Miracle-dz/UniFAR-FTUs huggingface dataset:
The Hidden Fortress: Structure and substructure of the complex strong lensing cluster SDSS J1029+2623

We present Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) and Wide Field Camera 3 (WFC3) observations of SDSS J1029+2623, a three-image quasar lens system produced by a foreground cluster at z = 0.584. Our strong lensing analysis reveals six additional multiply imaged galaxies in addition to the multiply imaged quasar. We confirm the complex nature of the mass distribution of the lensing cluster, with a bimodal dark matter distribution which deviates from the Chandra X-ray surface brightness distribution. The Einstein radius of the lensing cluster is estimated to be theta(E) = 15.2 +/- 0.5 arcsec for the quasar redshift of z = 2.197. We derive a radial mass distribution from the combination of strong lensing, HST/ACS weak lensing and Subaru/Suprime-cam weak lensing analysis results, finding a best-fitting virial mass of M-vir = 1.55(-0.35)(+0.40) x 10(14) h(-1) M-circle dot and a concentration parameter of c(vir) = 25.7(-7.5)(+14.1). The lensing mass estimate at the outer radius is smaller than the X-ray mass estimate by a factor of similar to 2. We ascribe this large mass discrepancy to shock heating of the intracluster gas during a merger, which is also suggested by the complex mass and gas distributions and the high value of the concentration parameter. In the HST image, we also identify a probable galaxy, GX, in the vicinity of the faintest quasar image C. In strong lens models, the inclusion of GX explains the anomalous flux ratios between the quasar images. The morphology of the highly elongated quasar host galaxy is also well reproduced. The best-fitting model suggests large total magnifications of 30 for the quasar and 35 for the quasar host galaxy, and has an AB time delay consistent with the measured value.
Global existence and decay to equilibrium for some crystal surface models

In this paper we study the large time behavior of the solutions to the following nonlinear fourth-order equations $$ \partial_t u=\Delta e^{-\Delta u}, $$ $$ \partial_t u=-u^2\Delta^2(u^3). $$ These two PDE were proposed as models of the evolution of crystal surfaces by J. Krug, H.T. Dobbs, and S. Majaniemi (Z. Phys. B, 97, 281-291, 1995) and H. Al Hajj Shehadeh, R. V. Kohn, and J. Weare (Phys. D, 240, 1771-1784, 2011), respectively. In particular, we find explicitly computable conditions on the size of the initial data (measured in terms of the norm in a critical space) guaranteeing the global existence and exponential decay to equilibrium in the Wiener algebra and in Sobolev spaces.
Linear dynamical systems on Hilbert spaces:
 typical properties and explicit examples

We solve a number of questions pertaining to the dynamics of linear operators on Hilbert spaces, sometimes by using Baire category arguments and sometimes by constructing explicit examples. In particular, we prove the following results. - A typical hypercyclic operator is not topologically mixing, has no eigenvalues and admits no non-trivial invariant measure, but is densely distributionally chaotic. - A typical upper-triangular operator is ergodic in the Gaussian sense, whereas a typical operator of the form "diagonal plus backward unilateral weighted shift" is ergodic but has only countably many unimodular eigenvalues, in particular, it is ergodic but not ergodic in the Gaussian sense. - There exist Hilbert space operators which are chaotic and $\mathcal U$-frequently hypercyclic but not frequently hypercyclic, Hilbert space operators which are chaotic and frequently hypercyclic but not ergodic, and Hilbert space operators which are chaotic and topologically mixing but not $\mathcal U$-frequently hypercyclic. We complement our results by investigating the descriptive complexity of some natural classes of operators defined by dynamical properties.
Exact lowest-Landau-level solutions for vortex precession in Bose-Einstein condensates

The Lowest Landau Level (LLL) equation emerges as an accurate approximation for a class of dynamical regimes of Bose-Einstein Condensates (BEC) in two-dimensional isotropic harmonic traps in the limit of weak interactions. Building on recent developments in the field of spatially confined extended Hamiltonian systems, we find a fully nonlinear solution of this equation representing periodically modulated precession of a single vortex. Motions of this type have been previously seen in numerical simulations and experiments at moderately weak coupling. Our work provides the first controlled analytic prediction for trajectories of a single vortex, suggests new targets for experiments, and opens up the prospect of finding analytic multi-vortex solutions.
Investigating a university library building evacuation in Pakistan during a semi‐announced fire drill

