On the set of limit points of conditionally convergent series

On rearrangements of conditionally convergent series

Rearrangement of a Conditionally Convergent Series

One of the surprising results in an elementary calculus course is that a rearrangement of a conditionaly convergent series may change its sum, even its very convergence. Observing typical textbook examples of this phenomenon, it turns out that during the rearrangement some of the terms are moved arbitrarily large distances from their original locations. Is this necessary? The answer is positive...

Changes of signs in conditionally convergent series on a small set

We consider ideals I of subsets of the set of natural numbers N such that for every conditionally convergent series of real numbers ∑ n∈N an and s ∈ R, then there is a sequence of signs δ = (δn)n∈N such that ∑ n∈N δnan = s and N(δ) := {n ∈ N : δn = −1} ∈ I. We give some properties of such ideals and characterize them in terms of extendability to a summable ideal.

the effect of taftan pozzolan on the compressive strength of concrete in the environmental conditions of oman sea (chabahar port)

cement is an essential ingredient in the concrete buildings. for production of cement considerable amount of fossil fuel and electrical energy is consumed. on the other hand for generating one tone of portland cement, nearly one ton of carbon dioxide is released. it shows that 7 percent of the total released carbon dioxide in the world relates to the cement industry. considering ecological issu...

the effect of task cognitive complexity and time limit on the performance of the learners with different proficiency levels in second language writing skill

this study investigated the effects of manipulating the cognitive complexity of tasks along +/- few elements and the time limits on l2 learners writing performance. to conduct the study, 60 iranian efl learners with two levels of proficiency, low and high intermediate, were selected and assigned to three groups based on the time devoted to task completion. the participants performed both a simp...