Previous Paper Research Articles

Fusion of irreducible modules in the periodic Temperley–Lieb algebra

We propose a new family \mathsf{Y}_{k,\ell,x,y,[z,w]}𝖸k,ℓ,x,y,[z,w] of modules over the enlarged periodic Temperley–Lieb algebra \mathsf{\mathcal EPTL}_N(\beta)ℰ𝖯𝖳𝖫N(β). These modules are built from link states with two marked points, similarly to the modules \mathsf{X}_{k,\ell,x,y,z}𝖷k,ℓ,x,y,z that we constructed in a previous paper. They however differ in the way that defects connect pairwise. We analyse the decomposition of \mathsf{Y}_{k,\ell,x,y,[z,w]}𝖸k,ℓ,x,y,[z,w] over the irreducible standard modules \mathsf{W}_{k,x}𝖶k,x for generic values of the parameters zz and ww, and use it to deduce the fusion rules for the fusion \mathsf{W} × \mathsf{W}𝖶×𝖶 of standard modules. These turn out to be more symmetric than those obtained previously using the modules \mathsf{X}_{k,\ell,x,y,z}𝖷k,ℓ,x,y,z. From the work of Graham and Lehrer, it is known that, for \beta = -q-q^{-1}β=−q−q−1 where qq is not a root of unity, there exists a set of non-generic values of the twist yy for which the standard module \mathsf{W}_{\ell,y}𝖶ℓ,y is indecomposable yet reducible with two composition factors: a radical submodule \mathsf{R}_{\ell,y}𝖱ℓ,y and a quotient module \mathsf{Q}_{\ell,y}𝖰ℓ,y. Here, we construct the fusion products \mathsf{W}×\mathsf{R}𝖶×𝖱, \mathsf{W}×\mathsf{Q}𝖶×𝖰 and \mathsf{Q} × \mathsf{Q}𝖰×𝖰, and analyse their decomposition over indecomposable modules. For the fusions involving the quotient modules \mathsf{Q}𝖰, we find very simple results reminiscent of \mathfrak{sl}(2)𝔰𝔩(2) fusion rules. This construction with modules \mathsf{Y}_{k,\ell,x,y,[z,w]}𝖸k,ℓ,x,y,[z,w] is a good lattice regularization of the operator product expansion in the underlying logarithmic bulk conformal field theory. Indeed, it fits with the correspondence between standard modules and connectivity operators, and is useful for the calculation of their correlation functions. Remarkably, we show that the fusion rules \mathsf{W}×\mathsf{Q}𝖶×𝖰 and \mathsf{Q}×\mathsf{Q}𝖰×𝖰 are consistent with the known fusion rules of degenerate primary fields.

Three-loop contributions to b → sγ associated with the current-current operators

In a recent work, we calculated all three-loop diagrams contributing to the decay amplitude for b → sγ where none of the gluons touch the b-leg. In the present paper, we complete the calculation by working out all remaining three-loop diagrams (of order αs2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\alpha}_s^2 $$\\end{document}) associated with the current-current operators O1 and O2 at the physical value of the charm-quark mass mc. Using the programs AMFlow and DiffExp to solve the differential equations for the master integrals, we obtained precise numerical results at 23 values for z=mc2/mb2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ z={m}_c^2/{m}_b^2 $$\\end{document}, ranging from z = 1/1000 to z = 1/5, along with asymptotic expansions around z = 0. For certain diagrams, the asymptotic expansion breaks down in the physical z-range, necessitating a Taylor expansion (which we do around z = 1/10). In all expansions, we retained power terms up to z20 and included the accompanying log(z) terms to all powers for asymptotic expansions. Numerical results for the sum of all diagrams (including those calculated in the previous paper) are presented in tabular form, while the mentioned expansions of individual diagram classes are provided electronically. We note that our results for the asymptotic expansions around z = 0 are in good agreement with those recently published by Fael et al. and Czaja et al.

Can ChatGPT help patients understand radiopharmaceutical extravasations?

