Christian Henriksen
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Christian Henriksen has a total of 48 co-authors. Here are the top co-authors by number of shared publications:
- Berta Fernández
Department of Physical Chemistry University of Santiago de Compostela Santiago de Compostela Spain
8 shared publications - Núria Fagella
Universitat de Barcelona, Spain
6 shared publications - Carsten Lunde Petersen
Department of Science and Environment Roskilde University
5 shared publications - Eva Uhre
University of Copenhagen
4 shared publications - Hubert Cybulski
Kazimierz Wielki Univ, Inst Phys, Ul Powstancow Wielkopolskich 2, PL-85090 Bydgoszcz, Poland
4 shared publications - Angelika Baranowska-Łączkowska
Faculty of Physics, Kazimierz Wielki University, Powstancow Wielkopolskich 2, 85-090 Bydgoszcz, Poland
3 shared publications
Latest Publications
- Open Access
- 22 June 2026
- Published by Wiley in Bulletin of the London Mathematical Society
- Vol. 58 (7)
Roots of polynomial sequences in root‐sparse regions
Given a family of polynomials, we call an open set root‐sparse if the number of zeros of is locally uniformly bounded on . We study the interplay between the individual zeros of the polynomials and those of the th derivatives in a root‐sparse open set , as . More precisely, if the root distributions of converge weak* to some compactly supported measure , whose potential is nowhere locally constant on a root‐sparse open set , then we link the roots of the th derivative , for an arbitrary , to the roots of and the critical points of the potential on compact subsets of . We apply this result in a polynomial dynamics setting to obtain convergence results for the roots of the th derivative of the iterates of a polynomial outside the filled‐in Julia set. We also apply our result in the setting of extremal polynomials.
- 22 June 2026
- Published by Wiley in Bulletin of the London Mathematical Society
- Vol. 58 (7)
Open AccessRoots of polynomial sequences in root‐sparse regions
Given a family of polynomials, we call an open set root‐sparse if the number of zeros of is locally uniformly bounded on . We study the interplay between the individual zeros of the polynomials and those of the th derivatives in a root‐sparse open set , as . More precisely, if the root distributions of converge weak* to some compactly supported measure , whose potential is nowhere locally constant on a root‐sparse open set , then we link the roots of the th derivative , for an arbitrary , to the roots of and the critical points of the potential on compact subsets of . We apply this result in a polynomial dynamics setting to obtain convergence results for the roots of the th derivative of the iterates of a polynomial outside the filled‐in Julia set. We also apply our result in the setting of extremal polynomials.
- Open Access
- 7 March 2026
- Published by Springer Nature in The Journal of Geometric Analysis
- Vol. 36 (4)
Zero Distributions of Derivatives of Polynomial Families Centering on a Set
Suppose $$C \subset {\mathbb {C}}$$ is compact. Let $$q_k$$ be a sequence of polynomials of degree $$n_k \rightarrow \infty $$ , such that the locus of roots of all the polynomials is bounded, and the number of roots of $$q_k$$ in any closed set L disjoint from C is uniformly bounded. Supposing that $$(q_k)_k$$ has an asymptotic root distribution $$\mu $$ we provide conditions on C and $$\mu $$ assuring the sequence of m th derivatives $$(q_k^{(m)})_k$$ has the same asymptotic root distribution $$\mu $$ for any $$m\ge 1$$ . This complements recent results of Totik, [19].- 7 March 2026
- Published by Springer Nature in The Journal of Geometric Analysis
- Vol. 36 (4)
Open AccessZero Distributions of Derivatives of Polynomial Families Centering on a Set
