of Boyan Dimitrov,
Associate Professor of Mathematics
RESEARCH
DIRECTED AND/OR PARTICIPATED IN
In
the area of Probability Theory I have published
works on:
A. Limit
Theorems (Mostly related with my PhD Thesis):
- Application
of Transfer theorems for random sums of random variables
in solving some limit problems of Renewal theory
(uniform renewal limit
theorems [11,12,17,105], in the study of
transient behavior in Branching
processes (with large number of ancestors) and
special type of service
systems (with fast service [6,10,13,18,22,23]).
These works study
conditions of the Gnedenko-Fahim theorem, or
leading-term asymptotic
expansion in the domain of attraction of the
steady state of a process,
to assess when to replace non-stationary
characteristics by stationary
ones, and how close the two are.
B.
Probability Distributions (an old interest,
and continuing research)
- Characterization
of Probability Distributions and Stability of
Characterization problems, namely
Exponential [45,49,60,71,75,79,93, 97,100],
Poisson [89,90,105,109], the logistic
distribution [105, and 111], and
the introduction of the Almost lack of memory
class of probability
distributions
[80,81,84,86,88,91,92,93,98,99,101,103,105,107,109,113,116],
which has a broad impact on applications in
environmental modeling,
insurance business, financial mathematics and
other fields.
C.
Stochastic Processes of Special Type and Its
Applications.
- Markov
Chains and its applications in Probability
Modeling. Here belongs the
most of the power of Probability Modeling for
Reliability, Queuing,
Inventory problems, the new Markov Arrival
Processes (invented recently by M.
Neuts), and more. My book [3] is devoted to this
techniques, and other books
[1,2,6,11] are illustrating it. The Methods of
Complementary event and complementary variable in
combination, proposed and used in most of my
works on priority queues are broadly based on the
ideas of searching an underlying Markov process.
- Studies
on Priority queues and Service with unreliable
servers
Here belongs
the monograph [1] on priority queues issued in
1973, Moscow University, in
collaboration with coauthors B.Gnedenko,
E.Danielyan, G.Klimov, and V.Matveev.
Also the monograph [2], issued in Sofia, 1973
with A.Obretenov and
E.Danielyan); the Handbook on Queues [4], 1978,
which was translated into
Polish in Poland [8], 1989. They reflect an
extensive work on Priority Queues I did in my
papers
[2,5,6,8,9,10,13,14,15,16,18,21,22,
23,24,25,26,27,30,31,32,33,35,38],
and more. As a main contribution here
I consider the
worked out Method of Complementary Events,
which allows an interpretation
of probability generating functions (the Laplace
transform and the conventional generating
function for discrete distributions), in
combination with the Method
of the Complementary Variables, broadly
exploited in the cited monographs, and in most of
the papers.
- Other
Queuing Problems developed to study
so called Closed Queuing Systems with Priorities
(papers [10,14,26,27,30,]), Asymptotic Methods in
Queues [22,23,35], Methods of Discretization
[38,39,52,54,57,64], and various approaches to
the Numerical Solutions for non-stationary
process characteristics
[34,36,38,39,48,54,56,64,65,68,74,101,103,111];
- Applications
of Queuing Theory for Modeling Computational
Systems and their
Optimization in a non-reliable environment -
were worked out mostly under contracts with
Engineers of Bulgarian computer industry, 1976 -
1990, and used later as a source of other
research projects. Here is my Doctorate on
Mathematical Methods in Queuing Theory,
acknowledged in 1986, most of the publications in
the previous topics, and also in
[34,36,40,41,42,48,51,63,66,70,78,82,101,104,111,117].
- Inventory
systems - training, lecturing and
supervising graduated projects for
students in economics at Economical University of
Sofia. Publications [10,21,44,47,59,67,72,85,96,112], and the
textbook [6] are results of my work in this
area.
