There is a well known interplay between the study of algebraic varieties and propositional calculus of various logics. Prime examples of this are boolean algebras and classical logic, and Heyting algebras and intuitionistic logic. After the class of Heyting algebras was generalized to the semi-Heyting algebras by H. Sankappanavar in [San08], its logic counterpart was developed by one of us in [...

A nite special and connuent string-rewriting system S is constructed such that it is undecidable in general whether a word equation is solvable mod S. Thus, (word) uniication mod S is undecidable.

In this paper we generalize the notion of Semi-continuity and MS-continuity and go on to study Semi-compactness, Semi-cocompactness, Semi-stability and Semi-costability in a ditopological texture space. We also extends the notion of Semi-compactness and Semi-cocompactness to a ditopological texture space modulo an ideal [13].

The 3x 1 problem can be viewed, starting with the binary form for any n ∈ N, as a string of “runs” of 1s and 0s, using methodology introduced by Błażewicz and Pettorossi in 1983. A simple system of two unary operators rewrites the length of each run, so that each new string represents the next odd integer on the 3x 1 path. This approach enables the conjecture to be recast as two assertions. I E...

A [semi-]continuous real function of a frame (locale) L has up to now been understood as a frame homomorphism from the frame L(R) of reals into L [as a frame homomorphism (modulo some conditions) from certain subframes of L(R) into L]. Thus, these continuities involve different domains. It would be desirable if all these continuities were to have L(R) as a common domain. This paper demonstrates...

RSA is a popular cryptography algorithm widely used in signing and encrypting operations for security systems. Generally, the software implementations of RSA algorithm are based on 2-prime RSA. Recently multi-prime RSA has been proposed to speed up RSA implementations. Both 2-prime and multi-prime implementations require squaring reduction and multiplication reduction of multi-precision integer...

Ensuring that p and q are very large prime numbers ensures the security of the system. Although multiplying large prime numbers is equivalent to multiplying any two large numbers, a trivial operation on a computer, its inverse is practically impossible. This operation is thus called a one-way function. This ensures that although one is given n, the product of the two prime numbers, discovering ...

It is shown that every commutative arithmetic ring R has λ-dimension ≤ 3. An example of a commutative Kaplansky ring with λ-dimension 3 is given. Moreover, if R satisfies one of the following conditions, semi-local, semi-prime, self f p-injective, zero-Krull dimensional, CF or FSI then λ-dim(R) ≤ 2. It is also shown that every zero-Krull dimensional commu-tative arithmetic ring is a Kaplansky r...