# Mirjana VukovicAcademy of Science and Arts of Bosnia and Herzegovina | ANUBiH · Department of Natural Sciences and Mathematics

Mirjana Vukovic

Academician - ANUBiH

A new issue of the journal "Sarajevo Journal of Mathematics" Vol. 18, No. 1 in 2022 has been prepared for publication.

## About

181

Publications

48,896

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

136

Citations

Citations since 2016

Introduction

Very nice news
1) my new book "MATHEMATICIANS -- MEMMBERS OF ACADEMY OF SCIENCES AND ARTS OF BOSNIA AND HERZEGOVINA is finished and will be soon published, by the ANUBiH.
It will be soon published:
2) a new issue of "Sarajevo Journal of Mathematics" dedicated to Prof. Mustafa Kulenović, member of the Editorial Board, on the occasion of his 70th birthday,

**Skills and Expertise**

Additional affiliations

December 2018 - present

**Academy of Science and Arts of Bosnia and Herzegovina**

Position

- academician

Description

- researcher in ANUBiH, Editor in Chief of "Sarajevo Journal of Mathematics", academician ANUBiH

October 2013 - October 2016

**University of East Sarajevo, Faculty of Philosophy, East Sarajevo**

Position

- Professor (Full)

Description

- From Octorber 2013, I taught many different courses at Department of Mathematics and Computer Science & Department of Mathematics and Physics of University of East Sarajevo.

December 2012 - June 2020

**Academy of Science and Arts of Bosnia and Herzegovina**

Position

- Full member of Academy of Sciences and Arts of BiH

Description

- researcher in ANUBiH, Full member of the ANUBiH

Education

April 2000 - December 2000

November 1997 - December 1997

**Technische Universität Wien**

Field of study

- Austrian Government Research Fellowship awarded under the program "Stipendien für die Universitäten Bosnia-Herzegowinas der Österreichi- schen Rectorkonkonferenz"

November 1977 - December 1977

**University "Pierre et Marie Curie" (Paris VI),**

Field of study

- Mathematics - Algebra

## Publications

Publications (181)

This is book about MAHMUT BAJRAKTAREVIĆ, MANOJLO MARAVIĆ, BRANISLAV MARTIĆ, FIKRET VAJZOVIĆ, and VESELIN PERIĆ, mathematicians members of ACADEMY OF SCIENCES AND ARTS OF BOSNIA AND HERZEGOVINA

It is cover page of new issue of "Sarajevo Journal of Mathemetics" prepared by two Editors in Chief: Academician Mirjana Vuković, ANUBiH and Prof. Mehmed Nurkanović, University of Tuzla

This textbook on Group Theori (Overview of Theory and Problems) is the product of many years of experience teaching this subject at the Faculty of Science and Mathematics of University of Sarajevo and Podgorica as well as at the Department of Mathematics of the Faculty of Philosopy of University of East Sarajevo of both authors

The authors of the papers published in this issue are: NICHOLAS H. BINGHAM AND ADAM J. OSTASZEWS, R. DIVYA AND P. CHITHRA DEVI, JOHN M. CAMPBEL, SONIA DOG, D. MARY FLORENCE, R. MURUGESAN AND P. NAMASIVAY, EDOARDO BALLICO, MAYAKRISHNAN MADHAN, SRINIVASAN SELVARANGAM AND ETHIRAJU THANDAPAN, SEL ̇IN C ̧ INAR AND KAM ̇IL DEM ̇IRC ̇I, FRANCISCO JAVIER A...

This is HOMMAAGE TO MY FIVE PROFESSORS and ACADEMICIANS -- MEMBERS OF
ACADEMY OF SCIENCES AND ARTS OF BOSNIA AND HERZEGOVINA
M.BAJRAKTAREVIĆ, M. MARAVIĆ, B. MARTIĆ, F. VAJZOVIĆ, AND V. PERIĆ
ON THE OCCASION OF 70 YEARS SINCE THE ESTABLISHMENT O

Marc Krasner investigating valued fields and observing a connection between them and their valuation rings using equivalence of valuations came to the fundamental notion of a corpoid in 1944-45 (series C.R. of Academy of Sciences of Paris notes) which represents the origin of the development forerunner of the general graded theory – a theory of hom...

