Miracle-dz/UniFAR-FTUs huggingface dataset:
Extrinsic rigidity theorems for compact submanifolds of the sphere.

In this paper we consider immersions X: M —> S of a compact oriented Riemannian n-manifold M into the standard unit m-sphere S, and wish to find conditions on X which imply that it is a standard isometric immersion of a constant curvature π-sphere into S, i.e., to find extrinsic rigidity theorems. Our principal tools are certain integral formulas. In § 1 we briefly discuss the problem of finding interesting integral formulas. As an example we derive a simple integral formula relating the scalar curvature to infinitesmal conformal transformations. In § 2 we derive some integral formulas for compact hypersurfaces of S (Theorem A) by means of a variant of Newton's formula, and use these integral formulas to prove our first rigidity theorem (Corollary A). In § 3 we generalize the first two formulas of Theorem A to the case of arbitrary codimension (Theorem B) and then derive an improvement of a rigidity theorem, originally due to De Giorgi and Simons, for compact minimal submanifolds of the sphere whose normal spaces are close enough to each other (Theorem C). In the appendix we prove a weaker form of Theorem C using the theory of elliptic partial differential equations (Theorem D). Notation and conventions. The inner product and norm in the Euclidean space E of dimension m + 1 are denoted by ( , ) and | |, respectively. All manifolds are assumed to be connected, and all immersions to be isometric. We denote the directional derivative of an E^valued function / along a vector v by FJ, which means componentwise differentiation. If e19 , en form a frame field for M we shall at times use the notation ftJ for Fejf, particularly if / is a component of a tensor. In all sections but the appendix we follow the index convention 1 < /, j , k,l < n. The author wishes to thank his advisor, Professor Shiing-Shen Chern, for many helpful suggestions and kind encouragement during the preparation of his dissertation, of which this paper forms a part. He also wishes to thank Professors Robert Gardner and David Gilbarg for several informative conversations.
CONSTRAINING THE MILKY WAY'S HOT GAS HALO WITH O vii AND O viii EMISSION LINES

The Milky Way hosts a hot (≈2 × 106 K), diffuse, gaseous halo based on detections of z = 0 O vii and O viii absorption lines in quasar spectra and emission lines in blank-sky spectra. Here we improve constraints on the structure of the hot gas halo by fitting a radial model to a much larger sample of O vii and O viii emission line measurements from XMM-Newton/EPIC-MOS spectra compared to previous studies (≈650 sightlines). We assume a modified β-model for the halo density distribution and a constant-density Local Bubble from which we calculate emission to compare with the observations. We find an acceptable fit to the O viii emission line observations with (dof) = 1.08 (644) for best-fit parameters of cm−3 kpc3β and β = 0.50 ± 0.03 for the hot gas halo and negligible Local Bubble contribution. The O vii observations yield an unacceptable (dof) = 4.69 (645) for similar best-fit parameters, which is likely due to temperature or density variations in the Local Bubble. The O viii fitting results imply hot gas masses of M(<50 kpc) = and M(<250 kpc) = , accounting for ≲50% of the Milky Way's missing baryons. We also explore our results in the context of optical depth effects in the halo gas, the halo gas cooling properties, temperature and entropy gradients in the halo gas, and the gas metallicity distribution. The combination of absorption and emission line analyses implies a sub-solar gas metallicity that decreases with radius, but that also must be ⩾0.3 Z☉ to be consistent with the pulsar dispersion measure toward the Large Magellanic Cloud.
Study of Menstrual Hygiene Practices Among Adolescent Girls in a Tribal Area of Central India

