Miracle-dz/UniFAR-FTUs huggingface dataset:
Strictly positive solutions for one-dimensional nonlinear elliptic problems

We study existence and nonexistence of strictly positive solutions for the elliptic problems of the form $Lu=m\left( x\right) u^{p}$ in a bounded open interval, with zero boundary conditions, where $L$ is a strongly uniformly elliptic differential operator, $p\in\left( 0,1\right) $, and $m$ is a function that changes sign. We also characterize the set of values $p$ for which the problem admits a solution, and in addition an existence result for other nonlinearities is presented.
On pairs of finitely generated subgroups in free groups

We prove that for arbitrary two finitely generated subgroups A and B having infinite index in a free group F, there is a subgroup H of finite index in B such that the subgroup generated by A and H has infinite index in F. The main corollary of this theorem says that a noncyclic free group of finite rank admits a faithful highly transitive action on an infinite set, whereas the restriction of this action to any finitely generated subgroup of infinite index in F has no infinite orbits.
Semiautomorphic inverse property loops

ABSTRACT We define a variety of loops called semiautomorphic, inverse property loops that generalize Moufang and Steiner loops. We first show an equivalence between a previously studied variety of loops. Next we extend several known results for Moufang and Steiner loops. That is, the commutant is a subloop and if a is in the commutant, then a2 is a Moufang element, a3 is a c-element and a6 is in the center. Finally, we give two constructions for semiautomorphic inverse property loops based on Chein’s and de Barros and Juriaans’ doubling constructions.
On Average Risk-sensitive Markov Control Processes

We introduce the Lyapunov approach to optimal control problems of average risk-sensitive Markov control processes with general risk maps. Motivated by applications in particular to behavioral economics, we consider possibly non-convex risk maps, modeling behavior with mixed risk preference. We introduce classical objective functions to the risk-sensitive setting and we are in particular interested in optimizing the average risk in the infinite-time horizon for Markov Control Processes on general, possibly non-compact, state spaces allowing also unbounded cost. Existence and uniqueness of an optimal control is obtained with a fixed point theorem applied to the nonlinear map modeling the risk-sensitive expected total cost. The necessary contraction is obtained in a suitable chosen seminorm under a new set of conditions: 1) Lyapunov-type conditions on both risk maps and cost functions that control the growth of iterations, and 2) Doeblin-type conditions, known for Markov chains, generalized to nonlinear mappings. In the particular case of the entropic risk map, the above conditions can be replaced by the existence of a Lyapunov function, a local Doeblin-type condition for the underlying Markov chain, and a growth condition on the cost functions.
Auroral Field‐Aligned Current Signatures in Jupiter's Magnetosphere: Juno Magnetic Field Observations and Physical Modeling

We analyze magnetic data obtained during northern high‐altitude traversals of Jovian middle magnetosphere (MM) field lines during the first 10 inbound data‐taking passes of the Juno spacecraft for azimuthal field perturbations associated with magnetosphere‐ionosphere coupling currents. Full traversals across the MM region occur on all 10 passes at radial distances ∼7 to 16 RJ (T1 traversals), followed in four cases by reversed traversals (T2) at ∼4 to 7 RJ. Signatures of upward field‐aligned currents were observed in all cases, closely collocated with the statistical main auroral oval when mapped along field lines to the ionosphere. Two T1 sheets carry currents ∼10 MA per radian of azimuth in ionospheric colatitudinal layers ∼1.2°, closely comparable with the ∼8.5 MA rad−1 theoretical model value of Cowley et al. (2008, https://doi.org/10.5194/angeo-26-4051-2008). The other T1 sheets typically carry half this current ∼5.1 MA rad−1 in layers half the width ∼0.56°, thus with comparable current densities ∼425 nA m−2. The T2 currents are smaller ∼3.4 MA rad−1 with current densities ∼120 nA m−2, a difference that may relate to locations on opposite sides of the main oval as reflected in near‐contemporaneous ultraviolet observations, though ionospheric field strengths are not greatly different. Comparison with northern near‐periapsis currents observed inside ∼2 RJ on the same passes by Kotsiaros et al. (2019, https://doi.org/10.1038/s41550-019-0819-7) yields a cross‐correlation coefficient ∼0.7 with our T1 currents, though Kotsiaros et al.’s mean current value of ∼3.8 MA rad−1 is somewhat less than our overall mean T1 value ∼6.2 MA rad−1. The differences may have spatial, temporal, or methodological origins.
Molecular and Pharmacological Characterization of β-Adrenergic-like Octopamine Receptors in the Endoparasitoid Cotesia chilonis (Hymenoptera: Braconidae)

