{"id":{"repo_id":"greece","oai_identifier":"oai:10442/1499"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/1499","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"ΑΝΙΣΟΤΗΤΕΣ BONFERRONI-ΑΚΟΛΟΥΘΙΕΣ ΜΕ ΑΥΤΟΣΥΣΧΕΤΙΣΗ ΜΗΔΕΝ","abstract":"IN THE FIRST PART OF THE DISSERTATION WE PRESENT A METHOD FOR DERIVING IMPROVEDBONFERRONI TYPE UPPER AND LOWER BOUNDS OF EVERY DEGREE M: I) FOR THE PROBABILITY OF THE UNION OF N NOT NECESSARILY EXCHANGEABLE EVENTS, II) FOR THE PROBABILITY THAT EXACTLY M AMONG N EVENTS OCCUR. WE ALSO PROVE THAT THE BONFERRONI, SOBEL-UPPULURI, GALAMBOS AND MARGARITES CN BOUNDS ARE SPECIAL CASES OF THE PROPOSEDBOUNDS. IN THE SECOND PART OF THIS DISSERTATION WE PROVE THAT GOLAY SEQUENCES OF LENGTH N=2.72T, T>0 DO NOT EXIST. WE ALSO DEVELOP ALGORITHMS FOR CONSTRUCTING COMPLEMENTARY SEQUENCES AND ESPECIALLY GOLAY, BASE AND TURYN SEQUENCES USING THE PROPERTIES OF THESE RESULTS: I) GOLAY SEQUENCES OF LENGTH N=98 DO NOT EXIST, II) BASE SEQUENCES OF LENGTHS N+1, N+1, N,N ARE CONSTRUCTED FOR ALL DECOMPOSITIONS OF 4N+2 INTO FOUR SQUARES FOR N=19,20,..,24 AND III) TURYN SEQUENCES OF LENGTHS N=18,...,27 DO NOT EXIST.","abstract_html":"IN THE FIRST PART OF THE DISSERTATION WE PRESENT A METHOD FOR DERIVING IMPROVEDBONFERRONI TYPE UPPER AND LOWER BOUNDS OF EVERY DEGREE M: I) FOR THE PROBABILITY OF THE UNION OF N NOT NECESSARILY EXCHANGEABLE EVENTS, II) FOR THE PROBABILITY THAT EXACTLY M AMONG N EVENTS OCCUR. WE ALSO PROVE THAT THE BONFERRONI, SOBEL-UPPULURI, GALAMBOS AND MARGARITES CN BOUNDS ARE SPECIAL CASES OF THE PROPOSEDBOUNDS. IN THE SECOND PART OF THIS DISSERTATION WE PROVE THAT GOLAY SEQUENCES OF LENGTH N=2.72T, T>0 DO NOT EXIST. WE ALSO DEVELOP ALGORITHMS FOR CONSTRUCTING