we consider the fundamental relation  on a semihypergroup  to interpret the lower and upper approximations as subsets of the fundamental semigroup  and we give some results in this connection. also, we introduce the notion of a bi-hyperideal to study the relationship between approximations and bi-hyperideals.

We prove Feasible Disjunction Property for modal propositional logics K, K4, K4Grz, GL, T, S4, and S4Grz, by a uniform and simple proof based on modular modal sequent proof systems. We derive Feasible Interpolation Theorem for all the logics. Our results are weaker than Hrubeš’ obtained in [9].

A modern mathematical proof is not very diierent from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details. Abstract In this paper the duality theory of Linear Optimization (LO) is built up based on ideas emerged from interior point methods. All we need is elementary calculus. We will embed the LO problem a...

backgroundfor using of complementary and alternative medicine methods (cam) in the leukemia pediatrics than other types of cancer, we have two great challenges; first challenge is their safety and risks and second challenge is study gaps in this field. regarding to these challenges, this study is a narrative review of some cam methods in the leukemia pediatrics from the perspective of their saf...

background and purpose: inappropriate complementary feeding practices are one of the causes of malnutrition worldwide. this study was aimed to determine the complementary feeding practices according to world health organization recommendation in sari, iran. materials and methods: this cross-sectional study on complementary feeding practices assayed the different aspect of infant feeding based o...

The detection of the optic nerve in retina images is a key element of detecting the anatomical structure of the retina. In this work we report on the fusion of two complementary optic nerve detection methods. The methods are complementary in the sense that they use different fundamental queues for locating the optic nerve. By fusing the methods through applying simple distance-based threshold, ...

The unique complementary switching behaviour of complementary resistive switches (CRSs) makes them very attractive for logic applications. The implementation of complete Boolean logic functions in a single CRS cell is certainly an extremely important step towards the commercialisation of related logic circuits, but it has not been accomplished to date. Here, we report two methods for the implem...