Suppose $$C \subset {\mathbb {C}}$$ is compact. Let $$q_k$$ be a sequence of polynomials of degree $$n_k \rightarrow \infty $$ , such that the locus of roots of all the polynomials is bounded, and the number of roots of $$q_k$$ in any closed set L disjoint from C is uniformly bounded. Supposing that $$(q_k)_k$$ has an asymptotic root distribution $$\mu $$ we provide conditions on C and $$\mu $$ assuring the sequence of m th derivatives $$(q_k^{(m)})_k$$ has the same asymptotic root distribution $$\mu $$ for any $$m\ge 1$$ . This complements recent results of Totik, [19]. - 18 February 2026
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 46 (6) , 1576-1586
Value distributions of derivatives of K -regular polynomial families
Let $\Omega \in \mathbb C$ be a domain such that $K:= \mathbb C \setminus \Omega $ is compact and non-polar. Let $(q_k)_{k>0}$ be a sequence of polynomials with $n_k$ , the degree of $q_k$ satisfying $n_k \to \infty $ , and let $(q_k^{(m)})_k$ denote the sequence of m th derivatives. We provide conditions which ensure that the preimages $(q_k^{(m)})^{-1}(\{a\})$ uniformly equidistribute on $\partial \Omega $ , as $k \to \infty $ , for every $a \in \mathbb C$ and every $m = 0, 1, \ldots .$- 18 February 2026
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 46 (6) , 1576-1586
Value distributions of derivatives of K -regular polynomial families
Let $\Omega \in \mathbb C$ be a domain such that $K:= \mathbb C \setminus \Omega $ is compact and non-polar. Let $(q_k)_{k>0}$ be a sequence of polynomials with $n_k$ , the degree of $q_k$ satisfying $n_k \to \infty $ , and let $(q_k^{(m)})_k$ denote the sequence of m th derivatives. We provide conditions which ensure that the preimages $(q_k^{(m)})^{-1}(\{a\})$ uniformly equidistribute on $\partial \Omega $ , as $k \to \infty $ , for every $a \in \mathbb C$ and every $m = 0, 1, \ldots .$- 8 December 2025
- Published by Springer Nature in Potential Analysis
- Vol. 64 (1) , 12
Convergence of Equilibrium Measures under K-regular Polynomial Sequences and their Derivatives
- 8 December 2025
- Published by Springer Nature in Potential Analysis
- Vol. 64 (1) , 12
Convergence of Equilibrium Measures under K-regular Polynomial Sequences and their Derivatives
- 14 January 2025
- Published by Edward Elgar Publishing
- p. 59-72
Student learning in the age of AI: principles and practices for using AI in higher education
This chapter explores the transformative potential of generative AI in higher education, particularly its promise in addressing Bloom’s “two-sigma problem.” The chapter discusses the capabilities of state-of-the-art AI models like GPT-4 in providing virtual tutoring that rivals human tutors in knowledge, empathy, and availability. It emphasizes the necessity for critical engagement with AI to enhance learning, rather than merely offloading tasks. Key principles for effective AI interaction - context provision, iteration, and human-like communication - are outlined. The chapter also presents practical use cases for AI, demonstrating its application in explaining complex concepts, conducting low-stakes testing, and bridging disciplinary gaps.
- 14 January 2025
- Published by Edward Elgar Publishing
- p. 59-72
Student learning in the age of AI: principles and practices for using AI in higher education
This chapter explores the transformative potential of generative AI in higher education, particularly its promise in addressing Bloom’s “two-sigma problem.” The chapter discusses the capabilities of state-of-the-art AI models like GPT-4 in providing virtual tutoring that rivals human tutors in knowledge, empathy, and availability. It emphasizes the necessity for critical engagement with AI to enhance learning, rather than merely offloading tasks. Key principles for effective AI interaction - context provision, iteration, and human-like communication - are outlined. The chapter also presents practical use cases for AI, demonstrating its application in explaining complex concepts, conducting low-stakes testing, and bridging disciplinary gaps.
