Miracle-dz/UniFAR-FTUs huggingface dataset:
On weakly $sigma$-permutable subgroups of finite groups

Let G be a finite group and {\sigma} = {{\sigma}_i, i \in I} be a partition of the set of all primes \mathbb{P}. A set \mathcal{H} of subgroups of G with 1 \in \mathcal{H} is said to be a complete Hall {\sigma}-set of G if every non-identity member of \mathcal{H} is a Hall {\sigma}_i-subgroup of G. A subgroup H of G is said to be {\sigma}-permutable if G possesses a complete Hall {\sigma}-set \mathcal{H} such that HA^x = A^xH for all A \in \mathcal{H} and all x \in G. We say that a subgroup H of G is weakly {\sigma}-permutable in G if there exists a {\sigma}-subnormal subgroup T of G such that G = HT and H \cap T \leq H_{\sigma}G. where H_{\sigma}G is the subgroup of H generated by all those subgroups of H which are {\sigma}-permutable in G. By using this new notion, we establish some new criterias for a group G to be a {\sigma}-soluble and supersoluble, and also we give the conditions under which a normal subgroup of G is hypercyclically embedded.
Weak Brill-Noether for rational surfaces

A moduli space of sheaves satisfies weak Brill-Noether if the general sheaf in the moduli space has no cohomology. Goettsche and Hirschowitz prove that on the projective plane every moduli space of Gieseker semistable sheaves of rank at least two and Euler characteristic zero satisfies weak Brill-Noether. In this paper, we give sufficient conditions for weak Brill-Noether to hold on rational surfaces. We completely characterize Chern characters on Hirzebruch surfaces for which weak Brill-Noether holds. We also prove that on a del Pezzo surface of degree at least 4 weak Brill-Noether holds if the first Chern class is nef.
Note on limit distribution of normalized return times and escape rate

In this note we discuss limit distribution of normalized return times for shrinking targets and draw a necessary and sufficient condition using sweep-out sequence in order for the limit distribution to be exponential with parameter $1$. The normalizing coefficients are the same as sizes of the targets. Moreover we study escape rate, namely the exponential decay rate of sweep-out sequence and prove that in $\psi$-mixing systems for a certain class of sets the escape rate is in limit proportional to the size of the set.
Gordian adjacency for torus knots

A knot K is called Gordian adjacent to a knot L if there exists an unknotting sequence for L containing K. We provide a sufficient condition for Gordian adjacency of torus knots via the study of knots in the thickened torus. We also completely describe Gordian adjacency for torus knots of index 2 and 3 using Levine-Tristram signatures as obstructions to Gordian adjacency. Finally, Gordian adjacency for torus knots is compared to the notion of adjacency for plane curve singularities.
Trial of an Intervention to Improve Acute Heart Failure Outcomes.

BACKGROUND Patients with acute heart failure are frequently or systematically hospitalized, often because the risk of adverse events is uncertain and the options for rapid follow-up are inadequate. Whether the use of a strategy to support clinicians in making decisions about discharging or admitting patients, coupled with rapid follow-up in an outpatient clinic, would affect outcomes remains uncertain. METHODS In a stepped-wedge, cluster-randomized trial conducted in Ontario, Canada, we randomly assigned 10 hospitals to staggered start dates for one-way crossover from the control phase (usual care) to the intervention phase, which involved the use of a point-of-care algorithm to stratify patients with acute heart failure according to the risk of death. During the intervention phase, low-risk patients were discharged early (in ≤3 days) and received standardized outpatient care, and high-risk patients were admitted to the hospital. The coprimary outcomes were a composite of death from any cause or hospitalization for cardiovascular causes within 30 days after presentation and the composite outcome within 20 months. RESULTS A total of 5452 patients were enrolled in the trial (2972 during the control phase and 2480 during the intervention phase). Within 30 days, death from any cause or hospitalization for cardiovascular causes occurred in 301 patients (12.1%) who were enrolled during the intervention phase and in 430 patients (14.5%) who were enrolled during the control phase (adjusted hazard ratio, 0.88; 95% confidence interval [CI], 0.78 to 0.99; P = 0.04). Within 20 months, the cumulative incidence of primary-outcome events was 54.4% (95% CI, 48.6 to 59.9) among patients who were enrolled during the intervention phase and 56.2% (95% CI, 54.2 to 58.1) among patients who were enrolled during the control phase (adjusted hazard ratio, 0.95; 95% CI, 0.92 to 0.99). Fewer than six deaths or hospitalizations for any cause occurred in low- or intermediate-risk patients before the first outpatient visit within 30 days after discharge. CONCLUSIONS Among patients with acute heart failure who were seeking emergency care, the use of a hospital-based strategy to support clinical decision making and rapid follow-up led to a lower risk of the composite of death from any cause or hospitalization for cardiovascular causes within 30 days than usual care. (Funded by the Ontario SPOR Support Unit and others; COACH ClinicalTrials.gov number, NCT02674438.).
On the q-Analogue of Gamma Functions and Related Inequalities

adiga@hotmail.comAbstractIn this paper, we obtain a q-analogue of a double inequality involving theEuler gamma function which was ﬁrst proved geometrically by Alsina andTom´as [1] and then analytically by S´andor [6]. Keywords and Phrases: Euler gamma function, q-gamma function.2000 AMS Subject Classiﬁcation: 33B15.
$L^{\Phi(A(x,\cdot))}$ estimate for the gradient in $W^{1,A(x,\cdot)}$

