@article{40371,
  abstract     = {{<jats:p>Multimode integrated interferometers have great potential for both spectral engineering and metrological applications. However, the material dispersion of integrated platforms constitutes an obstacle that limits the performance and precision of such interferometers. At the same time, two-colour nonlinear interferometers present an important tool for metrological applications, when measurements in a certain frequency range are difficult. In this manuscript, we theoretically developed and investigated an integrated multimode two-colour SU(1,1) interferometer operating in a supersensitive mode. By ensuring the proper design of the integrated platform, we suppressed the dispersion, thereby significantly increasing the visibility of the interference pattern. The use of a continuous wave pump laser provided the symmetry between the spectral shapes of the signal and idler photons concerning half the pump frequency, despite different photon colours. We demonstrate that such an interferometer overcomes the classical phase sensitivity limit for wide parametric gain ranges, when up to 3×104 photons are generated.</jats:p>}},
  author       = {{Ferreri, Alessandro and Sharapova, Polina R.}},
  issn         = {{2073-8994}},
  journal      = {{Symmetry}},
  keywords     = {{Physics and Astronomy (miscellaneous), General Mathematics, Chemistry (miscellaneous), Computer Science (miscellaneous)}},
  number       = {{3}},
  publisher    = {{MDPI AG}},
  title        = {{{Two-Colour Spectrally Multimode Integrated SU(1,1) Interferometer}}},
  doi          = {{10.3390/sym14030552}},
  volume       = {{14}},
  year         = {{2022}},
}

@article{30864,
  author       = {{Schulz, Andreas and Wecker, Christian and Inguva, Venkatesh and Lopatin, Alexey S. and Kenig, Eugeny Y.}},
  issn         = {{0009-2509}},
  journal      = {{Chemical Engineering Science}},
  keywords     = {{Applied Mathematics, Industrial and Manufacturing Engineering, General Chemical Engineering, General Chemistry}},
  publisher    = {{Elsevier BV}},
  title        = {{{A PLIC-based method for species mass transfer at free fluid interfaces}}},
  doi          = {{10.1016/j.ces.2021.117357}},
  volume       = {{251}},
  year         = {{2021}},
}

@article{30907,
  author       = {{Rodriguez, Alfonso and Otero, Andres and Platzner, Marco and De la Torre, Eduardo}},
  issn         = {{0018-9340}},
  journal      = {{IEEE Transactions on Computers}},
  keywords     = {{Computational Theory and Mathematics, Hardware and Architecture, Theoretical Computer Science, Software}},
  pages        = {{1--1}},
  publisher    = {{Institute of Electrical and Electronics Engineers (IEEE)}},
  title        = {{{Exploiting Hardware-Based Data-Parallel and Multithreading Models for Smart Edge Computing in Reconfigurable FPGAs}}},
  doi          = {{10.1109/tc.2021.3107196}},
  year         = {{2021}},
}

@article{34042,
  author       = {{Li, Jiaao and Ma, Yulai and Miao, Zhengke and Shi, Yongtang and Wang, Weifan and Zhang, Cun-Quan}},
  issn         = {{0095-8956}},
  journal      = {{Journal of Combinatorial Theory, Series B}},
  keywords     = {{Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Theoretical Computer Science}},
  pages        = {{61--80}},
  publisher    = {{Elsevier BV}},
  title        = {{{Nowhere-zero 3-flows in toroidal graphs}}},
  doi          = {{10.1016/j.jctb.2021.11.001}},
  volume       = {{153}},
  year         = {{2021}},
}

@article{31261,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>For a compact Riemannian locally symmetric space $\mathcal M$ of rank 1 and an associated vector bundle $\mathbf V_{\tau }$ over the unit cosphere bundle $S^{\ast }\mathcal M$, we give a precise description of those classical (Pollicott–Ruelle) resonant states on $\mathbf V_{\tau }$ that vanish under covariant derivatives in the Anosov-unstable directions of the chaotic geodesic flow on $S^{\ast }\mathcal M$. In particular, we show that they are isomorphically mapped by natural pushforwards into generalized common eigenspaces of the algebra of invariant differential operators $D(G,\sigma )$ on compatible associated vector bundles $\mathbf W_{\sigma }$ over $\mathcal M$. As a consequence of this description, we obtain an exact band structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions on the representations $\tau$ and $\sigma$ defining the bundles $\mathbf V_{\tau }$ and $\mathbf W_{\sigma }$, we obtain a very explicit description of the generalized common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections of $\mathbf W_{\sigma }$. Our methods of proof are based on representation theory and Lie theory.</jats:p>}},
  author       = {{Küster, Benjamin and Weich, Tobias}},
  issn         = {{1073-7928}},
  journal      = {{International Mathematics Research Notices}},
  keywords     = {{General Mathematics}},
  number       = {{11}},
  pages        = {{8225--8296}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces}}},
  doi          = {{10.1093/imrn/rnz068}},
  volume       = {{2021}},
  year         = {{2021}},
}