Octopamine (OA) is structurally and functionally similar to adrenaline/noradrenaline in vertebrates, and OA modulates diverse physiological and behavioral processes in invertebrates. OA exerts its actions by binding to specific octopamine receptors (OARs). Functional and pharmacological characterization of OARs have been investigated in several insects. However, the literature on OARs is scarce for parasitoids. Here we cloned three β-adrenergic-like OARs (CcOctβRs) from Cotesia chilonis. CcOctβRs share high similarity with their own orthologous receptors. The transcript levels of CcOctβRs were varied in different tissues. When heterologously expressed in CHO-K1 cells, CcOctβRs induced cAMP production, and were dose-dependently activated by OA, TA and putative octopaminergic agonists. Their activities were inhibited by potential antagonists and were most efficiently blocked by epinastine. Our study offers important information about the molecular and pharmacological properties of β-adrenergic-like OARs from C. chilonis that will provide the basis to reveal the contribution of individual receptors to the physiological processes and behaviors in parasitoids.
Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory

We extend the theory of Thom spectra and the associated obstruction theory for orientations in order to support the construction of the E∞ string orientation of tmf , the spectrum of topological modular forms. Specifically, we show that, for an E∞ ring spectrum A , the classical construction of gl1A , the spectrum of units, is the right adjoint of the functor Σ+∞Ω∞:ho(connectivespectra)⟶ho(E∞ringspectra). To a map of spectra f:b⟶bgl1A, we associate an E∞ A ‐algebra Thom spectrum Mf , which admits an E∞ A ‐algebra map to R if and only if the composition b⟶bgl1A⟶bgl1R is null; the classical case developed by May, Quinn, Ray, and Tornehave arises when A is the sphere spectrum. We develop the analogous theory for A∞ ring spectra: if A is an A∞ ring spectrum, then to a map of spaces f:B⟶BGL1A, we associate an A ‐module Thom spectrum Mf, which admits an R ‐orientation if and only if B⟶BGL1A⟶BGL1R is null. Our work is based on a new model of the Thom spectrum as a derived smash product.
The Association of Sex with Unplanned Cardiac Readmissions following Percutaneous Coronary Intervention in Australia: Results from a Multicentre Outcomes Registry (GenesisCare Cardiovascular Outcomes Registry)

Background and aim: Unplanned cardiac readmissions in patients with percutaneous intervention (PCI) is very common and is seen as a quality indicator of in-hospital care. Most studies have reported on the 30-day cardiac readmission rates, with very limited information being available on 1-year readmission rates and their association with mortality. The aim of this study was to investigate the impact of biological sex at 1-year post-PCI on unplanned cardiac readmissions. Methods and results: Patients enrolled into the GenesisCare Cardiovascular Outcomes Registry (GCOR-PCI) from December 2008 to December 2020 were included in the study. A total of 13,996 patients completed 12 months of follow-up and were assessed for unplanned cardiac readmissions. All patients with unplanned cardiac readmissions in the first year of post-PCI were followed in year 2 (post-PCI) for survival status. The rate of unplanned cardiac readmissions was 10.1%. Women had a 29% higher risk of unplanned cardiac readmission (HR 1.29, 95% CI 1.11 to 1.48; p = 0.001), and female sex was identified as an independent predictor of unplanned cardiac readmissions. Any unplanned cardiac readmission in the first year was associated with a 2.5-fold higher risk of mortality (HR 2.50, 95% CI 1.67 to 3.75; p < 0.001), which was similar for men and women. Conclusion: Unplanned cardiac readmissions in the first year post-PCI was strongly associated with increased all-cause mortality. Whilst the incidence of all-cause mortality was similar between women and men, a higher incidence of unplanned cardiac readmissions was observed for women, suggesting distinct predictors of unplanned cardiac readmissions exist between women and men.
An intrinsic characterization of C*-simplicity

