Miracle-dz/UniFAR-FTUs huggingface dataset:
Embeddings of Decomposition Spaces into Sobolev and BV Spaces

In the present paper, we investigate whether an embedding of a decomposition space $\mathcal{D}\left(\mathcal{Q},L^{p},Y\right)$ into a given Sobolev space $W^{k,q}(\mathbb{R}^{d})$ exists. As special cases, this includes embeddings into Sobolev spaces of (homogeneous and inhomogeneous) Besov spaces, ($\alpha$)-modulation spaces, shearlet smoothness spaces and also of a large class of wavelet coorbit spaces, in particular of shearlet-type coorbit spaces. Precisely, we will show that under extremely mild assumptions on the covering $\mathcal{Q}=\left(Q_{i}\right)_{i\in I}$, we have $\mathcal{D}\left(\mathcal{Q},L^{p},Y\right)\hookrightarrow W^{k,q}(\mathbb{R}^{d})$ as soon as $p\leq q$ and $Y\hookrightarrow\ell_{u^{\left(k,p,q\right)}}^{q^{\triangledown}}\left(I\right)$ hold. Here, $q^{\triangledown}=\min\left\{ q,q'\right\} $ and the weight $u^{\left(k,p,q\right)}$ can be easily computed, only based on the covering $\mathcal{Q}$ and on the parameters $k,p,q$. Conversely, a necessary condition for existence of the embedding is that $p\leq q$ and $Y\cap\ell_{0}\left(I\right)\hookrightarrow\ell_{u^{\left(k,p,q\right)}}^{q}\left(I\right)$ hold, where $\ell_{0}\left(I\right)$ denotes the space of finitely supported sequences on $I$. All in all, for the range $q \in (0,2]\cup\{\infty\}$, we obtain a complete characterization of existence of the embedding in terms of readily verifiable criteria. We can also completely characterize existence of an embedding of a decomposition space into a BV space.
Detector configuration of DECIGO/BBO and identification of cosmological neutron-star binaries

The primary target for the planned space-borne gravitational wave interferometers DECIGO/BBO (Decihertz Interferometer Gravitational Wave Observatory/Big Bang Observer) is a primordial gravitational wave background. However there exist astrophysical foregrounds, and among them, gravitational waves from neutron-star (NS) binaries are the solid and strong component that must be identified and subtracted. In this paper, we discuss the geometry of detector configurations preferable for identifying the NS/NS binary signals. As a first step, we analytically estimate the minimum signal-to-noise ratios of the binaries for several static detector configurations that are characterized by adjustable geometrical parameters, and determine the optimal values for these parameters. Next we perform numerical simulations to take into account the effect of detector motions, and find reasonable agreements with the analytical results. We show that, with the standard network formed by 4 units of triangle detectors, the proposed BBO sensitivity would be sufficient in receiving gravitational waves from all the NS/NS binaries at z{<=}5 with signal-to-noise ratios higher than 25. We also discuss the minimum sensitivity of DECIGO required for the foreground identification.
Reconstructing eruptive source parameters from tephra deposit: a numerical approach for medium-sized explosive eruptions

Since the seventies, several reconstruction techniques have been proposed, and are currently used, to extrapolate and quantify eruptive parameters from sampled deposit datasets. Discrete numbers of tephra ground loadings or stratigraphic records are usually processed to estimate source eruptive values. Reconstruction techniques like Pyle, Power law and Weibull are adopted as standard to quantify the erupted mass (or volume) whereas Voronoi for reconstructing the granulometry. Reconstructed values can be affected by large uncertainty due to complexities occurring within the atmospheric dispersion and deposition of volcanic particles. Here we want to quantify the sensitivity of reconstruction techniques, and to quantify how much estimated values of mass and grain size differ from emitted and deposited ones. We adopted a numerical approach simulating with a dispersal code a mild explosive event occurring at Mt. Etna, with eruptive parameters similar to those estimated for eruptions occurred in the last decade. Then we created a synthetic deposit by integrating the mass on the ground computed by the model over the computational domain (>50000 km2). Multiple samplings of the simulated deposit are used for generating a large dataset of sampling tests afterwards processed with standard reconstruction techniques. Results are then compared and evaluated through a statistical analysis, based on 2000 sampling tests of 100 samplings points. On average, all the used techniques underestimate deposited and emitted mass. A similar analysis, carried on Voronoi results, shows that information on the total grain size distribution is strongly deteriorated. Here we present a new method allowing an estimate of the deficiency in deposited mass for each simulated class. Finally a sensitivity study on eruptive parameters is presented in order to generalize our results to a wider range of eruptive conditions.
THE INITIAL MASS FUNCTION OF FIELD OB STARS IN THE SMALL MAGELLANIC CLOUD