@article{32810,
  author       = {{Li, Jiaao and Ma, Yulai and Shi, Yongtang and Wang, Weifan and Wu, Yezhou}},
  issn         = {{0195-6698}},
  journal      = {{European Journal of Combinatorics}},
  keywords     = {{Discrete Mathematics and Combinatorics}},
  publisher    = {{Elsevier BV}},
  title        = {{{On 3-flow-critical graphs}}},
  doi          = {{10.1016/j.ejc.2021.103451}},
  volume       = {{100}},
  year         = {{2021}},
}

@article{33657,
  author       = {{Mirhosseini, Hossein and Tahmasbi, Hossein and Kuchana, Sai Ram and Ghasemi, Alireza and Kühne, Thomas}},
  issn         = {{0927-0256}},
  journal      = {{Computational Materials Science}},
  keywords     = {{Computational Mathematics, General Physics and Astronomy, Mechanics of Materials, General Materials Science, General Chemistry, General Computer Science}},
  publisher    = {{Elsevier BV}},
  title        = {{{An automated approach for developing neural network interatomic potentials with FLAME}}},
  doi          = {{10.1016/j.commatsci.2021.110567}},
  volume       = {{197}},
  year         = {{2021}},
}

@article{34827,
  abstract     = {{<jats:title>Zusammenfassung</jats:title><jats:p>Zu den ersten geometrischen Begriffen, die Kinder bereits im Elementar- und Primarbereich lernen, zählen u. a. Viereck, Rechteck und Quadrat. Studien zeigen, dass Lernende bereits früh individuelle Vorstellungen, sog. <jats:italic>individuelle Begriffskonzepte,</jats:italic> zu diesen Begriffen aufbauen. Zwar wird die Entwicklung von Begriffsverständnis in verschiedenen mathematikdidaktischen Stufenmodellen dargestellt, diese sind jedoch generisch und beschreiben nicht explizit die Entwicklung der ersten <jats:italic>individuellen Begriffskonzepte </jats:italic>von Lernenden zu Viereck, Rechteck und Quadrat. Aus empirischer Sicht liegen verschiedene Studien vor, die einzelne Aspekte der individuellen Begriffskonzepte von Lernenden unterschiedlicher Altersgruppen zu diesen Begriffen ausleuchten. Um Begriffsbildungsprozesse aus empirischer Sicht detaillierter entlang der jeweils vorherrschenden individuellen Begriffskonzepte zu beschreiben, fehlen insbesondere Studien in der Grundschule, die alle vier Klassenstufen betrachten und dabei differenzierte Erkenntnisse zu verschiedenen theoretischen Indikatoren des Begriffsverständnisses liefern. Daher geht die vorliegende Studie der Frage nach, welches Verständnis der Begriffe Viereck, Rechteck und Quadrat Schülerinnen und Schüler der Jahrgangsstufen 1, 2, 3 und 4 zeigen. Dazu wurde eine Quasi-Längsschnittstudie mit <jats:italic>N</jats:italic> = 456 Grundschulkindern (ca. 100 pro Jahrgangsstufe) durchgeführt. Die Ergebnisse geben detaillierte Einblicke in die individuellen Begriffskonzepte der Lernenden und zeigen, dass Lernende zunehmend Eigenschaften der Figuren berücksichtigen, jedoch individuelle Begriffskonzepte über lange Zeit auch prototypisch geprägt sind. Implikationen dieser Ergebnisse für Forschung und Praxis werden diskutiert.</jats:p>}},
  author       = {{Bruns, Julia and Unterhauser, Elisabeth and Gasteiger, Hedwig}},
  issn         = {{0173-5322}},
  journal      = {{Journal für Mathematik-Didaktik}},
  keywords     = {{Education, General Mathematics}},
  number       = {{2}},
  pages        = {{581--623}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Geometrisches Begriffsverständnis in der Grundschule am Beispiel der Begriffe Viereck, Rechteck und Quadrat}}},
  doi          = {{10.1007/s13138-021-00185-4}},
  volume       = {{42}},
  year         = {{2021}},
}

