A Remark on Nets of Threshold Elements

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

A remark on boundedness of composition operators between weighted spaces of holomorphic functions on the upper half-plane

In this paper, we obtain a sucient condition for boundedness of composition operators betweenweighted spaces of holomorphic functions on the upper half-plane whenever our weights are standardanalytic weights, but they don't necessarily satisfy any growth condition.

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.

On Autonomous Logic Nets of Threshold Elements

A model of autonomous logic nets composed of n threshold elements is presented and several properties of a single threshold element are generalized to this model. The number of these nets is shown to be 2kn (-<k<l) for completely specified machines. The capacity of the net is defined and conjectured to be 2, similar to the case of a single threshold element. P and NPN Manuscript received Octobe...