Introduction Menstruation is an essential phenomenon in an adolescent girl's life. In India, females who are menstruating are considered impure and teenage girls are not allowed to undertake home chores or engage in religious or cultural events during their period. Up-to-date knowledge about menstruation, beginning in early adolescence, would improve safe practices and relieve the distress of millions of women. Material and methods A cross-sectional study was conducted among adolescent girls (10-19 years) residing in a tribal area of Nagpur District from January to March 2022. Three tribal residential schools (Ashram Shala) were selected from a total of six in Hingana Taluka of Nagpur District, using simple random sampling to fulfill the required sample size of 272. Demographic details, age at menarche, awareness of menstruation, sources of information about menstruation, menstrual hygiene practices, and restrictions observed during menstruation were assessed. Results The average age at menarche was 13.04+0.96 years (range 11-16 years). Only 45.17% of girls were aware of the menarche and menstrual cycle before its onset. The duration of the menstrual cycle ranged from 21-35 days in most of the girls (90.69%), and it was regular in 85.86% of girls. Duration of bleeding was two to six days for the majority of the girls (87.93%). Around 73.79% of girls were using sanitary pads, while 26.21% of girls were using clothes. The most important restrictions imposed on the girls during menstruation were not being allowed to attend religious functions (97.93%), followed by not being allowed to attend classes (65.86%). The use of sanitary pads was significantly more in late adolescent girls than in early adolescent girls (ꭓ2=14.97, p=0.0001), girls who have literate mothers than girls with illiterate mothers (ꭓ2=5.17, p=0.02), and girls belonging to higher socioeconomic classes (class I, II, III) than lower ones (class IV, V) (ꭓ2=44.23, p<0.0001). Conclusion The tribal adolescent girls still don't exercise proper hygiene throughout their periods. During menstruation, the majority of girls are still subjected to various restrictions.
Different realizations of kappa-momentum space and relative-locality effect

We consider different realizations for the momentum sector of kappa-Poincare Hopf algebra, which is associated with a curved momentum space. We show that the notion of the particle mass as introduced recently by Amelino-Camelia et al. in the context of relative-locality is realization independent for a wide class of realizations, up to linear order in deformation parameter l. On the other hand, the time delay formula clearly shows a dependence on the choice of realization.
Model for an optically thick torus in local thermodynamic equilibrium around a black hole

We propose a simple model for an optically thick radiative torus in local thermodynamic equilibrium around a Kerr black hole. The hydrodynamics structure, which is not affected by the radiation field, is the same as for the so--called polish doughnuts. Under the assumption of isentropic fluid and polytropic equation of state, a simple stationary and axisymmetric solution to the relativistic radiation hydrodynamics equations is possible, for which the temperature of the torus scales like the specific enthalpy. The astrophysical relevance of the model is briefly discussed.
Transient Electrical Characteristics of No-Insulation REBCO Coil Impregnated With GaInSn Liquid Metal

Due to higher critical current density and better self-protection, no-insulation (NI) high-temperature superconducting (HTS) coils wound by REBCO coated conductors have been widely studied and used in various superconducting magnets. When HTS coils are applied in rotating machines and high filed magnets, epoxy resin impregnation is indispensable to improve their mechanical stability. However, the use of epoxy resin may cause delamination problems and increase the turn-to-turn characteristic resistance when the epoxy penetrates through the winding turns. Although the solder impregnation method has been demonstrated to enhance the mechanical robust of NI coils, the solder needs to be heated and melted into a liquid before it can be used, which makes the impregnation process extremely inconvenient. The gallium−indium−tin (GaInSn) alloy is liquid at room temperature with a melting temperature of 10.5 °C. Therefore, GaInSn liquid metal alloy can be applied as impregnation material, which makes the impregnation process more convenient. In this article, NI HTS coils with and without GaInSn impregnation are fabricated and tested for comparison. The transient electrical characteristics including charging and sudden-discharging tests are conducted at 77 K. The critical current experiment shows that the conductor of the impregnated coil can be reused. These results can provide useful data for the potential application of GaInSn impregnated NI HTS coils.
PROTOPLANETARY DISK STRUCTURES IN OPHIUCHUS. II. EXTENSION TO FAINTER SOURCES

