Abstract The purpose of this paper is to compare the notion a Grzegorczyk point introduced in [19] (and thoroughly investigated [3, 14, 16, 18]) standard notions filter Boolean algebras and round contact algebras. In particular, we points filters ultrafilters atomic atomless We also prove how certain extra axiom influences topological spaces for Last but not least, do refrain from philosophical...

Stack filters are a special case of non-linear filters. They have a good performance for filtering images with different types of noise while preserving edges and details. A stack filter decomposes an input image into several binary images according to a set of thresholds. Each binary image is filtered by a Boolean function. The Boolean function that characterizes an adaptive stack filter is op...

Feedback Shift Registers (LFSR) is presented here. In this method, shift register structure used for polynomial modular division is combined with LFSR keystream generator to yield a new keystream generator with much higher periodicity. Security is brought into this structure by using the Boolean function to combine state bits of the LFSR keystream generator and taking the output through the Boo...

In this paper the concept of an $Omega$- Almost Boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $Omega$- Almost Boolean ring over a locally Boolean space.

Background: Advancements in gene expression technology allow acquiring cheap and abundant data for analyzing cell behavior. However, these technologies produce noisy, and often correlated, measurements on the transcriptional states of genes. The Boolean network model has been shown to be effective in capturing the complex dynamics of gene regulatory networks (GRNs). It is important in many appl...

The role of Boolean functions is prominent in several areas including cryptography, sequences, and coding theory. Therefore, various methods for the construction of Boolean functions with desired properties are of direct interest. New motivations on the role of Boolean functions in cryptography with attendant new properties have emerged over the years. There are still many combinations of desig...

one of the models that can be used to study the relationship between boolean random sets and explanatory variables is growth regression model which is defined by generalization of boolean model and permitting its grains distribution to be dependent on the values of explanatory variables. this model can be used in the study of behavior of boolean random sets when their coverage regions variation...

The forcing construction Pmax, invented by W. Hugh Woodin, produces a model whose collection of subsets of ω1 is in some sense maximal. In this paper we study the Boolean algebra induced by the nonstationary ideal on ω1 in this model. Among other things we show that the induced quotient does not have a simply definable form. We also prove several results about saturation properties of the ideal...