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On a theorem of forelli in a non-standard setting. (English) Zbl 07928448

Eyral, Christophe (ed.) et al., GKLW-workshop in singularity theory in memory of Stanisław Łojasiewicz. Selected papers, Warsaw, Poland, December 2022. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Cent. Publ. 128, 127-134 (2024).

MSC: 32A05 32A10 14P15 14P20

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Alkateeb, Mohamad; Rebelo, Julio

Examples of harmonic foliated currents and singular Levi-flats on the projective plane. (English) Zbl 07916596

Adv. Math. 452, Article ID 109792, 40 p. (2024).

MSC: 37F75 37Axx 32C07

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Baro, E.; Fernando, José F.; Gamboa, J. M.

Rings of differentiable semialgebraic functions. (English) Zbl 07902506

Sel. Math., New Ser. 30, No. 4, Paper No. 71, 56 p. (2024).

MSC: 14P10 46E25 12D15 13E99

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Belotto da Silva, André; Curmi, Octave; Rond, Guillaume

On the Nash points of subanalytic sets. (English) Zbl 07865143

J. Singul. 27, 68-88 (2024).

MSC: 13B10 14P20 32C07 13A18 13J05 32B20

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Carbone, Antonio; Fernando, José F.

Surjective Nash maps between semialgebraic sets. (English) Zbl 1537.14079

Adv. Math. 438, Article ID 109288, 57 p. (2024).

Reviewer: José Javier Etayo (Madrid)

MSC: 14P10 14P20 58A07 14E15 57R12

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Pan, Yifei; Zhang, Yuan

Continuous Sobolev functions with singularity on arbitrary real-analytic sets. arXiv:2406.04544

Preprint, arXiv:2406.04544 [math.AP] (2024).

MSC: 32C07 46E35 14E15

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Kocel-Cynk, Beata; Pawłucki, Wiesław; Valette, Anna

Semialgebraic Calderon-Zygmund theorem on regularization of the distance function. arXiv:2403.03135

Preprint, arXiv:2403.03135 [math.CA] (2024).

MSC: 14P20 57R35 14P10 32B20

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Kollár, János

Real analytic functions and monomial curves. (English) Zbl 1542.14074

Bull. Pol. Acad. Sci., Math. 71, No. 1, 53-63 (2023).

Reviewer: Tobias Kaiser (Passau)

MSC: 14P15 26E05 32C07

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Kocel-Cynk, Beata; Pawłucki, Wiesław; Valette, Anna

Approximation of singular semialgebraic sets by smooth ones with respect to the Hausdorff metric. (English) Zbl 1514.14071

Bull. Sci. Math. 185, Article ID 103270, 12 p. (2023).

Reviewer: Janusz Adamus (London, ON)

MSC: 14P10 14P20 14B07 58K60

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Fernando, José F.; Ueno, Carlos

On polynomial images of a closed ball. (English) Zbl 1521.14099

J. Math. Soc. Japan 75, No. 2, 679-733 (2023).

Reviewer: Jose Capco (Linz)

MSC: 14P10 41A10 52A20 52B99

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Kucharz, Wojciech; Kurdyka, Krzysztof

Regulous functions over real closed fields. (English) Zbl 1509.14112

Int. Math. Res. Not. 2023, No. 3, 2649-2664 (2023).

Reviewer: Alexander Kovačec (Coimbra)

MSC: 14P05 14P20 26C15 12D99 58A07

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Carbone, Antonio; Fernando, José F.

Strong desingularization of semialgebraic sets and applications. arXiv:2306.08093

Preprint, arXiv:2306.08093 [math.AG] (2023).

MSC: 14P10 14P20 14E15 14B05 57R12 57Q55

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Lebl, Jiří; Mernik, Luka

On Segre-degenerate Levi-flat hypervarieties. arXiv:2306.07259

Preprint, arXiv:2306.07259 [math.CV] (2023).

MSC: 32C07 32E20 32D10 14P15

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Savi, Enrico

A relative Nash-Tognoli theorem over \(\mathbb{Q}\) and application to the \(\mathbb{Q}\)-algebraicity problem. arXiv:2302.04673

Preprint, arXiv:2302.04673 [math.AG] (2023).

