Bayraktar, Turgay; Kişisel, Ali Ulaş Özgür Expected multivolumes of random amoebas. (English) Zbl 07799849 J. Complexity 80, Article ID 101802, 7 p. (2024). MSC: 14P25 14T05 60D05 PDFBibTeX XMLCite \textit{T. Bayraktar} and \textit{A. U. Ö. Kişisel}, J. Complexity 80, Article ID 101802, 7 p. (2024; Zbl 07799849) Full Text: DOI arXiv
Krasikov, Vitaly A. A survey on computational aspects of polynomial amoebas. (English) Zbl 07734146 Math. Comput. Sci. 17, No. 3-4, Paper No. 16, 19 p. (2023). MSC: 14J81 14P25 14Q15 14T90 32A08 68W40 PDFBibTeX XMLCite \textit{V. A. Krasikov}, Math. Comput. Sci. 17, No. 3--4, Paper No. 16, 19 p. (2023; Zbl 07734146) Full Text: DOI arXiv
Zhukov, T. A.; Sadykov, T. M. Computing the connected components of the complement to the amoeba of a polynomial in several complex variables. (English. Russian original) Zbl 1523.32004 Program. Comput. Softw. 49, No. 2, 91-99 (2023); translation from Programmirovanie 49, No. 2, 36-45 (2023). MSC: 32-04 32A08 PDFBibTeX XMLCite \textit{T. A. Zhukov} and \textit{T. M. Sadykov}, Program. Comput. Softw. 49, No. 2, 91--99 (2023; Zbl 1523.32004); translation from Programmirovanie 49, No. 2, 36--45 (2023) Full Text: DOI
Goucha, António Pedro; Gouveia, Joaõ The phaseless rank of a matrix. (English) Zbl 1510.14045 SIAM J. Appl. Algebra Geom. 5, No. 3, 526-551 (2021). MSC: 14P10 14T10 15A03 15A23 90C22 90C26 PDFBibTeX XMLCite \textit{A. P. Goucha} and \textit{J. Gouveia}, SIAM J. Appl. Algebra Geom. 5, No. 3, 526--551 (2021; Zbl 1510.14045) Full Text: DOI arXiv
Mikhalkin, Grigory; Rau, Johannes Spines for amoebas of rational curves. (English) Zbl 1464.14068 Enseign. Math. (2) 65, No. 3-4, 377-396 (2019). Reviewer: José Javier Etayo (Madrid) MSC: 14T20 14H50 30F15 PDFBibTeX XMLCite \textit{G. Mikhalkin} and \textit{J. Rau}, Enseign. Math. (2) 65, No. 3--4, 377--396 (2019; Zbl 1464.14068) Full Text: DOI arXiv
Nisse, Mounir; Sadykov, Timur Amoeba-shaped polyhedral complex of an algebraic hypersurface. (English) Zbl 1423.32010 J. Geom. Anal. 29, No. 2, 1356-1368 (2019). Reviewer: Piotr Pokora (Kraków) MSC: 32A60 32B20 PDFBibTeX XMLCite \textit{M. Nisse} and \textit{T. Sadykov}, J. Geom. Anal. 29, No. 2, 1356--1368 (2019; Zbl 1423.32010) Full Text: DOI arXiv
Johansson, Petter Some results on amoebas and coamoebas of affine spaces. (English) Zbl 1404.32013 Andersson, Mats (ed.) et al., Analysis meets geometry. The Mikael Passare memorial volume. Cham: Birkhäuser/Springer (ISBN 978-3-319-52469-6/hbk; 978-3-319-52471-9/ebook). Trends in Mathematics, 261-285 (2017). MSC: 32A60 PDFBibTeX XMLCite \textit{P. Johansson}, in: Analysis meets geometry. The Mikael Passare memorial volume. Cham: Birkhäuser/Springer. 261--285 (2017; Zbl 1404.32013) Full Text: DOI
Nisse, Mounir; Passare, Mikael Amoebas and coamoebas of linear spaces. (English) Zbl 1404.14072 Andersson, Mats (ed.) et al., Analysis meets geometry. The Mikael Passare memorial volume. Cham: Birkhäuser/Springer (ISBN 978-3-319-52469-6/hbk; 978-3-319-52471-9/ebook). Trends in Mathematics, 63-80 (2017). MSC: 14T05 32A60 PDFBibTeX XMLCite \textit{M. Nisse} and \textit{M. Passare}, in: Analysis meets geometry. The Mikael Passare memorial volume. Cham: Birkhäuser/Springer. 63--80 (2017; Zbl 1404.14072) Full Text: DOI arXiv