@article{47567,
  author       = {{Bruns, Bastian and Di Pretoro, Alessandro and Grünewald, Marcus and Riese, Julia}},
  issn         = {{0009-2509}},
  journal      = {{Chemical Engineering Science}},
  keywords     = {{Applied Mathematics, Industrial and Manufacturing Engineering, General Chemical Engineering, General Chemistry}},
  publisher    = {{Elsevier BV}},
  title        = {{{Flexibility analysis for demand-side management in large-scale chemical processes: An ethylene oxide production case study}}},
  doi          = {{10.1016/j.ces.2021.116779}},
  volume       = {{243}},
  year         = {{2021}},
}

@article{45962,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow and powers of mean and inverse mean curvature flow. Error estimates are proved for semidiscretizations and full discretizations for the generalized flow. The algorithm proposed and studied here combines evolving surface finite elements, whose nodes determine the discrete surface, and linearly implicit backward difference formulae for time integration. The numerical method is based on a system coupling the surface evolution to nonlinear second-order parabolic evolution equations for the normal velocity and normal vector. A convergence proof is presented in the case of finite elements of polynomial degree at least 2 and backward difference formulae of orders 2 to 5. The error analysis combines stability estimates and consistency estimates to yield optimal-order $H^1$-norm error bounds for the computed surface position, velocity, normal vector, normal velocity and therefore for the mean curvature. The stability analysis is performed in the matrix–vector formulation and is independent of geometric arguments, which only enter the consistency analysis. Numerical experiments are presented to illustrate the convergence results and also to report on monotone quantities, e.g. Hawking mass for inverse mean curvature flow, and complemented by experiments for nonconvex surfaces.</jats:p>}},
  author       = {{Binz, Tim and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{3}},
  pages        = {{2545--2588}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{A convergent finite element algorithm for generalized mean curvature flows of closed surfaces}}},
  doi          = {{10.1093/imanum/drab043}},
  volume       = {{42}},
  year         = {{2021}},
}

@article{45957,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>A proof of convergence is given for a bulk–surface finite element semidiscretisation of the Cahn–Hilliard equation with Cahn–Hilliard-type dynamic boundary conditions in a smooth domain. The semidiscretisation is studied in an abstract weak formulation as a second-order system. Optimal-order uniform-in-time error estimates are shown in the $L^2$- and $H^1$-norms. The error estimates are based on a consistency and stability analysis. The proof of stability is performed in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second-order system. Numerical experiments illustrate the theoretical results.</jats:p>}},
  author       = {{Harder, Paula and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{3}},
  pages        = {{2589--2620}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions}}},
  doi          = {{10.1093/imanum/drab045}},
  volume       = {{42}},
  year         = {{2021}},
}

@article{45961,
  author       = {{Nick, Jörg and Kovács, Balázs and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{4}},
  pages        = {{997--1000}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations}}},
  doi          = {{10.1007/s00211-021-01196-6}},
  volume       = {{147}},
  year         = {{2021}},
}

@article{45959,
  author       = {{Kovács, Balázs and Li, Buyang and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{3}},
  pages        = {{595--643}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{A convergent evolving finite element algorithm for Willmore flow of closed surfaces}}},
  doi          = {{10.1007/s00211-021-01238-z}},
  volume       = {{149}},
  year         = {{2021}},
}

@article{34629,
  author       = {{Hesse, Kerstin and Sloan, Ian H. and Womersley, Robert S.}},
  issn         = {{0377-0427}},
  journal      = {{Journal of Computational and Applied Mathematics}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  publisher    = {{Elsevier BV}},
  title        = {{{Local RBF-based penalized least-squares approximation on the sphere with noisy scattered data}}},
  doi          = {{10.1016/j.cam.2020.113061}},
  volume       = {{382}},
  year         = {{2021}},
}

