Miracle-dz/UniFAR-FTUs huggingface dataset:
Measuring Comodules and Enrichment

We study the existence of universal measuring comodules Q(M,N) for a pair of modules M,N in a braided monoidal closed category, and the associated enrichment of the global category of modules over the monoidal global category of comodules. In the process, we use results for general fibred adjunctions encompassing the fibred structure of modules over monoids and the opfibred structure of comodules over comonoids. We also explore applications to the theory of Hopf modules.
Bounds on spectral norms and barcodes

We investigate the relations between algebraic structures, spectral invariants, and persistence modules, in the context of monotone Lagrangian Floer homology with Hamiltonian term. Firstly, we use the newly introduced method of filtered continuation elements to prove that the Lagrangian spectral norm controls the barcode of the Hamiltonian perturbation of the Lagrangian submanifold, up to shift, in the bottleneck distance. Moreover, we show that it satisfies Chekanov type low-energy intersection phenomena, and non-degeneracy theorems. Secondly, we introduce a new averaging method for bounding the spectral norm from above, and apply it to produce precise uniform bounds on the Lagrangian spectral norm in certain closed symplectic manifolds. Finally, by using the theory of persistence modules, we prove that our bounds are in fact sharp in some cases. Along the way we produce a new calculation of the Lagrangian quantum homology of certain Lagrangian submanifolds, and answer a question of Usher.
On the maximum magnetic field amplification by the magnetorotational instability in core-collapse supernovae

Whether the magnetorotational instability (MRI) can amplify initially weak magnetic fields to dynamically relevant strengths in core collapse supernovae is still a matter of active scientific debate. Recent numerical studies have shown that the first phase of MRI growth dominated by channel flows is terminated by parasitic instabilities of the Kelvin-Helmholtz type that disrupt MRI channel flows and quench further magnetic field growth. However, it remains to be prop- erly assessed by what factor the initial magnetic field can be amplified and how it depends on the initial field strength and the amplitude of the perturbations. Different termination criteria leading to different estimates of the amplification factor were proposed within the parasitic model. To determine the amplification factor and test which criterion is a better predictor of the MRI termination, we perform three-dimensional shearing-disc and shearing-box simula- tions of a region close to the surface of a differentially rotating proto-neutron star in non-ideal MHD with two different numerical codes. We find that independently of the initial magnetic field strength, the MRI channel modes can amplify the magnetic field by, at most, a factor of 100. Under the conditions found in proto-neutron stars a more realistic value for the mag- netic field amplification is of the order of 10. This severely limits the role of the MRI channel modes as an agent amplifying the magnetic field in proto-neutron stars starting from small seed fields. A further amplification should therefore rely on other physical processes, such as for example an MRI-driven turbulent dynamo.
Rapidly converging formulae for $\zeta(4k\pm 1)$

We provide rapidly converging formulae for the Riemann zeta function at odd integers using the Lambert series $\mathscr{L}_q(s) = \sum_{n=1}^\infty n^{s} q^{n}/(1-q^n)$, $s=-(4k\pm 1)$. Our main formula for $\zeta(4k-1)$ converges at rate of about $e^{-\sqrt{15}\pi}$ per term, and the formula for $\zeta(4k+1)$, at the rate of $e^{-4\pi}$ per term. For example, the first order approximation yields $\zeta(3)\approx\frac{\pi ^3 \sqrt{15}}{100} +e^{-\sqrt{15} \pi }\left[\frac{9}{4}+\frac{4}{\sqrt{15}}\sinh (\frac{\sqrt{15} \pi }{2})\right]$ which has an error only of order $10^{-10}$.
Memorising Contemporary Piano Music as Described by Professional Pianists