COMPLEMENTARY SEQUENCES AND ESPECIALLY GOLAY, BASE AND TURYN SEQUENCES USING THE PROPERTIES OF THESE RESULTS: I) GOLAY SEQUENCES OF LENGTH N=98 DO NOT EXIST, II) BASE SEQUENCES OF LENGTHS N+1, N+1, N,N ARE CONSTRUCTED FOR ALL DECOMPOSITIONS OF 4N+2 INTO FOUR SQUARES FOR N=19,20,..,24 AND III) TURYN SEQUENCES OF LENGTHS N=18,...,27 DO NOT EXIST.","abstract_has_math":false,"creators":["Σωτηράκογλου, Κυριακή"],"institution":"Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1989,"date_issued":"1989","date_published":"1989","updated_at":"2026-07-24T02:24:59Z","subjects":["AUTOCORRELATION FUNCTION","BAS SEQUENCES","BONFERRONI INEQUALITIES","GOLAY SEQUENCES","TURYN SEQUENCES","UPPER AND LOWERBOUNDS","ΑΚΟΛΟΥΘΙΕΣ BASE","ΑΚΟΛΟΥΘΙΕΣ GOLAY","ΑΚΟΛΟΥΘΙΕΣ ΤΘΡΥΝ","ΑΝΙΣΟΤΗΤΕΣ BONFERRONI","ΑΝΩ ΚΑΙ ΚΑΤΩ ΦΡΑΓΜΑΤΑ","ΣΥΝΑΡΤΗΣΗ ΑΥΤΟΣΥΣΧΕΤΙΣΗΣ","Φυσικές Επιστήμες","Natural Sciences","Μαθηματικά","Mathematics"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1499"],"render_values":[{"text":"10.12681/eadd/1499","href":"https://doi.org/10.12681/eadd/1499","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/1499","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Σωτηράκογλου, Κυριακή"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1989"]},{"key":"dc:publisher","label":"Institution","values":["Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)","Aristotle University Of Thessaloniki (AUTH)"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["AUTOCORRELATION FUNCTION","BAS SEQUENCES","BONFERRONI INEQUALITIES","GOLAY SEQUENCES","TURYN SEQUENCES","UPPER AND LOWERBOUNDS","ΑΚΟΛΟΥΘΙΕΣ BASE","ΑΚΟΛΟΥΘΙΕΣ GOLAY","ΑΚΟΛΟΥΘΙΕΣ ΤΘΡΥΝ","ΑΝΙΣΟΤΗΤΕΣ BONFERRONI","ΑΝΩ ΚΑΙ ΚΑΤΩ ΦΡΑΓΜΑΤΑ","ΣΥΝΑΡΤΗΣΗ ΑΥΤΟΣΥΣΧΕΤΙΣΗΣ","Φυσικές Επιστήμες","Natural Sciences","Μαθηματικά","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["gre"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1499","http://hdl.handle.net/10442/hedi/1499"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["IN THE FIRST PART OF THE DISSERTATION WE PRESENT A METHOD FOR DERIVING IMPROVEDBONFERRONI TYPE UPPER AND LOWER BOUNDS OF EVERY DEGREE M: I) FOR THE PROBABILITY OF THE UNION OF N NOT NECESSARILY EXCHANGEABLE EVENTS, II) FOR THE PROBABILITY THAT EXACTLY M AMONG N EVENTS OCCUR. WE ALSO PROVE THAT THE BONFERRONI, SOBEL-UPPULURI, GALAMBOS AND MARGARITES CN BOUNDS ARE SPECIAL CASES OF THE PROPOSEDBOUNDS. IN THE SECOND PART OF THIS DISSERTATION WE PROVE THAT GOLAY SEQUENCES OF LENGTH N=2.72T, T>0 DO NOT EXIST. WE ALSO DEVELOP ALGORITHMS FOR CONSTRUCTING COMPLEMENTARY SEQUENCES AND ESPECIALLY GOLAY, BASE AND TURYN SEQUENCES USING THE PROPERTIES OF THESE RESULTS: I) GOLAY SEQUENCES OF LENGTH N=98 DO NOT EXIST, II) BASE SEQUENCES OF LENGTHS N+1, N+1, N,N ARE CONSTRUCTED FOR ALL DECOMPOSITIONS OF 4N+2 INTO FOUR SQUARES FOR N=19,20,..,24 AND III) TURYN SEQUENCES OF LENGTHS N=18,...,27 DO NOT EXIST.","ΣΤΟ ΠΡΩΤΟ ΜΕΡΟΣ ΤΗΣ ΔΙΑΤΡΙΒΗΣ, ΔΙΝΕΤΑΙ ΜΙΑ ΜΕΘΟΔΟΣ ΕΥΡΕΣΗΣ ΒΕΛΤΙΩΜΕΝΩΝ ΑΝΩ ΚΑΙ ΚΑΤΩ ΦΡΑΓΜΑΤΩΝ ΤΥΠΟΥ BONFERRONI ΟΛΩΝ ΤΩΝ ΒΑΘΜΩΝ: Ι) ΓΙΑ ΤΗΝ ΠΙΘΑΝΟΤΗΤΑ ΤΗΣ ΕΝΩΣΗΣ 'Η ΓΕΓΟΝΟΤΩΝ, ΙΙ) ΓΙΑ ΤΗΝ ΠΙΘΑΝΟΤΗΤΑ ΤΟΥΛΑΧΙΣΤΟΝ Μ ΑΠΟ 'Η ΓΕΓΟΝΟΤΑ ΝΑ ΣΥΜΒΑΙΝΟΥΝ ΚΑΙ ΙΙΙ) ΓΙΑ ΤΗΝ ΠΙΘΑΝΟΤΗΤΑ ΑΚΡΙΒΩΣ Μ ΑΠΟ 'Η ΓΕΓΟΝΟΤΑ ΝΑ ΣΥΜΒΑΙΝΟΥΝ. ΑΠΟΔΕΙΚΝΥΕΤΑΙ ΟΤΙ ΤΑ ΗΔΗ ΥΠΑΡΧΟΝΤΑ ΦΡΑΓΜΑΤΑ ΤΟΥ BONFERRONI, ΤΩΝ SOBET-UPPULURI, ΤΟΥ GALAMBOS Κ.