Przeglądaj Wydział Matematyki i Informatyki | Faculty of Mathematics and Computer Science według tytułu
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A family of hyperbolas associated to a triangle
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)In this note, we explore an apparently new one parameter family of conics associated to a triangle. Given a triangle we study ellipses whose one axis is parallel to one of sides of the triangle. The centers of these ellipses ... -
A few introductory remarks on line arrangements
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)Points and lines can be regarded as the simplest geometrical objects. Incidence relations between them have been studied since ancient times. Strangely enough our knowledge of this area of mathematics is still far from ... -
A Modest Review of a Great Deal of Work
(Wydawnictwo Uniwersytetu Łódzkiego, 2013) -
A non-containment example on lines and a smooth curve of genus 10
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)The containment problem between symbolic and ordinary powers of homogeneous ideals has stimulated a lot of interesting research recently. In the most basic case of points in P2 and powers I(3) and I2, there is a number of ... -
A note on divergence-free polynomial derivations in positive characteristic
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)In this paper we discuss an explicit form of divergence-free polynomial derivations in positive characteristic. It involves Jacobian derivations. -
A note on square-free factorizations
(Łódź University Press, 2017)We analyze properties of various square-free factorizations in greatest common divisor domains (GCD-domains) and domains satisfying the ascending chain condition for principal ideals (ACCP-domains). -
A note on the dependence of solutions on functional parameters for nonlinear sturm-liouville problems
(AGH University of Science and Technology Press, 2014)We deal with the existence and the continuous dependence of solutions on functional parameters for boundary valued problems containing the Sturm-Liouville equation. We apply these result to prove the existence of at least ... -
A note on the Łojasiewicz exponent of non-degenerate isolated hypersurface singularities
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)We prove that in order to find the value of the Łojasiewicz exponent ł(f) of a Kouchnirenko non-degenerate holomorphic function f : (Cn; 0) → (C; 0) with an isolated singular point at the origin, it is enough to find this ... -
A short proof that equisingular plane curve singularities are topologically equivalent
(Łódź University Press, 2017)We prove that if two plane curve singularities are equisingular, then they are topologically equivalent. The method we will use is P. Fortuny Ayuso’s who proved this result for irreducible plane curve singularities. -
An estimation of the jump of the Milnor number of plane curve singularities
(Wydawnictwo Uniwersytetu Łódzkiego, 2022)Skokiem liczby Milnora osobliwości izolowanej nazywamy najmniejszą niezerową różnicę między liczbą Milnora osobliwości a liczbą Milnora jednej z jej osobliwości. W pracy za pomocą diagramów Enriquesa wyznaczone zostały ... -
An integral formula for Riemannian G-structures with applications to almost Hermitian and almost contact structures
(Springer Nature, 2019)For a Riemannian G-structure, we compute the divergence of the vector field induced by the intrinsic torsion. Applying the Stokes theorem, we obtain the integral formula on a closed oriented Riemannian manifold, which we ... -
An invitation to the positivity and geometry of algebraic cycles
(Wydawnictwo Uniwersytetu Łódzkiego, 2022)The purpose of this work is an introduction and overview of geometric and numeric properties of algebraic cycles in smooth projective varieties. We recall or propose several problems, which we consider worth to study. We ... -
Analitic and Algebraic Geometry 4
(Wydawnictwo Uniwersytetu Łódzkiego, 2022)This volume (the fourth in the series) is dedicated to two mathematicians: Wojciech Kucharz, who celebrates 70th anniversary in 2022 and Tadeusz Winiarski who celebrated the 80th anniversary in 2020. These people were ... -
Andrzej Nowicki – Scientific biography
(Wydawnictwo Uniwersytetu Łódzkiego, 2019) -
Arkadiusz Płoski- Scientific biography
(Łódź University Press, 2017) -
Axial functions
(Wydawnictwo Uniwersytetu Łódzkiego, 2013) -
Baire Category Lower Density Operators with Borel Values
; Hejduk, Jacek
; (Springer Nature, 2023)
We prove that the lower density operator associated with the Baire category density points in the real line has Borel values of class Π<SUP>0</SUP><SUB>3</SUB> which is analogous to the measure case. We also introduce ... -
Best Proximity Point Theorem in Quasi-Pseudometric Spaces
(Hindawi, 2016)In quasi-pseudometric spaces (not necessarily sequentially complete), we continue the research on the quasi-generalized pseudodistances. We introduce the concepts of semiquasiclosed map and contraction of Nadler type with ... -
Bézout’s inequality for real polynomials
(Łódź University Press, 2017)Let F(X, Y ), G(X, Y ) be polynomials of degrees m, n > 0 respectively. We prove, that the set {(x, y) Є R² : F(x, y) = G(x, y) = 0} has at most mn connected components. -
Bilinear mappings – selected properties and problems
(Wydawnictwo Uniwersytetu Łódzkiego, 2013)