Abstract
I dedicate this article to Prof. Milenko Pikula, a dear colleague and friend from our student days, with a short retrospective of his life and professional career, including his
contribution to mathematics and bibliography.

The purpose of this article is to present certain results arising from a study of the paragraded rings-the most general graded rings introduced by M. Krasner and myself as a generalisation of general graded rings in Krasner's sense. Besides, we give some examples of paragraded rings that are not graded and some open questions concerning paragraded...

The textbook ALGEBRA I - GROUP THEORY (Review of Theory and Problems with Solutions) is intended primarily for students of mathematics, but also for others who need group theory. It was created as a culmination of many years of experience and work of both authors in teaching various subjects in the field of algebra, at the Department of Mathematics...

This is one of the rare photos of the great French mathematician of Jewish-Russian roots and a scientific portrait by Wisenportal -- Durch- suchen, 2014, which was a man of broad general culture and education and a passionate photographer of natural beauty.
I got this beautiful photo (taken in Marseille) thanks to dear colleague and friend Prof. A...

The purpose of this article is to present certain results arising from a study of the paragraded rings-the most general graded rings introduced by M. Krasner and myself as a generalisation of general graded rings in Krasner's sense. Besides, we give some examples of paragraded rings that are not graded and some open questions concerning paragraded...

This article is dedicated to dr Milenko Pikula, Professor and Professor Emeritus of the University of East Sarajevo -- dear colleague and friend from the student days, with a brief retrospective of his life and professional careers, including his contributions to mathematics.

In this issue of the "Sarajevo Journal of Mathematics" (SJM) Vol. 16 (29), No. 2 (2020), 145-269 are published the following papers: M. Vuković, Remembering academician Manojlo Maravić; Feng-Zhen Zhao, On the log-convexity of the difference sequence of a log-convex sequence; M. A. Pathan and Waseem A. Kha, Unified Apostol type Hermite-Bernoulli, He...

In mid-November 2019 it was one hundert years of birth, and in May 2020, twenty years since the death of Manojlo Maravić, professor at the Faculty of Civil Engineering of the University of Sarajevo and member of the Academy of Sciences and Arts of Bosnia and Herzegovina. On this occasion we devote this article to a brief retrospect of his life and...

Successful study of Bourbaki-Krasner's graded structures problems opened the way to paragraded structures for me. In this paper we study paragraded modules over noncommutative paragraded rings and as a main result prove the paragraded version of Schur's Lemma.

New issue of the "Sarajevo Journal of Mathematics" Vol. 16 (29), No. 1, (Sarajevo 2020) as the previous dedicated to the memory of two distinguished members of Editorial Board Academician Fikret Vajzović, member of ANUBiH and Prof. Harry Miller, foreign member of ANUBiH, who was the Editor-in-Chief, for many years is prepared and will be posted on...

This paper is dedicated to the 100th anniversary of the birth and 20 years since the death of Academician Manojlo Maravić .

It was Conference in organisation Academy of Sciences and Arts of Bosnia and Hrzegovina, University of Grenoble and University of Maribor, held in Dbrovnik (IUC-2016) dedicated to the Memory of Professor Marc Krasner, French mathematician Jewish-Russian born and its results in the theory of graded structures. We wanted to remind of his contribution...

This issue of the "Sarajevo Journal of Mathematics" (SJM) Vol. 15 (28), No.. 2 (2019), 129-322 is dedicated to the memory of two distinguished members of the Editorial Board Academician Fikret Vajzović, member of Academy of Sciences and Arts of Bosnia and Herzegovina and Professor Harry Miller, foreign member of Academy of Sciences and Arts of Bosn...

After a short review of Mihajlo Petrović Alas, the founder of the world-famous Belgrade School of Mathematics, I will speak about the Sarajevo School of Analysis that greaw out of the Belgrade School, and which consisted of Belgrade students: Vera Popović Šnajder -- the first female mathematician in Bosnia and Herzegovina and the author of the firs...

