**K.D. Tarkalanov's publications**

The corresponding titles from this list are also inserted directly into each one of the Research and the Teaching Statements. Some of these titles are supplied with an entire text or with detail abstracts. Others, for which there isn't an English text, are reflected in the first ones and so a sufficient integral description of the scientific and methods achievements is in one's disposition. A considerable part of
the scientific publications (marked additionally with [T1-27], [TK],
and [T-J] in this __List__) are already systematized in **[**42**]** (please see its blurb
there). The author could submit for a temporary official
purpose-oriented not commercial using a variant of the monograph at
an eventual request for that. Scanned pages of the remaining a few
papers which are not in English could be send at a request. Not all talks over the publications are covered in this list.

*Publications based upon dissertation research:*

* *

**[**T12**] **1W . *A Class of Partially Ordered Semigroups with a Solvable Inequality Problem***, Comp. Rendus de l'Academie Bulgare de Sciences,** t. 23. N 2 (1970), 129-132 ( in Russian).

*The idea is developed in # 4, # 12, # 22, # 23. It is reflected in # 30.*

* *

**[**T15**] **2. *On Partially Ordered Semigroups and Groups which are given with Determining Inequalities without Cycles*, **Math. Balk**. ( Beograd ), 4.116 (1974), 601-604 ( in Russian).

**[**T16**] **3. *On Partially Ordered Semigroups and Groups which are given with Determining Inequalities without Cycles***, Work Collection of the young scientific workers and students**, Plovdiv University, N 2 (1974), 203-206 ( in Bulgarian, Russian and German Summaries).

**[**T13**] **4W .* A Solution of the Inequality Problem in a Class of Partially Ordered Semigroups according to the Ossiipova's Method*, **Travaux scientific de l'Ecole Normale Superieure **"Paissii Hilendarski" - Plovdiv ( Bulgarie ), v.9,f.2 (1971)- Math., 37-43 ( in Russian, French summary).

*See # 30 please.*

* *

**[**T14**] **5W .* On the o-Isomorfism and Broken Line Problems and the Applicability of the Algorithm for Divisibility*,

a**) Dikladi Akademii Nauk** **Ukraine SSR,** A, N 6 (1976), 502-505 (in Russian, English summary),

b)** Dopovidi Akademii Nauk Ukraine SSR, **A, N 6 (1976), 501-504 (in Ukrainian, English summary),

c) *Authoreferat,* **Zbl.f. Math. u. ihre Gr**., N 338, 02027, s.16 (in English).

*You could see, or print, or save and print after that its text from*__e1-3__.

6W . *On the Recognition of the Applicability of a Certain Algorithm for Divisibility***, Travaux scientifiques de l'Universite de Plovdiv** ( Bulgarie ), v.12, N 1 (1974), 163-168 (in Bulgarian, Russian and French summaries).

7. *To the Divisibility and Word Problems for Semigroups with one Irreducible from left determining Relation*, **Collection Mathematika i matematichesko obrasovanie** (Collection Mathematics and mathematical Education, Reports of the 3rd Spring Conference of the Bulgarian Mathematical Society ), Sofia, Bulg. Ac. of Sc. (1976), 282-285 (in Bulgarian, Russian and German summaries).

**[**T1**] **8. *Strong Homomorphism of a Partially Ordered Group over another***, Travaux scientifiques de l'Ecole Normale Superieure** " Paissii Hilendarski " (Plovdiv, Bulgarie ), v.6, f. 1 (1968), 27-32 (in Bulgarian, Russian and German summaries).

*The idea is generalized in # 16: a persistence of the predicates in a reverse direction.*

**[**T19**] **9. *On Strongly Monotonously Homomorphic Images of a Partially Ordered Group***, Natura, ENS** (Plovdiv, Bulgarie), t.III, f. 1 (1970), 13-16 (in Russian, French summary).

**[**T20**] **10. *Strongly Homomorphic Images of the Partially Ordered Direct Product of Two Groups*, **Travaux scientifiques de l'Ecole Normale Superieure** " Paissii Hilendarski " (Plovdiv, Bulgarie ), v.8, f.1 (1970), 25-31 in Russian, French summary).

