We show that the operations addition and multiplication on the set C(Ω) of all real continuous functions on Ω ⊆ Rn can be extended to the set H(Ω) of all Hausdorff continuous interval functions on Ω in such a way that the algebraic structure of C(Ω) is preserved, namely, H(Ω) is a commutative ring with identity. The operations on H(Ω) are defined in three different but equivalent ways. This all...

Automorph class theory formalism is developed for the case of integral nonsingular quadratic forms in an odd number of variables. As an application, automorph class theory is used to construct a lifting of similitudes of quadratic Z-modules of arbitrary nondegenerate ternary quadratic forms to morphisms between certain subrings of associated Clifford algebras. The construction explains and gene...

Uf(a,ß,Y,x): Universal-logic-module for ternary functions, based upon Reed-Muller expansion, i.e. aodulo-algebra expansion Uh(c,n,x): basic Universal-logic-module for ternary function«, based upon modulo-algebra expansion uh(5,n,x) t ® n x F]: column vector whose entries are the 3 values of f(x), arranged in Increasing order of y, n-1 yI x^ 1-0 LgCK)]: coefficient column vector based upon modul...

In this age of modern era, the use of internet must be maximized. Yeah, internet will help us very much not only for important thing but also for daily activities. Many people now, from any level can use internet. The sources of internet connection can also be enjoyed in many places. As one of the benefits is to get the on-line thomas manns death in venice book, as the world window, as many peo...

We consider multi-variable functions defined over a fixed finite set A. A centralizing monoid M is a set of unary functions on A which commute with all members of some set F of functions on A, where F is called a witness of M . We show that every centralizing monoid has a witness whose arity does not exceed |A|. Then we present a method to count the number of centralizing monoids which have set...

A quantitative method is presented for creating a large number of classes of binary (256) and ternary (7.62 x 10(12)) textures. The binary textures are presented as black and white (contrasts -1 and 1). The ternary textures have three levels: black, white and the mean luminance gray (contrasts -1, 0 and 1). The ternary patterns in particular display a wide variety of properties, including depth...

experimental determination of solubility and ternary phase diagram of chiral compound are of tedious and time consuming tasks, and in many cases, there is not enough experimental data for different enantiomeric compositions to access the experimental ternary phase diagram. using thermodynamic models with predictive capability, having less dependency on experimental data, affords a great advanta...