This project is purelly theoretic and there are no any experiment.

It is the Cover page of "Sarajevo Journal of Mathematics" Vol. 15 (28), No. 1, -- journal of
Academy of Sciences and Arts of Bosnia and Hercegovina with Content of published research papers and authors of this pepers.
ISSN 1840-0655 (Printed edition)
ISSN 2233-1964 (Online edition)
The journal is presented also electronically on the address: www.a...

After a short review of Mihajlo Petrović Alas, the founder of the world -famous Belgrade School of Mathematics, I will speak about about the Sarajevo School of Analysis that grew out of the Belgrade School, and which consisted of Belgrade students : Vera Popović Šnajer, -- the first female mathematician in Bosnia and Herzegovina (BH) and the author...

Conference: "MODERN ALGEBRA AND ANALYSIS AND THEIR APPLICATIONS" (Dedicated to Professor Mirjana Vuković)
At: Academy of Sciences and Arts of Bosnia and Herzegovina, Bosnia and Herzegovina Sarajevo, September 20-22, 2018
In book: SARAJEVO JOURNAL OF MATHEMATICS
Journal: SARAJEVO JOURNAL OF MATHEMATICS Vol. 14 (27), No. 2
ISSN: 1840 - 0655 (Printed...

There are no experiments in this project. This is pure theory, i.e. abstract theoretical science

The paper, supplemented with a short historical dvelopment of graduation which begins with Krasner's famous notion of a corpoid, introduced in 1940s and general grded groups in Krasner's sense, more general than Bourbaki's, will present some results in the theory of Krasner-Vuković's para- and extra-graded groups including examples of paragraduatio...

The paper discuss three sangaku problems on relationship among circles inscribed in the sector of an annulus, which is due to its shape, called a fan.
In the period 17th to 19th century, so called Edo period, Japan closed its doors to the outer world traditional Japanese mathematics was developed, (wasan 和算). In Japan in that times, there was no o...

The lecture will include a short history of the graded rings that refers to Krasner's notion of corpoid. M. Krasner: Une généralisation de la conception de corps-corpoïde. Un corpoïde remarquable de la théorie des corps, C. R. Acad. Sci., Paris 219 (1944) and notion of general graded rings in Krasner's sense. M. Krasner: Le vieux qui est noef, Revu...

In my presentation, after a brieof Mathematicsf review of Mihailo Petrovic -- Alas, founder in the world of the famous Belgrade School of Mathematics, I will speak about the Sarajevo School which grew out of Belgrade School, made by Belgrade students: Vera Popović -- Šnajder (born 1904) -- the first mathematician from Bosnia and Herzegovina (B-H) w...

The Academy of Sciences and Arts of Bosnia and Herzegovina and its Department of Natural Sciences and Mathematics and myself organize International Scientific Conference "MODERN ALGEBRA AND ANALYSIS AND THEIR APPLICATIONS" which take place from 22th to 22nd September, 2018 in Sarajevo. The aim of this Conference was to present the least results in...

The Academy of Sciences and Arts of Bosnia and Herzegovina and its Department of Natural Sciences and Mathematics and myself organize International Scientific Conference "MODERN ALGEBRA AND ANALYSIS AND THEIR APPLICATIONS" which will take place from 22th to 22nd September, 2018 in Sarajevo. The aim of this Conference is to present the least results...

ALGEBRA -- THEORY OF GROUPS is my new book written joint with academician V. Perić
It will appear soon in bookstores.

In this paper we observe paragraded rings (first introduced by the famous French mathe-matician Marc Krasner and myself [Structures paragraduees (groups, anneaux, modules), Queen's Papers , No. 77, Queen's University, ONT, Canada, 1987), and then introduce different radicals of paragraded rings (Jacobson, prime, Kurosh -- Amitzur).
It is known tha...

However, the first relatively general definition of graded groups was given by
Bourbaki. But this definition was not general enough, because it was formu-lated with some unnecessarily restrictive conditions, i.e. Bourbaki's definition was based on the notion of the Abelian graded group [1].
Marc Krasner started his study on: Anneaux gradues generau...