Under appropriate assumptions on the $N(\Omega)$-fucntion, the $L^{\Phi(A(x,\cdot))}$ estimate for the gradient of the minimizers of a class of energy functional in Musielak-Orlicz-Sobolev space $W^{1,A(x,\cdot)}$ is presented by using Calder\'{o}n-Zygmund decomposition.
Quantization

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous probability distribution by a discrete distribution. It has broad application in signal processing and data compression. In this paper, first we define the uniform distributions on different curves such as a line segment, a circle, and the boundary of an equilateral triangle. Then, we give the exact formulas to determine the optimal sets of n-means and the nth quantization errors for different values of n with respect to the uniform distributions defined on the curves. In each case, we further calculate the quantization dimension and show that it is equal to the dimension of the object; and the quantization coefficient exists as a finite positive number. This supports the well-known result of Bucklew and Wise (1982), which says that for a Borel probability measure P with non-vanishing absolutely continuous part the quantization coefficient exists as a finite positive number.
The Representation Theory of the Increasing Monoid

We study the representation theory of the increasing monoid. Our results provide a fairly comprehensive picture of the representation category: for example, we describe the Grothendieck group (including the effective cone), classify injective objects, establish properties of injective and projective resolutions, construct a derived auto-duality, and so on. Our work is motivated by numerous connections of this theory to other areas, such as representation stability, commutative algebra, simplicial theory, and shuffle algebras.
Strichartz estimates for the Schrödinger flow on compact Lie groups

Every connected compact Lie group is the quotient by a finite central subgroup of a product of circles and compact simply connected simple Lie groups. Let each of the circles be equipped with a constant metric, and each of the simple groups be equipped a metric that is a constant multiple of the negative of the Cartan-Killing form, under the requirement that the periods of the Schrodinger flow on each component are rational multiples of each other. This metric on the covering group is pushed down to a metric on the original group, which is called a rational metric. This paper establishes scaling invariant Strichartz estimates for the Schrodinger flow on compact Lie groups equipped with rational metrics. The highlights of this paper include a Weyl differencing technique for rational lattices, the different decompositions of the Schrodinger kernel that accommodate different positions of the variable inside the maximal torus relative to the Weyl chamber walls, and the application of the BGG-Demazure operators to the estimate of the difference between characters.
Branching data for curves up to genus 48

An algorithm of Thomas Breuer produces complete lists of automorphism groups of curves for a fixed genus, and the code to execute this algorithm was written in the computer algebra package GAP and run by Breuer over a decade ago. For each curve $X$ of genus $g$ and a group $G$ acting on $X$, the branching data for the covering $X \to X/G$ is computed but was not record. We have added functionality to the code to output this data, and have translated the code to the computer algebra package Magma. This article provides an explanation of the code to add this branching data. Complete data from this modified program for curves up to genus 20, and data for genus up to 48 of groups $G$ so that $|G|>4(g-1)$ are available. We also include sample programs which provide a way to search the data for groups or actions with desired properties, these functions should be of use to researchers who want to find examples of group actions on lower genus curves with certain properties, or who need explicit examples of generating vectors for their research. The code also may be used to create generating vectors for higher genus curves, if the automorphism group and signature of the mapping $X \to X/G$ are already know.
Optimal density for values of generic polynomial maps

Abstract:We establish that the optimal bound for the size of the smallest integral solution of the Oppenheim Diophantine approximation problem $|Q(x)-\\xi|<\\epsilon$ for a generic ternary form $Q$ is $|x|\\ll\\epsilon^\{-1\}$. We also establish an optimal rate of density for the values of polynomials maps in a number of other natural problems, including the values of linear forms restricted to suitable quadratic surfaces, and the values of the polynomial map defined by the generators of the ring of conjugation-invariant polynomials on $M_3(\\Bbb\{C\})$. These results are instances of a general approach that we develop, which considers a rational affine algebraic subvariety of Euclidean space, invariant and homogeneous under an action of a semisimple Lie group $G$. Given a polynomial map $F$ defined on the Euclidean space which is invariant under a semisimple subgroup $H$ of the acting group $G$, consider the family of its translates $F\\circ g$ by elements of the group. We study the restriction of these polynomial functions to the integer points on the variety confined to a large Euclidean ball. Our main results establish an explicit rate of density for their values, for generic polynomials in the family. This problem has been extensively studied before when the polynomials in question are linear, in the context of classical Diophantine approximation, but very little was known about it for polynomial of higher degree. We formulate a heuristic pigeonhole lower bound for the density and an explicit upper bound for it, formulate a sufficient condition for the coincidence of the lower and upper bounds, and in a number of natural examples establish that they indeed match. Finally, we also establish a rate of density for values of homogeneous polynomials on homogeneous projective varieties.
Cyclic Demazure Modules and Positroid Varieties