A group is said to be C*-simple if its reduced C*-algebra is simple. We establish an intrinsic (group-theoretic) characterization of groups with this property. Specifically, we prove that a discrete group is C*-simple if and only if it has no non-trivial amenable uniformly recurrent subgroups. We further prove that a group is C*-simple if and only if it satisfies an averaging property considered by Powers.
Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces

There are two main aims of the paper. The first is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second is to extend the criterion for the precompactness of sets in the Lebesgue spaces Lp (ℝ n ), 1 ⩽ p < ∞, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces , into Lorentz-type spaces.
Duality for distributive space

The main source of inspiration for the present paper is the w ork of R. Rosebrugh and R.J. Wood on constructive complete distributive lattices where the aut hors employ elegantly the concepts of adjunction and module in their study of ordered sets. Both notions (suitably ad apted) are available in topology too, which permits us to investigate topological, metric and other kinds of space s in a similar spirit. Therefore, relative to a choice Φ of modules, we consider spaces which admit all colimits with we ight inΦ, as well as (suitably defined) Φ-distributive andΦ-algebraic spaces. We show that the category of Φ-distributive spaces and Φ-colimit preserving maps is dually equivalent to the idempotent splitting completion of a category of spaces and convergence relations between them. We explain the connection of these results to the tradi tional duality of spaces with frames, and conclude further duality theorems. Finally, we study properties and str uctures of the resulting categories, in particular monoida l (closed) structures.
The Role of Kemeny's Constant in Properties of Markov Chains

In a finite irreducible Markov chain with stationary probabilities {π i } and mean first passage times m ij (mean recurrence time when i = j) it was first shown, by Kemeny and Snell (1960), that is a constant, K, (Kemeny's constant) not depending on i. A variety of techniques for finding expressions and bounds for K are given. The main interpretation focuses on its role as the expected time to mixing in a Markov chain. Various applications are considered including perturbation results, mixing on directed graphs and its relation to the Kirchhoff index of regular graphs.
Ultrasound Diagnosis of a Retained Migrated Foreign Body Following Penetrating Injury to The Upper Thigh in a Child: A Case Report Demonstrating an Underused Indication for Diagnostic Ultrasound

Abstract We present a case of delayed diagnosis of retained glass foreign body in the inguinal region of a child using ultrasonography following penetrating trauma to the upper thigh. The foreign body had traversed significantly by the time of diagnosis, from the medial upper thigh to the inguinal region at the level of the inguinal ligament. Ultrasound can be an effective initial imaging modality for the diagnosis of foreign bodies in children, allowing the potential to reduce ionizing radiation exposure.
Integrable boundary conditions for multi-species ASEP

The first result of the present paper is to provide classes of explicit solutions for integrable boundary matrices for the multi-species ASEP with an arbitrary number of species. All the solutions we have obtained can be seen as representations of a new algebra that contains the boundary Hecke algebra. The boundary Hecke algebra is not sufficient to build these solutions. This is the second result of our paper.
Non compact conformal field theory and the a2(2)?> (Izergin–Korepin) model in regime III

The so-called regime III of the a2(2)? > Izergin–Korepin 19-vertex model has defied understanding for many years. We show in this paper that its continuum limit involves in fact a non compact conformal field theory (the so-called Witten Euclidian black hole CFT), which leads to a continuous spectrum of critical exponents, as well as very strong corrections to scaling. Detailed numerical evidence based on the Bethe ansatz analysis is presented, involving in particular the observation of discrete states in the spectrum, in full agreement with the string theory prediction for the black hole CFT. Our results have important consequences for the physics of the O(n) model, which will be discussed elsewhere.
A Flat Faint End of the Fornax Cluster Galaxy Luminosity Function