Some theories of star formation suggest massive stars may only form in clustered environments, which would create a deficit of massive stars in low-density environments. Observationally, Massey finds such a deficit in samples of the field population in the Small and Large Magellanic Clouds, with an initial mass function (IMF) slope of ΓIMF ∼ 4. These IMF measurements represent some of the largest known deviations from the standard Salpeter IMF slope of ΓIMF = 1.35. Here, we carry out a comprehensive investigation of the mass function above 20 M☉ for the entire field population of the Small Magellanic Cloud (SMC), based on data from the Runaways and Isolated O Type Star Spectroscopic Survey of the SMC (RIOTS4). This is a spatially complete census of the entire field OB star population of the SMC obtained with the IMACS multi-object spectrograph and MIKE echelle spectrograph on the Magellan telescopes. Based on Monte Carlo simulations of the evolved present-day mass function, we find the slope of the field IMF above 20 M☉ is ΓIMF = 2.3 ± 0.4. We extend our IMF measurement to lower masses using BV photometry from the OGLE II survey. We use a statistical approach to generate a probability distribution for the mass of each star from the OGLE photometry, and we again find ΓIMF = 2.3 ± 0.6 for stellar masses from 7 M☉ to 20 M☉. The discovery and removal of ten runaways in our RIOTS4 sample steepens the field IMF slope to ΓIMF = 2.8 ± 0.5. We discuss the possible effects of binarity and star formation history on our results, and conclude that the steep field massive star IMF is most likely a real effect.
EFFECTS OF THE SCATTER IN SUNSPOT GROUP TILT ANGLES ON THE LARGE-SCALE MAGNETIC FIELD AT THE SOLAR SURFACE

The tilt angles of sunspot groups represent the poloidal field source in Babcock–Leighton-type models of the solar dynamo and are crucial for the build-up and reversals of the polar fields in surface flux transport (SFT) simulations. The evolution of the polar field is a consequence of Hale's polarity rules, together with the tilt angle distribution which has a systematic component (Joy's law) and a random component (tilt-angle scatter). We determine the scatter using the observed tilt angle data and study the effects of this scatter on the evolution of the solar surface field using SFT simulations with flux input based upon the recorded sunspot groups. The tilt angle scatter is described in our simulations by a random component according to the observed distributions for different ranges of sunspot group size (total umbral area). By performing simulations with a number of different realizations of the scatter we study the effect of the tilt angle scatter on the global magnetic field, especially on the evolution of the axial dipole moment. The average axial dipole moment at the end of cycle 17 (a medium-amplitude cycle) from our simulations was 2.73 G. The tilt angle scatter leads to an uncertainty of 0.78 G (standard deviation). We also considered cycle 14 (a weak cycle) and cycle 19 (a strong cycle) and show that the standard deviation of the axial dipole moment is similar for all three cycles. The uncertainty mainly results from the big sunspot groups which emerge near the equator. In the framework of Babcock–Leighton dynamo models, the tilt angle scatter therefore constitutes a significant random factor in the cycle-to-cycle amplitude variability, which strongly limits the predictability of solar activity.
Psychological Test Development: Innovative Behavior at Work for Startup Employee

The majority of Indonesia's startup companies failed during the early phase of the company. One factor contributing to this failure is the lack of Innovation brought up by the company. Human resource in the company plays an important role in fostering Innovation. Studies showed employee innovative work behavior is the main factor that drives company innovation. This research aims to construct Innovative Behavior at Work scale that is reliable, valid, have good items and norms for score interpretation purposes. The research subjects were an employee who works in a startup company. The result showed that the scale has high internal consistency, valid, and the items discriminate individual capabilities. The norm used in this scale is within group norms with a standard score of M=10 and SD=3.
Normalizer, divergence type, and Patterson measure for discrete groups of the Gromov hyperbolic space

