We introduce the notions of anti fuzzy right ideal, anti fuzzy right k-ideal and intuitionistic fuzzy right k-ideal of semirings. We investigate the their properties and connections with right k-ideal, fuzzy right k-ideal, anti fuzzy right k-ideal. We characterize regular semiring through intuitionistic fuzzy right ideal. The semi regularity of semirings is characterized by intuitionistic fuzzy...

Let mIO(X) be the family of ⋆-open (resp. α-I-open, pre-I-open, semi-I-open, β-I-open, etc.) sets in an ideal topological space (X, τ, I). By using mIO(X), we introduce and investigate notions m-I-continuous multifunction F : I) → (Y, σ) mi⋆ -continuous σ, J). The notion -continuity is a generalization m-I-continuity i⋆-continuity [9].

We introduce a practical synchronous stream cipher with provable security named QUAD. The cipher relies on the iteration of a multivariate quadratic system of m equations in n < m unknowns over a finite field. The security of QUAD is provably reducible to the conjectured intractability of the MQ problem, namely solving a multivariate system of quadratic equations.

Let S be a Heegaard splitting surface of a compact orientable 3-manifold M. If S is strongly irreducible, the manner in which it can intersect a ball or a solid torus in M is very constrained and the allowable configurations are simple and useful. Splitting surfaces not conforming to these simple local pictures must be weakly reducible.

The word problem for discrete groups is well-known to be undecidable by a Turing Machine; more precisely, it is reducible both to and from and thus equivalent to the discrete Halting Problem. The present work introduces and studies a real extension of the word problem for a certain class of groups which are presented as quotient groups of a free group and a normal subgroup. Most important, thes...

It is shown that if M is a compact, connected, orientable hyperbolic 3-manifold whose boundary is a torus, and 7‘1, FZ are two slopes on i7M whose associated fillings are respectively a reducible manifold and one containing an essential torus, then the distance between these slopes is bounded above by 4. Under additional hypotheses this bound is improved Consequently the cabling conjecture is s...

The word problem for discrete groups is well-known to be undecidable by a Turing Machine; more precisely, it is reducible both to and from and thus equivalent to the discrete Halting Problem. The present work introduces and studies a real extension of the word problem for a certain class of groups which are presented as quotient groups of a free group and a normal subgroup. As main difference w...

An SO(4) gauge invariant model with extended field transformations is examined in four dimensional Euclidean space. The gauge field is (A µ) αβ = 1 2 t µνλ (M νλ) αβ where M νλ are the SO(4) generators in the fundamental representation. The SO(4) gauge indices also participate in the Euclidean space SO(4) transformations giving the extended field transformations. We provide the decomposition of...