$S$-limits and $A$-summability

On statistical A-summability

Let A = (ank)∞n,k=1 be an infinite matrix and x = (xk) ∞ k=1 a sequence of real or complex numbers. Then the A-transform of x is a sequence Ax = (An(x))where An(x) = ∑ ∞ k=1 ankxk provided that the series converges for each n; and the sequence x is said to be A-summable if Ax is convergent. In this paper we define statistical A-summability of x, that is, x is said to be statistically A-summable...

Limits on Quaoar ’ s Atmosphere

Here we present high cadence photometry taken by the Acquisition Camera on Gemini South, of a close passage by the ∼ 540 km radius Kuiper Belt Object, (50000) Quaoar, of a r’=20.2 background star. Observations before and after the event show that the apparent impact parameter of the event was 0.019±0.004”, corresponding to a close approach of 580±120 km to the centre of Quaoar. No signatures of...

Confronting Science ’ s Logical Limits

To anyone infected with the idea that the human mind is unlimited in its capacity to answer questions, a tour of 20th-century mathematics must be rather disturbing. In 1931 Kurt Gödel set forth his incompleteness theorem, which established that no system of deductive inference can answer all questions about numbers. A few years later Alan M. Turing proved an equivalent assertion about computer ...

Generalized Covering Groups and Direct Limits

Abel summability and angular convergence

We construct an example of a series that is Abel summable but whose associated power series does not converge on angular sectors. We also give some related results.