Random coincidence degree theory with applications to random differential inclusions

Enayet U, Tarafdar; P. Watson; George Xian-Zhi Yuan

Displaying similar documents to “Random coincidence degree theory with applications to random differential inclusions”

Some results on $L Σ (κ)$ -spaces

Fidel Casarrubias Segura, Oleg Okunev, Paniagua C. G. Ramírez (2008)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We present several results related to $L Σ (κ)$ -spaces where $κ$ is a finite cardinal or $ω$ ; we consider products and some constructions that lead from spaces of these classes to other spaces of similar classes.

On the cardinality and weight spectra of compact spaces, II

Istvan Juhász, Saharon Shelah (1998)

Fundamenta Mathematicae

Similarity:

Let B(κ,λ) be the subalgebra of P(κ) generated by ${[κ]}^{\leq λ}$ . It is shown that if B is any homomorphic image of B(κ,λ) then either $| B | < 2^{λ}$ or $| B | = {| B |}^{λ}$ ; moreover, if X is the Stone space of B then either $| X | \leq 2^{2^{λ}}$ or $| X | = | B | = {| B |}^{λ}$ . This implies the existence of 0-dimensional compact $T_{2}$ spaces whose cardinality and weight spectra omit lots of singular cardinals of “small” cofinality.

On infinite composition of affine mappings

László Máté (1999)

Fundamenta Mathematicae

Similarity:

Let $F_{i} = 1, . . ., N$ be affine mappings of $ℝ^{n}$ . It is well known that if there exists j ≤ 1 such that for every $σ_{1}, . . ., σ_{j} \in 1, . . ., N$ the composition (1) $F_{σ 1} \circ . . . \circ F_{σ_{j}}$ is a contraction, then for any infinite sequence $σ_{1}, σ_{2}, . . . \in 1, . . ., N$ and any $z \in ℝ^{n}$ , the sequence (2) $F_{σ 1} \circ . . . \circ F_{σ_{n}} (z)$ is convergent and the limit is independent of z. We prove the following converse result: If (2) is convergent for any $z \in ℝ^{n}$ and any $σ = σ_{1}, σ_{2}, . . .$ belonging to some subshift Σ of N symbols (and the limit is independent of z), then there exists j ≥ 1 such that for every $σ = σ_{1}, σ_{2}, . . . \in Σ$ the composition (1) is a contraction....

Intersection topologies with respect to separable GO-spaces and the countable ordinals

M. Jones (1995)

Fundamenta Mathematicae

Similarity:

Given two topologies, $T_{1}$ and $T_{2}$ , on the same set X, the intersection topologywith respect to $T_{1}$ and $T_{2}$ is the topology with basis $U_{1} \cap U_{2} : U_{1} \in T_{1}, U_{2} \in T_{2}$ . Equivalently, T is the join of $T_{1}$ and $T_{2}$ in the lattice of topologies on the set X. Following the work of Reed concerning intersection topologies with respect to the real line and the countable ordinals, Kunen made an extensive investigation of normality, perfectness and $ω_{1}$ -compactness in this class of topologies. We demonstrate that the majority of his results...

On the “zero-two” law for positive contractions in the Banach-Kantorovich lattice $L^{p} (\nabla, μ)$

Inomjon Ganiev, Farrukh Mukhamedov (2006)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In the present paper we prove the “zero-two” law for positive contractions in the Banach-Kantorovich lattices $L^{p} (\nabla, μ)$ , constructed by a measure $μ$ with values in the ring of all measurable functions.

Approximation of common random fixed points of finite families of N-uniformly $L_{i}$ -Lipschitzian asymptotically hemicontractive random maps in Banach spaces.

Moore, Chika, Nnanwa, C.P., Ugwu, B.C. (2009)

Banach Journal of Mathematical Analysis [electronic only]

Similarity:

A note on evaluations of some exponential sums

Marko J. Moisio (2000)

Acta Arithmetica

Similarity:

1. Introduction. The recent article [1] gives explicit evaluations for exponential sums of the form $S (a, p^{α} + 1) : = \sum_{x \in_{q}} χ (a x^{p^{α} + 1})$ where χ is a non-trivial additive character of the finite field $_{q}$ , $q = p^{e}$ odd, and $a \in *_{q}$ . In my dissertation [5], in particular in [4], I considered more generally the sums S(a,N) for all factors N of $p^{α} + 1$ . The aim of the present note is to evaluate S(a,N) in a short way, following [4]. We note that our result is also valid for even q, and the technique used in our proof can also be used to evaluate...

A problem of Galambos on Engel expansions

Jun Wu (2000)

Acta Arithmetica

Similarity:

1. Introduction. Given x in (0,1], let x = [d₁(x),d₂(x),...] denote the Engel expansion of x, that is, (1) $x = 1 / d ₁ (x) + 1 / (d ₁ (x) d ₂ (x)) + . . . + 1 / (d ₁ (x) d ₂ (x) . . . d_{n} (x)) + . . .$ , where $d_{j} (x), j \geq 1$ is a sequence of positive integers satisfying d₁(x) ≥ 2 and $d_{j + 1} (x) \geq d_{j} (x)$ for j ≥ 1. (See [3].) In [3], János Galambos proved that for almost all x ∈ (0,1], (2) $l i m_{n \to \infty} d_{n}^{1 / n} (x) = e .$ He conjectured ([3], P132) that the Hausdorff dimension of the set where (2) fails is one. In this paper, we prove this conjecture: Theorem. $d i m_{H} x \in (0, 1] : (2) f a i l s = 1$ . We use L¹ to denote the one-dimensional Lebesgue measure on (0,1] and $d i m_{H}$ to denote...

On the positivity of the number of t-core partitions

Ken Ono (1994)

Acta Arithmetica

Similarity:

A partition of a positive integer n is a nonincreasing sequence of positive integers with sum $n .$ Here we define a special class of partitions. 1. Let $t \geq 1$ be a positive integer. Any partition of n whose Ferrers graph have no hook numbers divisible by t is known as a t- core partitionof $n .$ The hooks are important in the representation theory of finite symmetric groups and the theory of cranks associated with Ramanujan’s congruences for the ordinary partition function [3,4,6]. If $t \geq 1$ and $n \geq 0$ ,...