There is an increasing need to forecast power generated by photovoltaic sources in day-ahead power system operation. The electrical energy generated by these renewable sources is an uncertain variable and depends on solar irradiance, which is out of control and depends on climate conditions. The stochastic programming based on various scenarios is an efficient way to deal with such uncertaintie...

A ring is called a Gelfand ring (pm ring ) if each prime ideal is contained in a unique maximal ideal. For a Gelfand ring R with Jacobson radical zero, we show that the following are equivalent: (1) R is Artinian; (2) R is Noetherian; (3) R has a finite Goldie dimension; (4) Every maximal ideal is generated by an idempotent; (5) Max (R) is finite. We also give the following resu1ts:an ideal...

It is consistent with the axioms of set theory that the circle T can be covered by א1 many closed sets of uniqueness while a much larger number of H-sets is necessary to cover it. In the proof of this theorem, the descriptive set theoretic phenomenon of overspill appears, and it is reformulated as a natural forcing preservation principle that persists through the operation of countable support ...

We consider boundary layer ows driven by either monochromatic progressive waves or standing waves. The forcing waves may be noisy from either phase or amplitude uctuations in these waves. The central issue addressed here is whether such ows are capable of developing spatial transport velocity patterns which persist over time. The existence of such patterns has two important consequences. First,...

Ideal on an arbitrary non-empty set $\Omega$ it's a family of subset $\mathfrak{I}$ the which satisfies following axioms: $\Omega \notin \mathfrak{I}$, if $A, B \in then $A \cup \mathfrak{I}$ and $D \subset A$, \mathfrak{I}$. The ideal theory is very popular branch modern mathematical research. In our paper we study some classes ideals all positive integers $\mathbb{N}$, namely statistical conv...