**[**T3**] **11*. The Context-free Languages and some Questions from Semigroup and Group Theory*, **Annals Union of the Scientific Workers in Bulgaria**, Br. Plovdiv, A Scientific Session of the young Scientific Workers, 1979(1980), 131-142 (in Bulgarian).

*Parts of this paper are included in # 30. They are well grounded from a methodological point of view in # 21.*

* *

**[**TK**] **12*. Partial Order and Algorithmic Problems in Semigroups and Groups***, Executive Summary of Ph.D. dissertation**, Bulgarian Academy of Sciences, Institute of Mathematics, Sofia - 1977(1978), (in Bulgarian).

*Parts of the Summary are included in # 30.*

**The scientific results included in the dissertation were reported at the International Conference in Partial Ordered Sets in Brno
(Czech republic, summer 1974), during the author’s specialization with a
Certificate in Theory of Languages and Programming at the Department of
Cybernetics of the Kiev University (Ukraine, then in USSR, spring 1976)
at the following seminars: the Seminar in Algebra at the Ukrainian Academy of Science (with a Leader then the Corresponding Member of the Academy Chernikov), the Seminar in Mathematical Logic at the Department of Mathematics of the Kiev University (with a Leader then Prof. Kalujnin), the Seminar in Algebra at the Department of Cybernetics of the Kiev University (with a Leader then Prof. Charyn), the Seminar of Theory of Languages and Processors at the Department of the Cybernetics of the Kiev University (with a Leader then Prof. Red’ko and with a Scientific Secretary then Prof. Anissimov), after that at the National Colloquium in Algebra (Rodopi mountain, Bulgaria, fall 1976) and at the National Seminar in Mathematical Logic of the Mathematical Institute of the Bulgarian Academy of Science (Sofia, Bulgaria, winter 1978).**

** **

** **

*Publications not based upon dissertation research:*

* *

**[**T17**]**** **13. a)* **Words in a Strongly Normal Form, Stable Congruence in a Free
Semigroup and Topological Sorting Performed by Determining Correlations
on Parts of the Word*,** International Congress of Mathematicians (August,
3-11, 1986, Berkeley, California, USA), Abstracts**,

*You could see, or print, or save and print after
that its text from *__e2-2__.*See # 20 also.*

b) *Words in a Strongly Normal Form, Stable Congruence in a Free Semigroup
and Topological Sorting*, **Modeli i sistemi obrabotki informatsii**,
Kiev University Publishing House " Vistcha Shkola ", Republican Interdepartamental
Collection, Ukraine SSR, vyp. 7 (1988), 23-28 (in Russian).

**[**T4**] **14*. Invariant Decoding Automata, Strongly Regular Vocabularies and Solvability of Algorithmic Problems in Semigroups***, Scientific Works of the Higher Popular Military School** " Vassil Levski " (Veliko T"rnovo, Bulgaria), Book 2 (1982), 143-150 (in Bulgarian).

*See # 30 please.*

* *

*
*

**[**T21**] ***15.** Over Some Questions of Context-free Languages in a Double Alphabet
and of Group Calculations*

a**) Sixth Congress of Balkan Mathematicians**, June 3-9, 1977, **Abstracts**,
p. 247 (in German).

b**) 9th Youth Symposium with International Participation**, May
17-19, 1977 (Plovdiv, Bulgaria), Abstracts, p. 48 (in Bulgarian).

c) **Work Collection of the Young Scientific Workers and Students**,
Plovdiv University (Bulgaria), N 5 (1977), 35-41 (in Bulgarian, Russian
and English summaries).

*You could see an abstract of a talk at the *__Logic__*
seminar over its part about group calculations.*

**[**T18**] **16. *Powerful Homomorphism of One Algebraic System Over Another Algebraic System*

a) **Vortragsauszuge und Teilnehmer verzeichnis der Wissenschaftlichen Jahrestagung **vom 9.-14.02.1970 (Mathematische Geselschaft der DDR), s. 55 (in German).

b) **Natura,** ENS (Plovdiv, Bulgarie), t. IV, f. 1 (1971), 5-8 (in German with Russian summary).