A previously published paper in the official journal of the Society of Nuclear Medicine and Molecular Imaging (SNMMI) concluded that the artificial intelligence chatbot ChatGPT may offer an adequate substitute for nuclear medicine staff informational counseling to patients in an investigated setting of 18F-FDG PET/CT. To ensure consistency with the previous paper, the author and a team of experts followed a similar methodology and evaluated whether ChatGPT could adequately offer a substitute for nuclear medicine staff informational counseling to patients regarding radiopharmaceutical extravasations. We asked ChatGPT fifteen questions regarding radiopharmaceutical extravasations. Each question or prompt was queried three times. Using the same evaluation criteria as the previously published paper, the ChatGPT responses were evaluated by two nuclear medicine trained physicians and one nuclear medicine physicist for appropriateness and helpfulness. These evaluators found ChatGPT responses to be either highly appropriate or quite appropriate in 100% of questions and very helpful or quite helpful in 93% of questions. The interobserver agreement among the evaluators, assessed using the Intraclass Correlation Coefficient (ICC), was found to be 0.72, indicating good overall agreement. The evaluators also rated the inconsistency across the three ChatGPT responses for each question and found irrelevant or minor inconsistencies in 87% of questions and some differences relevant to main content in the other 13% of the questions. One physician evaluated the quality of the references listed by ChatGPT as the source material it used in generating its responses. The reference check revealed no AI hallucinations. The evaluator concluded that ChatGPT used fully validated references (appropriate, identifiable, and accessible) to generate responses for eleven of the fifteen questions and used generally available medical and ethical guidelines to generate responses for four questions. Based on these results we concluded that ChatGPT may be a reliable resource for patients interested in radiopharmaceutical extravasations. However, these validated and verified ChatGPT responses differed significantly from official positions and public comments regarding radiopharmaceutical extravasations made by the SNMMI and nuclear medicine staff. Since patients are increasingly relying on the internet for information about their medical procedures, the differences need to be addressed.

Wilson Lines in the Abelian Lattice Higgs Model.

Lattice gauge theories are lattice approximations of the Yang-Mills theory in physics. The abelian lattice Higgs model is one of the simplest examples of a lattice gauge theory interacting with an external field. In a previous paper (Forsström et al. in Math Phys 4(2):257-329, 2023), we calculated the leading order term of the expected value of Wilson loop observables in the low-temperature regime of the abelian lattice Higgs model on with structure group for some In the absence of a Higgs field, these are important observables since they exhibit a phase transition which can be interpreted as distinguishing between regions with and without quark confinement. However, in the presence of a Higgs field, this is no longer the case, and a more relevant family of observables are so-called open Wilson lines. In this paper, we extend and refine the ideas introduced in Forsström et al. (Math Phys 4(2):257-329, 2023) to calculate the leading order term of the expected value of the more general Wilson line observables. Using our main result, we then calculate the leading order term of several natural ratios of expected values and confirm the behavior predicted by physicists.

Two complementary eigen-based geometric properties of a vortex

In our previous paper [V. Kolář and J. Šístek, “Orbitally compact and loose vortex regions,” Phys. Fluids 35, 121708 (2023)], the eigenvalue-based measure of orbital compactness of particle motion inside a vortex for compressible flows has been proposed. Here, a complementary eigenvector-based geometric property of cylindricity (three-dimensional /3D/ aspect) is introduced. This property is closely related to the local flow axisymmetry in the swirl plane (two-dimensional /2D/ aspect) which explains the positive response of the vortex-identification Δ-criterion, and closely related criteria swirling strength and Rortex (Liutex), for almost no vorticity and a large (without any limitation) rate-of-strain magnitude. A relatively high correlation between orbital compactness, cylindricity, and widely used vortex-identification criteria has been found for several flow examples.

Transformation of the tobacco product market in Japan, 2011–2023

ObjectiveThis study updates a previous paper that examined trends in the sale of cigarettes and heated tobacco products (HTPs) in Japan between 2011 and part way through 2019. The current study includes complete unit sales data through 2023.MethodsData on cigarette and HTP sales were obtained from public sources available from the websites and stockholder reports for the Tobacco Institute of Japan, Philip Morris International and Japan Tobacco. We used joinpoint regression using the parametric method to test for trends in both per capita and total sales for the three outcome variables assessed between 2011 and 2023: (1) cigarette sales, (2) HTP sales and (3) combined cigarette and HTP sales. Joinpoint regression identifies changes in trends and estimates the annual per cent change (APC) for each trend segment.ResultsBetween 2011 and 2023, per capita and total cigarette sales declined by 52.6% and 52.7%, respectively. From 2011 to 2015, per capita cigarette sales in Japan decreased −1.5% APC; from 2015 to 2018, the decline accelerated to −10.5% APC and continued to fall −7.3% APC between 2018 and 2023. Between 2016 and 2018, per capita HTP sales increased by 149.0% APC, and since 2018, they have increased by 8.1% APC.ConclusionWhile many factors may account for the decreased sale of cigarettes in Japan over the past 12 years, the increased sale of HTPs appears to be a factor.