Mikhalkin, Grigory Quantum indices and refined enumeration of real plane curves. (English) Zbl 1468.14092 Acta Math. 219, No. 1, 135-180 (2017). Reviewer: Eugenii I. Shustin (Tel Aviv) MSC: 14N10 14H50 14P05 14T15 PDFBibTeX XMLCite \textit{G. Mikhalkin}, Acta Math. 219, No. 1, 135--180 (2017; Zbl 1468.14092) Full Text: DOI arXiv
Welk, Martin; Kleefeld, Andreas; Breuß, Michael Quantile filtering of colour images via symmetric matrices. (English) Zbl 1469.68163 Math. Morphol., Theory Appl. 1, 136-174 (2016). MSC: 68U10 94A08 PDFBibTeX XMLCite \textit{M. Welk} et al., Math. Morphol., Theory Appl. 1, 136--174 (2016; Zbl 1469.68163) Full Text: DOI
González-Hidalgo, Manuel; Massanet, Sebastia; Mir, Arnau; Ruiz-Aguilera, Daniel Gaussian noise reduction using fuzzy morphological amoebas. (English) Zbl 1452.94005 Carvalho, Joao Paulo (ed.) et al., Information processing and management of uncertainty in knowledge-based systems. 16th international conference, IPMU 2016, Eindhoven, The Netherlands, June 20–24, 2016. Proceedings. Part I. Cham: Springer. Commun. Comput. Inf. Sci. 610, 660-671 (2016). MSC: 94A08 94D05 PDFBibTeX XMLCite \textit{M. González-Hidalgo} et al., Commun. Comput. Inf. Sci. 610, 660--671 (2016; Zbl 1452.94005) Full Text: DOI
Bogdanov, D. V.; Kytmanov, A. A.; Sadykov, T. M. Algorithmic computation of polynomial amoebas. (English) Zbl 1453.14145 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 18th international workshop, CASC 2016, Bucharest, Romania, September 19–23, 2016. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9890, 87-100 (2016). MSC: 14P25 14M25 14Q10 65H99 68U05 68W40 PDFBibTeX XMLCite \textit{D. V. Bogdanov} et al., Lect. Notes Comput. Sci. 9890, 87--100 (2016; Zbl 1453.14145) Full Text: DOI arXiv
Berkesch Zamaere, Christine; Forsgård, Jens; Matusevich, Laura Felicia Hypergeometric functions for projective toric curves. (English) Zbl 1350.32006 Adv. Math. 300, 835-867 (2016). Reviewer: Chrysoula G. Kokologiannaki (Patras) MSC: 32A17 33C70 14M25 14F10 PDFBibTeX XMLCite \textit{C. Berkesch Zamaere} et al., Adv. Math. 300, 835--867 (2016; Zbl 1350.32006) Full Text: DOI arXiv
Nisse, Mounir; Sottile, Frank Higher convexity for complements of tropical varieties. (English) Zbl 1369.14072 Math. Ann. 365, No. 1-2, 1-12 (2016). Reviewer: Keyvan Yaghmayi (Salt Lake City) MSC: 14T05 PDFBibTeX XMLCite \textit{M. Nisse} and \textit{F. Sottile}, Math. Ann. 365, No. 1--2, 1--12 (2016; Zbl 1369.14072) Full Text: DOI arXiv
Welk, Martin; Kleefeld, Andreas; Breuß, Michael Non-adaptive and amoeba quantile filters for colour images. (English) Zbl 1445.68323 Benediktsson, Jón Atli (ed.) et al., Mathematical morphology and its applications to signal and image processing. 12th international symposium, ISMM 2015, Reykjavik, Iceland, May 27–29, 2015. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9082, 398-409 (2015). MSC: 68U10 94A08 PDFBibTeX XMLCite \textit{M. Welk} et al., Lect. Notes Comput. Sci. 9082, 398--409 (2015; Zbl 1445.68323) Full Text: DOI
