A remark on ratios

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Remark on a Reply

1.1 In their original PNAS article Macy and Sato (2002) make it clear that their main point concerns social mobility (see, for instance, the abstract and the last section). Their central claim is the non-monotonic effect of mobility: with moderate mobility, they maintain, trust can be established; with too much mobility, trust and trustworthiness are undermined — and therefore their "warning fl...

A remark on Remainders of homogeneous spaces in some compactifications

‎We prove that a remainder $Y$ of a non-locally compact‎ ‎rectifiable space $X$ is locally a $p$-space if and only if‎ ‎either $X$ is a Lindel"{o}f $p$-space or $X$ is $sigma$-compact‎, ‎which improves two results by Arhangel'skii‎. ‎We also show that if a non-locally compact‎ ‎rectifiable space $X$ that is locally paracompact has a remainder $Y$ which has locally a $G_{delta}$-diagonal‎, ‎then...

A remark on the means of the number of divisors

‎We obtain the asymptotic expansion of the sequence with general term $frac{A_n}{G_n}$‎, ‎where $A_n$ and $G_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎Also‎, ‎we obtain some explicit bounds concerning $G_n$ and $frac{A_n}{G_n}$.

A short remark on the result of Jozsef Sandor

It is pointed out that, one of the results in the recently published article, ’On the Iyengar-Madhava Rao-Nanjundiah inequality and it’s hyperbolic version’ [3] by J´ozsef S´andor is logically incorrect and new corrected result with it’s proof is presented.