Through this study, the following has been proven, if is an algebraically paranormal operator acting on separable Hilbert space, then satisfies ( ) property and also for all . These results are achieved property. In addition, we prove that a polaroid with finite ascent after holds

We study statistics of records in a sequence of random variables. These identical and independently distributed variables are drawn from the parent distribution ρ. The running record equals the maximum of all elements in the sequence up to a given point. We define a superior sequence as one where all running records are above the average record expected for the parent distribution ρ. We find th...

The co-algebraic perspective on objects and classes in object-oriented programming is elaborated: classes are described as co-algebras, which may occur as models (implementations) of co-algebraic speciications. These speciications are much like deferred (or virtual) classes with assertions in Eiiel. An object belonging to a class is an element of the state space of the class, as co-algebra. We ...

Let G = Z4. We construct examples of G-equivariant entire rational maps from non-singular real algebraic G-varieties to Grassmannians with appropriate actions of G. These examples of strongly algebraicZ4 vector bundles facilitate a key step in the verification of Conjecture1.1 in the general cyclic group action case.