The convention of performing from memory is a well-established practice among pianists, but an exception is often made for contemporary piano repertoire. Even so, a number of renowned pianists continue performing highly demanding compositions of this genre from memory, and this practice is commended by contemporary composers. No research to date has systematically investigated musicians’ views on this matter and explored detailed accounts of how to prepare and memorise such repertoire. In this study six renowned professional pianists with experience in performing contemporary piano repertoire were interviewed on their approaches to learning and memorising this music. Interpretative Phenomenological Analysis of the pianists’ accounts revealed a variety of views on performing contemporary music from memory, with some pianists advocating benefits from performing by heart and others from using the score. The general practice strategies reported resembled approaches described by skilled musicians in relation to standard repertoire, with some variations related to different types of contemporary music styles. Memorisation accounts emphasised the importance of strategies such as mental rehearsal, chunking, and reliance on different types of memory and their combination.
Towards an M5-brane model I: A 6d superconformal field theory

We present an action for a six-dimensional superconformal field theory containing a non-abelian tensor multiplet. All of the ingredients of this action have been available in the literature. We bring these pieces together by choosing the string Lie 2-algebra as a gauge structure, which we motivated in previous work. The kinematical data contains a connection on a categorified principal bundle, which is the appropriate mathematical description of the parallel transport of self-dual strings. Our action can be written down for each of the simply laced Dynkin diagrams, and each case reduces to a four-dimensional supersymmetric Yang–Mills theory with corresponding gauge Lie algebra. Our action also reduces nicely to an M2-brane model which is a deformation of the Aharony-Bergman-Jafferis-Maldacena (ABJM) model. While this action is certainly not the desired M5-brane model, we regard it as a key stepping stone towards a potential construction of the (2, 0)-theory.
The Gaia-ESO Survey: lithium depletion in the Gamma Velorum cluster and inflated radii in low-mass pre-main-sequence stars

RDJ and RJJ acknowledge support from the UK Science and Technology Facilities Council (STFC). Based on data products from observations made with European Southern Observatory (ESO) Telescopes at the La Silla Paranal Observatory under programme ID 188.B-3002. These data products have been processed by the Cambridge Astronomy Survey Unit (CASU) at the Institute of Astronomy, University of Cambridge, and by the FLAMES/UVES reduction team at the Istituto Nazionale di Astrofisica (INAF)/Osservatorio Astrofisico di Arcetri. These data have been obtained from the Gaia-ESO Survey Data Archive, prepared and hosted by the Wide Field Astronomy Unit, Institute for Astronomy, University of Edinburgh, which is funded by the STFC. This publication makes use of data products from the TwoMicron All-Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. This work was partly supported by the European Union FP7 programme through European Research Council (ERC) grant number 320360 and by the Leverhulme Trust through grant RPG-2012- 541. We acknowledge the support from the INAF and Ministero dell’ Istruzione, dell’ Universita’ e della Ricerca (MIUR) in the ` form of the grant ‘ Premiale VLT 2012’. This research was partially supported by the INAF through a PRIN-2014 grant. The results presented here benefit from discussions held during the Gaia-ESO workshops and conferences supported by the European Science Foundation (ESF) through the Gaia Research for European Astronomy Training (GREAT) Research Network Programme.
Shape and orientation of the gas distribution in A1689

ABSTRACT Knowledge of intrinsic shape and orientation of galaxy clusters is crucial to understand theirformation and evolution. We propose a novel model which uses Bayesian inference to deter-mine the intrinsic form of the hot intracluster medium of galaxy clusters. The method exploitsX-ray spectroscopic and photometric data plus measurements of the Sunyaev-Zel’dovich ef-fect (SZe). The gas distribution is modelled with an ellipsoidal parametric proﬁle who can ﬁtobserved X-ray surface-brightness and temperature. Comparison with the SZ amplitude ﬁxesthe elongation along the line of sight. Finally, Bayesian inference allows us to deproject themeasured elongation and the projected ellipticity and constrain the intrinsic shape and orien-tation of the cluster. We apply the method to the rich cluster Abell 1689, which was targetedby the Chandra and XMM satellites as well as by several SZe observatories. Observationscover in detail a region < ∼ 1Mpc. Our analysis favours a mildly triaxial cluster with a mi-nor to major axis ratio of 0.70±0.15, preferentially elongated along the line of sight, asexpected for massive lensing clusters. The triaxial structure together with the orientation biascan reconcile X-ray with lensing analyses and supports the view of A1689 as a just slightlyover-concentrated massive cluster not so far from hydrostatic equilibrium.Key words: galaxies: clusters: general – cosmology: observations – me thods: statistical –galaxies: clusters: individual: Abell 1689
Limit theorems for some skew products with mixing base maps