BOSNIA-HERZEGOVINA WOMEN'S SCIENTISTS AND THEIR RESEARCH WORK
Abstract. The work is dedicated to Prof. Vera Šnajder, the woman who was the first woman mathematician in Bosnia and Herzegovina, as well as the first woman which served as the Dean of one faculty, not only in Bosnia and Herzegovina, but in all of former Yugoslavia. Besides, her first s...

The work is dedicated to Vera Šnajder, the woman who was the first mathematician in Bosnia and Herzegovina and the first female dean of a faculty , not only in Bosnia and Herzegovina, but also in the former Yugoslavia . In addition, her first scientific paper, published in Comtes Rendus de l'Academie des Sciences de Paris in 1931, was the first pub...

The paper is dedicated to Professor Vera Šnajder, the woman who was the first woman mathematician in Bosnia and Herzegovina, as well as the first woman which served as the Dean of one faculty, not only in Bosnia and Herzegovina, but in former Yugoslavia as well. Further, her first scientific paper(published in Comtes Rendus de l'Académie des Scienc...

Obituary: Academician Fikret Vajzovic was born on the 1st of May 1928 in Konjic. and died on 4th November 2017 in Sarajevo.
It can certainly be said that Prof. Vajzovic was one of the founders of modern mathematical analysis and mathematics in general in this region, as well as one of the best mathematicians ever to be associated with the Departmen...

This presentation begin with definition of a paragraded rings, then we give an example of paragraded ring that is not graded ring and discuss prime and Jacobson radicals of paragraded rings.

This is not just Cover of „SARAJEVO JOURNAL OF MATHEMATICS“. Vol. 12 (25), No. 2 Supplement, in which are published papers from the Conference "Graded Structures in Algebra and their Applications" dedicated to the memory of Professor Marc Krasner, Officier des Palmes de l'Academie des Sciences de Paris, on the occasion of the 30th anniversary of hi...

This issue is dedicated to the memory of Professor Marc Krasner, Officier des Palmes de l'Academie des Sciences de Paris on the ocasion of the 30th anniversary of his death.
All mauscripts of this issue were presented at International Scientific Conference "Graded Structures in Algebra and their Applications" held in Inter University Center, Dubrov...

In this paper we prove that there exist paragraded rings which are not graded and we discuss prime and Jacobson radicals of paragraded rings. In particular, we prove that paragraded counterparts of prime and Jacobson radicals are the largest paragraded ideals contained in them

This work is dedicated to the memory of Professor Marc Krasner, "Officier des Palmes de l' Académie des Sciences de Paris" on the occasion of the 30th anniversary of his death.
He was Professor and Professor Emeritus of the University „Pierre et Marie Curie“ from Paris passed away. Marc Krasner, a Russian-born, eminent French mathematician of Jewis...

In this paper, we prove the paragraded version of the Wedderburn–Artin theorem. Following the methods known from the abstract case, we first prove the density theorem and observe the matrix rings whose entries are from a paragraded ring. However, in order to arrive at the desired structure theorem, we introduce the notion of a Jacobson radical of a...

Applying Parseval's formula for the G-summability of eigenfunction expansion is proved one theorem which is an analogue of Avadhani' s theorem for the Riesz method of summability.

This issue is ddicated to the memory of Academician Mahmut Bajraktarevic
It is thirty years since Mahmut Bajraktarevi´c - Maˇso, professor at the Natural Sciences and Mathematics Faculty of the University of Sarajevo and member of the Academy of Sciences and Arts of Bosnia and Herzegovina (ANUBiH) passed away.

This is BOOK OF ABSTRACTS, BIBLIOGRAFIES, and PROGRAMME of CONFERENCE

Abstract. We discuss the general theory of radicals of paragraded
rings, establish that the ADS-Theorem holds, and characterize para-
graded normal radicals. It is known that any special radical of a ring
can be described by the appropriate class of modules over that ring. In
this note we show that all special paragraded radicals of paragraded ring...