Evacuation models represent one of the main tools used to assess building fire safety. Existing evacuation models are based on data from evacuation drills in western and developed countries, while there is a need for data from South Asian and developing countries (in general). This paper presents the results of an evacuation drill carried out in a library of a developing country in South Asia (Pakistan). The data of 85 student evacuees were recorded and analysed. Pre‐evacuation and walking speed data have been reported in this paper which are compared with the available data for library evacuations in other countries. The average pre‐evacuation time of 24.3 s (± standard deviation [SD] = 19.83 s) obtained in this study was shorter than previously published data for similar building types in other parts of the world. Furthermore, unimpeded horizontal speeds (mean = 0.74 m/s, SD = 0.28 m/s) were also smaller than the values reported in the available literature. Stair descending speeds (mean = 0.97 m/s, SD = 0.36 m/s) were within the ranges of stair movement data listed in previous studies. These findings represent a pioneering dataset for future building designs and evacuation simulations in developing countries.
Topological tensor product of bimodules, complete Hopf algebroids and convolution algebras

Given a finitely generated and projective Lie–Rinehart algebra, we show that there is a continuous homomorphism of complete commutative Hopf algebroids between the completion of the finite dual of its universal enveloping Hopf algebroid and the associated convolution algebra. The topological Hopf algebroid structure of this convolution algebra is here clarified, by providing an explicit description of its topological antipode as well as of its other structure maps. Conditions under which that homomorphism becomes an homeomorphism are also discussed. These results, in particular, apply to the smooth global sections of any Lie algebroid over a smooth (connected) manifold and they lead a new formal groupoid scheme to enter into the picture. In the appendices we develop the necessary machinery behind complete Hopf algebroid constructions, which involves also the topological tensor product of filtered bimodules over filtered rings.
Researching Finnish library responses to Covid-19 digital literacy challenges through the employment of reflective practice

Social distancing restrictions due to the Covid-19 pandemic were declared in Finland in March 2020. Libraries followed Government recommendations resulting in limited library service delivery across a variety of sectors. This research investigates challenges experienced by public, special and academic libraries in the Helsinki metropolitan area focussing on library staff reflections of digital literacy services offered during the pandemic. A multiple case study, with an emergent mixed methods research design was utilised. All data was gathered online due to Covid-19 restrictions: Quantitative data originated from an online survey of library staff; library websites were also audited. Qualitative data originated from semi-structured interviews. Triangulation of the data enabled a clear understanding of digital literacy challenges and responses. Overall, the mixed methods design and the data collection techniques, encouraged reflection upon experience, which in return informed a rich picture of the multiple case study. Results demonstrated that digital literacy challenges existed, particularly related to reaching library customers requiring digital support. Finnish libraries did not differentiate information literacy from digital literacy, as both were perceived as part of library service. Library staffs’ reflections corroborated similar research, for example, the impact of teleworking, on technology use and social aspects of working from home. Recommendations include undertaking further research on special libraries and promoting reflective practice as a mechanism for better understanding the views of library staff.
On Amalgamation in NTP2 Theories and Generically Simple Generics

We prove a couple of results on NTP2 theories. First, we prove an amalgamation statement and deduce from it that the Lascar distance over extension bases is bounded by 2. This improves previous work of Ben Yaacov and Chernikov. We propose a line of investigation of NTP2 theories based on S1 ideals with amalgamation and ask some questions. We then define and study a class of groups with generically simple generics, generalizing NIP groups with generically stable generics.
The equation div$u$+$\langle a, u \rangle=f$

