we study interior operators and interior structures in a fuzzy setting.we investigate systems of “almost open” fuzzy sets and the relationshipsto fuzzy interior operators and fuzzy interior systems.

One of the most fundamental operations in biological sequence analysis is multiple sequence alignment (MSA). It is a critical tool for biologists to identify the relationships between species and also possibly predict the structure and functionality of biological sequences. The general multiple sequence alignment problem is known to be NP-hard, and hence the problem of finding the best possible...

We give some inequalities related to a large class of operator norms, the so-called Q norms, for a (not necessary commutative) family of bounded linear operators acting on a Hilbert space that are related to the classical Schwarz inequality. Applications for vector inequalities are also provided.

Representing and manipulating sequences in description logics (DLs) h as typically been achieved through the use of new sequence-specific operators or by relying on host-language functions. This paper shows that it is not necessary to add additional features to a DL to handle sequences, and instead describes an approach for dealing with sequences as first-class entities directly within a DL wit...

The invertibility of second-order finite-difference operators with constant operator coefficients acting in the Banach space two-sided vector sequences is proved under condition their uniform injectivity (in particular, left invertibility), or surjectivity right Fredholm property.

We introduce the notion of weighted A-statistical convergence of a sequence, where A represents the nonnegative regular matrix. We also prove the Korovkin approximation theorem by using the notion of weighted A-statistical convergence. Further, we give a rate of weighted A-statistical convergence and apply the classical Bernstein polynomial to construct an illustrative example in support of our...

In this paper we deal with the connection of frames with the class of Hilbert Schmidt operators. First we give an easy criteria for operators being in this class using frames. It is the equivalent to the criteria using orthonormal bases. Then we construct Bessel sequences frames and Riesz bases for the class of Hilbert Schmidt operators using the tensor product of such sequences in the original...

In this note we investigate the operators associated with frame sequences in a Hilbert space H, i.e., the synthesis operator T : l (N) → H , the analysis operator T ∗ : H → l (N) and the associated frame operator S = TT ∗ as operators defined on (or to) the whole space rather than on subspaces. Furthermore, the projection P onto the range of T , the projection Q onto the range of T ∗ and the Gr...

A canonical quantitative view of transcriptional regulation holds that the only role of operator sequence is to set the probability of transcription factor binding, with operator occupancy determining the level of gene expression. In this work, we test this idea by characterizing repression in vivo and the binding of RNA polymerase in vitro in experiments where operators of various sequences we...