Modeling and Analyzing of CMOS Cross-Coupled Differential-Drive Rectifier for Ultra-Low-Power Ambient RF Energy Harvesting

This paper models and analyzes the Complementary Metal Oxide Semiconductor (CMOS) cross-coupled differential-drive (CCDD) rectifier for Ultra-Low-Power ambient radio-frequency energy harvesters (RFEHs) working in the subthreshold region. In this paper, two closed-form equations of CCDD rectifier output voltage and input resistance in the subthreshold region were derived based on BSIM4 models of NMOS and PMOS. The model give insight to specify circuit parameters according to different inputs, transistor sizes, threshold voltages, numbers of stages, load conditions and compensation voltages, which can be used to optimize the rectifier circuit. There is a good agreement between the simulation results and these models, and these models have a maximum deviation of 10% in comparison with the simulation results in the subthreshold region. The measurement results of a single-stage CCDD rectifier reported in a previous paper were adopted to verify the model. The output voltage and input resistance predicted by these models provide excellent consistency with corresponding measurement results. The model can be employed to optimize the CCDD rectifier without expensive calculation in the design stage.

On the necessity of accounting for age structure in human malaria transmission modeling

Malaria is one of the most common mosquito-borne diseases widespread in tropical and subtropical regions, causing thousands of deaths every year in the world. In a previous paper, we formulated an age-structured model containing three structural variables: (i) the chronological age of human and mosquito populations, (ii) the time since they are infected, and (iii) humans waning immunity (i.e. the progressive loss of protective antibodies after recovery). In the present paper, we expand the analysis of this age-structured model and focus on the derivation of entomological and epidemiological results commonly used in the literature, following the works of Smith and McKenzie. We generalize their results to the age-structured case. In order to quantify the impact of neglecting structuring variables such as chronological age, we assigned values from the literature to our model parameters. While some parameters values are readily accessible from the literature, at least those about the human population, the parameters concerning mosquitoes are less commonly documented and the values of a number of them (e.g. mosquito survival in the presence or in absence of infection) can be discussed extensively. Our analysis, informed by parameter values from the literature, demonstrates that overlooking those structural variables of human and mosquito populations may result in inaccurate epidemiological predictions and suboptimal control strategies. We highlight the epidemiological implications of these findings and emphasize the necessity of considering age structure in future malaria control programs.

Three-dimensional eigensolutions of the unsteady compressible boundary-region equations

A previous paper of the authors (Duck & Stephen, J. Fluid Mech., vol. 917, 2021, A56) considered the effect of three-dimensional, temporally periodic, linear and incompressible disturbances on a Blasius boundary layer, in particular when the disturbance wavelength is both comparable to and longer than the boundary-layer thickness. This previous study revealed that, unlike the two-dimensional counterpart, a mode exists that exhibits regimes of downstream spatial growth. In this paper we extend the analysis to the compressible regime, based on the boundary-region equations methodology. The aforementioned unstable mode is seen to persist into the compressible regime, and is studied using a combination of numerical and asymptotic methods. The paper adopts several approaches. First is a numerical approach in which the spatial development of the disturbances is assessed. This then leads to a consideration of the far-downstream behaviour, using (several) asymptotic limits. Of some note, in addition to unstable modes found in the incompressible case, is the existence of a further class of instability, not found in the incompressible case (which is also analysed asymptotically), corresponding to what amounts to an inviscid instability. The far-downstream analysis enables a (sub-)classification into entropy and non-entropy modes. The former, according to this analysis, are spatially damped, with one caveat, as revealed by our marching procedure, which highlights how spatial development of disturbances can be important.