For a non-elementary discrete isometry group $G$ of divergence type acting on a proper geodesic $\delta$-hyperbolic space, we prove that its Patterson measure is quasi-invariant under the normalizer of $G$. As applications of this result, we have: (1) under a minor assumption, such a discrete group $G$ admits no proper conjugation, that is, if the conjugate of $G$ is contained in $G$, then it coincides with $G$; (2) the critical exponent of any non-elementary normal subgroup of $G$ is strictly greater than half of that for $G$.
Constraining the gravitational-wave energy density of the Universe in the range 0.1 Hz to 1 Hz using the Apollo Seismic Array

In this paper, we describe an analysis of Apollo era lunar seismic data that places an upper limit on an isotropic stochastic gravitational-wave background integrated over a year in the frequency range 0.1\,Hz -- 1\,Hz. We find that because the Moon's ambient noise background is much quieter than that of the Earth, significant improvements over an Earth based analysis were made. We find an upper limit of $\Omega_{\rm GW}<1.2\times 10^{5}$, which is three orders of magnitude smaller than a similar analysis of a global network of broadband seismometers on Earth and the best limits in this band to date. We also discuss the benefits of a potential Earth-Moon correlation search and compute the time-dependent overlap reduction function required for such an analysis. For this search, we find an upper limit an order of magnitude larger than the Moon-Moon search.
Degree growth of monomial maps and McMullen's polytope algebra

We compute all dynamical degrees of monomial maps by interpreting them as mixed volumes of polytopes. By exploiting further the isomorphism between the polytope algebra of P. McMullen and the universal cohomology of complete toric varieties, we construct invariant positive cohomology classes when the dynamical degrees have no resonance.
Decomposing edge-coloured complete symmetric digraphs into monochromatic paths

Confirming and extending a conjecture by Guggiari, we show that every countable $(r+1)$-edge-coloured complete symmetric digraph containing no directed paths of edge-length $\ell_i$ for any colour $i\leq r$ can be covered by $\prod_{i\leq r} \ell_i$ pairwise disjoint monochromatic directed paths in colour $r+1$.
A Generalization of a Bin-Based Modification to the Stochastic Simulation Algorithm

In a 1996 paper, See$\beta$elberg, Trautmann and Thorn modified Gillespie's (1975) Monte Carlo algorithm which is used to stochastically simulate the collision and coalescence process. Their modification reduces the storage requirements of the simulation by several orders of magnitude. However, their modification creates unphysical and potentially fatal conditions when used with common initial distributions. We identify those conditions and propose a solution to maintain physically real conditions for all state variables during the evolution of any initial distribution.
Boundary Regularity for the $\infty$-Heat Equation

We study the boundary regularity for the normalised $\infty$-heat equation $u_t = \Delta_{\infty}^Nu$ in arbitrary domains. Perron's Method is used for constructing solutions. We characterize regular boundary points with barrier functions, and prove an Exterior Ball result. A Petrovsky-like criterion is established.
Data analysis methods for the cosmic microwave background

In this review, we give an overview of some of the major aspects of data reduction and analysis for the cosmic microwave background (CMB). Since its prediction and discovery in the last century, the CMB radiation has proven itself to be one of our most valuable tools for precision cosmology. Recently, and especially when combined with complementary cosmological data, measurements of the CMB anisotropies have provided us with a wealth of quantitive information about the birth, evolution and structure of our Universe. We begin with a simple, general introduction to the physics of the CMB, including a basic overview of the experiments which record CMB data. The focus, however, will be the data analysis treatment of CMB data sets.
A New Diagnostic Criteria and Grading System of Rhino-Maxillary Mucormycosis based on Cone Beam Computed Tomographic Findings