We obtain a central limit theorem, local limit theorems and renewal theorems for stationary processes generated by skew product maps $T(\unicode[STIX]{x1D714},x)=(\unicode[STIX]{x1D703}\unicode[STIX]{x1D714},T_{\unicode[STIX]{x1D714}}x)$ together with a $T$-invariant measure whose base map $\unicode[STIX]{x1D703}$ satisfies certain topological and mixing conditions and the maps $T_{\unicode[STIX]{x1D714}}$ on the fibers are certain non-singular distance-expanding maps. Our results hold true when $\unicode[STIX]{x1D703}$ is either a sufficiently fast mixing Markov shift with positive transition densities or a (non-uniform) Young tower with at least one periodic point and polynomial tails. The proofs are based on the random complex Ruelle–Perron–Frobenius theorem from Hafouta and Kifer [Nonconventional Limit Theorems and Random Dynamics. World Scientific, Singapore, 2018] applied with appropriate random transfer operators generated by $T_{\unicode[STIX]{x1D714}}$, together with certain regularity assumptions (as functions of $\unicode[STIX]{x1D714}$) of these operators. Limit theorems for deterministic processes whose distributions on the fibers are generated by Markov chains with transition operators satisfying a random version of the Doeblin condition are also obtained. The main innovation in this paper is that the results hold true even though the spectral theory used in Aimino, Nicol and Vaienti [Annealed and quenched limit theorems for random expanding dynamical systems. Probab. Theory Related Fields162 (2015), 233–274] does not seem to be applicable, and the dual of the Koopman operator of $T$ (with respect to the invariant measure) does not seem to have a spectral gap.
THE MEDIATING EFFECT OF SCHOOL CLIMATE ON THE RELATIONSHIP BETWEEN TEACHER COMMUNICATION BEHAVIOR AND STUDENT ENGAGEMENT

The purpose of this study was to determine the mediating effect of school climate on the relationship between teacher communication behavior and student engagement. Utilizing quantitative, non-experimental design via correlational technique, data were obtained from 300 respondents of the study who are students who belong to the senior high school department, particularly Grade levels 11 and 12 of the three national high schools under the division of Davao Del Sur in the province of Davao Del Sur. The researcher utilized a stratified random sampling technique and an online survey mode of data collection. The researcher also utilized the statistical tools mean, Pearson r, and Medgraph using Sobel z-test. From the results of the study, it was found that there is a high level of mean score for teacher communication behaviour and very high levels of mean scores for school climate and student engagement. Also, results revealed that there is a significant relationship between teacher communication behaviour and student engagement, a significant relationship between teacher communication behaviour and school climate and a significant relationship between school climate and student engagement. Further, it was revealed that there was full mediation on the effect of school climate on the relationship between teacher communication behaviour and student engagement. This implies that the teacher’s communication behaviour conveys the school climate.
Generalized Stokes laws for active colloids and their applications

The force per unit area on the surface of a colloidal particle is a fundamental dynamical quantity in the mechanics and statistical mechanics of colloidal suspensions. Here we compute it in the limit of slow viscous flow for a suspension of N spherical active colloids in which activity is represented by surface slip. Our result is best expressed as a set of linear relations, the ‘generalized Stokes laws’, between the coefficients of a tensorial spherical harmonic expansion of the force per unit area and the surface slip. The generalized friction tensors in these laws are many-body functions of the colloidal configuration and can be obtained to any desired accuracy by solving a system of linear equations. Quantities derived from the force per unit area—forces, torques and stresslets on the colloids and flow, pressure and entropy production in the fluid—have succinct expressions in terms of the generalized Stokes laws. Most notably, the active forces and torques have a dissipative, long-ranged, many-body character that can cause phase separation, crystallization, synchronization and a variety of other effects observed in active suspensions. We use the results above to derive the Langevin and Smoluchowski equations for Brownian active suspensions, to compute active contributions to the suspension stress and fluid pressure, and to relate the synchrony in a lattice of harmonically trapped active colloids to entropy production. Our results provide the basis for a microscopic theory of active Brownian suspensions that consistently accounts for momentum conservation in the bulk fluid and at fluid-solid boundaries.
Inverse scattering transforms and N-double-pole solutions for the derivative NLS equation with zero/non-zero boundary conditions.