*The idea of a persistence of the
predicates in a reverse direction is well grounded from methodological
point of view in # 21. It is a generalization of that one in # 8. It is
more developed for ordered group in # 9 and # 10.*

* *

**[**T23**] **17.* **Some Questions from Pair Algebra and from Consecutive Machines*,**Annals Union of the Scientific Workers in Bulgaria**, Br. Plovdiv, A
Session of the Young Scientific Workers,

*A part of this paper about factor automata is reflected
in a *__talk__*
(you could read its text *__only__** )**.

* *

**[**T25**] **18*. Retaining the Properties of the Invariant Decoding Automata
without Overtaking after their Homomorphic Displaing and Consecutive
Connecting*,

a) **Second International Conference on Discrete. Mathematics and Applications**, Blagoevgrad (Bulgaria), June 5-10, 1990, Abstracts, p. 31-32 (in Russian).

b) **Year-book of Higher Pedagogical Institute - Blagoevgrad** (Bulgaria), Department of Mathematics, Physics and Chemistry. Mathematics, v. VII, b. 2 (1990), 82-87 (in Russian).

*Parts of this paper are reflected in # 30. A changed title of this publication is included in the Web site http://home.swu.bg/shtrakov/icdma/icdma2/index.html .*

*
*

**[**T24**] **19. a)* Homomorphisms of Semigroup-Automata and those of their State-Semigroups*,

*You could see, or print, or save and print after
that its text from *__e5-01__*,*__e5-02__*,*__e5-03__,__e5-04__*,*__e5-05__,__e5-06__,__e5-07__,__e5-08__,__e5-09__,__e5-10__.* It has been reflected by Zentralblatt in Section 20M35 (Semigroups in Automata Theory, Linguistics, etc.). *

b) *Coincidence of the Splittings of the State-Group of a Strongly
Group-Automaton with its Decompositions in Co-classes Concerning its Subgroups,***
International Congress of Mathematicians** (August 21-29, 1990, Kyoto,
Japan ), **Abstracts**, p. 239 (included in (a) above).

*You could see, or print, or save and print after
that it from *__e4-2__.

**[**T27**] **20.* Utilisation of Push-down Store Automata for Reducing a Word to
its Only One Strongly Normal Form which is Equal to the Initial One in
a Semigroup with a Partial Commutativity*,** Collection of Scientific
Works: Anniversary Scientific Session,** 35 Years Technical University in
Varna

**You could see itstext. **

**[**T5**] **21. *Study of the Prototypes in my Mathematical Works .*

**The publication is marked in the french catalog "SUDOC". Both 21. and 27. are included in a french reference indication.**

**[**T-J**] **22W
. - Co-authored with St.D. Jeleva (second author*), To the Problem of the Inequality for Partially Ordered Semigroups, Part I*, **Travaux scientifiques de l'Ecole normale superieure** " Paissii Hilendarski " (Plovdiv, Bulgarie), v. 9, f. 3 (1971), 25-32 (in Bulgarian, Russian and German summaries).

**[**T-J**] **23W
. - Co-authored with St.D. Jeleva (second author*), To the Problem of the Inequality for Partially Ordered Semigroups, Part II***, Travaux scientifiques de l'Universite de Plovdiv**, (Bulgarie), v. 10, f. 2 ( 1972), 9-14 (in Bulgarian, Russian and German summaries).

24. - Co-authored with ½__Chr. Dimov½__(second author) , *Coordinated Module Homomorphisms*,

a)** 10th Anniversary Youth Symposium with International Participation**, May 19, 1979, Plovdiv (Bulgaria),** Abstracts**, p.39 (in Bulgarian).

b) deposed in the Organizing Committee ( according to the regulation - five pages in Bulgarian).

25*. Algebraic Properties of Power Series Modules and Rings***, Travaux scientifiques de l'Universite de Plovdiv** " Paissii Hilendarski ", (Bulgarie) - Math., v. 19, f. 1 (1981), 17-25 ( in Bulgarian, Russian and German summaries).

26*. A Criterion for Completion of the Work of a Program, Represented
by an Oriented Graph. A Mechanical Solution of Another Problem of Artificial
Intelligence Concerning the Banana***, First. International Conference
on Discrete Mathematics and Applications, **December 03-06, 1987, **Year-Book
of Higher Pedagogical Institute** - Blagoevgrad (Bulgaria), Department
of Polytechnical Education, Mathematics, v. IV, b. 1 (1987), 71-79 (in
English, Russian summary).