- Open Access
Roots of polynomial sequences in root-sparse regions
Given a family $(q_k)_k$ of polynomials, we call an open set $U$ root-sparse if the number of zeros of $q_k$ is locally uniformly bounded on $U$. We study the interplay between the individual zeros of the polynomials $q_k$ and those of the $m$th derivatives $q_k^{(m)}$, in a root-sparse open set $U$, as $k\to\infty$. More precisely, if the root distributions $μ_k$ of $q_k$ converge weak* to some compactly supported measure $μ$, whose potential is nowhere locally constant on a root-sparse open set $U$, then we link the roots of the $m$th derivative $q_k^{m}$, for an arbitrary $m>0$, to the roots of $q_k$ and the critical points of the potential $p_μ$ on compact subsets of $U$. We apply this result in a polynomial dynamics setting to obtain convergence results for the roots of the $m$th derivative of iterates of a polynomial outside the filled-in Julia set. We also apply our result in the setting of extremal polynomials.Open AccessRoots of polynomial sequences in root-sparse regions
Given a family $(q_k)_k$ of polynomials, we call an open set $U$ root-sparse if the number of zeros of $q_k$ is locally uniformly bounded on $U$. We study the interplay between the individual zeros of the polynomials $q_k$ and those of the $m$th derivatives $q_k^{(m)}$, in a root-sparse open set $U$, as $k\to\infty$. More precisely, if the root distributions $μ_k$ of $q_k$ converge weak* to some compactly supported measure $μ$, whose potential is nowhere locally constant on a root-sparse open set $U$, then we link the roots of the $m$th derivative $q_k^{m}$, for an arbitrary $m>0$, to the roots of $q_k$ and the critical points of the potential $p_μ$ on compact subsets of $U$. We apply this result in a polynomial dynamics setting to obtain convergence results for the roots of the $m$th derivative of iterates of a polynomial outside the filled-in Julia set. We also apply our result in the setting of extremal polynomials. - Open Access
- 18 July 2024
- Published by Cambridge University Press (CUP) in Mathematics in Industry Repository
Preventing food waste: Forecasting the number of meals for canteen kitchens
\textbf{Cheffr ApS} is a Danish development company that focuses on minimizing food and resource waste in canteen kitchens. Currently, %up to one-third of the produced food ends up in the trash [reference?] up to 20\% of food served in the food service sector is wasted which has negative consequences for both the environment and the economy. To address this issue, Cheffr has developed \texttt{CheffrBook}, a digital application for booking and cancelling meals which assists kitchen managers in reducing daily food waste. The Study Group is asked to propose optimal algorithms to turn existing user data into more reliable predictions which can help kitchen managers minimise food waste at the cooking and serving stage of food delivery. The goal is to develop forecasting functionality for the \texttt{CheffrBook} application based historical information such as bookings and attendance, as well as related data like vacations, seasons, and individual diner profiles.
- 18 July 2024
- Published by Cambridge University Press (CUP) in Mathematics in Industry Repository
Open AccessPreventing food waste: Forecasting the number of meals for canteen kitchens
\textbf{Cheffr ApS} is a Danish development company that focuses on minimizing food and resource waste in canteen kitchens. Currently, %up to one-third of the produced food ends up in the trash [reference?] up to 20\% of food served in the food service sector is wasted which has negative consequences for both the environment and the economy. To address this issue, Cheffr has developed \texttt{CheffrBook}, a digital application for booking and cancelling meals which assists kitchen managers in reducing daily food waste. The Study Group is asked to propose optimal algorithms to turn existing user data into more reliable predictions which can help kitchen managers minimise food waste at the cooking and serving stage of food delivery. The goal is to develop forecasting functionality for the \texttt{CheffrBook} application based historical information such as bookings and attendance, as well as related data like vacations, seasons, and individual diner profiles.