We present new results from a significant extension of our previous high angular resolution (0.″3 ≈ 40 AU) submillimeter array survey of the 340 GHz (880 μm) thermal continuum emission from dusty circumstellar disks in the ∼1 Myr old Ophiuchus star-forming region. An expanded sample is constructed to probe disk structures that emit significantly lower millimeter luminosities (hence dust masses), down to the median value for T Tauri stars. Using a Monte Carlo radiative transfer code, the millimeter visibilities and broadband spectral energy distribution for each disk are simultaneously reproduced with a two-dimensional parametric model for a viscous accretion disk that has a surface density profile Σ ∝ (R/Rc)−γexp [ − (R/Rc)2−γ]. We find wide ranges of characteristic radii (Rc = 14–198 AU) and disk masses (Md = 0.004–0.143 M☉), but a narrow distribution of surface density gradients (γ = 0.4–1.1) that is consistent with a uniform value 〈γ〉 = 0.9 ± 0.2 and independent of mass (or millimeter luminosity). In this sample, we find a correlation between the disk luminosity/mass and characteristic radius, such that fainter disks are both smaller and less massive. We suggest that this relationship is an imprint of the initial conditions inherited by the disks at their formation epoch, compare their angular momenta with those of molecular cloud cores, and speculate on how future observations can help constrain the distribution of viscous evolution timescales. No other correlations between disk and star properties are found. The inferred disk structures are briefly compared with theoretical models for giant planet formation, although resolution limitations do not permit us to directly comment on material inside R ≈ 20 AU. However, there is some compelling evidence for the evolution of dust in the planet formation region: 4/17 disks in the sample show resolved regions of significantly reduced millimeter optical depths within ∼20–40 AU of their central stars.
Assessment of Waste Marble Powder on the Mechanical Properties of High-Strength Concrete and Evaluation of Its Shear Strength

Currently, the costs of building materials, especially cement, are increasing. Waste marble powder (WMP) could be used as a cement replacement material to produce environmentally friendly concrete to help preserve resources and reduce environmental pollution. The study’s goals are (1) to evaluate the effects of using marble powder in place of cement in high-strength concrete (HSC) on the material’s mechanical properties and durability characteristics. (2) The study is expanded to assess the effect of using partial WMP on the shear behavior of HSC beams under static loads. Eight half-scale simply supported reinforced beams with and without WMP have been tested. Each beam’s cross-section was 120 × 200 mm, and each beam had a total length of 1000 mm. The ratios of the used WMP were 0%, 2.5%, 5%, 7.5% by weight, and two different stirrup ratios, 0% and 0.47%, were used. When applied to HSC beams with and without WMP, the shear strength provisions of two of the most used codes, such as the locally used Egyptian Code (ECP 207) and the internationally used American Concrete Institute’s (ACI-2019), were examined. Using the ABAQUS software, the experimental results were compared to the findings of the nonlinear finite element analysis. The results established that partial replacement of cement by WMP led to increases in the concrete’s compressive and tensile strengths of about 15% and 16%, respectively. When tested specimens were exposed to acid attack, there were slight losses in weight and compressive strength (1.25% to 2.47%) for both with and without the addition of WMP. Both the concrete with and without WMP showed the same level of water absorption. Additionally, WMP led to an enhancement in the shear capacities for all beams. Increasing the WMP ratio from 0% to 2.5%, 5%, and 7.5% increased the shear capacity by about 13%, 20%, and 28%, respectively, for beams without stirrups, while for beams with stirrups, the shear capacity improved by 12%, 19%, and 25%, respectively. The enhancement in the beams’ shear capacities could be attributed to the advanced concrete matrix produced by WMP’s extremely small particle size.
KELVIN–HELMHOLTZ INSTABILITY IN CORONAL MAGNETIC FLUX TUBES DUE TO AZIMUTHAL SHEAR FLOWS

Transverse oscillations of coronal loops are often observed and have been theoretically interpreted as kink magnetohydrodynamic (MHD) modes. Numerical simulations by Terradas et al. suggest that shear flows generated at the loop boundary during kink oscillations could give rise to a Kelvin–Helmholtz instability (KHI). Here, we investigate the linear stage of the KHI in a cylindrical magnetic flux tube in the presence of azimuthal shear motions. We consider the basic, linearized MHD equations in the β = 0 approximation and apply them to a straight and homogeneous cylindrical flux tube model embedded in a coronal environment. Azimuthal shear flows with a sharp jump of the velocity at the cylinder boundary are included in the model. We obtain an analytical expression for the dispersion relation of the unstable MHD modes supported by the configuration, and compute analytical approximations of the critical velocity shear and the KHI growth rate in the thin tube limit. A parametric study of the KHI growth rates is performed by numerically solving the full dispersion relation. We find that fluting-like modes can develop a KHI in timescales comparable to the period of kink oscillations of the flux tube. The KHI growth rates increase with the value of the azimuthal wavenumber and decrease with the longitudinal wavenumber. However, the presence of a small azimuthal component of the magnetic field can suppress the KHI. Azimuthal motions related to kink oscillations of untwisted coronal loops may trigger a KHI, but this phenomenon has not been observed to date. We propose that the azimuthal component of the magnetic field is responsible for suppressing the KHI in a stable coronal loop. The required twist is small enough to prevent the development of the pinch instability.
DENSE CORE PROPERTIES IN THE INFRARED DARK CLOUD G14.225-0.506 REVEALED BY ALMA

