List of

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, p. 317.

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, 1979(1980), 143-151 (in Bulgarian).

A part of this paper about factor automata is reflected in a talk (you could read its text only).An example from #19 is indicated in it. Parts of this paper are reflected in # 30 also.

 

[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,Scientific Works of the Plovdiv University " Paissii Hilendarski "(Plovdiv, Bulgaria), v. 32, b. 3 (1995), 51-60.

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 (Bulgaria), October 16-18, 1997, v. 5, Varna (2001), 3-8.

You could see itstext.


[T5] 21. Study of the Prototypes in my Mathematical Works. Collection Philosophie et Mathematiques. Seminaire de l'Ecole Normale Superieure - Paris, Edite par l'I.R.E.M. Paris-Nord, Universite Paris XIII, N 81 (1992), 9 pages, ISBN: 2 86240 581 4, ISSN: 0294-6777 (in French).

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 ½Chr. 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 cashed Web library book catalog as treating a general scientific conception. It appears also in Google e-Books Library. Both [21] and [27] are included in a french reference indication.

 

[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

 
The cover pages of this Conference program are 1 , 2, 3. The same abstract 4 is a beginning of the full text of this solution of a long time not solved discussion and it is a next Theory of Science application of the methodological approach from 27, 21, 29, and 28.

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), 2010, 314-319. (ISBN: 978-954-423-621-2, 508 pp.) http://fmi.uni-plovdiv.bg/GetResource?id=684  

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.

You could read its abstract here or to see or print the corresponding page of the Section.
 
b) Homomorphisms of the Semigroups of Program Models Induced by an Insertion of Equivalencies in Their Common Operator Symbols Free Semigroup, Scientific Researches of the Union of Scientist in Bulgaria - Plovdiv, ISSN 1311-9192, Volume IV, Series B. Natural Sciences and the Humanities, Scientific Session . Section Physics and Mathematics, October 24, 2003, pp. 26-31, Plovdiv (2004) (Russian Summary).

You can see the scanned pages 26-27, 28-29, 30-31 of this publication. The paper has a conceptual relation to papers 21,16, and 19.

 

[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. The following statement is proved in the second section of this publication [41]: A correspondence of a semigroup in another one is a homomorphism if and only if when the entire prototype of the product of images contains the product of their entire prototypes. We have reach it following the indicated general approach of ours for studying the prototypes which started with [8], [9], [10], passed through [16], [12], [11], [14] to its philosophy of science substantiation [21] (and therefore - of the just indicated statement), and continued with [30], [36]. It uses as a connection to comparing entire prototypes at regular languages substitutions in the third section of [41] which substitutions  are playing an important role in theoretical and practical aspects of computer science.

 

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 , athttp://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.

00A30Philosophy 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, 68R15Combinatorics 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 [11], [12], and [30] as it was indicated above. This congruence but again much later and without generalizations of its was used by Parkes and Thomas ("Communications in Algebra") for a description of the group languages as this is indicated in [36]. The posters for [21] and [27] appeared in a survey of the activities of the same Seminar. The papers [1], [4], [5], [6], [22], [23] are included in the series Perspectives in Mathematical Logic, edited by the Omega-group, v. III and IV, Springer-Verlag, Berlin Heidelberg, 1987.The publications [21] and [27] are marked in the french catalog "SUDOC". It is indicated in a cashed Web library book catalog as treating a general scientific conception. It appears also in Google e-Books Library. Both [21] and [27] are included in a french reference indication. Our work over Algorithmic Problems in Algebra but without its connecting with Theories of Languages and Automata has been reflected before the publications [30] and [36] at a Symposium of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence, August 1995.
The following statement is proved in the second section of the publication [41]: A correspondence of a semigroup in another one is a homomorphism if and only if when the entire prototype of the product of images contains the product of their entire prototypes. We have reach it following the indicated general approach of ours for studying the prototypes which started with [8], [9], [10], passed through [16], [12], [11], [14] to its philosophy of science substantiation [21] (and therefore - of the just indicated statement), and continued with [30], [36]. It uses as a connection to comparing entire prototypes at regular languages substitutions in the third section of [41] which substitutions  are playing an important role in theoretical and practical aspects of computer science.

 

 

 

 

TEXTBOOKS, MANUALS FOR EXERCISES AND METHODS PUBLICATIONS
 
 
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 9th National Conference of the Council On Undergraduate Research, Connecticut College, USA, June 19-22, 2002, Abstracts, p. 34.
 
You could read here the text of the abstract or to see (print) the corresponding page where it is published.
 
      b) Mathematics in Human Practice through the Ages, Springfield College, Boston Campus of Human Services (Edited as Xerox copies for teaching a student Seminar during 2003/2004 Academic Year), Fall 2003. 
 
You could see here its cover page and read this enlargement of the indicated in a) poster. Two pictures from its presentation at the indicated Conference are attached here.

 

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.

 

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), 2010, 314-319. (ISBN: 978-954-423-621-2, 508 pp.) http://fmi.uni-plovdiv.bg/GetResource?id=684  

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 6th 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 combinationThe 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, Summer1999.


You could read the story here. The cover page of the collection is here.