Significant role of secondary electrons in the formation of a multi-body chemical species spur produced by water radiolysis.

Scientific insights into water photolysis and radiolysis are essential for estimating the direct and indirect effects of deoxyribonucleic acid (DNA) damage. Secondary electrons from radiolysis intricately associated with both effects. In our previous paper, we simulated the femtosecond (1 × 10- 15s) dynamics of secondary electrons ejected by energy depositions of 11-19eV into water via high-energy electron transport using a time-dependent simulation code. The results contribute to the understanding of simple "intra-spur" chemical reactions of tree-body chemical species (hydrated electrons, hydronium ion and OH radical) in subsequent chemical processes. Herein, we simulate the dynamics of the electrons ejected by energy depositions of 20-30eV. The present results contribute to the understanding of complex "inter-spur" chemical reactions of the multi-body chemical species as well as for the formation of complex DNA damage with redox site and strand break on DNA. The simulation results present the earliest formation mechanism of an unclear multi-body chemical species spur when secondary electrons induce further ionisations or electronic excitations. The formation involves electron-water collisions, i.e. ionisation, electronic excitation, molecular excitation and elastic scattering. Our simulation results indicate that (1) most secondary electrons delocalise to ~ 12nm, and multiple collisions are sometimes induced in a water molecule at 22eV deposition energy. (2) The secondary electrons begin to induce diffuse band excitation of water around a few nm from the initial energy deposition site and delocalise to ~ 8nm at deposition energies ~ 25eV. (3) The secondary electron can cause one additional ionisation or electronic excitation at deposition energies > 30eV, forming a multi-body chemical species spur. Thus, we propose that the type and density of chemical species produced by water radiolysis strongly depend on the deposition energy. From our results, we discuss formation of complex DNA damage.

The “Notch” in Unstable Layers and the Stability Minimum in the Tropics

Abstract In a previous paper, we identified a “notch” in unstable layers at Koror (7.3 0N, 134.5 0E), where there was a relative deficiency in thin unstable layers and a corresponding relative excess in thicker layers, at altitudes centered at 12 km. We hypothesized that this feature was associated with the previously identified stability minimum in the tropics at that same altitude. In this paper, we extend our studies of this “notch” and its association with the tropical stability minimum by examining other stations in the deep tropics and also some stations at higher latitudes within the tropics. We find that this “notch” feature is found at all the other radiosonde stations in the deep tropics that we examined. We also find that the annual variations in unstable layer occurrences at stations at higher latitudes within the tropics show variations consistent with our hypothesis that this “notch” is associated with the region of minimum stability in the tropics at altitudes centered around 12 km, in that the annual variation in this “notch” feature is consistent with the annual variation of minimum stability in this region. Two factors contribute to the “notch” feature. One is that the data quality control procedure of the analysis rejects many thin layers due to the small trend-to-noise ratio in the region of minimum stability. The other is that the cloud-top outflow, which was previously identified with the stability minimum, advects thicker unstable layers throughout the deep tropics at the altitudes of the “notch.”

On decision problems concerning contextual insertions and deletions

The notions of stability, anti-stability, and error-correctability of a language that is modified by making contextual insertions in the words of the language were introduced in a previous paper by Bottoni et al. in 2011, where it was shown that these properties are decidable for regular languages. The authors proposed investigating the decidability of these properties for other classes of languages. Here, we derive necessary and sufficient conditions for a class of languages to have decidable stable, anti-stable, and error-correctable properties, and use these conditions to exhibit general classes of languages (strictly greater than the regular languages) for which the properties are decidable, and also simple classes (the first such classes) for which the properties are undecidable. We obtain identical results for the case when contextual deletions (instead of insertions) are made in the words of the language, and also with mixes of insertions and deletions. Our constructions also demonstrate that certain general problems involving nondeterministic generalized sequential machines (GSMs) applied to languages accepted by deterministic machine models are decidable, which is surprising as the deterministic language families do not need to be closed under GSM mappings.

