{"id":1345,"date":"2018-03-19T09:12:32","date_gmt":"2018-03-19T08:12:32","guid":{"rendered":"https:\/\/www.pmfst.unist.hr\/znanost\/?p=1345"},"modified":"2021-03-25T09:07:23","modified_gmt":"2021-03-25T08:07:23","slug":"grupa-za-teoriju-brojeva","status":"publish","type":"post","link":"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/grupa-za-teoriju-brojeva\/","title":{"rendered":"Grupa za teoriju brojeva"},"content":{"rendered":"
[vc_row][vc_column width=”1\/3″][mk_title_box color=”#1e73be” font_family=”none”]Voditelj grupe<\/b>[\/mk_title_box][mk_employees style=”boxed” column=”1″ employees=”11917″][mk_title_box color=”#1e73be” font_family=”none”]\u010clanovi grupe<\/b>[\/mk_title_box][mk_employees style=”boxed” column=”1″ employees=”11918″][vc_column_text css=”.vc_custom_1524469272596{margin-bottom: 0px !important;}”]Lucija Ru\u017eman, prof., KTF, Split[\/vc_column_text][\/vc_column][vc_column width=”2\/3″][mk_title_box color=”#1e73be” font_family=”none”]Odjel\/Katedra:\u00a0<\/strong>Odjel za matematiku[\/mk_title_box][vc_column_text css=”.vc_custom_1522914016490{margin-bottom: 0px !important;}”]\n

Podru\u010dje istra\u017eivanja:<\/h4>\n

– diofantske jednad\u017ebe (Thueove jednad\u017ebe, indeksne jednad\u017ebe, sustavi pellovskih jednad\u017ebi, Diofantove m-torke)
\n– diofantske aproksimacije (primjena Bakerove teorije, hipergeoretrijska metoda, veri\u017eni razlomci)
\n– kanonskih brojevni sustavi.
\n[\/vc_column_text][vc_column_text css=”.vc_custom_1520591748316{margin-bottom: 0px !important;}”]\n

Opis istra\u017eivanja:<\/h4>\n

Istra\u017euju se problemi povezani s odre\u0111ivanjem minimalnog indeksa, te svih elemenata s minimalnim indeksom za razna pro\u0161irenja od Q. Tako\u0111er, promatraju se i analogni problemi za relativna pro\u0161irenja. Za dano pro\u0161irenje, navedeni problemi se svode na rje\u0161avanje odgovaraju\u0107e diofantske jednad\u017ebe koja se naziva indeksna jednad\u017eba. Za neke vrste pro\u0161irenja, pokazano je da se rje\u0161avanje indeksne jednad\u017ebe reducira na rje\u0161avanje nekih jednostavnijih tipova diofantskih jednad\u017ebi kao \u0161to su Thueove jednad\u017ebe ili sustavi pellovskih jednad\u017ebi. Tako\u0111er, prou\u010davaju se i problemi povezani s odre\u0111ivanjem kanonskih brojevnih sustava (CNS) u prstenovima cijelih brojeva razli\u010ditih polja K, \u0161to je problem usko povezan s prethodnim problemom. Isto tako prou\u010dava se i problem Diofantskih m-torki, posebno u cjelobrojnom slu\u010daju i nad kvadratnim poljima. Zanimljiva su nam i poop\u0107enja problema na polinomijalni slu\u010daj. Dosada\u0161nji rezultati idu u prilog dokazivanju otvorenih problema vezanih za veli\u010dinu mogu\u0107eg skupa u cjelobrojnom slu\u010daju.
\nPri rje\u0161avanju ovih problema koriste se raznovrsne metode iz diofantske analize i algebarske teorije brojeva.<\/p>\n[\/vc_column_text][vc_column_text css=”.vc_custom_1520591959083{margin-bottom: 0px !important;}”]\n

Kontakti s akademskim i drugim institucijama:<\/strong><\/h4>\n

\u2013 PMF-Matemati\u010dki odsjek, Sveu\u010dili\u0161te u Zagrebu
\n\u2013 Gra\u0111evinski fakultet, Sveu\u010dili\u0161te u Zagrebu
\n\u2013 Odjel za matematiku, Sveu\u010dili\u0161te u Rijeci
\n\u2013 Matemati\u010dki institut, Sveu\u010dili\u0161te u Debrecenu, Ma\u0111arska
\n\u2013 Institut za analizu i teoriju brojeva, TU-Graz, Austrija
\n\u2013 Matemati\u010dki odjel, Sveu\u010dili\u0161te u Salzburgu, Austria
\n\u2013 Institut za napredna istra\u017eivanja u matematici, Sveu\u010dili\u0161te u Strasbourgu, Francuska
\n\u2013 Glavni laboratorij za numeri\u010dke simulacije, Neijiang Normal University, Se\u010duan, Kina
\n\u2013 Matemati\u010dki odjel, Purdue University North Central, SAD
\n\u2013 Pedago\u0161ki fakultet, Sveu\u010dili\u0161te u Biha\u0107u, BIH<\/p>\n[\/vc_column_text][vc_column_text css=”.vc_custom_1520591973324{margin-bottom: 0px !important;}”]\n