We have performed a dense core survey toward the Infrared Dark Cloud G14.225-0.506 at 3 mm continuum emission with the Atacama Large Millimeter/Submillimeter Array (ALMA). This survey covers the two hub-filament systems with an angular resolution of (∼0.03 pc). We identified 48 dense cores. 20 out of the 48 cores are protostellar due to their association with young stellar objects (YSOs) and/or X-ray point-sources, while the other 28 cores are likely prestellar and unrelated with known IR or X-ray emission. Using APEX 870 μm continuum emission, we also identified the 18 clumps hosting these cores. Through virial analysis using the ALMA N2H+ and VLA/Effelsberg NH3 molecular line data, we found a decreasing trend in the virial parameter with decreasing scales from filaments to clumps, and then to cores. The virial parameters of 0.1–1.3 in cores indicate that cores are likely undergoing dynamical collapse. The cumulative core mass function for the prestellar core candidates has a power law index of , with masses ranging from 1.5 to 22 . We find no massive prestellar or protostellar cores. Previous studies suggest that massive O-type stars have not been produced yet in this region. Therefore, high-mass stars should be formed in the prestellar cores by accreting a significant amount of gas from the surrounding medium. Another possibility is that low-mass YSOs become massive by accreting from their parent cores that are fed by filaments. These two possibilities might be consistent with the scenario of global hierarchical collapse.
Antimicrobial Activity of Lactobacillus Species Against Carbapenem-Resistant Enterobacteriaceae

Objective This study aims to identify suitable lactobacilli that have anti-carbapenem-resistant Enterobacteriaceae (CRE) activity with in vitro tolerance to pepsin and bile salts. Methods Fifty-seven Lactobacillus spp. strains encompassing nine species were collected for investigation. Their viabilities in the presence of pepsin and bile salts were tested using tolerance tests. Their anti-CRE effects were assessed by agar well diffusion and broth microdilution assay, as well as time-kill test. Results Of the 57 Lactobacillus isolates collected, 31 had a less than 2-log reduction in their viability in both pepsin and bile salt tolerance tests. Of these 31 isolates, 5 (LUC0180, LUC0219, LYC0289, LYC0413, and LYC1031) displayed the greatest anti-CRE activity with a CRE zone of inhibition greater than 15 mm in agar well diffusion assays. The minimal inhibitory percentages of supernatants from these five strains against CREs ranged from 10 to 30%. With the exception of LUC0180, which had a minimal bactericidal percentage ≥ 40%, the bactericidal percentage of all the strains ranged from 20 to 40%. The inhibitory effect of the cell-free culture supernatants from these Lactobacillus strains did not change after heating but was abolished as the pH changed to 7.0. After a 24-h incubation, five of the Lactobacillus strains at a concentration of 108 CFU/ml totally inhibited the growth of carbapenem-resistant Escherichia coli (CRE316) and Klebsiella pneumoniae (CRE632). After a 48-h incubation, the growth of CRE316 was completely inhibited under each concentration of lactobacilli based on time-kill test. Furthermore, when the concentration of lactobacilli was at 108 CFU/ml, the decline in pH was faster than at other concentrations. Conclusion Some Lactobacillus strains exhibit anti-CRE activity, which suggests potential applications for controlling or preventing CRE colonization or infection.
Physiotherapists’ Attitudes, and Barriers of Delivering Cardiopulmonary Rehabilitation for Patients with Heart Failure in Saudi Arabia: A Cross-Sectional Study