We study the solutions $u$ to the equation $$ \begin{cases} \operatorname{div} u + \langle a , u \rangle = f & \textrm{ in } \Omega,\\ u=0 & \textrm{ on } \partial \Omega, \end{cases} $$ where $a$ and $f$ are given. We significantly improve the existence results of [Csat\'o and Dacorogna, A Dirichlet problem involving the divergence operator, \textit{Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire}, 33 (2016), 829--848], where this equation has been considered for the first time. In particular, we prove the existence of a solution under essentially sharp regularity assumptions on the coefficients. The condition that we require on the vector field $a$ is necessary and sufficient. Finally, our results cover the whole scales of Sobolev and H\"older spaces.
Third Mac Lane cohomology

Abstract MacLane cohomology is an algebraic version of the topological Hochschild cohomology. Based on the computation of the third author (see Appendix) we obtain an interpretation of the third Mac Lane cohomology of rings using certain kind of crossed extensions of rings in the quadratic world. Actually we obtain two such interpretations corresponding to the two monoidal structures on the category of square groups.
Antibacterial activity of galam soap (Melaleuca cajuputi) against Salmonella typhi as a form of ethnoscience based learning

Central Kalimantan has abundant biodiversity, one of which is galam which is often found in swampy areas in Central Kalimantan. One example of the use of galam is processing it into soap products as an effort to manage plant-based waste typical of Central Kalimantan. This study aims to determine the antibacterial activity of galam soap (Melaleuca cajuputi) against Salmonella typhi bacteria, where the results of this study have the potential to be developed as a learning resource for the application of ethnoscience-based learning. This study used an experimental research method using the disc method and the research design was a Completely Randomized Design (CRD). The results showed that galam soap was effective in inhibiting the growth of Salmonella typhi bacteria. The results of these studies can be used as a learning resource in lecture activities as a form of implementation of ethnoscience-based learning using the results of recent research, because ethnoscience-based learning is expected to help create meaningful learning activities.Abstrak Kalimantan Tengah memiliki keanekaragaman hayati yang melimpah, salah satunya berupa galam yang seringkali ditemui pada wilayah rawa di Kalimantan Tengah. Salah satu contoh pemanfaatan galam diantaranya diolah manjadi produk sabun sebagai upaya untuk pengelolaan limbah berbasis tumbuhan khas yang ada di Kalimantan Tengah. Penelitian ini bertujuan untuk mengetahui aktivitas anti bakteri sabun galam (Melaleuca cajuputi) terhadap bakteri Salmonella typhi, dimana hasil penelitian tersebut sangat berpotensi untuk dikembangkan sebagai sumber belajar untuk penerapan pembelajaran berbasis etnosains. Penelitian ini menggunakan metode penelitian eksperimen dengan menggunakan metode cakram serta desain penelitiannnya berupa Rancangan Acak Lengkap (RAL). Hasil penelitian menunjukkan bahwa sabun galam terbukti efektif dalam menghambat pertumbuhan bakteri Salmonella typhi. Hasil penelitian tersebut dapat dimanfaatkan sebagai sumber belajar pada kegiatan perkuliahan sebagai bentuk implementasi dari pembelajaran berbasis etnosains menggunakan hasil-hasil penelitian terkini, karena pembelajaran berbasis etnosains diharapkan dapat membantu menciptakan kegiatan pembelajaran yang bermakna.
INFLUENCE OF THE NONLINEARITY PARAMETER ON THE SOLAR WIND SUB-ION MAGNETIC ENERGY SPECTRUM: FLR–LANDAU FLUID SIMULATIONS

The cascade of kinetic Alfvén waves (KAWs) at sub-ion scales in the solar wind is simulated numerically using a fluid approach that retains ion and electron Landau damping, together with ion finite Larmor radius (FLR) corrections. Assuming initially equal and isotropic ion and electron temperatures, and an ion beta equal to unity, different simulations are performed by varying the propagation direction and the amplitude of KAWs that are randomly driven at a transverse wavenumber k0 such that k 0 d i = 0.18 ? > (where di is the proton inertial length), in order to maintain a prescribed level of turbulent fluctuations. The resulting turbulent regimes are characterized by the nonlinearity parameter, defined as the ratio of the characteristic times of Alfvén wave propagation and of the transverse nonlinear dynamics. The corresponding transverse magnetic energy spectra display power laws with exponents spanning a range of values consistent with spacecraft observations. The meandering of the magnetic field lines and the homogenization of ion temperature along these lines are shown to be related to the strength of the turbulence, measured by the nonlinearity parameter. The results are interpreted in terms of a recently proposed phenomenological model where the homogenization process along field lines induced by Landau damping plays a central role.
HUMAN RESOURCE ASPECTS AND PERFORMANCE OF CHILD DEVELOPMENT CENTRE PROJECTS IN ARUA CITY, UGANDA

