For two normed algebras $A$ and $B$ with the character space   $bigtriangleup(B)neq emptyset$  and a left $B-$module $X,$  a certain class of bounded linear maps from $A$ into $X$ is introduced. We set $CMH_B(A, X)$  as the set of all non-zero $B-$character module homomorphisms from $A$ into $X$. In the case where $bigtriangleup(B)=lbrace varphirbrace$ then $CMH_B(A, X)bigcup lbrace 0rbrace$ is...

The strength of a homogeneous polynomial (or form) is the smallest length an additive decomposition expressing it whose summands are reducible forms. Using functors, we show that set forms with bounded not always Zariski-closed. More specifically, if ground field algebraically closed, prove quartics ≤3 Zariski-closed for large number variables.

We show that for a continuous map of a closed interval to itself, if the set of periodic points is closed, then every recurrent point is periodic. If, furthermore, the set of least periods of the periodic points is finite, then every nonwandering point is periodic. This answers a question of L. Block [Proc. Amer. Math. Soc. 67 (1977), 357-360]. Introduction. In [1] and [2], L. Block studied con...

A fuzzy bag is a bag in which each occurrence of an element is associated with a grade of membership. This notion can be viewed as a generalization of the concepts of set, fuzzy set and bag. The set of fuzzy integers (Nf ) provides a general characterization in which all these different concepts are treated in a uniform way and can then be composed. In the field of databases, the use of fuzzy b...

This paper summarizes various formulations of the standard rough set theory. It demonstrates how those formulations can be adopted to develop different generalized rough set theories. The relationships between rough set theory and other theories are discussed. 1 Formulations of Standard Rough Sets The theory of rough sets can be developed in at least two different manners, the constructive and ...