- Reliability
studies - theoretical and practical
works related to redundancy systems [2,3,4,6,7,11,19,117],
statistical criterions for testing hypotheses in
view of the specific information from reliability
data [28,29,37,50,53,59,83,96]; optimization
problems when work with non-reliable servers and
other items were mentioned in the Applications of
the Queuing Theory above. The new stuff
essentially is concentrated on the introduction
of models with check-points that may save
execution time, the use of methods of
discretization, the selection of specific
statistical methods for standardized use, and the
new point of view on reliability systems with
random redundancy introduced in [91,117],
important for communication systems and
computer networks. The development of
standardization
documentation
for practicing reliability and specialized
computer packages for purposes of the Applied
Statistics was actively made in years, and
reflected in the papers
[53,58,59,62,72,76,83,112]. In addition, most of
my works in Statistics are related with the
respective practical reliability problems
[28,29,37,50,53,58,83].
D. Warranty
Analysis.
- Probability
Models in Warranty Analysis (with Dr.
S.Chukova), is
an approach to incorporate the qualitative and
quantitative marketing,
technical and economical product characteristics in an
integrated model and
objective function to determine the optimal
behavioral parameters of the
corresponding models and processes in
real world systems. It has
been started by Grant 43 - 87 of Bulgarian Science
Foundation, and still
continues. The works in the field of reliability, noticed
above, and the specific works in this field
[77,89,90,94,108,110, plus the Dr. Chukova's works]
brought us to the collaboration with world known experts
like V. Rykov [94], W.Blischke and D.N.P.Murthy (BOOKS #
10, and [108]). Recently an unexpected relationship
between warranty modeling and studies on probability
distributions in periodic random environment is noticed
[90,114,116], and promise good field of application for
our class of Almost-Lack-of-Memory probability
distributions. In this way, the processes used in
warranties, and environmental and financial processes in
the insurance mathematics will
be linked, and many
problems may mutually gain from the solution for the
others. The work continues in collaboration with
colleagues and graduate students from Concordia
University, Montreal on projects for Cost
Analysis in Related Models.
E.
Environmental Studies.
My interests on
Environmental Probability and
Statistical Models
and methods of their study were
initiated. Modeling for
periodic random
data related to water pollution and statistics
for parameters
of Probability Distributions
with Almost lack of memory property for Studying
Environmental Properties, had
proved fruitful in most of the work of myself and
involved other
colleagues. Here belong the most resent papers
[88,90,92,98,103,105,107,109,114,115,116,117].
Statistical Studies.
Related to
Standardization, Applied Statistics, Reliability and
Quality
- The work on Standards
in Applied Statistics, StatisticalMethods
in Reliability and Quality Control brought
to me a lot of practical
experience (1975-1991). Being head of the Laboratory
on Statistical Quality
Control we developed International (for the
former "East
Countries"), and National (for Bulgaria) Standards
as follows: Standards
on Applied Statistics(e.g.
Probability Distributions for Applied Statistics, Regression
Analysis, Methods of comparing statistical samples), Standards
on Reliability (e.g. Estimations of reliability characteristics,
Terminology and Symbols, Design of experiments and testing, Tolerances
and admissibility),Standards on
Statistical Quality Control (SQC)(e.g.
terminology and symbols, Statistical estimations of
quality parameters of the outgoing production, Methods of
statistical sampling from bulk products, Methods of
statistical on-line control) and other documents related
to the standardization. I wrote methodic (documentation)
for practical implementationof the standardized
mathematical methods, algorithmic and computational supervision for
these methods. Computer programs for SQC, Reliability and
Applied Statistics have been created in support of these
practically directed works. My Ph.D. student Dimitar Christozov got his
degree for the successfully developedprogram
package RELIA-SOFT, where reliability
characteristics are estimated from experimentally
collected data, and/or field data for item performance.
Also Grant #43 (1987-1991) with Bulgarian Science
Foundation was awarded in relation to this subject, and
involved more researchers in this work. Many of my
publications in this field were related with the needs of
specific standardization requirements, and with the
statistical establishment when these requirements are
met. These are the publications from the list
[28,29,37,50,53,55,58,83 - for reliability], and
[43,50,53,58,59,61,62,69,72,76,83,112 - for quality].
