相关论文: Why most papers on filters are really trivial (inc…

This short article contains the construction of a construction that generalizes the concept of the derivative of a function of one variable, using the theory of filters. The paper presents a new concept, demonstrates that it really…

The paper is withdrawn because we realized triviality of the main considered example. Less trivial examples are provided in other our papers on the subject.

Two results on product of compact filters are shown to be the common principle behind a surprisingly large number of theorems.

The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…

This contribution is devoted to the comparison of various resampling approaches that have been proposed in the literature on particle filtering. It is first shown using simple arguments that the so-called residual and stratified methods do…

In this article, we define the notion of a filtration and then give the basic theorems on initial and progressive enlargements of filtrations.

The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cleaner than the "standard" proof.

In this paper, we introduce the concept of filter on IL-algebra. It is proved that this concept generalizes the notion of filter on Residuated Lattices. Prime filters on IL-algebra are defined and few interesting properties are obtained. It…

The purpose of this paper is to describe and elaborate the philosophical ideas behind hyperstructures and structure formation in general and emphasize the key ideas of the Hyperstructure Program.

The aim of this note is to emphasize the fact that in many papers on invexity published in prestigious journals there are not clear definitions, trivial or not clear statements and wrong proofs. We also point out the unprofessional way of…

To present a survey on known results from the theory of transposed Poisson algebras, as well as to establish new results on this subject, are the main aims of the present paper. Furthermore, a list of open questions for future research is…

Many classes of maps are characterized as (possibly multi-valued) maps preserving particular types of compact filters.

This is a mostly expository paper, intended to explain a very natural relationship between two a priori distinct notions appearing in the literature: Generic Vanishing in the context of vanishing theorems and birational geometry, and…

This note develops some fundamental properties of resultants and related notions. It represents my own personal exploration of this domain, which I found more instructive than seeking answers in the standard literature. Consequently,…

The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…

Although the results are correct, it was pointed out that the results follow from some previously known results. Accordingly, this version of the paper is withdrawn by the authors.

A little general abstract combinatorial nonsense delivered in this note is a presentation of some old and basic concepts, central to discrete mathematics, in terms of new words. The treatment is from a structural and systematic point of…

The purpose of this note is to present a formulation of a given nonlinear ordinary differential equation into an equivalent system of linear ordinary differential equations. It is evident that the easiness of a such procedure would be able…

The goal of this paper is to provide some basic structure information on derivations in finite semirings.

The filter quotient construction is a particular instance of a filtered colimit of categories. It has primarily been considered in the context of categorical logic, where it has been used effectively to construct non-trivial models, for…