Background Cardiopulmonary rehabilitation (CR) is an effective management approach for heart failure (HF) patients and is delivered by multidisciplinary teams including physiotherapists (PTs). PT attitudes about delivering CR and barriers that might affect referral have not been explored. Thus, this study is aimed to explore PT attitudes about delivering CR programs to patients with HF and identify factors and barriers that might affect referral decisions. Methods A cross-sectional online survey was disseminated to all PTs in Saudi Arabia between 19 February and 27 June, 2022. The characteristics of the respondents were described using descriptive statistics. Percentages and frequencies were used to report categorical variables. Results Overall, 553 PTs, 289 (52.30%) male and 264 (47.70%) females, completed the online survey. Of these, 360 (65.1%) strongly agreed that CR would improve patients’ physical fitness and 334 (60.4%) strongly agreed that CR would reduce breathlessness in patients with HF. The majority of PTs (321, 58%) strongly agreed that CR would improve HF patients’ palpitation and fatigue. Out of 553 PTs, 349 (63.1%) strongly agreed that CR would improve patients’ ability to perform daily activities. A hospital-supervised program was the preferred mode of delivering CR programs by 499 (90.20%) of the respondents. Apart from the exercise component, stress management was perceived by 455 (82.30%) as an essential component of CR programs. The most common patient-related factor that strongly influenced referral decisions was “fatigue related to disease” (42%). A lack of CR centers was reported by 59.90% as the most common referring barrier. Conclusion PTs perceived CR as a successful strategy for patients with HF. Although a supervised hospital-based program with stress management as an essential component aside from the exercise component was perceived as the preferred mode of delivery, CR was lacking, which caused a significant barrier to CR referral from the PTs’ perspective.
Thermal Energy Storage (TES) Prototype Based on Geopolymer Concrete for High-Temperature Applications

Thermal energy storage (TES) systems are dependent on materials capable of operating at elevated temperatures for their performance and for prevailing as an integral part of industries. High-temperature TES assists in increasing the dispatchability of present power plants as well as increasing the efficiency in heat industry applications. Ordinary Portland cement (OPC)-based concretes are widely used as a sensible TES material in different applications. However, their performance is limited to operation temperatures below 400 °C due to the thermal degradation processes in its structure. In the present work, the performance and heat storage capacity of geopolymer-based concrete (GEO) have been studied experimentally and a comparison was carried out with OPC-based materials. Two thermal scenarios were examined, and results indicate that GEO withstand high running temperatures, higher than 500 °C, revealing higher thermal storage capacity than OPC-based materials. The high thermal energy storage, along with the high thermal diffusion coefficient at high temperatures, makes GEO a potential material that has good competitive properties compared with OPC-based TES. Experiments show the ability of geopolymer-based concrete for thermal energy storage applications, especially in industries that require feasible material for operation at high temperatures.
Rational maps without Herman rings

Let $f$ be a rational map with degree at least two. We prove that $f$ has at least $2$ disjoint and infinite critical orbits in the Julia set if it has a Herman ring. This result is sharp in the following sense: there exists a cubic rational map having exactly two critical grand orbits but also having a Herman ring. In particular, $f$ has no Herman rings if it has at most one infinite critical orbit in the Julia set. These criterions derive some known results about the rational maps without Herman rings.
Non-linear energy transfers in accretion discs MRI turbulence. I. Net vertical field case

The magnetorotational instability (MRI) is believed to be responsible for most of the angular momentum transport in accretion discs. However, molecular dissipation processes may drastically change the efficiency of MRI turbulence in realistic astrophysical situations. The physical origin of this dependency is still poorly understood as linear and quasi linear theories fail to explain it. In this paper, we look for the link between molecular dissipation processes and MRI transport of angular momentum in unstratified shearing box simulations, including a mean vertical field. We show that magnetic helicity is unimportant in the model we consider. We perform a spectral analysis on the simulations tracking energy exchanges in spectral space when turbulence is fully developed. We find that the energy exchanges are essentially direct (from large to small scale) whereas some non-linear interactions appear to be non-local in spectral space. We speculate that these non-local interactions are responsible for the correlation between turbulent transport and molecular dissipation. We argue that this correlation should then disappear when a significant scale separation is achieved, and we discuss several methods by which one can test this hypothesis.