MSC: 14P05 14P25 14P20 57R99 14E15 14M15

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Ghiloni, Riccardo; Savi, Enrico

The topology of real algebraic sets with isolated singularities is determined by the field of rational numbers. arXiv:2302.04142

Preprint, arXiv:2302.04142 [math.AG] (2023).

MSC: 14P05 14P10 14P20

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Koike, Satoshi; Paunescu, Laurentiu

On finiteness theorems of polynomial functions. (English) Zbl 1491.14082

Eur. J. Math. 8, Suppl. 1, S214-S234 (2022).

MSC: 14P10 32S15 32S45 57R45 14P20

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Lebl, Jiří

Segre-degenerate points form a semianalytic set. (English) Zbl 1487.32037

Proc. Am. Math. Soc., Ser. B 9, 159-173 (2022).

MSC: 32C07 32B20 14P15

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Bochnak, Jacek; Kucharz, Wojciech

Algebraic surfaces determine analyticity of functions. (English) Zbl 1482.14058

Arch. Math. 118, No. 1, 57-63 (2022).

MSC: 14P05 14P20 58A07 32C05 32C25

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Bilski, Marcin; Scheiblechner, Peter

Effective approximation of the solutions of algebraic equations. (English) Zbl 1476.14104

J. Symb. Comput. 109, 144-176 (2022).

Reviewer: Sonia Pérez Díaz (Madrid)

MSC: 14Q99 32B10 32C07 65H10 68W30

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Kucharz, Wojciech; Kurdyka, Krzysztof

Arc-meromorphous functions. (English) Zbl 1479.14073

Ann. Pol. Math. 127, No. 1-2, 51-62 (2021).

MSC: 14P10 14P20 32B10 58A07

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Valette, Anna

Stratified \({{\mathcal{C}}}^P\)-semialgebraic triviality. (English) Zbl 1468.14100

Manuscr. Math. 166, No. 1-2, 315-322 (2021).

MSC: 14P10 14P20 57R35

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Kucharz, Wojciech; Kurdyka, Krzysztof; El-Siblani, Ali

Separately Nash and arc-Nash functions over real closed fields. (English) Zbl 1465.14054

Bull. Lond. Math. Soc. 53, No. 2, 426-441 (2021).

MSC: 14P10 14P20 32B20 58A07

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Valette, Anna; Valette, Guillaume

Approximations in globally subanalytic and Denjoy-Carleman classes. (English) Zbl 1467.14142

Adv. Math. 385, Article ID 107764, 32 p. (2021).

Reviewer: Fujita Masato (Kure)

MSC: 14P10 32B20 41A30 58A07

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Kucharz, Wojciech; Kurdyka, Krzysztof

Rational representation of real functions. (English) Zbl 1460.14126

Pure Appl. Math. Q. 17, No. 1, 249-268 (2021).

MSC: 14P05 14P10 26C15

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Spodzieja, Stanisław

A geometric model of an arbitrary differentially closed field of characteristic zero. (English) Zbl 1465.12007

Trans. Am. Math. Soc. 374, No. 1, 663-686 (2021).

Reviewer: Gerhard Pfister (Kaiserslautern)

MSC: 12H05 13N15 14P20 14P10

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Adamus, Janusz; Patel, Aftab

Equisingular algebraic approximation of real and complex analytic germs. (English) Zbl 1519.32005

J. Singul. 20, 289-310 (2020).

MSC: 32S05 32S10 32B99 32C07 14P15 14P20 13H10 13C14

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Berraho, Mourad

On a problem concerning the ring of Nash germs and the Borel mapping. (English) Zbl 1484.32011

AIMS Math. 5, No. 2, 923-929 (2020).

MSC: 32C07 13F25 14P20

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Domitrz, Wojciech; Mormul, Piotr; Pragacz, Piotr

Order of tangency between manifolds. (English) Zbl 1451.14014

Hu, Jianxun (ed.) et al., Schubert calculus and its applications in combinatorics and representation theory. Selected papers presented at the “International Festival in Schubert Calculus”, Guangzhou, China, November 6–10, 2017. Singapore: Springer. Springer Proc. Math. Stat. 332, 27-42 (2020).

MSC: 14C17 14M15 14N10 14N15 14P10 14P20 32B20 32C07

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Fichou, Goulwen; Monnier, Jean-Philippe; Quarez, Ronan

Substitution property for the ring of continuous rational functions. (English) Zbl 1441.14190

Ishikawa, Masaharu (ed.) et al., Singularities – Kagoshima 2017. Proceedings of the 5th Franco-Japanese-Vietnamese symposium on singularities, Kagoshima, Japan, October 27 – November 3, 2017. Hackensack, NJ: World Scientific. 71-93 (2020).

MSC: 14P05 14P20 11E25 26C15

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Nguyen, Nhan; Trivedi, Saurabh

Transversality of smooth definable maps in o-minimal structures. (English) Zbl 1447.32015

Math. Proc. Camb. Philos. Soc. 168, No. 3, 519-533 (2020).

MSC: 32C07 14P10 32B20

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El-Siblani, Ali; Kurdyka, Krzysztof

On the regularity of a semialgebraic function. (English) Zbl 1448.14057

Ann. Pol. Math. 125, No. 1, 25-46 (2020).

MSC: 14P10 14P20 32B20 58A07

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Priziac, Fabien

Quotients and invariants of \(\mathcal{AS}\)-sets equipped with a finite group action. (English) Zbl 1454.14135

Math. Ann. 377, No. 3-4, 1015-1055 (2020).

MSC: 14P05 14P10 14P20 14L24 57S17

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Bürgisser, Peter; Lerario, Antonio

Probabilistic Schubert calculus. (English) Zbl 1436.32029

J. Reine Angew. Math. 760, 1-58 (2020).

MSC: 32C07 14N15 14P15

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Kurdyka, Krzysztof; Spodzieja, Stanisław; Szlachcińska, Anna

Correction to: Metric properties of semialgebraic mappings. (English) Zbl 1453.14142

Discrete Comput. Geom. 62, No. 4, 990-991 (2019).

MSC: 14P10 32C07 14P20

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Ishikawa, Goo; Yamashita, Tatsuya

Leibniz complexity of Nash functions on differentiations. (English) Zbl 1441.14198

J. Math. Soc. Japan 71, No. 3, 709-726 (2019).

MSC: 14P20 58A07 32C07

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Elazar, Boaz

Quasi-Nash varieties and Schwartz functions on them. (English) Zbl 1458.14066

Isr. J. Math. 232, No. 2, 589-629 (2019).

Reviewer: Alexander Kovačec (Coimbra)

MSC: 14P20 14P05 14P10 46E99

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Bochnak, Jacek; Kucharz, Wojciech

Global variants of Hartogs’ theorem. (English) Zbl 1472.32002

Arch. Math. 113, No. 3, 281-290 (2019).

Reviewer: Zofia Denkowska (Angers)

MSC: 32A10 14A10 32C07 32C15

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Fernando, José F.; Ghiloni, Riccardo

Differentiable approximation of continuous semialgebraic maps. (English) Zbl 1472.14067

Sel. Math., New Ser. 25, No. 3, Paper No. 46, 30 p. (2019).

Reviewer: James Madden (Baton Rouge)

MSC: 14P10 57Q55 14P05 14P20

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Baro, Elías; de Vicente, Juan; Otero, Margarita

Locally \(\mathbb{C}\)-Nash groups. (English) Zbl 1440.14263

Rev. Mat. Complut. 32, No. 2, 531-558 (2019).

MSC: 14P10 14P20 03C64

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Campesato, Jean-Baptiste; Fukui, Toshizumi; Kurdyka, Krzysztof; Parusiński, Adam

Arc spaces, motivic measure and Lipschitz geometry of real algebraic sets. (English) Zbl 1436.14094

Math. Ann. 374, No. 1-2, 211-251 (2019).

Reviewer: Immanuel Halupczok (Leeds)

MSC: 14P20 26A16 14E18 14B05

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Gérard, Christian; Wrochna, Michał

Analytic Hadamard states, Calderón projectors and Wick rotation near analytic Cauchy surfaces. (English) Zbl 1414.58002

Commun. Math. Phys. 366, No. 1, 29-65 (2019).

