibonacci, pseudo-irreducible, geometric functors?