Opis dosada\u0161nje suradnje:<\/strong><\/h4>\n

Suradnja s kolegama na navedenim institucijama je ostvarena prvenstveno preko zajedni\u010dkog znanstveno-istra\u017eiva\u010dkog rada u okviru nacionalnih ili bilateralnih projekata. Zajedni\u010dki znanstveno-istra\u017eiva\u010dki rad rezultirao je publiciranjem vi\u0161e znanstvenih radova u me\u0111unarodnim \u010dasopisima. Suradnja je ostvarena i preko kra\u0107ih obostranih posjeta u sklopu kojih je odr\u017eano nekoliko predavanja u okviru odgovaraju\u0107ih seminara ili kolokvija.
\n[\/vc_column_text][vc_column_text css=”.vc_custom_1521113815978{margin-bottom: 0px !important;}”]\n

Planovi budu\u0107ih istra\u017eivanja:<\/strong><\/h4>\n

Planiraju se nastaviti istra\u017eivanja prije spomenutih problema.
\n[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text css=”.vc_custom_1520603890149{margin-bottom: 0px !important;}”]\n

Popis odabranih znanstvenih radova:<\/h4>\n

1. A. Dujella and B. Jadrijevi\u0107, A parametric family of quartic Thue equations, Acta Arith. 101 (2002), 159-170;
\n2. A. Dujella and B. Jadrijevi\u0107, A family of quartic Thue inequalities, Acta Arith., 111 (2004), 61-76;
\n3. B. Jadrijevi\u0107, A system of Pellian equations and related two-parametric family of quartic Thue equations, Rocky Mountain J. Math. 35, No. 2 (2005), 547-572;
\n4. B. Jadrijevi\u0107 and V. Ziegler, A system of relative Pellian equations and a related family of relative Thue equations, Int. J. Number Theory 2, No. 4 (2006), 569-590;
\n5. C. Fuchs and B. Jadrijevi\u0107, On a parametric family of Thue inequalities over function fields, Math. Proc. Cambridge Philos. Soc. 143 (2007), 9-23;
\n6. B. Jadrijevi\u0107, Establishing the minimal index in a parametric family of bicyclic biquadratic fields, Period. Math. Hungar. 58 (2) (2009), 2; 155-180.
\n7. B. He, B. Jadrijevi\u0107 and A. Togb\u00e9, Solutions of a class of quartic Thue inequalities, Glas. Mat., 44 (2009), 2; 309-321;
\n8. A. Dujella, B. Ibrahimpa\u0161i\u0107 and B. Jadrijevi\u0107, Solving a family of quartic Thue inequalities using continued fractions, Rocky Mountain J. Math. 41 (2011), 1173-1182.;
\n9. B. Jadrijevi\u0107, On elements with index of the form 2^a3^b in a parametric family of biquadratic fields, Glas. Mat., 50 (2015), 1, 43-63;
\n10. M. Bliznac, A. Filipin, An upper bound for the number of Diophantine quintuple, Bulletin of the Australian Mathematical Society, 94 (2016), 3; 384-394.;
\n10. I. Gaal, B. Jadrijevi\u0107, Determining elements of minimal index in an in\ufb01nite family of totally real bicyclic biquadratic number \ufb01elds, JP Journal of Algebra, Number Theory and Applications, 39 (2017), 3; 307-326.;
\n11. Z. Franu\u0161i\u0107, B. Jadrijevi\u0107, Computing relative power integral bases in a family of quartic extensions of imaginary quadratic fields, Publicationes Mathematicae Debrecen, 92 (2018), 3-4; 293-315;
\n12. M . Bliznac Trebje\u0161anin, A. Filipin, A. Jurasi\u0107, On the polynomial quadruples with the property D(\u22121 ; 1), Tokyo Journal of Mathematics (prihva\u0107en za objavljivanje);
\n13. M . Bliznac Trebje\u0161anin, A. Filipin, Nonexistence of D(4)-quintuples, (u postupku recenzije);
\n14. I. Gaal, B. Jadrijevi\u0107, L. Remete, Totally real Thue equations over imaginary quadratic \ufb01elds, (u postupku recenzije);
\n15. I. Gaal, B. Jadrijevi\u0107, L. Remete, Simplest quartic and simplest sextic Thue equations over imaginary quadratic fields, (u postupku recenzije)<\/p>\n[\/vc_column_text][\/vc_column][\/vc_row]\n<\/div>","protected":false},"excerpt":{"rendered":"

