An old question of T. Jech and K. Prikry asks if an existence of a precipitous ideal implies necessary existence of a normal precipitous ideal. The aim of the paper is to prove some results in the positive direction. Thus, it is shown that under some mild assumptions, an existence of a precipitous ideal over א1 implies an existence of a normal precipitous ideal over א1 once a Cohen subset is ad...

Nanoparticles are often measured using atomic force microscopy or other scanning probe microscopy methods. For isolated nanoparticles on flat substrates, this is a relatively easy task. However, in real situations, we often need to analyze nanoparticles on rough substrates or nanoparticles that are not isolated. In this article, we present a simple model for realistic simulations of nanoparticl...

the rings considered in this article are commutative with identity $1neq 0$. by a proper ideal of a ring $r$,  we mean an ideal $i$ of $r$ such that $ineq r$.  we say that a proper ideal $i$ of a ring $r$ is a  maximal non-prime ideal if $i$ is not a prime ideal of $r$ but any proper ideal $a$ of $r$ with $ isubseteq a$ and $ineq a$ is a prime ideal. that is, among all the proper ideals of $r$,...

harvesting practices of potato is one of the most difficult, troublesome and sensitive stages. potatoes enter the machine with huge amounts of clod and stones: in the meantime separation of potato some stone and clod, which are the same size as of that the potatoes, shall be confide red a major problem. many methods of study by investigators are based on physical properties of potato, stone and...

One of the most common tools for achieving optimization and adequate production process management is linear programming (LP) in various forms. However, there are specific cases application when implies several potential solutions instead one. Exactly such a problem solved this paper, which integrates Multi-Criteria Decision-Making (MCDM) model. First, was applied to optimize lying on line segm...

In this paper, three types of (philosophical, optimistic and pessimistic) multigranulation single valued neutrosophic (SVN) covering-based rough set models are presented, and these three models are applied to the problem of multi-criteria group decision making (MCGDM).Firstly, a type of SVN covering-based rough set model is proposed.Based on this rough set model, three types of mult...

fuzzy rough n-ary subhypergroups are introduced and characterized.

To tackle the problem with inexact, uncertainty and vague knowl- edge, constructive method is utilized to formulate lower and upper approx- imation sets. Rough set model over dual-universes in fuzzy approximation space is constructed. In this paper, we introduce the concept of rough set over dual-universes in fuzzy approximation space by means of cut set. Then, we discuss properties of rough se...