Among the papers related to reliability I would like to
mention [50] and [55] where the statistical estimators
proposed have the shape of the theoretical intensity
function, as stated in the original problem.
- Studies on Statistical
Optimization Problems underIncomplete
Information [67,87,109]. This topic appeals
to a resurrection of the known Markov-Tchebyshev moment
problem in the construction of probability measures, and
is one of the prospectives for research in the nearest
future. Moreover, it has a clear connection with the
construction of an Integral Indexes for the Quality of
Products (started in [63] with M.Varbanova, I.Stefanov
and L.Boneva and continuing be developed in [112]),
Contract with INFORMA
and the Laboratory of Statistical Quality Control
initiated this work, but it is also a good field for
further studies. The
recent Wuerzburg Workshop (March '99) has shown the
actuality and importance of this direction.
IMPACT OF THE
RESEARCH ON CURRICULA
AND/OR STUDENTS
Research
related to my teaching.
University
Textbooks combine teaching and research
experience.
- After years of
teaching and practicing Statistics I wrote the book Mathematical
Statistics, 1982 (see BOOKS # 5) and the statistical part of the
textbook Probability and Statistics for students of natural
science at Bulgarian universities (see BOOKS, # 9, and #
12). Another textbook Statistics for non-mathematical
students with an emphasize on
statistical models and manipulations for non-numerical
data is issued at
Southwestern Bulgarian University in Blagoevgrad in 1993 (see BOOKS #
10). Also my teaching courses on Markov Processes at the
University of Sofia for students in mathematics lead me
to the book # 3, and the courses on Inventory Models and
Quality Control for graduate students and post-graduate
students at the University of Economics and World Economy in Sofia
lead me to the writing of the books # 6 and # 7.
- Work on the
Curriculum for university students
is a collective work.
- While heading the
Department of Probability and Statistics at the Faculty of
Mathematics and Informatics at Sofia University (and 2 years as Dean of
the Faculty) Computational Stochastics was added to the curricula
for students and specialization at the Department was
introduced. And it was result of the collective work of
all members of the Department. Also curricula for other
specializations in mathematics have
been work out (Informatica, new specializations in
Mechanics, Post-university education for high-school
teachers), and this was result of the work of all
departments and of the Faculty Senate.
Warranty models for
complex technical items are
field of my new interests too.
The PhD thesis work of my
student, now colleague, Dr. S. Chukova and my
collaboration with her gave the result [Books # 11],
which is very useful for thesis work of graduate students
in Engineering. High-school
Textbooks reflect some teaching
experience and personal feeling of the need.
- Through my textbooks
for high school students (listed under
# 13-17), basic
statistical aspects were introduced to high school
students for the first
time in Bulgaria.
Teaching
and consulting Statistics, Modeling, or SQC at the
University.
- During my first
visits at Concordia University I taught
Industrial Statistics
and Quality Control, and worked under
Contracts with the Center for
Building Engineering, where I worked out methods
for Statistical
simulation of dependent random components in
cost analysis
problems (ref. to Dr. Z. Khalil, and
Dr. Osama Moselhi, Tel. (514)
848-3190). Also a model for
Statistical factor analysis of
real data was
explored. Add
here my teaching experience with students of the
specialization Probability and Statistics, the teaching
of Quality Control, Reliability and Operations Research
for students at the Division for Post-Universityy Education and Training of the
Economical University of Sofia, my long term tenure as a
head of the Laboratory on Statistical Quality Control,
the work experience with International Standardization
Organization, etc., and you'll understand what brought me
to the idea to open The Statistics Clinic at Kettering
University for free statistical consulting. It was open
in the Fall of 1998 at the Science and Mathematics
Department of Kettering University.