ABSTRACT In this talk we present some results from the radical theory of paragraded rings, structures introduced by Krasner and Vuković [M. Krasner, M. Vuković, Queen’s Papers in pure and applied Mathematics, No.77, Ontario, 1987] (see also [M. Vuković, Prepublication, de l’Institute Fourier,No. 436, Grenoble, 2001]). We also examine properties of...

Vers to Marc Krasne: About the works and the results of the great and the famous French mathematician of world renown, Mark Krasner, on the occasion of 30 th years of death

We discuss the general theory of radicals of paragraded rings, establish that the ADS-Theorem holds, and characterize para-graded normal radicals. It is known that any special radical of a ring can be described by the appropriate class of modules over that ring. In this note we show that all special paragraded radicals of paragraded rings can be de...

We discuss the general theory of radicals of paragraded rings, establish that the ADS-Theorem holds, and characterize paragraded normal radicals. It is known that any special radical of a ring
can be described by the appropriate class of modules over that ring. In this note we show that all special paragraded radicals of paragraded rings
can be des...

International Scientific Conference "Graded Structures in Algebra and their Applications" was Dedicated to the memory of Professor Marc Krasner, famous French mathematician.
Thematically, the Conference was dedicated, primarily, to the graded structures, which were introduced first by N. Bourbaki, and the final form of the definition was given by...

SARAJEVO JOURNAL OF MATHEMATICS
DOI: 10.5644/SJM.12.3.05
Vol.12 (25), No.2, (2016), 317–324, Suppl.
A NOTE ON GENERAL RADICALS OF PARAGRADED
RINGS
EMIL ILI
́
C-GEORGIJEVI
́
C AND MIRJANA VUKOVI
́
C
Dedicated to the memory of Professor Marc Krasner
Abstract. We discuss the general theory of radicals of paragraded rings, establish that the ADS-Theore...

R E P O R T
about the International Scientific Conference GRADED STRUCTURES IN ALGEBRA AND THEIR APPLICATIONS Dedicated to the Memory of Professor Marc Krasner Dubrovnik, 22-24 September 2016
http://www.iuc.hr/conference-details.php?id=283
At the Conference organized by the Department of Natural Sciences and Mathematics of the Academy of Sciences a...

In this paper are given definitions of Krasner-Vuković definition of paragraded ring, Jacobsonov radical, act densely and act densely on M, proved the following theorems, as well as: Density theorem, Paragraded Schoor’s lemma, Paragraded matrix rind and Paragraded Artin-Wedderburn theorem

GROUPS OF GEOMETRIC MAPPINGS. by Mirjana Vukovic and Emil Ilic-Georgijevic
This book intended for students who are already familiar with basic knowledge of geometry and group theory is divided into seven chapters, as follows:
1. Groups (basic)
2. Orthogonal mappings and mappings of similarities
3. Affine mappings
4. Projective mappings
5. Affine an...

Резюме: Дoкaзaн приблизительный peзyльтaт для билинейной Гильбертoвoй тpaнcформации кoтopый пользуется для обратной билинейной Гильбертoвoй тpaнcформации. р-Лебегoвы точки (р > либo = 1) pассмaтринывaютc я тoже.
Abstract: An approximation result for the bilinear Hilbert transform is proved and used for the inverse of the bilinear Hilbert transfor...

Резюме: Дoкaзaн приблизительный peзyльтaт для билинейной Гильбертoвoй тpaнcформации кoтopый пользуется для обратной билинейной Гильбертoвoй тpaнcформации. р-Лебегoвы точки (р > либo = 1) pассмaтринывaютc я тoже.
Abstract: An approximation result for the bilinear Hilbert transform is proved and used for the inverse of the bilinear Hilbert transfor...

The current applicant's scienentific profil comprises the following key topics:
- the connection between Krasner-Vuković' s paragraded structures (groups, rings, modules) and Lie super-
algebras (examined at the host institution by Prof. Dušan Pagon);
- In their common paper 3 - 5, and monograph 6, M. Krasner and M. Vukovic first introduced a theo...

