this paper deals with continuous frames and continuous riesz bases. we introduce continuous riesz bases and give some equivalent conditions for a continuous frame to be a continuous riesz basis. it is certainly possible for a continuous frame to have only one dual. such a continuous frame is called a riesz-type frame [13]. we show that a continuous frame is riesz-type if and only if it is a con...

We consider a sequence of independent and identicaly distributed (iid) random variables with absolutely continuous distribution function F(x) and probability density function (pdf) f(x). Let Rnl be the largest observation after observing nth record and R(ns) be the smallest observation after observing the nth record. Then we say Wnr = Rnl− R(ns), n > 1, as the nth record range. We will c...

in this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $x$,  where $x$ is a $c$-distinguished topological space. then, we show that their dual spaces can be identified in a natural way with certain spaces of radon measures.

laguerre function has many advantages such as good approximation capability for different systems, low computational complexity and the facility of on-line parameter identification. therefore, it is widely adopted for complex industrial process control. in this work, laguerre function based adaptive model predictive control algorithm (ampc) was implemented to control continuous stirred tank rea...

In this study, we present a continuous-valued logical approach to generalize the sigmoid function. Our starting point is kappa function, which known as unary operator in logic. First extend function (a,b) interval, and then interpret generalized limit of extended when b tend negative positive infinity, respectively. Since induced by an additive generator strict t-norm or t-conorm, dependent. Ba...