@article{53363,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>In this survey paper we aim to provide an overview of research on mathematics textbooks and, more broadly, curriculum resources as instruments for change related to mathematical content, instructional goals and practices, and student learning of mathematics. In particular, we elaborate on the following themes: (1) The role of curriculum resources as instruments for change from a theoretical perspective; (2) The design of curriculum resources to mediate the implementation of reform ideas and innovative practice; (3) Teachers’ influence on the implementation of change through curriculum resources; (4) Students’ influence on the implementation of change through curriculum resources; and (5) Evidence of curriculum resources yielding changes in student-related factors or variables. We claim that, whilst textbooks and curriculum resources are influential, they alone cannot change teachers’ teaching nor students’ learning practices in times of curricular change. Moreover, more knowledge is needed about features of curriculum resources that support the implementation of change. We contend that curriculum innovations are likely to be successful, if teachers and students are supported to co- and re-design the relevant curriculum trajectories and materials in line with the reform efforts and their own individual needs.</jats:p>}},
  author       = {{Rezat, Sebastian and Fan, Lianghuo and Pepin, Birgit}},
  issn         = {{1863-9690}},
  journal      = {{ZDM – Mathematics Education}},
  keywords     = {{General Mathematics, Education}},
  number       = {{6}},
  pages        = {{1189--1206}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Mathematics textbooks and curriculum resources as instruments for change}}},
  doi          = {{10.1007/s11858-021-01309-3}},
  volume       = {{53}},
  year         = {{2021}},
}

@article{44683,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>One of the most prevalent features of digital mathematics textbooks, compared to traditional ones, is the provision of automated feedback on students’ solutions. Since feedback is regarded as an important factor that influences learning, this is often seen as an affordance of digital mathematics textbooks. While there is a large body of mainly quantitative research on the effectiveness of feedback in general, very little is known about how feedback actually affects students’ individual content specific learning processes and conceptual development. A theoretical framework based on Rabardel’s theory of the instrument and Vergnaud’s theory of conceptual fields is developed to study qualitatively how feedback actually functions in the learning process. This framework was applied in a case study of two elementary school students’ learning processes when working on a probability task from a German 3rd grade digital textbook. The analysis allowed detailed reconstruction of how students made sense of the information provided by the feedback and adjusted their behavior accordingly. This in-depth analysis unveiled that feedback does not necessarily foster conceptual development in the desired way, and a correct solution does not always coincide with conceptual understanding. The results point to some obstacles that students face when working individually on tasks from digital mathematics textbooks with automated feedback, and indicate that feedback needs to be developed in design-based research cycles in order to yield the desired effects.</jats:p>}},
  author       = {{Rezat, Sebastian}},
  issn         = {{1863-9690}},
  journal      = {{ZDM Mathematics Education}},
  keywords     = {{General Mathematics, Education}},
  number       = {{6}},
  pages        = {{1433--1445}},
  publisher    = {{Springer}},
  title        = {{{How automated feedback from a digital mathematics textbook affects primary students’ conceptual development: two case studies}}},
  doi          = {{10.1007/s11858-021-01263-0}},
  volume       = {{53}},
  year         = {{2021}},
}

@article{35778,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>The aim of the special issue is to bring together important current international research on innovative teaching and learning practices in mathematics in engineering education, and to develop deeper understandings of the characteristics of current teaching and learning practices that can inform the design and implementation of future innovative practice. The focus of this review paper is to provide a state-of-the-art overview of this emerging field at the cross-roads between mathematics and engineering education, in addition to introducing the papers of this special issue. To guide this paper, we posed three review questions: (1) How can current (teaching/learning/study) practices of mathematics in engineering education be characterized with a view towards innovation?; (2) What are the ‘resources’ (cognitive, material, digital, social) used, and what are those that appear also well suited for innovative courses?; (3) What are promising innovative practices in mathematics in engineering education, and what are the implications for curriculum reform? Looking back across the studies we summarized in the review, we conclude that they are lagging behind the more fundamental changes that are happening in engineering education, whilst addressing selected aspects of innovative changes within the current system of engineering education. At the same time, the nine papers of this special issue contribute new perspectives for innovative practices in mathematics in engineering education, for a better understanding of current practices and for future research.</jats:p>}},
  author       = {{Pepin, Birgit and Biehler, Rolf and Gueudet, Ghislaine}},
  issn         = {{2198-9745}},
  journal      = {{International Journal of Research in Undergraduate Mathematics Education}},
  keywords     = {{Education, Mathematics (miscellaneous)}},
  number       = {{2}},
  pages        = {{163--188}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Mathematics in Engineering Education: a Review of the Recent Literature with a View towards Innovative Practices}}},
  doi          = {{10.1007/s40753-021-00139-8}},
  volume       = {{7}},
  year         = {{2021}},
}

