A remark on the contraction principle

A remark of contraction semigroups on Banach spaces

Let X be a complex Banach space and let J : X → X∗ be a duality section on X (i.e. 〈x, J(x)〉 = ‖J(x)‖‖x‖ = ‖J(x)‖2 = ‖x‖2). For any unit vector x and any (C0) contraction semigroup T = {e tA : t ≥ 0}, Goldstein proved that if X is a Hilbert space and if |〈T (t)x, J(x)〉| → 1 as t → ∞, then x is an eigenvector of A corresponding to a purely imaginary eigenvalue. In this article, we prove the simi...

0 Remark on the Second Principle of Thermodynamics

All presently available results lead to the conclusion that nonextensivity, in the sense of nonextensive statistical mechanics (i.e., q = 1), does not modify anything to the second principle of thermodynamics, which therefore holds in the usual way. Moreover, some claims in the literature that this principle can be violated for specific anomalous systems (e.g., granular materials) can be shown ...

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.

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