We systematically report a rigorous theory of the inverse scattering transforms (ISTs) for the derivative nonlinear Schrodinger (DNLS) equation with both zero boundary condition (ZBC)/non-zero boundary conditions (NZBCs) at infinity and double poles of analytical scattering coefficients. The scattering theories for both ZBC and NZBCs are addressed. The direct problem establishes the analyticity, symmetries and asymptotic behavior of the Jost solutions and scattering matrix, and properties of discrete spectra. The inverse problems are formulated and solved with the aid of the matrix Riemann-Hilbert problems, and the reconstruction formulae, trace formulae and theta conditions are also posed. In particular, the IST with NZBCs at infinity is proposed by a suitable uniformization variable, which allows the scattering problem to be solved on a standard complex plane instead of a two-sheeted Riemann surface. The reflectionless potentials with double poles for the ZBC and NZBCs are both carried out explicitly by means of determinants. Some representative semi-rational bright-bright soliton, dark-bright soliton, and breather-breather solutions are examined in detail. These results will be useful to further explore and apply the related nonlinear wave phenomena.
One-loop $\mathbf{\beta}$ function of noncommutative scalar $QED_{4}$

In this paper, we consider the $\beta$ function at one-loop approximation for noncommutative scalar QED. The renormalization of the full theory, including the basic vertices, and the renormalization group equation are fully established. Next, the complete set of the one-loop diagrams corresponding to the first-order radiative corrections to the basic functions is considered: gauge, charged scalar and ghost fields self-energies, and three- and four-point vertex functions $\left $ and $\left $, respectively. We pay special attention to the noncommutative contributions to the renormalization constants. To conclude, the one-loop $\beta$ function of noncommutative scalar QED is then computed and comparison to known results is presented.
Which finite groups act smoothly on a given 4-manifold?

We prove that for any closed smooth $4$-manifold $X$ there exists a constant $C$ with the property that each finite subgroup $G<Diff(X)$ has a subgroup $N$ which is abelian or nilpotent of class $2$, and which satisfies $[G:N]\leq C$. We give sufficient conditions on $X$ for $Diff(X)$ to be Jordan, meaning that there exists a constant $C$ such that any finite subgroup $G<Diff(X)$ has an abelian subgroup $A$ satisfying $[G:A]\leq C$. Some of these conditions are homotopical, such as having nonzero Euler characteristic or nonzero signature, others are geometric, such as the absence of embedded tori of arbitrarily large self-intersection arising as fixed point components of periodic diffeomorphisms. Relying on these results, we prove that: (1) the symplectomorphism group of any closed symplectic $4$-manifold is Jordan, and (2) the automorphism group of any almost complex closed $4$-manifold is Jordan.
CLASSROOM TEACHERS' PERCEPTIONS OF OUT-OF-SCHOOL LEARNING ENVIRONMENTS

The present study aims to investigate classroom teachers’ perceptions of out-of-school learning environments. The study was designed around a survey model. The sample of the study was comprised of 359 classroom teachers determined with random sampling method, working in the central districts of Denizli province in the 2021-2022 academic year, and who completely responded to the questions in the data collection tool. The data collection tool used in the study consisted of two parts as "Personal Information" and "Out of School Learning Regulation Scale". Looking at the classroom teachers’ responses to out of school learning regulation scale and its dimensions, the highest mean was found in the "application" dimension and indicated a high-level perception while the lowest mean was in the "planning” dimension and indicated a medium level. It was also seen that the classroom teachers’ perceptions were at a medium level in the “information” dimension, high in the “evaluation” dimension and high in the overall scale, and it was understood that the teachers were generally at a good level in this area. The classroom teachers’ perceptions of out-of-school learning regulation did not differ according to their teaching experience, education level and receiving training related to out-of-school learning environments; however, their perceptions differed according to their gender, age, marital status, the district where they work, and studying the out-of-school learning environments guidebook. Article visualizations:
Psychometric Evidences of the Entrepreneurial Behavior Scale in University Students from Northern Peru