The study assessed the levels of human resource aspects, examined performance levels of Child Development Centre (CDC’s) Projects and ascertained the influence of human resource aspects on the performance of CDC Projects in Arua city. It was hypothesized that there was no significant influence of human resource aspects on the performance of CDC Projects in Arua city. The study employed descriptive research designs; data were obtained from 72 respondents through questionnaires, interviews and follow-up interviews. The study revealed that generally, the level of human resource aspects in CDC’s in Arua city was high as shown by a grand Mean of 3.62 (72.4%), and the level of performance of CDC Projects in Arua city was high as shown by a grand mean of 3.78 (75.6%). The study further found out that human resource aspects: staff competences (B=.485; p=.000) and motivation (B=.347; p=.000) significantly influenced the performance of CDC Projects in Arua city while health and safety (B=.002; p=.689) had statistically insignificant influence on the performance of CDC projects in Arua city. However, overall, Human resource aspects (R=.673, R2=.452; P=.000) significantly influenced the performance of CDC Projects in Arua city. The null hypothesis that there was no significant influence of human resource aspects on the performance of CDC Projects in Arua city was rejected because the P-values of 0.000 was found to be less than the level of significance of 0.05. Therefore, it was recommended that CDC Projects in Arua city improve the levels of human resource aspects such as staff competences, motivation, health and safety to further increase their performance. Additional studies are carried out on other factors contributing to 54.8% in influencing the performance of CDC Projects in Arua city. Article visualizations:
A map of Ramanujan expansions

A map is a panorama in small scale. In this half-survey, half-research paper we give general results on Ramanujan expansions. We don't include the ocean of results from the literature on the two classes (see Schwarz-Spilker Book, also Lucht's survey for these) of additive and multiplicative functions while we include, say, the two new (not simply connected) lands of finite Ramanujan expansions (see my paper, with Murty & Saha) and of shift-Ramanujan expansions (see my subsequent paper, with Murty) .
The W, Z scale functions kit for first passage problems of spectrally negative Lévy processes, and applications to control problems

In the last years there appeared a great variety of identities for first passage problems of spectrally negative Lévy processes, which can all be expressed in terms of two “q-harmonic functions” (or scale functions) W and Z. The reason behind that is that there are two ways of exiting an interval, and thus two fundamental “two-sided exit” problems from an interval (TSE). Since many other problems can be reduced to TSE, researchers developed in the last years a kit of formulas expressed in terms of the “W, Z alphabet”. It is important to note – as is currently being shown – that these identities apply equally to other spectrally negative Markov processes, where however the W, Z functions are typically much harder to compute. We collect below our favorite recipes from the “W, Z kit”, drawing from various applications in mathematical finance, risk, queueing, and inventory/storage theory. A small sample of applications concerning extensions of the classic de Finetti dividend problem is offered. An interesting use of the kit is for recognizing relationships between problems involving behaviors apparently unrelated at first sight (like reflection, absorption, etc.). Another is expressing results in a standardized form, improving thus the possibility to check when a formula is already known.
Exhaustion of isoperimetric regions in asymptotically hyperbolic manifolds with scalar curvature $R\geq -6$