Welk, Martin Analysis of amoeba active contours. (English) Zbl 1357.94028 J. Math. Imaging Vis. 52, No. 1, 37-54 (2015). MSC: 94A08 68U10 PDFBibTeX XMLCite \textit{M. Welk}, J. Math. Imaging Vis. 52, No. 1, 37--54 (2015; Zbl 1357.94028) Full Text: DOI arXiv
Brugallé, Erwan; Shaw, Kristin Obstructions to approximating tropical curves in surfaces via intersection theory. (English) Zbl 1329.14112 Can. J. Math. 67, No. 3, 527-572 (2015). Reviewer: Emilia Mezzetti (Trieste) MSC: 14T05 14M25 PDFBibTeX XMLCite \textit{E. Brugallé} and \textit{K. Shaw}, Can. J. Math. 67, No. 3, 527--572 (2015; Zbl 1329.14112) Full Text: DOI arXiv
Theobald, Thorsten; De Wolff, Timo Approximating amoebas and coamoebas by sums of squares. (English) Zbl 1318.14054 Math. Comput. 84, No. 291, 455-473 (2015). Reviewer: Aris Daniilidis (Santiago) MSC: 14P10 14Q10 90C22 PDFBibTeX XMLCite \textit{T. Theobald} and \textit{T. De Wolff}, Math. Comput. 84, No. 291, 455--473 (2015; Zbl 1318.14054) Full Text: DOI arXiv
Bushueva, Natalia A.; Kuzvesov, Konstantin V.; Tsikh, Avgust K. On the asymptotic of homological solutions to linear multidimensional difference equations. (English) Zbl 1525.39007 J. Sib. Fed. Univ., Math. Phys. 7, No. 4, 417-430 (2014). MSC: 39A14 39A45 PDFBibTeX XMLCite \textit{N. A. Bushueva} et al., J. Sib. Fed. Univ., Math. Phys. 7, No. 4, 417--430 (2014; Zbl 1525.39007) Full Text: MNR
Krichever, I. Amoebas, Ronkin function, and Monge-Ampère measures of algebraic curves with marked points. (English) Zbl 1364.32008 Buchstaber, V. M. (ed.) et al., Topology, geometry, integrable systems and mathematical physics. Novikov’s seminar: 2012–2014. Selected papers of the seminar, Moscow, Russia, 2012–2014. Dedicated to S. P. Novikov on the occasion of his 75th birthday. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-1871-7/hbk). Translations. Series 2. American Mathematical Society 234. Advances in the Mathematical Sciences 67, 265-278 (2014). MSC: 32B20 PDFBibTeX XMLCite \textit{I. Krichever}, Transl., Ser. 2, Am. Math. Soc. 234, 265--278 (2014; Zbl 1364.32008) Full Text: DOI arXiv
Kiselman, Christer O. Questions inspired by Mikael Passare’s mathematics. (English) Zbl 1300.32006 Afr. Mat. 25, No. 2, 271-288 (2014). MSC: 32C30 32A60 14T05 14P25 14H45 32U05 90C10 90C15 PDFBibTeX XMLCite \textit{C. O. Kiselman}, Afr. Mat. 25, No. 2, 271--288 (2014; Zbl 1300.32006) Full Text: DOI
Martin, Bernd; Pochekutov, Dmitry Yu. Discriminant and singularities of logarithmic Gauss map, examples and application. (English) Zbl 1523.14100 J. Sib. Fed. Univ., Math. Phys. 6, No. 1, 74-85 (2013). Reviewer: Aleksandr G. Aleksandrov (Moskva) MSC: 14P99 14B05 14M25 14J70 14-04 PDFBibTeX XMLCite \textit{B. Martin} and \textit{D. Yu. Pochekutov}, J. Sib. Fed. Univ., Math. Phys. 6, No. 1, 74--85 (2013; Zbl 1523.14100) Full Text: arXiv MNR
Theobald, Thorsten; de Wolff, Timo Amoebas of genus at most one. (English) Zbl 1330.14090 Adv. Math. 239, 190-213 (2013). Reviewer: Martin Ulirsch (Bonn) MSC: 14M25 14Q10 14T05 52B20 PDFBibTeX XMLCite \textit{T. Theobald} and \textit{T. de Wolff}, Adv. Math. 239, 190--213 (2013; Zbl 1330.14090) Full Text: DOI arXiv