Failed supernova explosions increase the duration of star formation in globular clusters

The duration of SF in GC is an essential aspect for understanding their formation. Contrary to previous presumptions that all stars above 8 $M_ explode as CCSN recent evidence suggests a more complex scenario. We analyse iron spread observations from 55 GC to estimate the number of CCSN explosions before SF termination, thereby determining the SF duration. This work for the first time takes the possibility of failed CCSN into account, when estimating the SF duration. Two scenarios are considered: one where all stars explode as CCSN and another where only stars below 20 $M_ lead to CCSN as most CCSN models predict that no failed CCSN happen below 20 $M_ odot$. This establishes a lower ($ Myr$) and an upper ($ Myr$) limit for the duration of SF . Extending the findings of our previous paper, this study indicates a significant difference in SF duration based on CCSN outcomes, with failed CCSN extending SF by up to a factor of three. Additionally, a new code is introduced to compute the SF duration for a given CCSN model. The extended SF has important implications on GC formation, including enhanced pollution from stellar winds and increased binary star encounters. These results underscore the need for a refined understanding of CCSN in estimating SF durations and the formation of multiple stellar populations in GC

Editorial

This issue of RERM includes four papers that boldly attempt to propose ways in which educational research practices, traditions and methods might be enacted differently. They take seemingly foundational research methods (reviewing literature, ethnographic observation, walking methodologies) and transform them in to something less familiar that invite our readers to stutter and reappraise how else research might be done and with what outcomes. Firstly, researching from Danish inner cities, Staunæs and Vertelyte draw on affect theory and a concern with moods and felt pedagogies in education to explore how hopes and anxieties are woven through school objects and architecture. Through minor interventions the authors propose that there are abundant possibilities to improve the inclusion of racialized students in the inbetween, and often pathologised spaces of school. This holds the potential to radically shift perceptions, prejudices and behaviours that are not always identifiable but that can be sensed through the minor gesture. The authors attend to the significance of language and what happens through translation and diffractive readings. They stress that concepts that travel require careful consideration when transposed into alternative geopolitical contexts. They take Ahmed’s ‘happy objects’ as a case in point to make visible the specificities of local context and what that means for advancing theory that can pay closer attention to time and space. The next two papers address ways in which literature reviews – a staple element to any research project – can be up-ended and reimagined when post-foundational theories and practices are put to work. Naomi Pears-Scown makes use of Baradian theoretical concepts to think-with literature rather than merely review what is already known and organize a corpus of knowledge into useful categories. Through literature cartographies, Pears-Scown develops a mapping strategy that makes visible her affective engagement with literature through the crafting of found-poems which tell stories of the ways in which place shapes approaches to arts therapy in various geopolitical contexts. This novel approach to engaging with and encountering literature disrupts received wisdom about how literature should be reviewed and instead invites the reader to sit with the discomforts of expanding how literature stories can be told. In resonance with Pears-Scown, the next paper written by co-authors Boks-Vlemmix and Aspfors, offers a similar challenge to orthodoxies surrounding what a literature review is and how it should be undertaken. In their experimental piece the authors offer glimpses into what gets generated when the emphasis concerns processes and practices of doing a literature review rather than what it represents. Like the previous paper, the authors are inspired by a cartographic approach that holds the potential to map the processes involved in becoming deeply immersed and affect with a body of literature. They take literature on Teacher Educator Professional Learning as a case in point to explore how mapping and tracing entangled concepts can generate unanticipated insights and present new lines of thought. Finally, Louisa Allen explores the potential of smell, with all the senses and beyond the human, for educational research. She takes the reader on ‘smellwalks’ which presented themselves as an unlikely research method during pandemic lockdown. Allen provides detailed accounts of the ways in which smellwalks came into being in a small coastal town in Aotearoa-New Zealand and enabled a deep exploration of pandemic-transformed life at a daily and local level. The paper offers a theoretical examination of smellwalk methodology as a means to consider smell through multisensory conceptualisations where human senses are understood as distinct but overlapping. Further, the paper theorises the act of smelling as unbounded and ultimately, always more-than-human. A series of research moments are examined to demonstrate how smelling involves a multisensory experience that emerges with/through the material landscape. Together these papers offer important ways to reappraise approaches to research methodology in education that have become so deeply embedded that they unwittingly shape conventional expectations of how research should be done, has always be done. Each of these papers offer exciting invitations to interrupt this routine way of thinking. Respond to the invitation to pause, to ask, must we do it that way? The way it has always been done? What happens if we question and dare to experiment with alternative approaches? When theory is mobilized through research that seeks to pursue alternative lines of inquiry, what then? When theoretical concepts are taken up in/to ‘foreign’ spaces what happens to them? How do they travel? What do they agitate? What do they make possible? Aligned with the aims of this journal, these papers individually and collectively, invite a pause to business-as-usual in educational research. Jayne Osgood Camilla Andersen Mona-Lisa Angell Ann Merete Otterstad Editors