[vc_row][vc_column width=”1\/3″][mk_title_box color=”#1e73be” font_family=”none”]Voditelj grupe[\/mk_title_box][mk_employees style=”boxed” column=”1″ employees=”11917″][mk_title_box color=”#1e73be” font_family=”none”]\u010clanovi grupe[\/mk_title_box][mk_employees style=”boxed” column=”1″ employees=”11918″][vc_column_text css=”.vc_custom_1524469272596{margin-bottom: 0px !important;}”]Lucija Ru\u017eman, prof., KTF, Split[\/vc_column_text][\/vc_column][vc_column width=”2\/3″][mk_title_box color=”#1e73be” font_family=”none”]Odjel\/Katedra:\u00a0Odjel za matematiku[\/mk_title_box][vc_column_text css=”.vc_custom_1522914016490{margin-bottom: 0px !important;}”] Podru\u010dje istra\u017eivanja: – diofantske jednad\u017ebe (Thueove jednad\u017ebe, indeksne jednad\u017ebe, sustavi pellovskih jednad\u017ebi, Diofantove m-torke) – diofantske aproksimacije (primjena Bakerove teorije, hipergeoretrijska metoda, veri\u017eni razlomci) – kanonskih […]<\/p>\n","protected":false},"author":1,"featured_media":1384,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"rs_blank_template":"","rs_page_bg_color":"","slide_template_v7":"","footnotes":""},"categories":[3],"tags":[],"class_list":["post-1345","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-odjel-za-matematiku-istrazivacka-grupa"],"acf":[],"yoast_head":"\nGrupa za teoriju brojeva - Odjel za matematiku<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/grupa-za-teoriju-brojeva\/\" \/>\n<meta property=\"og:locale\" content=\"hr_HR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Grupa za teoriju brojeva - Odjel za matematiku\" \/>\n<meta property=\"og:description\" content=\"[vc_row][vc_column width=”1\/3″][mk_title_box color=”#1e73be” font_family=”none”]Voditelj grupe[\/mk_title_box][mk_employees style=”boxed” column=”1″ employees=”11917″][mk_title_box color=”#1e73be” font_family=”none”]\u010clanovi grupe[\/mk_title_box][mk_employees style=”boxed” column=”1″ employees=”11918″][vc_column_text css=”.vc_custom_1524469272596{margin-bottom: 0px !important;}”]Lucija Ru\u017eman, prof., KTF, Split[\/vc_column_text][\/vc_column][vc_column width=”2\/3″][mk_title_box color=”#1e73be” font_family=”none”]Odjel\/Katedra:\u00a0Odjel za matematiku[\/mk_title_box][vc_column_text css=”.vc_custom_1522914016490{margin-bottom: 0px !important;}”] Podru\u010dje istra\u017eivanja: – diofantske jednad\u017ebe (Thueove jednad\u017ebe, indeksne jednad\u017ebe, sustavi pellovskih jednad\u017ebi, Diofantove m-torke) – diofantske aproksimacije (primjena Bakerove teorije, hipergeoretrijska metoda, veri\u017eni razlomci) – kanonskih […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/grupa-za-teoriju-brojeva\/\" \/>\n<meta property=\"og:site_name\" content=\"Odjel za matematiku\" \/>\n<meta property=\"article:published_time\" content=\"2018-03-19T08:12:32+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-03-25T08:07:23+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/wp-content\/uploads\/sites\/24\/2018\/03\/teorijabrojeva.png\" \/>\n\t<meta property=\"og:image:width\" content=\"335\" \/>\n\t<meta property=\"og:image:height\" content=\"190\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"autor\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Napisao\/la\" \/>\n\t<meta name=\"twitter:data1\" content=\"autor\" \/>\n\t<meta name=\"twitter:label2\" content=\"Procijenjeno vrijeme \u010ditanja\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/grupa-za-teoriju-brojeva\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/grupa-za-teoriju-brojeva\/\"},\"author\":{\"name\":\"autor\",\"@id\":\"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/#\/schema\/person\/8c4957fe31fd46303be41a1bd068040a\"},\"headline\":\"Grupa za teoriju brojeva\",\"datePublished\":\"2018-03-19T08:12:32+00:00\",\"dateModified\":\"2021-03-25T08:07:23+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/grupa-za-teoriju-brojeva\/\"},\"wordCount\":906,\"commentCount\":0,\"image\":{\"@id\":\"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/grupa-za-teoriju-brojeva\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/wp-content\/uploads\/sites\/24\/2018\/03\/teorijabrojeva.png\",\"articleSection\":[\"Odjel za matematiku\"],\"inLanguage\":\"hr\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/grupa-za-teoriju-brojeva\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/grupa-za-teoriju-brojeva\/\",\"url\":\"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/grupa-za-teoriju-brojeva\/\",\"name\":\"Grupa za teoriju brojeva - 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