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On smooth hypersurfaces containing a given subvariety

Jelonek, Zbigniew (Wydawnictwo Uniwersytetu Łódzkiego, 2013)

We reprove some results about affine complete intersections.

On C0-sufficiency of jets

Osińska-Ulrych, Beata; Skalski, Grzegorz; Spodzieja, Stanisław (Wydawnictwo Uniwersytetu Łódzkiego, 2013)

The paper presents some details of the proofs by Kuiper and Kuo, and Bochnak and Łojasiewicz that refer to the impact of the Łojasiewicz exponent of gradient mappings on C0-sufficiency of jets.

Euclidean algorithm and polynomial equations after Labatie

García Barroso, Evelia Rosa; Płoski, Arkadiusz (Wydawnictwo Uniwersytetu Łódzkiego, 2013)

We recall Labatie's effective method of solving polynomial equations with two unknowns by using the Euclidean algorithm.

Necessary conditions for irreducibility of algebroid plane curves

Brzostowski, Szymon (Wydawnictwo Uniwersytetu Łódzkiego, 2013)

Let K be an algebraically closed field of characteristic 0 and let ƒ ϵ K[[X]] [Y] be monic. Using the properties of approximate roots given in [J. Algebra 343 (2011), pp. 143-159] we propose some necessary conditions for ...

Geometric desingularization of curves in manifolds

Łojasiewicz, Stanisław (Wydawnictwo Uniwersytetu Łódzkiego, 2013)

Preface

Krasinski, Tadeusz; Spodzieja, Stanisław (Wydawnictwo Uniwersytetu Łódzkiego, 2013)

On Chouikha’s isochronicity criterion

Strelcyn, Jean-Marie (Wydawnictwo Uniwersytetu Łódzkiego, 2013)

Recently A.R.Chouikha gave a new characterization of isochronicity of center at the origin for the equation x'' + g(x) = 0, where g is a real smooth function de_ned in some neighborhood of 0 ϵ R. We present some new ...

Introduction to the local theory of plane algebraic curves

Płoski, Arkadiusz (Wydawnictwo Uniwersytetu Łódzkiego, 2013)

We consider the algebroid plane curves de ned by formal power series of two variables with coe cients in an algebraically closed eld. Using quadratic transformations we prove the local normalization theorem. Then we study ...

Multiple zeta values and the WKB method

Zakrzewski, Michał; Żołądek, Henryk (Wydawnictwo Uniwersytetu Łódzkiego, 2013)

The multiple zeta values ζ(d1, . . . , dr ) are natural generalizations of the values ζ(d) of the Riemann zeta functions at integers d. They have many applications, e.g. in knot theory and in quantum physics. It turns ...