In this paper, aimed at exploring the fundamental properties of isoperimetric region in $3$-manifold $(M^3,g)$ which is asymptotic to Anti-de Sitter-Schwarzschild manifold with scalar curvature $R\geq -6$, we prove that connected isoperimetric region $\{D_i\}$ with $\mathcal{H}_g ^3(D_i)\geq \delta_0>0$ cannot slide off to the infinity of $(M^3,g)$ provided that $(M^3,g)$ is not isometric to the hyperbolic space. Furthermore, we prove that isoperimetric region $\{D_i\}$ with topological sphere $\{\partial D_i\}$ as boundary is exhausting regions of $M$ if Hawking mass $m_H(\partial D_i)$ has uniform bound. In the case of exhausting isoperimetric region, we obtain a formula on expansion of isoperimetric profile in terms of renormalized volume.
On the interplay among maximum principles, compact support principles and Keller-Osserman conditions on manifolds

This paper is about the influence of Geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, in particular by the study of entire graphs with prescribed mean curvature, we consider classes of coercive differential inequalities of the form $$ \mathrm{div}\left( \frac{\varphi(|\nabla u|)}{|\nabla u|} \nabla u\right) \ge b(x)f(u) l(|\nabla u|) \qquad \text{(respectively, $\le$ or $=$)} $$ on domains of a manifold $M$, for suitable $\varphi,b,f,l$, with emphasis on mean curvature type operators. We investigate the validity of strong maximum principles, compact support principles and Liouville type theorems; in particular, the goal is to identify sharp thresholds, involving curvatures or volume growth of geodesic balls in $M$, to guarantee the above properties under appropriate Keller-Osserman type conditions, and to discuss the geometric reasons behind the existence of such thresholds. The paper also aims to give a unified view of recent results in the literature. The bridge with Geometry is realized by studying the validity of weak and strong maximum principles at infinity, in the spirit of Omori-Yau's Hessian and Laplacian principles and subsequent improvements.
Analytic components for the hadronic total cross-section: Fractional calculus and Mellin transform

In high-energy hadron-hadron collisions, the dependence of the total cross-section ($\sigma_{tot}$) with the energy still constitutes an open problem for QCD. Phenomenological analyses usually relies on analytic parameterizations provided by the Regge-Gribov formalism and fits to the experimental data. In this framework, the singularities of the scattering amplitude in the complex angular momentum plane determine the asymptotic behavior of $\sigma_{tot}$ in terms of the energy. Usual applications connect simple and triple pole singularities with asymptotic power and logarithmic-squared functions of the energy, respectively. More restrict applications have considered as a leading component for $\sigma_{tot}$ an empirical function consisting of a logarithmic raised to a real exponent, which is treated as a free fit parameter. With this function, data reductions lead to good descriptions of the experimental data and real (not integer) values of the exponent. In this paper, making use of two independent formalisms (fractional calculus and Mellin transform), we first show that the singularity associated with this empirical function is a branch point and then we explore the mathematical consequences of the result and possible physical interpretations. After reviewing the determination of the singularities from asymptotic forms of interest through the Mellin transform, we demonstrate that the same analytic results can be obtained by means of the Caputo fractional derivative, leading, therefore, to fractional calculus interpretations. Besides correlating Mellin transform, non-local fractional derivatives and exploring the generalization from integer to real exponents and derivative orders, this fractional calculus result may provide insights for physical interpretations on the asymptotic rise of $\sigma_{tot}$.
The Effects of Solvents Polarity on the Phenolic Contents and Ferric Reducing Antioxidant Power of Cassytha filiformis, Commiphora schlechteri, Ochna natalitias and Pavetta assimilis

In the present study, the levels of Total Phenols compounds (TPC) and the antioxidant capacity of different extracts from leaves of Cassytha filiformis (C. filiformis), Commiphora schlechteri (C. schlechterii), Ochna natalitias (O. natalitia) and Pavetta assimilis (P. assimilis) were evaluated by the Folin-Ciocalteu and ferric ion reduction methods, respectively. The extracts evaluated were prepared with solvents of different polarities (n-hexane, dichloromethane, ethyl acetate and aqueous methanol). The total phenols found in all samples increase with solvent polarity. The reduction power found was linearly proportional to the concentration and is greater the greater the content of total phenolics. All extracts of the species O. natalitia (DCM, EtAcO and MetOH) showed higher antioxidant capacity than the other species. Thus, the promising results found in the present study suggest a high potential of these species as a source for the development of therapeutically useful natural antioxidants.