@article{35702,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>Mathematics Learning Support Centres are becoming more and more common in higher education both internationally and in Germany. Whereas it is clear that their quality largely depends on a functioning interaction in consultations, little is known about how such consultations proceed in detail. On the basis of models from the literature and recorded support sessions (N = 36), we constructed a process model that divides consultations into four ideal–typical phases. In the individual consultations, forward or backward leaps occur, but overall the model seems to describe the data well. A high intercoder reliability shows that it can be applied consistently on real data by different researchers. An analysis of the consultations between students and tutors shows that both mainly work on past attempts or thoughts of the students to solve the exercise or problems and on concrete strategies to solve a problem within the session. In contrast, very little time is dedicated to summarizing and reflecting the solution. The data allows for a more in-depth discussion of what constitutes quality in advising processes and how it might be further explored. Practically, the model may structure support sessions and help in focussing on different goals in different phases.</jats:p>}},
  author       = {{Schürmann, Mirko and Panse, Anja and Shaikh, Zain and Biehler, Rolf and Schaper, Niclas and Liebendörfer, Michael and Hilgert, Joachim}},
  issn         = {{2198-9745}},
  journal      = {{International Journal of Research in Undergraduate Mathematics Education}},
  keywords     = {{Education, Mathematics (miscellaneous)}},
  number       = {{1}},
  pages        = {{94--120}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Consultation Phases in Mathematics Learning and Support Centres}}},
  doi          = {{10.1007/s40753-021-00154-9}},
  volume       = {{8}},
  year         = {{2021}},
}

@article{35781,
  author       = {{Podworny, Susanne and Biehler, Rolf}},
  issn         = {{1098-6065}},
  journal      = {{Mathematical Thinking and Learning}},
  keywords     = {{Developmental and Educational Psychology, Education, General Mathematics}},
  number       = {{4}},
  pages        = {{291--311}},
  publisher    = {{Informa UK Limited}},
  title        = {{{The process of actively building a model for a randomization test – insights into learners’ modeling activities based on a case study}}},
  doi          = {{10.1080/10986065.2021.1922837}},
  volume       = {{24}},
  year         = {{2021}},
}

@article{37443,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>The range of teaching materials now available is becoming increasingly diverse. Despite this, however, the use and influence of textbooks in teaching still remains very high. When instructing reading comprehension, teachers often use textbooks as the basis for teaching in language lessons. Establishing a good match between textbooks and the skills to be acquired is therefore essential. In this paper, I investigate whether textbooks used in Austrian schools can adequately support the teaching of reading comprehension skills. Since reading comprehension is the basis for acquiring knowledge in all subjects, science textbooks are examined in addition to (German) language lesson textbooks. Thus, the content pages of four language textbooks and four science textbooks for fourth and sixth grade were analysed in terms of five different categories, i.e. general structural setup, learning goals, text types, text structures, and activities. The results reveal clear variations with respect to learning goals in language textbooks. For example, the extent to which reading comprehension is addressed ranges from 13.64 to 69.70%, depending on the book used. Although not addressed as a learning goal in the science textbooks, reading comprehension is often presupposed, especially in sixth grade. While the instruction of reading comprehension ought to entail coverage of reading strategies, this is often neglected, or only dealt with indirectly. Given the diversity of textbooks analysed, it seems all the more important to stress that teachers should: 1) clarify the goals and teaching strategies of a book before using it, 2) become aware of strategies that support the development of students' reading comprehension, and 3) use textbooks as a complementary (and not sole) tool to support reading comprehension in all subjects.</jats:p>}},
  author       = {{Seifert, Susanne}},
  issn         = {{2211-1662}},
  journal      = {{Technology, Knowledge and Learning}},
  keywords     = {{Computer Science Applications, Human-Computer Interaction, Education, Mathematics (miscellaneous)}},
  number       = {{2}},
  pages        = {{383--405}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Is Reading Comprehension Taken for Granted? An Analysis of Austrian Textbooks in Fourth and Sixth Grade}}},
  doi          = {{10.1007/s10758-021-09490-w}},
  volume       = {{26}},
  year         = {{2021}},
}