- Open Access
Zero distributions of derivatives of polynomial families centering on a set
Suppose $C \subset \mathbb{C}$ is compact. Let $q_k$ be a sequence of polynomials of degree $n_k \to \infty$, such that the locus of roots of all the polynomials is bounded, and the number of roots of $q_k$ in any closed set $L$ not meeting $C$ is uniformly bounded. Supposing that $(q_k)_k$ has an asymptotic root distribution $μ$ we provide conditions on $C$ and $μ$ assuring the sequence of $m$th derivatives $(q_k^{(m)})_k$ also has asymptotic root distribution $μ$ for any $m\geq 1$. This complements recent results of Totik.Open AccessZero distributions of derivatives of polynomial families centering on a set
Suppose $C \subset \mathbb{C}$ is compact. Let $q_k$ be a sequence of polynomials of degree $n_k \to \infty$, such that the locus of roots of all the polynomials is bounded, and the number of roots of $q_k$ in any closed set $L$ not meeting $C$ is uniformly bounded. Supposing that $(q_k)_k$ has an asymptotic root distribution $μ$ we provide conditions on $C$ and $μ$ assuring the sequence of $m$th derivatives $(q_k^{(m)})_k$ also has asymptotic root distribution $μ$ for any $m\geq 1$. This complements recent results of Totik. - 25 May 2022
- Published by Taylor & Francis in Journal of Difference Equations and Applications
- Vol. 28 (6) , 771-776
Geometric limits of mixed families
Letting f and h denoting rational maps of degree at least 2 and 1 respectively, and denote by the nth iterate of f. We give upper and lower bounds on the set of accumulation points of the Julia sets with respect to the Hausdorff metric on non-empty compact subsets of the sphere.- 25 May 2022
- Published by Taylor & Francis in Journal of Difference Equations and Applications
- Vol. 28 (6) , 771-776
Geometric limits of mixed families
Letting f and h denoting rational maps of degree at least 2 and 1 respectively, and denote by the nth iterate of f. We give upper and lower bounds on the set of accumulation points of the Julia sets with respect to the Hausdorff metric on non-empty compact subsets of the sphere.- Open Access
- 10 May 2022
- Published by Cambridge University Press (CUP) in Mathematics in Industry Repository
Correction of Fluorescent Probe Degradation in Biodistribution Studies
Fluorescence microscopy can be used for evaluating distribution of medical compounds in animal tissue. Fluorescence intensity decays in time and due to scanning, but correcting for this can improve accuracy. We present a mixed-effects model for fluorescence microscopy intensity reconstruction. Model parameters are estimated via maximum likelihood estimation, taking into account biological variability between animals and measurement uncertainty. The initial fluorescence intensity is reconstructed by decay correction. The model is tested using different data sets. When estimating initial intensities from intensities measured on samples subjected to chemical degradation, decay rate estimates are found to be robust against variation in the ratio of measurement-induced variance to biological variance. Photobleaching rates are found to have only modest significance. A synthetic data set consistent with previously determined parameters is generated, and a forward model is applied; the maximum likelihood estimates accurately recover the parameters, demonstrating the consistency of the model.
- 10 May 2022
- Published by Cambridge University Press (CUP) in Mathematics in Industry Repository
Open AccessCorrection of Fluorescent Probe Degradation in Biodistribution Studies
Fluorescence microscopy can be used for evaluating distribution of medical compounds in animal tissue. Fluorescence intensity decays in time and due to scanning, but correcting for this can improve accuracy. We present a mixed-effects model for fluorescence microscopy intensity reconstruction. Model parameters are estimated via maximum likelihood estimation, taking into account biological variability between animals and measurement uncertainty. The initial fluorescence intensity is reconstructed by decay correction. The model is tested using different data sets. When estimating initial intensities from intensities measured on samples subjected to chemical degradation, decay rate estimates are found to be robust against variation in the ratio of measurement-induced variance to biological variance. Photobleaching rates are found to have only modest significance. A synthetic data set consistent with previously determined parameters is generated, and a forward model is applied; the maximum likelihood estimates accurately recover the parameters, demonstrating the consistency of the model.