Background: Mucormycosis is a rare opportunistic fungal infection, which has a rapidly progressive and fulminant course with fatal outcome. It is the need of the hour to diagnose and treat the increasing cases urgently. Aim: The aim of this article is to study the common radiographic features of rhinomaxillary mucormycosis (RMM), find diagnostic criteria, and grade the disease according to the radiographic features. Settings: This study was conducted at Face Three-Dimensional Cone-Beam Computed Tomography (CBCT) Center, Aurangabad, Maharashtra. Materials and Methods: CBCT scans of 30 patients who were referred for CBCT scanning of suspected RMM were retrospectively evaluated for relevant radiological data. Results: The most common CBCT features of RMM were osteolytic lesions in alveolar bone, palate, nose and nasal cavity, and zygoma along with involvement of paranasal sinuses. About 76.66% of patients had a history of COVID-19 infection. Conclusion: According to the collected data, the scans of probable rhinomaxillary mucormycosis were graded in three groups – mild, moderate, and severe. The goal of this article is to emphasize the most overlook diagnostic entity – CBCT and its significant importance in early diagnosis, treatment, and prognosis of RMM. Early diagnosis of RMM can save the patients from the extent of morbidity and mortality.
The Market Reaction to Corporate News in Emerging Markets: Evidence from India

In the context of market efficiency, the stock market reaction to arrival of corporate news has been widely researched in the context of developed markets. However, developed markets are distinct from emerging markets. In this paper, we employ a unique dataset of firm-specific news and examine the market reaction associated with the arrival of different firm-specific corporate news in the public domain in the context of India, an emerging market. We study the price and trading volume reaction associated with firm-specific news for a sample of stocks listed on the National Stock Exchange of India using the event study methodology. We observe that the Indian equity market incorporate new information through firm-specific corporate news releases promptly. Besides, our results underscore the role of earnings news and analyst calls in reducing information asymmetry among investors in an emerging market context. Our study reveals that the observations in the context of developed markets cannot be generalized in the context of the India. 3
Comments, Shares, or Likes: What Makes News Posts Engaging in Different Ways

In a digital media environment where content distribution is shaped by technology companies’ algorithms and user behaviors, news organizations try to post content that can prompt user engagement in forms such as comments, shares, and likes or reactions. This study employs a content analysis of 1,600 messages and analyses of engagement metrics for 157,962 messages to examine to what extent and how Facebook messages of US and Israeli news organizations differ in the engagement modes they generate: commenting versus sharing versus liking/reacting. Drawing on the participation paradigm in audience research, news value theory, and literature on engagement enhancers, the study shows that certain content characteristics are associated with each of the examined engagement modes in more than one country while other content characteristics are associated with particular modes, but not with all of them. It offers a nuanced understanding of user interaction with news-related content and helps think about content units as more engaging or less engaging than others, or as engaging in different ways.
On the semiduals of local isometry groups in 3d gravity

We use factorisations of the local isometry groups arising in 3d gravity for Lorentzian and Euclidean signatures and any value of the cosmological constant to construct associated bicrossproduct quantum groups via semidualisation. In this way we obtain quantum doubles of the Lorentz and rotation groups in 3d, as well as kappa-Poincare algebras whose associated r-matrices have spacelike, timelike and lightlike deformation parameters. We confirm and elaborate the interpretation of semiduality proposed in [13] as the exchange of the cosmological length scale and the Planck mass in the context of 3d quantum gravity. In particular, semiduality gives a simple understanding of why the quantum double of the Lorentz group and the kappa-Poincare algebra with spacelike deformation parameter are both associated to 3d gravity with vanishing cosmological constant, while the kappa-Poincare algebra with a timelike deformation parameter can only be associated to 3d gravity if one takes the Planck mass to be imaginary.
On categories of slices

In this paper we give an algebraic description of the category of $n$-slices for an arbitrary group $G$, in the sense of Hill-Hopkins-Ravenel. Specifically, given a finite group $G$ and an integer $n$, we construct an explicit $G$-spectrum $W$ (called an isotropic slice $n$-sphere) with the following properties: (i) the $n$-slice of a $G$-spectrum $X$ is equivalent to the data of a certain quotient of the Mackey functor $\underline{[W,X]}$ as a module over the endomorphism Green functor $\underline{[W,W]}$; (ii) the category of $n$-slices is equivalent to the full subcategory of right modules over $\underline{[W,W]}$ for which certain restriction maps are injective. We use this theorem to recover the known results on categories of slices to date, and exhibit the utility of our description in several new examples. We go further and show that the Green functors $\underline{[W,W]}$ for certain slice $n$-spheres have a special property (they are "geometrically split") which reduces the amount of data necessary to specify a $\underline{[W,W]}$-module. This step is purely algebraic and may be of independent interest.
Infra-solvmanifolds of $\Sol_1^4$-geometry