Madani, Farid; Nisse, Mounir Generalized logarithmic Gauss map and its relation to (co)amoebas. (English) Zbl 1284.14089 Math. Nachr. 286, No. 14-15, 1510-1513 (2013). Reviewer: Martin Ulirsch (Providence) MSC: 14T05 32A60 PDFBibTeX XMLCite \textit{F. Madani} and \textit{M. Nisse}, Math. Nachr. 286, No. 14--15, 1510--1513 (2013; Zbl 1284.14089) Full Text: DOI arXiv
Madani, Farid; Nisse, Mounir On the volume of complex amoebas. (English) Zbl 1303.14068 Proc. Am. Math. Soc. 141, No. 4, 1113-1123 (2013). Reviewer: Eugenii I. Shustin (Tel Aviv) MSC: 14T05 32A60 PDFBibTeX XMLCite \textit{F. Madani} and \textit{M. Nisse}, Proc. Am. Math. Soc. 141, No. 4, 1113--1123 (2013; Zbl 1303.14068) Full Text: DOI arXiv
Bushueva, N. A.; Tsikh, A. K. On amoebas of algebraic sets of higher codimension. (English. Russian original) Zbl 1312.14135 Proc. Steklov Inst. Math. 279, 52-63 (2012); translation from Tr. Mat. Inst. Steklova 279, 59-71 (2012). Reviewer: Ivan Bazhov (Carouge) MSC: 14P25 14M10 32C99 14T05 PDFBibTeX XMLCite \textit{N. A. Bushueva} and \textit{A. K. Tsikh}, Proc. Steklov Inst. Math. 279, 52--63 (2012; Zbl 1312.14135); translation from Tr. Mat. Inst. Steklova 279, 59--71 (2012) Full Text: DOI
Itenberg, I.; Mikhalkin, G. Geometry in the tropical limit. (English) Zbl 1253.14058 Math. Semesterber. 59, No. 1, 57-73 (2012). Reviewer: Eugenii I. Shustin (Tel Aviv) MSC: 14T05 14N10 14N35 81Q05 82B30 PDFBibTeX XMLCite \textit{I. Itenberg} and \textit{G. Mikhalkin}, Math. Semesterber. 59, No. 1, 57--73 (2012; Zbl 1253.14058) Full Text: DOI arXiv
Welk, Martin; Breuß, Michael; Vogel, Oliver Morphological amoebas are self-snakes. (English) Zbl 1255.94029 J. Math. Imaging Vis. 39, No. 2, 87-99 (2011). MSC: 94A08 68U10 PDFBibTeX XMLCite \textit{M. Welk} et al., J. Math. Imaging Vis. 39, No. 2, 87--99 (2011; Zbl 1255.94029) Full Text: DOI
Welk, Martin; Breuß, Michael; Vogel, Oliver Differential equations for morphological amoebas. (English) Zbl 1252.94025 Wilkinson, Michael H. F. (ed.) et al., Mathematical morphology and its application to signal and image processing. 9th international symposium, ISMM 2009, Groningen, The Netherlands, August 24–27, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-03612-5/pbk). Lecture Notes in Computer Science 5720, 104-114 (2009). MSC: 94A08 65D18 92C55 PDFBibTeX XMLCite \textit{M. Welk} et al., Lect. Notes Comput. Sci. 5720, 104--114 (2009; Zbl 1252.94025) Full Text: DOI
Gathmann, Andreas Tropical algebraic geometry. (English) Zbl 1109.14038 Jahresber. Dtsch. Math.-Ver. 108, No. 1, 3-32 (2006). Reviewer: Eugenii I. Shustin (Tel Aviv) MSC: 14N10 05C99 12J10 12J25 14A10 14M25 14N35 14P99 PDFBibTeX XMLCite \textit{A. Gathmann}, Jahresber. Dtsch. Math.-Ver. 108, No. 1, 3--32 (2006; Zbl 1109.14038) Full Text: arXiv
Mikhalkin, Grigory Tropical geometry and its applications. (English) Zbl 1103.14034 Sanz-Solé, Marta (ed.) et al., Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, August 22–30, 2006. Volume II: Invited lectures. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-022-7/hbk). 827-852 (2006). Reviewer: Eugenii I. Shustin (Tel Aviv) MSC: 14P99 14H50 14N10 52B20 PDFBibTeX XMLCite \textit{G. Mikhalkin}, in: Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, August 22--30, 2006. Volume II: Invited lectures. Zürich: European Mathematical Society (EMS). 827--852 (2006; Zbl 1103.14034) Full Text: arXiv