Abstract We analyse the photometric properties of the early-type Fornax cluster dwarf galaxy population (MV > −17 mag), based on a wide field imaging study of the central cluster area in V and I band-passes with IMACS/Magellan at Las Campanas Observatory. We create a fiducial sample of ~ 100 Fornax cluster dwarf ellipticals (dEs) with −16.6 < MV < −8.8 mag in the following three steps: (1) To verify cluster membership, we measured I-band surface brightness fluctuations (SBF) distances to candidate dEs known from previous surveys; (2) We re-assessed morphological classifications for those candidate dEs that are too faint for SBF detection; and (3) We searched for new candidate dEs in the size-luminosity regime close to the resolution limit of previous surveys. The resulting fiducial dE sample follows a well-defined surface brightness – magnitude relation, showing that Fornax dEs are about 40% larger than Local Group dEs. The sample also defines a colour-magnitude relation similar to that of Local Group dEs. The early-type dwarf galaxy luminosity function in Fornax has a very flat faint end slope α ≃ −1.1 ± 0.1. We compare the number of dwarfs per unit mass with those in other environments and find that the Fornax cluster fits well into a general trend of a lack of high-mass dwarfs in more massive environments.
Assessment of raptor species relative abundance in Hadejia Nguru Wetlands, Nigeria

Birds of prey are some of the most threatened vertebrate taxa, and in the last three decades many species have experienced severe population declines or faced extinction. The global loss of raptors per se is worrying, not just because of their charisma and flagship role, but also because reduced abundance of raptors can have cascading effects on ecosystem functioning. Raptor decline may also lead to loss of ecosystem services, sometimes acutely impacting human well-being. Therefore, population distribution, diversity and abundance of birds of prey demand investigation for potential conservation interventions. The study aimed to determine the abundance of birds of prey in Hadejia-Nguru wetlands, carried out in March to August, 2021, with a view to providing information in a bid to establish a baseline for conservation for this group of birds. Transect line method was used for the bird survey. This involved moving slowly along the transect line and recording all birds seen in and around the transect line. The survey was carried out for a period of six (6) months and each site was surveyed twice every month during the study period. Bird observation was carried out twice daily; morning between 6:00 to 10:00 a.m. and evening between 3pm to 6p.m. A pair of binoculars with magnification 7X50 was used for identification of birds visually alongside with field guide “Birds of West Africa” for identification of birds. Relative abundance and t-test were used for data analysis. The total number of birds was calculated as the number of birds seen. Transect line survey method detected a total of 1,562 individual birds of prey that belong to twenty four (24) species of 2 families. Accipitridae with 20 species and Falconidae with 4 species. The most abundant species, Yellow billed kite, black shouldered kite and gabar goshawk comprised 68.5% of all individuals seen in all wetlands in all seasons. Out of the 24 species recorded 16 are resident, 5 Palearctic migrant and 3 intra-African migrant. Four species of global conservation concern were also recorded; the Vulnerable Tawny eagle (Aquila rapax) the near threatened Red-necked falcon (Falco chicquera) and Pallid harrier (Circus macrourus) and the endangered Martial eagle (Polemaetus bellicosus ). Public awareness should be raised to inform the local populace about the importance of these species to the environment vis-à-vis protecting the man-made structures used by the bird species.
Random perturbations of heteroclinic attractors

Estimates are derived for the mean recurrence time of orbits in the neighborhood of an attracting homoclinic orbit or heteroclinic cycle in an ordinary differential equation, subject to small additive random noise. The theory presented is illustrated with numerical simulations of several systems, including ones invariant under symmetry groups, for which such heteroclinic attractors are structurally stable. The physical implications of the work presented are briefly discussed.
The Influence of Venture Capital on Growth through Innovation and the Use of Internet Technology in Micro and Small Industries (MSIs) in Indonesia

One challenge that Micro and Small Industries (MSIs) face is financing. Venture capital is one of the financing options to overcome capital problems by providing financial and non-financial support. This study aims to analyze the influence of venture capital on the growth of Micro and Small Industries (MSIs) in Indonesia through innovation and internet technology as the intervening variables. The research data were collected from a survey (Statistics Indonesia) in 2019 with 83,161 Micro and Small Industries (MSIs) as the samples. This research used the STATA logistic regression method and the Sobel test. The results showed that venture capital had a direct positive but insignificant influence on growth. Meanwhile, innovation could mediate the effect of venture capital on growth, yet the use of internet technology could not mediate the impact of venture capital on growth. This study proves that venture capital increases innovation activities and accelerates growth.
Robot navigation in crowds via deep reinforcement learning with modeling of obstacle uni-action

