Abstract Here we review the notion of polar analyticity introduced in a previous paper and successfully applied Mellin analysis for quadrature formulae over positive real axis. This approach provides simple way describing functions which are analytic on part Riemann surface logarithm. New results also obtained.

let$ p_{n}(x)= sum_{i=0}^{n} a_{i}x^{i}$ be a random algebraicpolynomial, where $a_{0},a_{1}, cdots $ is a sequence of independent random variables belong to the domain of attraction of the normal law. thus $a_j$'s for $j=0,1cdots $ possesses the characteristic functions $exp {-frac{1}{2}t^{2}h_{j}(t)}$, where $h_j(t)$'s are complex slowlyvarying functions.under the assumption that th...

The development of synthesis procedures for passing from a prescribed rational positive real function or matrix to a linear lumped network of passive components possessing the prescribed quantity as its impedance has been one of the major problems confronting network theorists in the past. One of the earliest such synthesis procedures is the Brune synthesis, see Reference 1 and for more recent ...

in this paper, a novel hybrid method based on learning algorithmof fuzzy neural network and newton-cotesmethods with positive coefficient for the solution of linear fredholm integro-differential equation of the second kindwith fuzzy initial value is presented. here neural network isconsidered as a part of large field called neural computing orsoft computing. we propose alearning algorithm from ...

this paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

in this paper, we define and study the notion of the real-valued functions on a frame $l$. we show that $f(l) $, consisting of all frame homomorphisms from the power set of $mathbb{r}$ to a frame $ l$, is an $f$-ring, as a generalization of all functions from a set $x$ into $mathbb r$. also, we show that $f(l) $ is isomorphic to a sub-$f$-ring of $mathcal{r}(l)$, the ring of real-valued continu...