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Refinement of X‐ray and electron diffraction crystal structures using analytical Fourier transforms of Slater‐type atomic wavefunctions in Olex2 (2024)
Journal Article
Kleemiss, F., Peyerimhoff, N., & Bodensteiner, M. (2024). Refinement of X‐ray and electron diffraction crystal structures using analytical Fourier transforms of Slater‐type atomic wavefunctions in Olex2. Journal of Applied Crystallography, 57, 161-174. https://doi.org/10.1107/s1600576723010981

An implementation of Slater‐type spherical scattering factors for X‐ray and electron diffraction for elements in the range Z = 1–103 is presented within the software Olex2. Both high‐ and low‐angle Fourier behaviour of atomic electron density and ele... Read More about Refinement of X‐ray and electron diffraction crystal structures using analytical Fourier transforms of Slater‐type atomic wavefunctions in Olex2.

Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms (2023)
Journal Article
Egidi, M., Gittins, K., Habib, G., & Peyerimhoff, N. (2023). Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms. Journal of Spectral Theory, 13(4), 1297-1343. https://doi.org/10.4171/JST/480

In this paper we introduce the magnetic Hodge Laplacian, which is a generalization of the magnetic Laplacian on functions to differential forms. We consider various spectral results, which are known for the magnetic Laplacian on functions or for the... Read More about Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms.

Bakry–Émery Curvature Sharpness and Curvature Flow in Finite Weighted Graphs. Implementation (2023)
Journal Article
Cushing, D., Kamtue, S., Liu, S., Münch, F., Peyerimhoff, N., & Snodgrass, B. (2023). Bakry–Émery Curvature Sharpness and Curvature Flow in Finite Weighted Graphs. Implementation. Axioms, 12(6), Article 577. https://doi.org/10.3390/axioms12060577

In this paper, we discuss the implementation of a curvature flow on weighted graphs based on the Bakry–Émery calculus. This flow can be adapted to preserve the Markovian property and its limits as time goes to infinity turn out to be curvature sharp... Read More about Bakry–Émery Curvature Sharpness and Curvature Flow in Finite Weighted Graphs. Implementation.

Going round in circles: Geometry in the early years (2023)
Journal Article
Oughton, R. H., Wheadon, D. M., Bolden, D. S., Nichols, K., Fearn, S., Darwin, S., Dixon-Jones, S., Mistry, M., Peyerimhoff, N., & Townsend, A. (2023). Going round in circles: Geometry in the early years. Mathematics teaching, 286, 29-34

The research described here came from a collaboration between university-based mathematicians and early years (EY) educators. The project emerged naturally, driven by the felt need of the EY educators to develop a broader understanding and appreciati... Read More about Going round in circles: Geometry in the early years.

Parameterized Counting and Cayley Graph Expanders (2023)
Journal Article
Peyerimhoff, N., Roth, M., Schmitt, J., Stix, J., Vdovina, A., & Wellnitz, P. (2023). Parameterized Counting and Cayley Graph Expanders. SIAM Journal on Discrete Mathematics, 37(2), 405-486. https://doi.org/10.1137/22m1479804

Given a graph property \Phi , we consider the problem \# EdgeSub(\Phi ), where the input is a pair of a graph G and a positive integer k, and the task is to compute the number of k-edge subgraphs in G that satisfy \Phi . Specifically, we study the pa... Read More about Parameterized Counting and Cayley Graph Expanders.

Rigidity properties of the hypercube via Bakry–Émery curvature (2022)
Journal Article
Liu, S., Münch, F., & Peyerimhoff, N. (2024). Rigidity properties of the hypercube via Bakry–Émery curvature. Mathematische Annalen, 388(2), 1225-1259. https://doi.org/10.1007/s00208-022-02537-y

We give rigidity results for the discrete Bonnet–Myers diameter bound and the Lichnerowicz eigenvalue estimate. Both inequalities are sharp if and only if the underlying graph is a hypercube. The proofs use well-known semigroup methods as well as new... Read More about Rigidity properties of the hypercube via Bakry–Émery curvature.

Developing ‘deep mathematical thinking’ in geometry with 3- and 4-year-olds: A collaborative study between early years teachers and University-based mathematicians (2022)
Journal Article
Oughton, R., Nichols, K., Bolden, D. S., Dixon-Jones, S., Fearn, S., Darwin, S., Mistry, M., Peyerimhoff, N., & Townsend, A. (2024). Developing ‘deep mathematical thinking’ in geometry with 3- and 4-year-olds: A collaborative study between early years teachers and University-based mathematicians. Mathematical Thinking and Learning, 26(3), 306-325. https://doi.org/10.1080/10986065.2022.2119497

Mathematics in early years settings is often restricted to learning to count and identifying simple shapes. This is partly due to the narrow scope of many early years curricula and insufficient teacher training for exploring deeper mathematical conce... Read More about Developing ‘deep mathematical thinking’ in geometry with 3- and 4-year-olds: A collaborative study between early years teachers and University-based mathematicians.

Refinement of anomalous dispersion correction parameters in single-crystal structure determinations (2022)
Journal Article
Meurer, F., Dolomanov, O. V., Hennig, C., Peyerimhoff, N., Kleemiss, F., Puschmann, H., & Bodensteiner, M. (2022). Refinement of anomalous dispersion correction parameters in single-crystal structure determinations. IUCrJ, 9(5), https://doi.org/10.1107/s2052252522006844

Correcting for anomalous dispersion is part of any refinement of an X-ray dif­fraction crystal structure determination. The procedure takes the inelastic scattering in the diffraction experiment into account. This X-ray absorption effect is specific... Read More about Refinement of anomalous dispersion correction parameters in single-crystal structure determinations.