Generalized juggling patterns, quiver Grassmannians and affine flag varieties

The goal of this paper is to clarify the connection between certain structures from the theory of totally nonnegative Grassmannians, quiver Grassmannians for cyclic quivers and the theory of local models of Shimura varieties. More precisely, we generalize the construction from our previous paper relating the combinatorics and geometry of quiver Grassmannians to that of the totally nonnegative Grassmannians. The varieties we are interested in serve as realizations of local models of Shimura varieties. We exploit quiver representation techniques to study the quiver Grassmannians of interest and, in particular, to describe explicitly embeddings into affine flag varieties which allow us to realize our quiver Grassmannians as a union of Schubert varieties therein.

A simple model of magnetic universe without singularity associated with a quadratic equation of state

A model of magnetic universe based on nonlinear electrodynamics has been introduced by Kruglov (Phys Rev D 92:123523, 2015). This model describes an early inflation era followed by a radiation era. We show that this model is related to the model of universe based on a quadratic equation of state introduced in our previous paper (Chavanis in Universe 1:357, 2015). This correspondence may provide a more fundamental justification of our equation of state. It may arise from quantum corrections to linear electrodynamics when the electromagnetic field becomes very high. We discuss two quantitatively different models of early universe. In Model I, the primordial density of the universe is identified with the Planck density. At t=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t=0$$\\end{document}, the universe had the characteristics of a Planck black hole (“planckion” particle). During the inflation, which takes place on a Planck timescale, the size of the universe evolves from the Planck length to a size comparable to the Compton wavelength of the neutrino. If we interpret the radius of the universe at the end of the inflation (neutrino’s Compton wavelength) as a minimum length related to quantum gravity and use Zeldovich’s first formula of the vacuum energy, we obtain the correct value of the cosmological constant. In Model II, the primordial density of the universe is identified with the electron density as a consequence of nonlinear electrodynamics. At t=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t=0$$\\end{document}, the universe had the characteristics of an electron. This can be viewed as a refinement of the “primeval atom” of Lemaître. During the inflation, which takes place on a gravitoelectronic timescale, the size of the universe evolves from the electron’s classical radius to a size comparable to the size of a dark energy star of the stellar mass. If we interpret the radius of the universe at the beginning of the inflation (electron’s classical radius) as a minimum length related to quantum gravity and use Zeldovich’s second formula of the vacuum energy, we obtain the correct value of the cosmological constant. This provides an accurate form of Eddington’s relation between the cosmological constant and the mass of the electron. We use these arguments to show that the present universe contains about 1080\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{80}$$\\end{document} protons (Eddington’s number). We also introduce a nonlinear electromagnetic Lagrangian that describes simultaneously the early inflation, the radiation era, and the dark energy era. It may account for a form of “generalized radiation” that is present from the beginning to the end of the cosmic evolution. Baryonic and dark matter are treated as independent noninteracting species. The dark energy era is due to the electromagnetic vacuum energy (zero-point radiation). In this approach, both the early inflation and the late acceleration of the universe (dark energy) arise as a consequence of nonlinear electrodynamics. This leads to a simple model of magnetic universe without singularity (aioniotic universe).

