ON n-TO-ONE CONTINUOUS IMAGES OF βN

Approximation of Fixed Points of Strongly Pseudocontractive Maps without Lipschitz Assumption

In the present paper, the following result is shown: Let X be a real Banach space with a uniformly convex dual X∗, and let K be a nonempty closed convex and bounded subset of X. Assume that T : K → K is a continuous strong pseudocontraction. Let {αn}∞n=1 and {βn}∞n=1 be two real sequences satisfying (i) 0 < αn, βn < 1 for all n ≥ 1; (ii) ∑∞ n=1 αn = ∞; and (iii) αn → 0, βn → 0 as n→∞. Then the ...

On Van Douwen Spaces and Retracts of Βn

Eric van Douwen [vD93] produced a maximal crowded extremally disconnected regular space and showed that its Stone-Čech compactification is an at most two-to-one image of βN. We prove that there are non-homeomorphic such images. We also develop some related properties of spaces which are absolute retracts of βN expanding on earlier of work in [BBS94, Sim87].

Investigating the Effects of Exposure to Continuous White Noise on SLC26A4 Gene Expression Levels in Male Rat Cochlea

Background and purpose: Irreversible damage to the inner ear is known as noise-induced hearing loss (NIHL). Exposure to excessive noise can affect the expression of genes in molecules involved in development of NIHL. SLC26A4 gene or PDS is responsible for causing both syndromic and non-syndromic deafness and is located at DFNB site. The aim of this study was to investigate the expression level ...

On images of continuous functions from a compact manifold to Euclidean space

Continuous Homomorphisms on βN and Ramsey Theory

We consider the question of the existence of a nontrivial continuous homomorphism from (βN,+) into N∗ = βN\N. This problem is known to be equivalent to the existence of distinct p and q in N∗ satisfying the equations p+ p = q = q + q = q + p = p+ q. We obtain certain restrictions on possible values of p and q in these equations and show that the existence of such p and q implies the existence o...