The purpose of this paper is to classify all compact manifolds modeled on the 4-dimensional solvable Lie group $Sol_1^4$. The maximal compact subgroup of $Isom(Sol_1^4)$ is $D_4=\mathbb Z_4\rtimes\mathbb Z_2$. We shall exhibit an infra-solvmanifold with $Sol_1^4$-geometry whose holonomy is $D_4$. This implies that all possible holonomy groups do occur; $\{1\}$, $\mathbb Z_2$ (5 families), $\mathbb Z_4$, $\mathbb Z_2\times\mathbb Z_2$ (5 families),and $\mathbb Z_4\rtimes\mathbb Z_2$ (2 families). This includes the classification of 3-dimensional infra-$Sol$ manifolds.
A Study of Phonemic Awareness, Letter Sound Knowledge, and Word Reading in Struggling Adolescent Students

ABSTRACT Phonemic awareness is thought to be a causal factor predicting early reading acquisition while its influence diminishes as other reading skills develop. This is a descriptive study of 74, primarily African American, fifth- through eighth-grade students attending a small, inner-city school. The study sought to determine the relationship between phonemic awareness, developmental spelling, pseudoword reading, and sight word reading in adolescent students who struggle with reading. Correlation results showed statistically significant relations among all four variables with the largest between phonemic awareness and developmental spelling. Regression results revealed phonemic awareness predicted significant variance in developmental spelling (R2 = .51), but not pseudo- or sight word reading. A discontinuity test determined that the influence of phonemic awareness on developmental spelling was consistent across all levels of attainment. Results are discussed from a developmental perspective.
The Hochschild–Kostant–Rosenberg Isomorphism for Quantized Analytic Cycles

In this article, we provide a detailed account of a construction sketched by Kashiwara in an unpublished manuscript concerning generalized HKR isomorphisms for smooth analytic cycles whose conormal exact sequence splits. It enables us, among other applications, to solve a problem raised recently by Arinkin and C\u{a}ld\u{a}raru about uniqueness of such HKR isomorphisms in the case of the diagonal injection. Using this construction, we also associate with any smooth analytic cycle endowed with an infinitesimal retraction a cycle class which is an obstruction for the cycle to be the vanishing locus of a transverse section of a holomorphic vector bundle.
Modeling Urban Impact on Zhengzhou Storm on July 20, 2021

The heavy storm event that occurred from 18 to 22 July 2021, in Henan province caused severe floods and casualties, especially in the provincial city, Zhengzhou. While the impacts of large‐scale synoptic systems and local‐scale orographic effects on the storm event have been studied, the role of urbanization remains unexplored. Using Weather Research and Forecasting model, the study designed two numerical experiments, differentiated by the presence of urban land cover, to investigate the urban impact on the storm event over Henan province, with a focus on Zhengzhou. Urbanization increases precipitation in the major urban area of Zhengzhou and its south, western Kaifeng, and western Xuchang, where the largest increases reach from 188.2 to 304.4 mm. Further investigation into Zhengzhou city reveals that urbanization leads to shifted precipitation center and stagnation in the major urban area, resulting in earlier peak rainfall time and more concentrated precipitation. Elevated surface temperature and sensible heat are identified before the peak rainfall arrives, which leads to increased planet boundary layer height, suggesting the contribution of the urban heat island effect. Thermal perturbation and increased surface roughness over urban areas promote vertical uplift and moisture convergence, increasing water vapor and forming storm system drags during the peak precipitation time, thus bringing earlier and higher amounts of precipitation to the major urban area and its south. The study calls for the consideration of the urban effect of extreme storm events and the precaution against waterlogging over urban areas in rapid‐developing cities.
Norm of the Bergman projection

This paper deals with the the norm of the weighted Bergman projection operator $P_\alpha:L^\infty\to \mathcal{B}$ where $\alpha>-1$ and $\mathcal{B}$ is the Bloch space of the unit ball of the complex space $\mathbf{C}^n$. We consider two Bloch norms, the standard Bloch norm and invariant norm w.r. t. automorphisms of the unit ball. Our work contains as a special case the main result of the recent paper \cite{Perala}.