Volichenko-type metasymmetry of braided Majorana qubits

Abstract This paper presents different mathematical structures connected with the parastatistics of braided Majorana qubits and clarifies their role; in particular, "mixed-bracket" Heisenberg-Lie algebras are introduced. These algebras belong to a more general framework than the Volichenko algebras defined in 1990 by Leites-Serganova as metasymmetries which do not respect even/odd gradings and lead to mixed brackets interpolating ordinary commutators and anticommutators.
In a previous paper braided Z2-graded Majorana qubits were first-quantized within a graded Hopf algebra framework endowed with a braided tensor product. The resulting system admits truncations at 
roots of unity and realizes, for a given integer s=2,3,4, ..., an interpolation between ordinary Majorana fermions (recovered at s=2) and bosons (recovered in the s →∞ limit); it implements a parastatistics where at most s-1 indistinguishable particles are accommodated in a multi-particle sector.
The structures discussed in this work are:
- the quantum group interpretation of the roots of unity truncations recovered from a (superselected) set of reps of the quantum superalgebra Uq(osp(1|2));
- the reconstruction, via suitable intertwining operators, of the braided tensor products as ordinary tensor products
(in a minimal representation, the N-particle sector of the braided Majorana qubits is described by 2N x 2N;
- the introduction of mixed brackets for the braided creation/annihilation operators which define generalized Heisenberg-Lie algebras;
- the s→∞ untruncated limit of the mixed-bracket Heisenberg-Lie algebras producing parafermionic oscillators;
- (meta)symmetries of ordinary differential equations given by matrix Schrödinger equations in 0+1 dimension induced by the braided creation/annihilation operators;
- in the special case of a third root of unity truncation, a nonminimal realization of the intertwining operators defines the system
as a ternary algebra.

DMRG-Tailored Coupled Cluster Method in the 4c-Relativistic Domain: General Implementation and Application to the NUHFI and NUF3 Molecules.

Heavy atom compounds represent a challenge for computational chemistry due to the need for simultaneous treatment of relativistic and correlation effects. Often such systems also exhibit strong correlation, which hampers the application of perturbation theory or single-reference coupled cluster (CC) methods. As a viable alternative, we have proposed externally correcting the CC method using the density matrix renormalization group (DMRG) wave functions, yielding the DMRG-tailored CC method. In a previous paper [J. Chem. Phys. 2020, 152, 174107], we reported a first implementation of this method in the relativistic context, which was restricted to molecules with real double group symmetry. In this work, we present a fully general implementation of the method, covering complex and quaternion double groups as well. The 4c-TCC method thus becomes applicable to polyatomic molecules, including heavy atoms. For the assessment of the method, we performed calculations of the chiral uranium compound NUHFI, which was previously studied in the context of the enhancement of parity violation effects. In particular, we performed calculations of a cut of the potential energy surface of this molecule along the stretching of the N-U bond, where the system exhibits strong multireference character. Since there are no experimental data for NUHFI, we have performed also an analogous study of the (more symmetric) NUF3 molecule, where the vibrational frequency of the N-U bond can be compared with spectroscopic data.

Global Existence in the Critical Space for the Space-Time Monopole Equations

We prove the global existence of solutions in the critical space \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1({\\mathbb {R}})$$\\end{document} for space-time monopole equations under the Lorenz gauge condition. The existence of a global solution was showed in our previous paper. Here we adapt a different function space to allow for a simplified proof. We first prove the local existence in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1({\\mathbb {R}})$$\\end{document} and extend the local solution to the global one.

Teachers as CALL Customizers: exploring teachers’ perceptions of conceptualizing and customizing CALL materials

A common issue in the second/foreign language (L2) classroom is that teachers’ insights are not often included in the development of CALL materials. To understand how teachers can customize CALL materials that meet the needs of their students, our previous conceptual paper proposed a three-level approach to show how teachers can leverage basic computers skills to categorize pre-existing digital materials to stimulate L2 interaction, namely by using them as-is, modifying them, and/or using online tools to create them from scratch. This one-group mixed-methods study implements these ideas by: (1) examining the types of CALL materials teachers can customize to stimulate L2 interaction, and (2) assessing participants’ perceptions of how they used the approach. The study took place in a CALL teacher training course for eight weeks at an English-speaking university in Montréal and featured readings, lectures, lab sessions, and projects directed at customizing CALL materials. To understand the types of CALL materials participants could customize (goal #1), mixed-methods data were collected in the form of online ESL courses built by participants and a design-choice log where they recorded details about the tools they used, providing an overview of each activity. A reflective discussion was held using the Socratic-Wheel technique to understand how participants used the approach (goal #2). The results indicate that participants customized CALL materials at all three levels, targeting L2 interaction with (e.g. online flashcards) and through (e.g. synchronous messages) computers. Responses from the reflective discussion revealed that participants perceived becoming aware of their abilities in CALL, thus endorsing the pedagogical effectiveness of the approach.