Passare, Mikael; Sadykov, Timur; Tsikh, August Singularities of hypergeometric functions in several variables. (English) Zbl 1080.33012 Compos. Math. 141, No. 3, 787-810 (2005). Reviewer: Vasily A. Chernecky (Odessa) MSC: 33C70 PDFBibTeX XMLCite \textit{M. Passare} et al., Compos. Math. 141, No. 3, 787--810 (2005; Zbl 1080.33012) Full Text: DOI arXiv
Gross, Mark Amoebas of complex curves and tropical curves. (English) Zbl 1083.14061 Guest, Martin (ed.) et al., UK-Japan winter school 2004—Geometry and analysis towards quantum theory.; Lecture notes from the school, University of Durham, Durham, UK, January 6–9, 2004. Yokohama: Keio University, Department of Mathematics. Seminar on Mathematical Sciences 30, 24-36 (2004). Reviewer: Jose Manuel Gamboa (Madrid) MSC: 14N10 14P10 14N35 PDFBibTeX XMLCite \textit{M. Gross}, Semin. Math. Sci. 30, 24--36 (2004; Zbl 1083.14061)
Itenberg, Ilia Amoebas of algebraic varieties and curves counting (following G. Mikhalkin). (Amibes de variétés algébriques et dénombrement de courbes (d’après G. Mikhalkin).) (French) Zbl 1059.14067 Bourbaki seminar. Volume 2002/2003. Exposes 909–923. Paris: Société Mathématique de France (ISBN 2-85629-156-2/pbk). Astérisque 294, 335-361, Exp. No. 921 (2004). Reviewer: Eugenii I. Shustin (Tel Aviv) MSC: 14N35 14P25 12J25 14J26 14N10 PDFBibTeX XMLCite \textit{I. Itenberg}, Astérisque 294, 335--361, Exp. No. 921 (2004; Zbl 1059.14067)
Mikhalkin, Grigory; Rullgård, Hans Amoebas of maximal area. (English) Zbl 0994.14032 Int. Math. Res. Not. 2001, No. 9, 441-451 (2001). Reviewer: J.M.Gamboa (Madrid) MSC: 14P15 14H45 32C05 PDFBibTeX XMLCite \textit{G. Mikhalkin} and \textit{H. Rullgård}, Int. Math. Res. Not. 2001, No. 9, 441--451 (2001; Zbl 0994.14032) Full Text: DOI arXiv
Passare, Mikael; Rullgård, Hans Multiple Laurent series and polynomial amoebas. (English) Zbl 1038.32001 Raby, Gilles (ed.) et al., Proceedings of the conference on complex analysis. In honor of Jean-Baptiste Poly, Université de Poitiers, Poitiers-Futuroscope, France, March 25–28, 1999. Poitiers: Atlantique (ISBN 2-911320-14-X/pbk). 123-129 (2000). Reviewer: Eleonora Storozhenko (Odessa) MSC: 32A05 32A07 PDFBibTeX XMLCite \textit{M. Passare} and \textit{H. Rullgård}, in: Actes des rencontres d'analyse complexe. En l'honneur de Jean-Baptiste Poly, Université de Poitiers, Poitiers-Futuroscope, France, March 25--28, 1999. Poitiers: Atlantique; Futuroscope: E.S.A. CNRS 6086 ``Groupes de Lie et Géométrie''. 123--129 (2000; Zbl 1038.32001)
Forsberg, Mikael; Passare, Mikael; Tsikh, August Laurent determinants and arrangements of hyperplane amoebas. (English) Zbl 1002.32018 Adv. Math. 151, No. 1, 45-70 (2000). MSC: 32S22 PDFBibTeX XMLCite \textit{M. Forsberg} et al., Adv. Math. 151, No. 1, 45--70 (2000; Zbl 1002.32018) Full Text: DOI Link
Abramson, Fred G. A simplicity theorem for amoebas over random reals. (English) Zbl 0446.03040 Proc. Am. Math. Soc. 78, 409-413 (1980). MSC: 03E15 03E35 28A20 PDFBibTeX XMLCite \textit{F. G. Abramson}, Proc. Am. Math. Soc. 78, 409--413 (1980; Zbl 0446.03040) Full Text: DOI