*You could see, or print, or save and print after
that its English text from *__e3-02__,__e3-03__,__e3-04__,__e3-05__,__e3-06__,__e3-07__,__e3-08__.

**[**T7**] **27. *Number Theory in Science of Logic by Hegel***, Collection Philosophie et Mathematiiques. Seminaire de l'Ecole Normale Superieure** **- **Paris,
Edite par l'I.R.E.M. Paris-Nord, Universite Paris XIII, N 66 (1990), 7
pages, ISBN: 2 86240 566 8, ISSN: 0294-6777 (in French).

**You could see here the ****announcement**** for this Conference which has been posted at ENS-Paris. The publication is marked in the french catalog "SUDOC". It is indicated in a**

**[**T9**] **28*. Substantiation of the Real World Fundamental Mathematical Models
Following Hegel's Reflexive Way***, Collection of Scientific Works:
Anniversary Scientific Session, 35 Years Technical University in Varna**
(Bulgaria), October 16-18, 1997, **v. 5**,** **Varna** (2001)**,
9-16.

*You could see its *__text__.

**[**T8**] **29. a) *Reflexive Substantiation of One-Way Ascendancy of Mathematics Over Ethics*, **PAIDEIA Twentieth World Congress of Philosophy**, Copley Place Boston, Massachusetts USA, August 10-16, 1998, **Abstracts**, p. 197.

b) *Reflexive Substantion of an One-Way Ascendancy of Mathematics over Ethics*, **The Paideia Project: Proceedings of the Twentieth World Congress of Philosophy**, Boston, Massachusetts, USA, August 10-16, 1998, __http://www.bu.edu/wcp/Papers/Math/MathTark.htm__ (February 11, 2000) or through __http://www.noesis.evanswille.edu/Author_Index/T__
.

** **

**It
could be reached also through the Schedulehttp://www.bu.edu/wcp/MainMath.htm of the Philosophy of Mathematics Section of the World Congress of
Philosophy.**

** **

**[**T10**]**** **37. *A Common Reflexive Basis for Studying the Degree of Certainty of Mathematical Models*, **Northeastern Section of the Mathematical Association of America, Fall 2006 Meeting**, November 17-18, 2006, Sacred Heart University, Fairfield, Connecticut, **Contributed Papers Session III, Abstract** (__4__
) or

http://faculty.sacredheart.edu/molitiernoj/nes/faculty_abstracts

**Another
information about this talk appears at http://www.providence.edu/mcs/fpf/maa/spr07/full.pdf, p. 9.**

** **

**[**T11**] **38. **a) ***Arithmetical Rules fir Rising the Chromatic and
Diatonic Scales, the Musical Circle of the Fifths, and for Rotation in
the Basic Chords*, **Northeastern Section of the Mathematical Association of America, Fall **__meeting__** ~ November 16-17, 2007, Framingham State College, Contributed Paper Session**, Abstracts, __p. 13__. or __http://www.framingham.edu/faculty/smabrouk/Nes_maa/Fall_2007/Program/doc/Contributed_Papers.pdf__

*You could read here this abstract in *__htm__* format, see a geometrical interpretation of diatonic and chromatic scales from the paper, and to read its entire text in *__pdf__* format.*

*Author owns a video clip of this presentation. You could read the *__projected__* text and hear *__his__*
voice from it (it is still not enough laud and needs some amplifying).
You could figure out which parts of the this text have been
consecutively shown then on the screen, when a *__geometrical__* interpretation has been used, and when a piano *__board__*
image with sound has been shown for a demonstration of the rules for
receiving piano chords. It is impossible for now to upload the clip here
due to its size but you could see a photography *__which__* has been shot from its beginning.*

*One more methodical exposition of its directed
to the synergetic and reflective aspects of the treated problems about
rising the diatonic scale from the chromatic one in only one way, about
the musical circle of the fifths and the rules for rotation in the basic
musical chords is realized in [*__38b__*].*