Here I work with
computers and use almost any available statistical
package in my Statistics Clinic, to serve as a consulting
office for students, faculty and staff at Kettering
University. It really gathers my experience in teaching,
theoretical and practical work in years, and also offers
(sometimes) new challenging problems to think on. Here
also some software I developed for myself in
collaboration with Dr. D. Christozov and other colleagues
from Bulgaria is
available to be demonstrated.
Ph.D.
THESES ADVISED
- Priority
queues with finite sources and priorities (Dr.
Khristo Karapenev). Optimal control of the
service in systems with unreliable server (Dr.
Krasimir Barosov). Numerical approaches in the
study of queuing systems with priority, based on
time and phase
Discretization (Dr. Chavdar Dokev). Minimization
of the total processing time in non-reliable process
with implicit or explicit breakdowns and repeat
actions (Dr. Nikolai Kolev). RELIA - SOFT program
system for computing the statistical
reliability of operating products (Dr. Dimitar
Christozov). Optimization of the inventory
characteristics under incomplete information (Dr.
Tran Zoan Fu). Optimal control of
Winner processes with external actions (Dr.
Mariana Beleva). Methods of discretization
in the study of queuing systems with unreliable
server and
priorities (Dr. Petko Ruskov). Probability models
in Warranty Analysis (Dr. Stefanka Chukova).
Informative parameters in quality studies (Plamen
Petrov), others.
Ph.D.
students: Krasimir Barosov, Dimitar
Christozov, Tran
Zoan Fu,
Mariana Beleva, Nikolai Kolev, Tchavdar Dokev.
Master students: At Concordia - Laila De Normand and Faiz Ahmad,
and many more back to Bulgaria.
COLLABORATION
WITH OTHERS
Within
the Department
At the SM
Department of Kettering University I enjoy the
collaboration in almost all the areas of my
research with Dr. Stefanka Chukova, in the area
of Queuing and Production Modeling with Dr.
Srinivas Chakravarthy, and in the area of
Characterization by analytical means and
Optimization (where mostly the technique of
differential equations is involved) with Dr.
David Green, Jr. Our joint publications in the
resent years may give the evidence for the
results of this collaboration. This collaboration
is an important part of the surrounding that
makes me feel better and provides conditions to
do research in the frame of very limited time
left from our duty to teach much more than
colleagues from other universities do.
Within
the Institute
The Statistics
Clinic is a good source of contacts with
colleagues from other departments at Kettering
University, to help them in solving their
particular problems, and to start working on
prospective joint projects. In this way a
fruitful collaboration with Prof. Etim Ubong from
the Department of Mechanical Engineering, was
initiated in 1998, and some results on Design of
Experiment (DOE) for a study of the fuel control
of a V-6 Buick motor engine have been obtained. A
Technical Report is expected, and a paper is in
preparation for our findings. One of the most
important discovery was that the left bank of
this motor is poorly fuel-fed than the right
bank, no matter what the fuel speed or load is.
This collaboration continues with other projects
involving statistics, or DOE in the work of an
engineer researcher.
With
researchers outside the Institute.
I like work in
collaboration with others. It helps me
immediately to adopt the current issue, to get a
new challenging idea, or just an appeal, to share
immediately my results with the closest expert in
the field. It started with the collaboration with
Dr. Eduard Danielyan during my PhD work in
Moscow, Russia, it continued with the
collaboration with many others, it continued in
Bulgaria in closed collaborative work with my PhD
students Khristo Karapenev, Chavdar Dokev, Kosta
Yanev, Nikolai Kolev, Tran Zoan Fu, and to
certain extend, with Dr. Chukova. This
collaboration gave lots of results in my work
with the colleagues Apostol Obretenov, Svetlozar
Rachev, Maria Varbanova, Ivan Mirazchiiski,
Liliana Boneva, Nikolai Yanev, Gero Gerov,
Zaprian Zaprianov, Elena Karashtranova, and
others. Thanks to them I always felt the
friendly, nice and productive environment a young
researcher needs in his or her career,
especially when starting and gaining experience.