Reviewer: Gabor Etesi (Budapest)

MSC: 58A07 32C07 35Q40

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Czarnecki, Aleksander

Maximal ideals of regulous functions are not finitely generated. (English) Zbl 1402.14075

J. Pure Appl. Algebra 223, No. 3, 1161-1166 (2019).

Reviewer: Jie Wang (Beijing)

MSC: 14P10 26C15 14P20

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Kucharz, Wojciech; Kurdyka, Krzysztof

From continuous rational to regulous functions. (English) Zbl 1441.14191

Sirakov, Boyan (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2018, Rio de Janeiro, Brazil, August 1–9, 2018. Volume II. Invited lectures. Hackensack, NJ: World Scientific; Rio de Janeiro: Sociedade Brasileira de Matemática (SBM). 719-747 (2018).

MSC: 14P05 14P10 14E18 26C15 57R22 58A07

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Elazar, Boaz; Shaviv, Ary

Schwartz functions on real algebraic varieties. (English) Zbl 1445.14078

Can. J. Math. 70, No. 5, 1008-1037 (2018).

Reviewer: Maria Infusino (Konstanz)

MSC: 14P05 14P20 22E45 46A11 46F05

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Adamus, Janusz; Seyedinejad, Hadi

On solutions of linear equations with polynomial coefficients. (English) Zbl 1423.14330

Ann. Pol. Math. 121, No. 1, 1-6 (2018).

MSC: 14P10 14P20

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Rond, Guillaume

Local topological algebraicity with algebraic coefficients of analytic sets or functions. (English) Zbl 1400.32014

Algebra Number Theory 12, No. 5, 1215-1231 (2018).

MSC: 32S05 32C07 14B05 32A05 32B10

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Fernando, José F.

On Nash images of Euclidean spaces. (English) Zbl 1397.14074

Adv. Math. 331, 627-719 (2018).

Reviewer: Zofia Denkowska (Angers)

MSC: 14P20 58A07 14P10 14E15

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Bekka, K.; Trotman, D.

Corrigendum: “Briançon-Speder examples and the failure of weak Whitney regularity”. (English) Zbl 1391.32045

J. Singul. 17, 214-215 (2018).

MSC: 32S25 32C07

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Adamus, Janusz; Seyedinejad, Hadi

Extensions of arc-analytic functions. (English) Zbl 1430.14106

Math. Ann. 371, No. 1-2, 685-693 (2018).

Reviewer: Eugenii I. Shustin (Tel Aviv)

MSC: 14P10 14P20 14P99

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Fernando, José F.; Gamboa, José M.; Ueno, Carlos

Polynomial, regular and Nash images of Euclidean spaces. (English) Zbl 1390.14177

Broglia, Fabrizio (ed.) et al., Ordered algebraic structures and related topics. International conference at CIRM, Luminy, France, October 12–16, 2015. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2966-9/pbk; 978-1-4704-4222-4/ebook). Contemporary Mathematics 697, 145-167 (2017).

MSC: 14P10 54C30 12D15

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Acquistapace, Francesca; Broglia, Fabrizio; Fernando, José F.

Some results on global real analytic geometry. Dedicated to Murray Marshall, in memoriam. (English) Zbl 1390.14180

Broglia, Fabrizio (ed.) et al., Ordered algebraic structures and related topics. International conference at CIRM, Luminy, France, October 12–16, 2015. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2966-9/pbk; 978-1-4704-4222-4/ebook). Contemporary Mathematics 697, 1-21 (2017).

MSC: 14P15 58A07 32C25 26E05 32C20

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Spodzieja, Stanisław; Szlachcińska, Anna

Łojasiewicz exponent of overdetermined semialgebraic mappings. (English) Zbl 1386.14200

Krasiński, Tadeusz (ed.) et al., Analytic and algebraic geometry. 2. Dedicated to the memory of Arkadiusz Płoski, Kamil Rusek and Krzysztof Kurdyka on the occasion of their 70th and 60th birthdays. Łódź: Łódź University Press (ISBN 978-83-8088-922-4/hbk; 978-83-8088-923-1/ebook). 179-188 (2017).

MSC: 14P20 14P10 32C07

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Kurdyka, Krzysztof

Analytic arcs and real analytic singularities. (English) Zbl 1403.14091

Bekka, K. (ed.) et al., Real algebraic geometry. Paris: Société Mathématique de France (SMF) (ISBN 978-2-85629-857-2/pbk). Panoramas et Synthèses 51, 79-106 (2017).

Reviewer: Tien-Son Pham (Dalat)

MSC: 14P20 14-02 32B10 14J17