* *b)* Methodical
Arithmetical Justification of Rising the Chromatic Scale and Inversely
of the Diatonic one from It, of the Rules for the Musical Circle of the
Fifths, and for Rotation in the Basic Chords***, **in** Synergetics and Reflection in Mathematics Education, Proceedings of the Anniversary International Conference** Celebrating Prof. Sava Grozdev's 60th Anyversary, September 10-12, 2010, Bachinovo, Bulgaria, University Press "Paissii Hilendarski", Plovdiv (Bulgaria),

**You could read the projected text and hear the voice from its presentation. Another information about the Conference and this presentation could be found in http://www.cphpvb.net/other/6417-photos-from-srem2010 . **

** **

**[**T6**]**** **30. a) *Connecting Algorithmic Problems in Semigroups with the Theories of Languages and* Automata, **Studia Univ. "Babesh-Bolyai", Mathematica, v. XLIV, No 1**, March **1999**, 95-100.

You could see here consequently its pages __95__, __96__, __97__, __98__, __99__, and __100__.*This
paper reflects parts of papers 1, 4, 14, 11, 12, 18, and 17. It has a
conceptual relation to 21 and 19. It has been reflected by Zentralblattin Section Computer Science (68Q70 Algebraic Theory of Automata).
*

b) *Connecting Algorithmic Problems in Semigroups with Theories of Languages* *and* *Automata*, **Collection of Papers Presented at the Jubilee Scientific Session** (1998) **of** **the Union of the Scientists in Bulgaria - Branch Plovdiv**, **Academic** **Publishing House of** **the Higher Institute of Agriculture - Plovdiv (Bulgaria), 1999**, Volume Three, **Section:** **Natural Sciences**, 121-124 (in Bulgarian, English Summary).

*You could see an enlarged text *__in English__. *This
paper reflects parts of papers 1, 4, 14, 11, 12, 18, and 17. It has a
conceptual relation to 21 and 19. There are obvious very small
corrections of the indexation at the HTML formatting. It is possible to
receive scanned pages at a wish.*

**[**T26**] **31. a) *Homomorphisms of the Free Semigroups of Program Models Induced by an* *Insertion of Equivalencies in Their Common Operator Symbols Semigroup*, **2001 Greater** **Boston Logic Conference**, **Massachusetts Institute of Technology**, May 11-13, 2001, **Section: Abstracts of the Contributed Talks**.

b)

*You can see the scanned pages *__26-27__, __28-29__, __30-31__** of this publication**

* *

**[**T22**] **36. *Prefix-Free Languages, Simple Grammars Representing a Group Element, Languages of Partial Order in a Group*, **Studia Univ. Babes-Bolyai, Informatica, Volume LI, ** **Number 1, 2006**, 59-68. __http://www.cs.ubbcluj.ro/~studia-i/2006-1/07-Tarkalanov.pdf__

**Its abstract has been used as a revue in MR and in Zentralblatt this time in Section Computer Science (68Q45 Formal Languages).**

**Its abstract appears also at http://www.studia.ubbcluj.ro/arhiva/abstract.php?editie=INFORMATICA&nr=1&an=2006&id_art=3026.**

**An information about its appearance is athttp://www.studia.ubbcluj.ro/arhiva/autori_art.php?id=2604&name=KRASSIMIR%20D.%20TARKALANOV too.**

** **

**[**T2**] **41.* Comparing Entire Prototypes at Semigroup Homomorphisms and Specifically at Regular Languages Substitutions*, in** Research and Education in Mathematics, Informatics, and their Applications **REMIA 2010, **Proceedings **of the Anniversary International Conference. Dedicated to the 40th Anniversary of the Faculty of Mathematics and Informatics, Plovdiv University, 10-12 December **2010**, Plovdiv, Bulgaria, Published by University Press "Paissii Hilendarski", Plovdiv (Bulgaria), 201-207. (ISBN: 978-954-423-648-9, 492 pp); http://www.fmi-plovdiv.org/GetResource?id=470 or through http://sci-gems.math.bas.bg/jspui/handle/10525/2103/browse?type=author&order=ASC&rpp=95&value=Tarkalanov%2C+Krassimir

**You can hear the voice from the corresponding clip and read the colored text for this presentation. **

* *

42.* Structural Prototypes, Language Prototypes and Algorithmic
Problems*, **LAMBERT Academic Publishing AV Akademikerverlag**
GmbH& Co. KG Verlag, Saarbrücken **2013**, ISBN:
978-3-659-50320-7, 168 pp. Information at

https://www.lap-publishing.com/catalog/details//store/gb/book/978-3-659-50320-7/structural-prototypes,-language-prototypes-and-algorithmic-problems , at__http://www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Dstripbooks&field-keywords=Krassimir%20Tarkalanov__ ,
etc.

