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Żywilla Fechner

Publications and source records attributed to Żywilla Fechner.

6 recordsLinked to original sources
arXiv2026

Why Do Students (Not) Choose Second-Cycle Mathematics Studies? Questionnaire and Graduate-Tracking Evidence from Poland

The Bologna Process has substantially reshaped higher education systems across Europe, including the structure of mathematical studies in Poland. One of the increasingly visible consequences of these transformations is the relatively low retention rate between first- and second-cycle studies. The aim of this paper is to investigate selected factors associated with students' willingness to continue mathematical education after obtaining a Bachelor's degree. The study combines questionnaire-based research conducted among mathematics students from 13 Polish higher education institutions with an auxiliary analysis of nationwide graduate-tracking data obtained from the Polish Graduate Tracking System (ELA). The survey investigated students' opinions on general and specialized courses, perceived labour-market usefulness of studies and future educational intentions. The results indicate that students willing to continue second-cycle studies evaluate both the substantive quality and practical usefulness of their studies more positively than students intending to leave mathematics or change institutions. Satisfaction with the chosen specialization emerged as one of the strongest differentiating factors between the analysed groups. At the same time, a substantial proportion of respondents expressed doubts regarding the professional utility of continuing mathematical education, despite administrative labour-market data suggesting several advantages associated with obtaining a Master's degree. The findings suggest that retention in mathematics is shaped not only by academic difficulty, but also by the perceived relationship between university curricula, specialization structures and labour-market expectations. We conclude with recommendations regarding curriculum design, cooperation with external stakeholders and other aspects of second-cycle mathematical education.

math.HO↗
arXiv2022

Moment functions of higher rank on polynomial hypergroups

In this paper we consider generalized moment functions of higher order. These functions are closely related to the well-known functions of binomial type which have been investigated on various abstract structures. In our former paper we investigated the properties of generalized moment functions of higher order on commutative groups. In particular, we proved the characterization of generalized moment functions on a commutative group as the product of an exponential and composition of multivariate Bell polynomial and a sequence additive functions. In the present paper we continue the study of generalized moment function sequences of higher order in the more abstract setting, namely we consider functions defined on a hypergroup. We characterize these functions on the polynomial hypergroup in one variable by means of partial derivatives of a composition of polynomials generating the polynomial hypergroup and an analytic function. As an example, we give an explicit formula for moment generating functions of rank at most two on the Tchebyshev hypergroup.

math.CO↗
arXiv2021

Moment functions and exponential monomials on commutative hypergroups

The purpose of this paper is to prove that if on a commutative hypergroup an exponential monomial has the property that the linear subspace of all sine functions in its variety is one dimensional, then this exponential monomial is a linear combination of generalized moment functions.

math.SP↗
arXiv2020

Moment functions on groups

The main purpose of this work is to prove characterization theorems for generalized moment functions on groups. According one of the main results these are exponential polynomials that can be described with the aid of complete (exponential) Bell polynomials. These characterizations will be immediate consequences of our main result about the characterization of generalized moment functions of higher rank.

math.CA↗
arXiv2015

Sine functions on hypergroups

In a recent paper we introduced sine functions on commutative hypergroups. These functions are natural generalizations of those functions on groups which are products of additive and multiplicative homomorphisms. In this paper we describe sine functions on different types of hypergroups, including polynomial hypergroups, Sturm--Liouville hypergroups, etc. A non-commutative hypergroup is also considered.

math.FA↗