The closeness
of my research interests with to those of
researchers from other institutions and the
occasional contacts with some of them at
International meetings gathered me with
professors Zohel Khalil and Jose Garrido from
Concordia University in Montreal, Canada, with
Prof. Jean-Pierre Dion from Universite de Quebec
a Montreal, with Prof. Elart von Collani, from
Wuerzburg University in Germany, with Prof.
Mohammed El-Saidi from Ferris State, Big Rapids,
Michigan. Discussions, contacts, live interest to
the subjects gave results in a series of joint
publications with these researchers. I thank all
of them for the good collaboration, for the
mutual respect and permanent support and interest
in what we were doing, and in what we project to
do in the nearest future. Especially I like to
thank colleagues from Montreal for their constant
initiatives during the years and for the support
they gave in the periods if time I needed at
most.
PROFESSIONAL
ACTIVITIES
Reviewer
of dissertations on Applied Probability and Applied
Statistics, Stochastic
Processes, Reliability, Queuing, Quality Control, Education in
Stochastics and others.
Cchairman of
the National Stochastic Seminar at the Union of the Bulgarian
Mathematicians, 1979 - 1991. Associate
Editor of "ECONOMIC QUALITY
CONTROL" - Journal and Newsletter for Quality
and Reliability with managing Editor Prof. Dr. Elart von Collani,
Inst. fur Angewandte Mathematik und Statistik, Sanderring 2,
D-8700, Wurzburg, GERMANY. Dean of
the Math. Faculty at Sofia University, 1989 - 1991.
Head of
the Department of Probability and Statistics, Math. Faculty at Sofia
University, since 1989.
Awards: Bulgarian Committee of
Sciences, Grant 43 - 87, 1987-1991. Mathematical
methods for quality control and reliability
studies; Also Grands
with Bulgarian Council of Higher Education,
1988 - 1990
(Statistical methods in quality control);
With the National
Bulgarian Science Foundation,
Grant MM 60 - 91, (Risk
theory and applications).
New Faculty Development
Grant (NFPDG 160009) at GMI 1995 - 1997.
Granted proposal for an
Applied Mathematics Computer Laboratory
at Kettering
University, August - September 1996, in collaboration
with Prof. Joe Salacuse
from SM Dept. The Laboratory started in July 1997.
REFERENCES
Prof.
Jose Garrido, Dept. of Math. &
Statist. Concordia Univ.,
7141 Sherbrooke
Str. West, MONTREAL H4B 1R6, CANADA,
Tel.(514)848-3252
(office) and (514)747-7026 (home).
e-mail:
GARRIDO@VAX2.CONCORDIA.CA Prof.
Atanas Radenski, R. J. Reynolds
Professor of Computer Sci.
Dept. of
Computer Science, Winston-Salem State University,
Winston-Salem,
North Carolina 27110,
Tel. (919)750-2480, e-mail:
RADENSKI@RAMSUN.ACC.WSSU.EDU Prof.
Spiridon Penev, School of Mathematics,
Dept. of Statist.
The Univ. of
New South Wales, P.O.Box 1, Kensington NSW 2033,
Australia. Tel.
(612)697-2693 (home); (612) 398-8162 (office).
e-mail: spiro@hydra.maths.unsw.edu.au, Prof.
Vladimir Tonchev, Dept. of Math.
Sciences College of
Sci. &
Arts, Michigan Technological Univ., 1400 Townsend
Drive,
Houghton, MI
49931-1295, (906) 487-2068 e-mail:
TONCHEV@MATH.MTU.EDU Prof.
Jean-Pierre Dion, UQAM, Dept. of Math.,
Montreal,
C.P. 8888,
Canada H3C 3P8; Tel. (514) 987-6166 (office);
(514) 671-2423
(home). e-mail: DION@MATH.UQAM.CA Prof.
Zohel Khalil, Dept. of Math. and
Statistics, Concordia,
Tel. (514)
848-3247 (office); (514) 697-6681 (home).
e-mail:
KHALILZ@VAX2.CONCORDIA.CA