# Aneta VelkoskaUniversity for Information Science and Technology "St. Paul the Apostle" · Faculty of Communication Networks and Security

Aneta Velkoska

PhD of Mathematics

## About

28

Publications

11,829

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31

Citations

Introduction

Additional affiliations

Education

November 2011 - February 2015

**Faculty of Natural Sciences and Mathematics Ss. Cyril and Methodius University Skopje**

Field of study

- Theoretical Mathematics

September 2002 - October 2009

**Faculty of Natural Sciences and Mathematics Ss. Cyril and Methodius University Skopje**

Field of study

- Theoretical Mathematics

## Publications

Publications (28)

In this paper, by using the geometrical classification of the types of linear equations or systems of two equations, we determine a method for solving systems of linear equations. The analysis specifically refers to systems of linear equations that reduce to a quadratic system of the second or third order in which all determinants of the system are...

In this article, by using the notion of chain, we give some characterizations of totally separated spaces. Then, we give some examples, study the properties of those spaces and give new proofs. Furthermore, by using the notion of chain, we introduce the notions of totally weakly chain separated and totally chain separated sets in a topological spac...

The Internet of Things (IoT) is a cutting-edge technology that enables virtual and physical objects to connect and communicate, resulting in new digitized services that enhance our quality of life. Despite its many advantages, the current centralized architecture of IoT poses various challenges such as single point of failure, security concerns, pr...

The paper gives a generalization of connectedness and chain
connectedness of a space that is more general than a topological space and it
consists of a set and a family of coverings of the set. In these spaces we define
the notions of connected and chain connected sets, that are generalization of
the notions with the same name in a topological spac...

In this paper we introduce the notion of pair of weakly chain separated sets in a topological space. If two sets are chain separated in the topological space, then they are weakly chain separated in the same space. We give an example of weakly chain separated sets in a topological space that are not chain separated in the space. Then we study the p...

The de Rham theorem gives a natural isomorphism between De Rham cohomology and singular cohomology on a paracompact differentiable manifold. We proved this theorem on a wider family of subsets of Euclidean space, on which we can define inner differentiability. Here we define this family of sets called tangentially locally linearly independent sets,...

Using the intrinsic definition of shape based on proximate sequences for compact and all topological spaces based on proximate nets indexed by open coverings in the paper Shekutkovski [5] we define proximate fundamental group. In this paper will be introduced proximate groups of higher order and it will be shown that these groups are invariants of...

Shekutkovski's paper [5] compares two definitions of connectedness: the standard one and a definition using coverings. The second definition seems to be an effective description of quasicomponents. In our paper rather than as a space, we generalize the notion of connectedness as a set in a topological space called chain connected set. We also intro...

The De Rham theorem gives a natural isomorphism between De Rham co-homology [4] and singular cohomology [3] on a paracompact differentiable man-ifold. This is very important fact as singular cohomology is very topological theory and De Rham cohomology is much more analytical. It comes from differential forms on manifolds and the exterior derivate....

Transmission of confidential messages over wireless networks between a transmitter and a receiver in the presence of illegitimate receivers called eavesdroppers is an active area of research. Cooperation by jamming can improve information-theoretic secrecy in wireless networks. However, randomly chosen jammers can have a negative impact on the secr...

The objective of teaching any subject, including mathematics is an active and creative proficiency of knowledge that will be durable and applicable in practice. Therefore, in addition to the appropriate educational contents, the relevant modern teaching tools, the adequate school supplies and the motivation among the parents and the students, it is...

Achieving reliability, availability, efficient node repair
and security of the data stored in a Distributed Storage System
(DSS) is of great importance for improving the functioning of
these systems. In this work, we apply a data distribution concept,
Twin-code framework, and compare it with a DSS that uses
minimum bandwidth regenerating (MBR) and...

Based on the intrinsic definition of shape by functions continuous over a covering and corresponding homotopy we will define proximate fundamental group. We prove that proximate fundamental group is an invariant of pointed intrinsic shape of a space.

The notion of shape was introduced by K. Borsuk in 1968 as a new classiﬁcation of spaces from the point of view of their most important global topological properties. In the past 45 years thousand of papers are published concerning shape theory. One of the most important invariants of (pointed) shape are shape groups.
Main references about shape a...

Using the intrinsic definition of shape based on proximate sequences for compact and all topological spaces based on proximate nets indexed by open coverings in the paper Shekutkovski et all. [1] we define proximate fundamental group. In this paper will be introduced the higher order proximate groups and it will be shown that these groups are invar...

Transmission of confidential messages over wireless
networks between a transmitter and a receiver in the presence of
illegitimate receivers called eavesdroppers is an active area of
research. Cooperation by jamming can improve informationtheoretic
secrecy in wireless networks. However, randomly
chosen jammers can have a negative impact on the secre...

The intrinsic definition of shape based on proximate sequences for compact metric spaces and for paracompact spaces based on proxi-mate nets indexed by open coverings directed by refinement of cover-ings are presented in the papers “Intrinsic definition of strong shape for compact metric spaces”, N. Shekutkovski, (2012) and “Maps of quasicomponents...

Understanding probability and statistics is essential in the modern world, where the print and electronic media are full of statistical information and interpretation. The probability and statistics lessons should provide to the students the ability to collect, organize and analyze numerical data, and to understand chance. Appropriate use of techno...

Оваа книга ја содржи предвидената материја со наставниот план и програма на факултет по Информатика во прва година на Првиот Приватен Европски Универзитет на Република Македонија, Скопје, по предметот Математика 1. Но, истата можат да ја користат и студентите од други сродни факултети, бидејќи се опфатени неопходните познавања од Математичка логика...

Оваа книга ја содржи предвидената материја со наставниот план и програма на економскиот факултет во прва година на Првиот Приватен Европски Универзитет на Република Македонија, Скопје, по предметот Математика за бизнис. Истата можат да ја користат и студентите од други сродни факултети, бидејќи се опфатени неопходните поими од Елементарна алгебра,...

Оваа книга ја содржи предвидената материја со наставниот план и програма на факултет по Информатика во третта година на Првиот Приватен Европски Универзитет на Република Македонија, Скопје. Но, истата можат да ја користат и студентите од други сродни факултети, бидејќи се опфатени неопходните методи на Статистичката анализа и заклучување.
Материја...

Оваа книга ја содржи предвидената материја со наставниот план и програма на економскиот факултет во прва година на Првиот Приватен Европски Универзитет на Република Македонија, Скопје. Но, истата можат да ја користат и студентите од други сродни факултети, бидејќи се опфатени неопходните методи на Статистичката анализа и заклучување.
Материјалот в...

The De Rham theorem answers one of the first questions which appear when discussing singular and De Rham cohomology . Are they related in any way? The De Rham theorem gives a natural isomorphism between De Rham cohomology and singular cohomology on a paracompact differentiable manifold . In other words The De Rham theorem says that they will produc...