Analytic and Algebraic Geometry 2

The volume is dedicated to three mathematicians celebrating in 2017 the jubilees of 70th and 60th birth anniversaries: Arkadiusz Ptoski, Kamil Rusek and Krzysztof Kurdyka. They all have contributed significantly to the success of the annual conferences Analytic and Algebraic Geometry since 1983 till now.

Preface 7 DEDICATIONS 9 Arkadiusz Płoski, Photo of Arkadiusz Płoski 11 Arkadiusz Płoski – Scientific biography 13 Kamil Rusek, Photo of Kamil Rusek 15 Kamil Rusek – Scientific biography 17 Krzysztof Kurdyka, Photo of Krzysztof Kurdyka 19 Krzysztof Kurdyka – Scientific biography 21 Shreeram Shankar Abhyankar, Photo of Shreeram Shankar Abhyankar 23 Note about Shreeram Shankar Abhyankar (1930–2012) 25 Poem: Shreeram S. Abhyankar, Polynomials and power series 27 Poem: Shreeram S. Abhyankar, Wielomiany i szeregi potęgowe (translation into Polish by Michał Szurek) 29 Poem: Shreeram S. Abhyankar, Wielomiany i szeregi potęgowe (translation into Polish by Tadeusz Krasiński) 33 SCIENTIFIC ARTICLES 35 Szymon Brzostowski, Tadeusz Krasiński, and Justyna Walewska, A short proof that equisingular plane curve singularities are topologically equivalent 37 Szymon Brzostowski and Tomasz Rodak, The Łojasiewicz exponent via the valuative Hamburger-Noether process 51 Stanisław Janeczko, Zbigniew Jelonek, and Maria Aparecida Soares Ruas, On a generic symmetry defect hypersurface 67 Zbigniew Jelonek, Wojciech Kucharz, and Krzysztof Kurdyka, Vector bundles and blowups 75 Piotr Jędrzejewicz, Łukasz Matysiak, and Janusz Zieliński, A note on square-free factorizations 79 Wojciech Kucharz and Krzysztof Kurdyka, Rationality of semialgebraic functions 85 Jean Moulin Ollagnier and Andrzej Nowicki, Rational constants of cyclotomic derivations 97 Andrzej Nowicki, Divergence-free polynomial derivations 123 Beata Osińska-Ulrych and Grzegorz Skalski, The Cauchy-Kowalevski Theorem 145 Arkadiusz Płoski, Formal and convergent solutions of analytic equations 161 Arkadiusz Płoski and Maciej Sękalski, Bézout’s inequality for real polynomials 175 Stanisław Spodzieja and Anna Szlachcińska, Łojasiewicz exponent of overdetermined semialgebraic mappings 179