Α. ΠΡΟΚΥΠΤΟΥΝ ΣΑΝ ΕΙΔΙΚΕΣ ΠΕΡΙΠΤΩΣΕΙΣ ΤΩΝ ΠΡΟΤΕΙΝΟΜΕΝΩΝ ΦΡΑΓΜΑΤΩΝ. ΣΤΟ ΔΕΥΤΕΡΟ ΜΕΡΟΣ ΤΗΣ ΔΙΑΤΡΙΒΗΣ ΑΥΤΗΣ, ΑΠΟΔΕΙΚΝΥΕΤΑΙ Η ΜΗ-ΥΠΑΡΞΗ ΑΚΟΛΟΥΘΙΩΝ GOLAY ΜΗΚΟΥΣ Ν=2.72Τ, Τ>0. ΕΠΙΣΗΣ ΑΝΑΠΤΥΣΣΟΝΤΑΙ ΑΠΟΤΕΛΕΣΜΑΤΙΚΟΙ ΑΛΓΟΡΙΘΜΟΙ ΚΑΤΑΣΚΕΥΗΣ ΣΥΜΠΛΗΡΩΜΑΤΙΚΩΝ ΑΚΟΛΟΥΘΙΩΝ ΚΑΙ ΙΔΙΑΙΤΕΡΑ ΑΚΟΛΟΥΘΙΩΝ GOLAY, BASE ΚΑΙ TURYN, ΧΡΗΣΙΜΟΠΟΙΩΝΤΑΣ ΤΙΣ ΙΔΙΟΤΗΤΕΣ ΤΩΝ ΑΚΟΛΟΥΘΙΩΝ ΑΥΤΩΝ. ΕΦΑΡΜΟΖΟΝΤΑΣ ΤΟΥΣ ΠΑΡΑΠΑΝΩ ΑΛΓΟΡΙΘΜΟΥΣ ΣΤΟΝ Η/Υ ΕΧΟΥΜΕ ΤΑ ΑΚΟΛΟΥΘΑ ΑΠΟΤΕΛΕΣΜΑΤΑ: Ι) ΔΕΝ ΥΠΑΡΧΟΥΝ ΑΚΟΛΟΥΘΙΕΣGOLAY ΜΗΚΟΥΣ Ν=19,20, 24 ΓΙΑ ΟΛΕΣ ΤΙΣ ΑΝΑΛΥΣΕΙΣ ΤΟΥ 4Ν+2 ΣΕ ΤΕΣΣΕΡΑ ΤΕΤΡΑΓΩΝΑ ΚΑΙ ΙΙΙ) ΔΕΝ ΥΠΑΡΧΟΥΝ ΑΚΟΛΟΥΘΙΕΣ TURYN ΓΙΑ ΟΛΑ ΤΑ ΜΗΚΗ Ν=18,19,...,27."]},{"key":"dc:title","label":"Title","values":["ΑΝΙΣΟΤΗΤΕΣ BONFERRONI-ΑΚΟΛΟΥΘΙΕΣ ΜΕ ΑΥΤΟΣΥΣΧΕΤΙΣΗ ΜΗΔΕΝ","BONFERRONI INEQUALITIES-SEQUENCES WITH ZERO AUTOCORRELATION"]}]}],"canonical_facts":{"dc:creator":["Σωτηράκογλου, Κυριακή"],"dc:date":["1989"],"dc:description":["IN THE FIRST PART OF THE DISSERTATION WE PRESENT A METHOD FOR DERIVING IMPROVEDBONFERRONI TYPE UPPER AND LOWER BOUNDS OF EVERY DEGREE M: I) FOR THE PROBABILITY OF THE UNION OF N NOT NECESSARILY EXCHANGEABLE EVENTS, II) FOR THE PROBABILITY THAT EXACTLY M AMONG N EVENTS OCCUR. WE ALSO PROVE THAT THE BONFERRONI, SOBEL-UPPULURI, GALAMBOS AND MARGARITES CN BOUNDS ARE SPECIAL CASES OF THE PROPOSEDBOUNDS. IN THE SECOND PART OF THIS DISSERTATION WE PROVE THAT GOLAY SEQUENCES OF LENGTH N=2.72T, T>0 DO NOT EXIST. WE ALSO DEVELOP ALGORITHMS FOR CONSTRUCTING COMPLEMENTARY SEQUENCES AND ESPECIALLY GOLAY, BASE AND TURYN SEQUENCES USING THE PROPERTIES OF THESE RESULTS: I) GOLAY SEQUENCES OF LENGTH N=98 DO NOT EXIST, II) BASE SEQUENCES OF LENGTHS N+1, N+1, N,N ARE CONSTRUCTED FOR ALL DECOMPOSITIONS OF 4N+2 INTO FOUR SQUARES FOR N=19,20,..,24 AND III) TURYN SEQUENCES OF LENGTHS N=18,...,27 DO NOT EXIST.","ΣΤΟ ΠΡΩΤΟ ΜΕΡΟΣ ΤΗΣ ΔΙΑΤΡΙΒΗΣ, ΔΙΝΕΤΑΙ ΜΙΑ ΜΕΘΟΔΟΣ ΕΥΡΕΣΗΣ ΒΕΛΤΙΩΜΕΝΩΝ ΑΝΩ ΚΑΙ ΚΑΤΩ ΦΡΑΓΜΑΤΩΝ ΤΥΠΟΥ BONFERRONI ΟΛΩΝ ΤΩΝ ΒΑΘΜΩΝ: Ι) ΓΙΑ ΤΗΝ ΠΙΘΑΝΟΤΗΤΑ ΤΗΣ ΕΝΩΣΗΣ 'Η ΓΕΓΟΝΟΤΩΝ, ΙΙ) ΓΙΑ ΤΗΝ ΠΙΘΑΝΟΤΗΤΑ ΤΟΥΛΑΧΙΣΤΟΝ Μ ΑΠΟ 'Η ΓΕΓΟΝΟΤΑ ΝΑ ΣΥΜΒΑΙΝΟΥΝ ΚΑΙ ΙΙΙ) ΓΙΑ ΤΗΝ ΠΙΘΑΝΟΤΗΤΑ ΑΚΡΙΒΩΣ Μ ΑΠΟ 'Η ΓΕΓΟΝΟΤΑ ΝΑ ΣΥΜΒΑΙΝΟΥΝ. ΑΠΟΔΕΙΚΝΥΕΤΑΙ ΟΤΙ ΤΑ ΗΔΗ ΥΠΑΡΧΟΝΤΑ ΦΡΑΓΜΑΤΑ ΤΟΥ BONFERRONI, ΤΩΝ SOBET-UPPULURI, ΤΟΥ GALAMBOS Κ.Α. ΠΡΟΚΥΠΤΟΥΝ ΣΑΝ ΕΙΔΙΚΕΣ ΠΕΡΙΠΤΩΣΕΙΣ ΤΩΝ ΠΡΟΤΕΙΝΟΜΕΝΩΝ ΦΡΑΓΜΑΤΩΝ. ΣΤΟ ΔΕΥΤΕΡΟ ΜΕΡΟΣ ΤΗΣ ΔΙΑΤΡΙΒΗΣ ΑΥΤΗΣ, ΑΠΟΔΕΙΚΝΥΕΤΑΙ Η ΜΗ-ΥΠΑΡΞΗ ΑΚΟΛΟΥΘΙΩΝ GOLAY ΜΗΚΟΥΣ Ν=2.72Τ, Τ>0. ΕΠΙΣΗΣ ΑΝΑΠΤΥΣΣΟΝΤΑΙ ΑΠΟΤΕΛΕΣΜΑΤΙΚΟΙ ΑΛΓΟΡΙΘΜΟΙ ΚΑΤΑΣΚΕΥΗΣ ΣΥΜΠΛΗΡΩΜΑΤΙΚΩΝ ΑΚΟΛΟΥΘΙΩΝ ΚΑΙ ΙΔΙΑΙΤΕΡΑ ΑΚΟΛΟΥΘΙΩΝ GOLAY, BASE ΚΑΙ TURYN, ΧΡΗΣΙΜΟΠΟΙΩΝΤΑΣ ΤΙΣ ΙΔΙΟΤΗΤΕΣ ΤΩΝ ΑΚΟΛΟΥΘΙΩΝ ΑΥΤΩΝ. ΕΦΑΡΜΟΖΟΝΤΑΣ ΤΟΥΣ ΠΑΡΑΠΑΝΩ ΑΛΓΟΡΙΘΜΟΥΣ ΣΤΟΝ Η/Υ ΕΧΟΥΜΕ ΤΑ ΑΚΟΛΟΥΘΑ ΑΠΟΤΕΛΕΣΜΑΤΑ: Ι) ΔΕΝ ΥΠΑΡΧΟΥΝ ΑΚΟΛΟΥΘΙΕΣGOLAY ΜΗΚΟΥΣ Ν=19,20, 24 ΓΙΑ ΟΛΕΣ ΤΙΣ ΑΝΑΛΥΣΕΙΣ ΤΟΥ 4Ν+2 ΣΕ ΤΕΣΣΕΡΑ ΤΕΤΡΑΓΩΝΑ ΚΑΙ ΙΙΙ) ΔΕΝ ΥΠΑΡΧΟΥΝ ΑΚΟΛΟΥΘΙΕΣ TURYN ΓΙΑ ΟΛΑ ΤΑ ΜΗΚΗ Ν=18,19,...,27."],"dc:identifier":["10.12681/eadd/1499","http://hdl.handle.net/10442/hedi/1499"],"dc:language":["gre"],"dc:publisher":["Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)","Aristotle University Of Thessaloniki (AUTH)"],"dc:subject":["AUTOCORRELATION FUNCTION","BAS SEQUENCES","BONFERRONI INEQUALITIES","GOLAY SEQUENCES","TURYN SEQUENCES","UPPER AND LOWERBOUNDS","ΑΚΟΛΟΥΘΙΕΣ BASE","ΑΚΟΛΟΥΘΙΕΣ GOLAY","ΑΚΟΛΟΥΘΙΕΣ ΤΘΡΥΝ","ΑΝΙΣΟΤΗΤΕΣ BONFERRONI","ΑΝΩ ΚΑΙ ΚΑΤΩ ΦΡΑΓΜΑΤΑ","ΣΥΝΑΡΤΗΣΗ ΑΥΤΟΣΥΣΧΕΤΙΣΗΣ","Φυσικές Επιστήμες","Natural Sciences","Μαθηματικά","Mathematics"],"dc:title":["ΑΝΙΣΟΤΗΤΕΣ BONFERRONI-ΑΚΟΛΟΥΘΙΕΣ ΜΕ ΑΥΤΟΣΥΣΧΕΤΙΣΗ ΜΗΔΕΝ","BONFERRONI INEQUALITIES-SEQUENCES WITH ZERO AUTOCORRELATION"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:24:59Z"}