The study establishes the psychometric evidences of the Entrepreneurial Behavior Scale (EBS) in a sample of university students (N = 865) where 526 (60.8%) were women and 339 (39.2%) were men. Evidences of Aiken's content validity (p<.01 or p<.05) were found, indicating that the items are clear, coherent and relevant; as well as of internal structure, verifying the three-dimensional model, with adequate fit indices (RMR = .05, AGFI = .94, NFI = .92, RFI = .91, PNFI = .84). Finally, reliability by internal consistency was found with the Omega coefficient (ω > .70). It is concluded that the Entrepreneurial Behavior Scale (EBS) presents adequate evidences of validity and reliability. Received: 18 August 2022 / Accepted: 19 October 2022 / Published: 5 November 2022
Integrated science teaching materials with local wisdom insights to improve students' critical thinking ability

Critical thinking in science learning emphasizes students' knowledge and understanding of scientific concepts and processes needed to make decisions in real conditions. Students who have the ability to think critically are expected to be able to face problems and make decisions intelligently and based on information to live a better life. This study aims to improve students' critical thinking skills by developing teaching materials based on local wisdom. The results showed that the learning carried out significantly affected the level of critical thinking of students, both viewed as a whole (z=-4.731; p-value=0.000<0.05) or based on three aspects of critical thinking separately (p-value=0.000<0.05). The results of this study recommend that the use of teaching materials with local wisdom in science learning materials, especially materials that make up the ecosystem, must be optimized, both at the school and university levels.Abstrak Berpikir kritis dalam pembelajaran sains menekankan pada pengetahuan dan pemahaman mahasiswa terhadap konsep-konsep ilmiah dan proses yang diperlukan untuk mengambil keputusan dalam kondisi nyata. Mahasiswa yang memiliki kemampuan berpikir kritis diharapkan mampu menghadapi masalah serta mengambil keputusan secara cerdas dan berbasis informasi agar dapat menjalani kehidupan yang lebih baik. Penelitian ini bertujuan untuk meningkatkan keterampilan berpikir kritis mahasiswa dengan mengembangkan bahan ajar berwawasan kearifan lokal. Hasil penelitian menunjukkan bahwa pembelajaran yang dilakukan mempengaruhi tingkat berpikir kritis mahasiswa secara signifikan, baik dilihat secara keseluruhan (z=-4,731; p-value=0,000<0,05), maupun berdasarkan tiga aspek berpikir kritis secara terpisah (p-value=0,000<0,05). Hasil penelitian ini merekomendasikan agar penggunaan bahan ajar berwawasan kearifan lokal dalam materi pembelajaran sains khususnya materi yang membentuk ekosistem perlu dioptimalkan, baik dalam level sekolah maupun pada tingkat perguruan tinggi.
Awake intubation with C-MAC video-stylet versus fibreoptic bronchoscope in predicted difficult airway patients: Comparative randomised study

ABSTRACT Background This work was conducted to examine the efficiency of using C-MAC video stylet (VS) in awake intubation by comparing it to the standard method using fibreoptic bronchoscope (FOB). Patients and methodology Eighty patients were included in this study and divided into two groups according to the device used for awake intubation: VS group and FOB group. Results The intubation time ranged between 25 and 245 s with median of 45.5 s in VS group, while in the FOB group, it ranged between 36 and 279 s with median of 80 s with P value < 0.001. Successful intubation was done in 36 patients (90%) on the first attempt in VS group versus 29 patients in the FOB group (72.5%) with P value 0.04. As regard SpO2, insignificant difference was found all through measurement times. Heart rate and mean arterial blood pressure showed significant increase in FBO group more than in CMAC-VS group at 1 and 5 min after intubation with P value < 0.001. Conclusion Using the C-MAC VS in awake intubation proved to be easier and more successful than using the FOB.