**BLURB**:
The monograph can be used for different tasks - from student special
courses to a basis for further research. It presents a significant
part (NB:**[**T1-27**]**, parts of __[__TK**]**, **[**T-J**]**)
of the author's papers. The results were reported at scientific
conferences and congresses. Their formal or semantic connection is
indicated. They are united by a study of prototypes at structure and
automaton homomorphisms. The most original of the methods for that
are grouped into an initial section with indications of their
distribution to the separate chapters and sections. This approach
allows a philosophy of science and mathematical motivation,
substantiation, and advanced indication of the advisability of the
received results. They unite different mathematical subjects from
Logic, Algebra, and Theoretical Computer Science. This task is
difficult, motivated and requires original approaches. One of them is
the realized connection between solving algorithmic problems in
Theory of Semigroups and Theory of Languages on the basis of a study
of language prototypes. Prototypes of concepts with an important role
in Computer science are also studied.

**VITA**:
Krassimir Tarkalanov, PhD, Bulgarian Assoc. Professor in Math Logic.
Textbook. A manual as an Adjunct Professor in US. Teaching method -
activating dialog. The publications connect different subjects in
Logic, Algebra, Computer Science and are substantiated as a returning
to prototypes. Conferences. Collaborator, TJX Companies, Framingham,
MA, USA.

**SUBJECT
CLASSIFICATION:**

*The
2010 AMS Mathematics Subject Classification*:** 01-02**
Research exposition (monographs, survey articles): **00A30,****03A10, 03C95, 03D03, 03D05, 03D40, 03E02, 06F05, 06F15, 20M05,
20M15, 20M35, 20F10, 08A30, 68P30, 68Q42, 68Q45, 68Q70, 68R10, 68R15,
00A65**; etc.

**00A30**Philosophy of mathematics,** 03A10** Logic in the philosophy
of science,** 03C95** Abstract model theory,** 03D03** Thue and
Post systems, etc., **03D05 **Automata and formal grammars in
connection with logical questions, **03D40** Word problems, etc. ,**03E02** Partition relations, **06F05** Ordered semigroups and
monoids, **06F15** Ordered groups, **20M05** Free semigroups,
generators and relations, word problems, **20M15** Mappings of
semigroups, **20M35 **Semigroups in automata theory, linguistics,
etc., **20F10** Word problems, other decision problems,
connections with logic and automata,** 08A30** Subalgebras,
congruence relations, **68P30** Coding and information theory
(compaction, compression, models of communication, encoding schemes,
etc.), **68Q42** Grammars and rewriting systems, **68Q45**
Formal languages and automata, **68Q70** Algebraic theory of
languages and automata,** 68R10** Graph theory, **68R15**Combinatorics on words, **00A65** Mathematics and music; etc.

*The
1998 CR Categories and Descriptors:*** F.4.2 [Grammars and Other
Rewri-ting Systems]**: Decision problems, Grammar types, Thue
systems;** F.4.3 [Formal Languages**]: Algebraic language theory,
Classes defined by grammars or automata, Operations on languages;
G.2.1 [Combinatorics]: Combinatorial algorithms.

*The
2012 ACM Computing Classification System toc:*
Theory of computation-Formal languages and
automata theory-Formalisms-Algebraic language theory, Rewrite
systems; Theory of
computation-Formal languages and automata
theory-Grammars and context-free languages, Regular languages;
Mathematics of computing-Discrete
mathematics-Graph
theory-Trees.

**A more
detailed information about the content with an indication of the
included in it papers and entire references can be found in**** [42]****. The
author could submit to an Institution for a temporary official
purpose-oriented not commercial using a variant of the monograph at
an eventual request for that.**

* *

*43. **Logicism
Lite's Rule Does Not Eliminate the Use of Arithmetical Laws*,**Abstract** only **in [42]**, p. 136.

