there are many different ways to subdivide the spectrum of a bounded linear operator; some of them aremotivated by applications to physics (in particular, quantum mechanics). in this study, the relationship betweenthe subdivisions of spectrum which are not required to be disjoint and goldberg's classification are given.moreover, these subdivisions for some summability methods are studied.

Due to its extensive potential applications, model management has attracted many research interests and gained great progress. To provide easy-to-use interfaces, we have proposed a graph transformation-based model management approach that provides intuitive interfaces for manipulation of graphical data models. The approach consists of two levels of graphical operators: low-level customizable op...

We introduce twisted differential calculus of negative level and prove a descent theorem: Frobenius pullback provides an equivalence between finitely presented modules endowed with topologically quasi-nilpotent connection minus one those zero. explain how this is related to the existence Cartier operator on prismatic crystals. For sake readability, we limit ourselves case dimension one.

In this contribution we investigate the evolution of operators for Genetic Programming by means of Genetic Programming. Metaevolution of recombination operators in graph-based GP is applied and compared to other methods for the variation of recombination operators in graph-based GP. We demonstrate that a straightforward application of recombination operators onto themselves does not work well. ...

Pairwise F-tests provided an efficient approach for aggregating large numbers of species into a manageable number of groups for developing diameter increment functions. The first stage of the two-stage procedure identified the number of groups required and the species defining these groups; the second stage aggregated all remaining species into the most appropriate group. Although there is no g...

‎let $x,y$ be normed spaces with $l(x,y)$ the space of continuous‎ ‎linear operators from $x$ into $y$‎. ‎if ${t_{j}}$ is a sequence in $l(x,y)$,‎ ‎the (bounded) multiplier space for the series $sum t_{j}$ is defined to be‎ [ ‎m^{infty}(sum t_{j})={{x_{j}}in l^{infty}(x):sum_{j=1}^{infty}%‎ ‎t_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $s:m^{infty}(sum t_{j})rightarrow y$ associat...

Weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operat...