In this paper, applying Parseval ' s formula, we prove a G -- summability analogue of Avadhani's theorem for the Riesz -- summability of the eigen-function expansion. A crucial step in our proof of this theorem was to �find a function g(x) that would lead us to the kernel of the G- summability
G -- summability, which is more complex than the kernel...

Paragraded rings are introduced as rings (A,+,.) equipped with a para-graduation π such that for any x, y∈Δ there is a z∈Δ such that AxAy⊂Az. From a semihomogeneous point of view an explicit characterization of paragraded rings is formulated by a list of 5 conditions.
Paraneids, extraneids, quasineids, paragraded modules, extragraded modules are...

In this paper we discuss the primary decomposition in the case of general graded modules – moduloids, a generalization of already done work for general graded rings – anneids. These structures, introduced by Marc Krasner are more general than graded structures of Bourbaki since they do not require the associativity nor the commutativity nor the uni...

We analyze quasiasymptotic boundedness of distributions and their wavelet transforms, in general, as well as for a class of α− exponentially bounded distributions and their wavelet transforms in particular. The main idea of this paper is to use, instead of the quasiasymptotic behaviour, the notion of quasiasymptotic boundedness. In this way we obta...

ABSTRACT: We study various classes of distribution semigroups on the
spaces of functions Fr, r ∈ R distinguished by their behavior at the origin.
AMS Mathematics Subject Classification (2000): 47D06; 47D62
Key words and phrases: Integrated semigroups, distribution semigroups,
smooth distribution semigroups

In this paper, we prove the paragraded version of the Wedderburn–Artin theorem. Following the methods known from the abstract case, we first prove the density theorem and observe the matrix rings whose entries are from a paragraded ring. However, in order to arrive at the desired structure theorem, we introduce the notion of a Jacobson radical of a...

In the present paper, we prove (applying Parseval’ s formla) the analogue of Avadhani’ s theorem for the Avakumovich’ s G – summability and obtained that the this G – summability of egenfunction expansion is a local property of f (x) at the considered point xo if kapa > or = k/2. A crutial step in our proof of this theorem was to find a function g...

Abstract: Face detection is very important topic in image processing. In this paper we propose a method for face detection based on skin detection for initial potential regions detection and Hu invariant moments as region descriptors. Seven Hu moments present complex relations among different skin regions and neural network is used for face or non-...

In this paper, we prove the paragraded version of the Wedderburn-Artin theorem. Following the methods known from the abstract case, we first prove the density theorem and observe the matrix rings whose entries are from a paragraded ring. However, in order to arrive at the desired structure theorem, we introduce the notion of a Jacobson radical of a...

One of recent innovations in the family of swarm intelligence metaheuristics is the firefly algorithm. It is inspired by nocturnal luminous insects called fireflies, more accurately by their mating and social behavior. Original Yang's algorithm was designed for unconstrained optimization problems. Because of its promising performance it was later s...

## Questions

Questions (15)

## Projects

Projects (5)

GOAL: Will be studied problems of functional analysis and algebra, such as integrated (semi-) group of operators in Banach spaceses, then generalization of Hilbert integral transformations and their generalizations and features a very limited continuous cosine operator functions, including in particular the review of the infinitesimal generators of such spektar of cosine functions.

Conference in Dubrovnik, 22-24 September 2016, IUC-2016
Dedicated to the memory Prof.Marc Krasner, Professor Emeritus of University "Pierre et Marie Curie" (Paris VI)
About this Project all is possible find on webb-site:
https://www.researchgate.net/project/International-Scientific-Conference-Graded-Structures-in-Algebra-and-their-applications-dedicated-to-the-memory-of-Professor-Marc-Krasner-which-should-take-place-from-22nd-to-24th-September-2016-in

The research in this project are related to the field of algebra and functional analysis, more precisely to the
1) extra- and para- graded structures: groups, rings and modules;
2) inegrated semigroups of operators and cosine operator functions;
In addition to the project leader Prof. Dr. Mirjana Vukovic and Academician Fikret Vajzović were engaged two young researcher Hadzic Aldijana and Manuela Musika - Dizdarevic, assistant at Department of Mathematics of Faculty of Sciences and Mathematics of Sarajevo Universityand