Mobile robots operating in public environments require the ability to navigate among humans and obstacles in a socially compliant and safe manner. Previous work has shown the power of deep reinforcement learning (DRL) techniques by employing them to train efficient policies for robot navigation. However, most DRL-based robot navigation methods only consider dynamic pedestrians and do not take static obstacles into account. The ability to approach pedestrians and obstacles differently will improve a robot's navigation efficiency. In this work, we propose a novel network, the obstacle-robot uni-action (ORU) network, to encode the one-way direct effects of obstacles on the robot. Obstacles' indirect effects on the robot, represented by the obstacle-human uni-action (OHU), together with human–human interaction (HHI), are concatenated to a human–robot interaction (HRI) network to obtain the features of a crowd's effects on the robot. We also implement a variable reaching goal reward and an approaching goal reward in our model, which can enhance the method's performance in terms of navigation time. Results of test experiments in both simulation and real datasets demonstrate that the proposed method outperforms state-of-the-art methods. GRAPHICAL ABSTRACT
Beyond Traditional Use of Alchemilla vulgaris: Genoprotective and Antitumor Activity In Vitro

Alchemilla vulgaris L. (lady’s mantle) was used for centuries in Europe and Balkan countries for treatments of numerous conditions and diseases of the reproductive system, yet some of the biological activities of lady’s mantle have been poorly studied and neglected. The present study aimed to estimate the potential of A. vulgaris ethanolic extract from Southeast Serbia to prevent and suppress tumor development in vitro, validated by antioxidant, genoprotective, and cytotoxic properties. A total of 45 compounds were detected by UHPLC–HRMS analysis in A. vulgaris ethanolic extract. Measurement of antioxidant activity revealed the significant potential of the tested extract to scavenge free radicals. In addition, the analysis of micronuclei showed an in vitro protective effect on chromosome aberrations in peripheral human lymphocytes. A. vulgaris extract strongly suppressed the growth of human cell lines derived from different types of tumors (MCF-7, A375, A549, and HCT116). The observed antitumor effect is realized through the blockade of cell division, caspase-dependent apoptosis, and autophagic cell death. Our study has shown that Alchemilla vulgaris L. is a valuable source of bioactive compounds able to protect the subcellular structure from damage, thus preventing tumorigenesis as well as suppressing tumor cell growth.
Comparison of the real and the complex Green functions, and sharp estimates of the Kobayashi distance

We extend the upper estimates obtained by M. Carlehed and B. -Y. Chen about the ratio of the classical and pluricomplex Green functions to the case of $\mathcal C^2$-smooth locally $\mathbb C$-convexifiable domains of finite type. We also give some lower estimates. In order to obtain those results, and because it is of independent interest, we refine and unify some classical estimates about the Kobayashi distance and the Lempert function in such domains.
Thermodynamic limit of random partitions and dispersionless Toda hierarchy

We study the thermodynamic limit of random partition models for the instanton sum of 4D and 5D supersymmetric U(1) gauge theories deformed by some physical observables. The physical observables correspond to external potentials in the statistical model. The partition function is reformulated in terms of the density function of Maya diagrams. The thermodynamic limit is governed by a limit shape of Young diagrams associated with dominant terms in the partition function. The limit shape is characterized by a variational problem, which is further converted to a scalar-valued Riemann–Hilbert problem. This Riemann–Hilbert problem is solved with the aid of a complex curve, which may be thought of as the Seiberg–Witten curve of the deformed U(1) gauge theory. This solution of the Riemann–Hilbert problem is identified with a special solution of the dispersionless Toda hierarchy that satisfies a pair of generalized string equations. The generalized string equations for the 5D gauge theory are shown to be related to hidden symmetries of the statistical model. The prepotential and the Seiberg–Witten differential are also considered.