* It and the entire text
of this note are here*.

** **

** **

**The second author of [ 22] and [23] used the indicated above method ([1], [4], [12]) in her dissertation thesis. Vassiliev wrote in the Journal of Logic Programming that his method is applicable to [16]. Much later factor-automata [17]
were constructed by Kloss ("Kibernetika") in the particular case of
automata without exit. A generalization of the Rabin and Scott's
syntactic congruence was introduced and used by us in [**

* *

* *

* *

* *

32. a) *Set Theory and Mathematical Logic (Textbook and Manual for Exercises*), Plovdiv University Press, Plovdiv 1991, ISSN: 954-423-006-8 (in Bulgarian).

You could see a program __329__, __330__, __331__ *in
the algorithmic language Basic from the book. It transforms a binary
function into a disjunctive normal form of its. It is not necessary to
translate the explanations "REM".** *

b) *Lectures on Elements of Set Theory and Mathematical Logic*, Edited by the Plovdiv University, Plovdiv 1980 (in Bulgarian, included in (a) above).

c) *Exercises on Elements of Set Theory and of the Propositional Calculus*, Edited by the Plovdiv University, Plovdiv 1983 (in Bulgarian, included in (a) above).

33. *An Illustrative Example of a Directing, Correcting and Complementing Dialogue Introduced Long Ago but Still Used Now*, **Paissii Hilendarski Plovdiv University, Ljuben Karavelov K"rdjali Branch, Anniversary scientific/practical Conference**
(on Dialogism and Education Process), May 26-27, 1995, Mathematics and
Informatics Section), Report Collection (1996), 132-136 ( in Bulgarian).

34.a) *Examples from History of Mathematics Excite an Interest in it or its Applications among Students in Human Services*, A __poster__ at **9**^{th} National Conference of the Council On Undergraduate Research, Connecticut College, USA, June 19-22, 2002, **Abstracts, **p. 34.

** **

35. *Activating Teaching Can Generate the Use of Basic Mathematical Knowledge in the Daily Service Practice of Some Students*, **Crossing Boundaries. Innovations in Undergraduate Research. Council on Undergraduate Research. Tenth National Conference. **University of Wisconsin - La Crosse, June 23-26, 2004**. Workshop and Poster Abstracts**, __p__. 23, or __http://www.cur.org/conferences/UW-LaCrosse/cur2004workshopabstracts.pdf__ , p.23.

**You could see its** __entire text too__ *and *__two__ __pictures__ *from the presentation at the indicated Conference.*

* *

**You could read the projected text and hear the voice from its presentation. Another information about the Conference and this presentation could be found in http://www.cphpvb.net/other/6417-photos-from-srem2010 . **

* *

* *

39. *Combining Non-Formal and Formal Discussion Has a Psychological Effect on Student Participation in Solving Problems*, in **Proceedings of the 6 ^{th} Mediterranean Conference on Mathematics Education, 22-26 April 2009, Plovdiv, Bulgaria**,
Editors Athanasios Gagatsis (University of Cyprus, Cyprus Mathematical
Society) and Sava Grozdev (Bulgarian Academy of Science), Organizers:
Cyprus Mathematical Society and University of Plovdiv, Published by
Faculty of Mathematics and Informatics, Plovdiv University, ISBN:
978-9963-9277-9-1. 475 pp, 315-322., http://fmi.uni-plovdiv.bg/GetResource?id=563 .

**You could read here the **__submitted__* text or its scanning 315, 316-317, 318-319, 320-321, 322 from the publication itself. The program of this Conference has been posted at http://medconf2009.fmi-plovdiv.org/programme.php .Our participation (Section Mathematics Education at University Level) has have been with a mailed video clip. My voice is not reading the parts of the projected text in brown. The coloring of this text separates formal and not-formal discussions and indicates the psychological impact at their combination. The entire texts in it follows exactly the text of the indicated above submitted one for the referees. It is impossible for now to upload the clip here due to its size but you could see a photography which has been shot from its beginning.*

* *

*
*

**A SHORT STORY**

** **

40.* His T-Line*, in** Words with Wings**, A Collection of Student Writings,
Ed. By YMCA of Greater Boston, International Learning Center, Summer**1999**.