Concerning an approximation of Copson

Recent Developments concerning Entropy and Approximation Numbers

Dataset concerning the analytical approximation of the Ae3 temperature

In this paper we present a new polynomial function for calculating the local phase transformation temperature (Ae3 ) between the austenite+ferrite and the fully austenitic phase fields during heating and cooling of steel:[Formula: see text] The dataset includes the terms of the function and the values for the polynomial coefficients for major alloying elements in steel. A short description of t...

Approximation of an additive mapping in various normed spaces

In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of the following Cauchy-Jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem t...

Issues Concerning the Approximation Underlying the Spectral Representation Theorem

In many important textbooks the formal statement of the Spectral Representation Theorem is followed by a process version, usually informal, stating that any stationary stochastic process f (t), t 2 T g is the limit in quadratic mean of a sequence of processes fS(n, t), t 2 T g, each consisting of a finite sum of harmonic oscillations with stochastic weights. The natural issues, whether the appr...

On a Simultaneous Approximation Problem concerning Binary Recurrences

Let Rn (n = 0, 1, 2, . . .) be a second order linear recursive sequence of rational integers defined by Rn = ARn−1+BRn−2 for n > 1, where A and B are integers and the initial terms are R0 = 0, R1 = 1. It is known, that if α, β are the roots of the equation x2 −Ax−B = 0 and |α| > |β|, then Rn+1/Rn −→ α as n −→ ∞. Approximating α with the rational number Rn+1/Rn, it was shown that ∣∣∣α− Rn+1 Rn ∣...