A positroid variety is an intersection of cyclically rotated Grassmannian Schubert varieties. Each graded piece of the homogeneous coordinate ring of a positroid variety is the intersection of cyclically rotated (rectangular) Demazure modules, which we call the cyclic Demazure module. In this note, we show that the cyclic Demazure module has a canonical basis, and define the cyclic Demazure crystal.
Eigenvalues of compactly perturbed operators via entropy numbers

We derive new estimates for the number of discrete eigenvalues of compactly perturbed operators on Banach spaces, assuming that the perturbing operator is an element of a weak entropy number ideal. Our results improve upon earlier results by the author and by Demuth et al. The main tool in our proofs is an inequality of Carl. In particular, in contrast to all previous results we do not rely on tools from complex analysis.
INDIRECT EVIDENCE FOR ESCAPING IONIZING PHOTONS IN LOCAL LYMAN BREAK GALAXY ANALOGS

A population of early star-forming galaxies is the leading candidate for the re-ionization of the universe. It is still unclear, however, what conditions and physical processes would enable a significant fraction of the ionizing (Lyman continuum) photons to escape from these gas-rich galaxies. In this paper we present the results of the analysis of Hubble Space Telescope Cosmic Origins Spectrograph far-UV (FUV) spectroscopy plus ancillary multi-waveband data of a sample of 22 low-redshift galaxies that are good analogs to typical star-forming galaxies at high redshift. We measure three parameters that provide indirect evidence of the escape of ionizing radiation (leakiness): (1) the residual intensity in the cores of saturated interstellar low-ionization absorption lines, which indicates incomplete covering by that gas in the galaxy; (2) the relative amount of blueshifted Lyα line emission, which can indicate the existence of holes in the neutral hydrogen on the front-side of the galaxy outflow, and (3) the relative weakness of the [S ii] optical emission lines that trace matter-bounded H ii regions. We show that our residual intensity measures are only negligibly affected by infilling from resonance emission lines. We find all three diagnostics agree well with one another. We use these diagnostics to rank-order our sample in terms of likely leakiness, noting that a direct measure of escaping Lyman continuum has recently been made for one of the leakiest members of our sample. We then examine the correlations between our ranking and other proposed diagnostics of leakiness. We find a good correlation with the equivalent width of the Lyα emission line, but no significant correlations with either the flux ratio of the [O iii]/[O ii] emission lines or the ratio of star-formation rates derived from the (dust-corrected) FUV and Hα luminosities. Turning to galaxy properties, we find the strongest correlations with leakiness are with the compactness of the star-forming region (Star formation rate/area) and the speed of the galactic outflow. This suggests that extreme feedback—a high intensity of ionizing radiation and strong pressure from both radiation and a hot galactic wind—combines to create significant holes in the neutral gas. These results not only shed new light on the physical mechanisms that can allow ionizing radiation to escape from intensely star-forming galaxies, they also provide indirect observational indicators that can be used at high redshift where direct measurements of escaping Lyman continuum radiation are impossible.
Frobenius splitting of valuation rings and
F-singularities of centers

Using a local monomialization result of Knaf and Kuhlmann, we prove that the valuation ring of an Abhyankar valuation of a function field over a perfect ground field of prime characteristic is Frobenius split. We show that a Frobenius splitting of a sufficiently well-behaved center lifts to a Frobenius splitting of the valuation ring. We also investigate properties of valuations centered on arbitrary Noetherian domains of prime characteristic. In contrast to [arXiv:1507.06009], this paper emphasizes the role of centers in controlling Frobenius properties of valuations rings in prime characteristic.
THE EFFECTS OF USING SELF-VIDEO RECORDING ON EFL HIGH SCHOOL STUDENTS’ LEXICON KNOWLEDGE

This study aims to investigate the effects of using self-video recording on EFL high school students’ lexicon knowledge. Participants include 80 EFL high school students in the Mekong Delta divided into two groups, namely the control and experimental group. Pretest and posttest were done to collect quantitative data before and after the treatment. After the treatment, the results of the experimental groups were higher than that of the control one in terms of lexicon knowledge. Therefore, this study gives recommendations for further studies in other aspects of speaking skills or speaking skills in general. <p> </p><p><strong> Article visualizations:</strong></p><p><img src="/-counters-/edu_01/0946/a.php" alt="Hit counter" /></p>
Braid-positive Legendrian links

Any link that is the closure of a positive braid has a natural Legendrian representative. These were introduced in [15], where their Chekanov– Eliashberg contact homology was also evaluated. In this paper we rephrase and improve that computation using a matrix representation. In particular, we present a way of finding all augmentations of such Legendrians, construct an augmentation which is also a ruling, and find surprising + + + +
Balanced truncation and singular perturbation approximation model order reduction for stochastically controlled linear systems

When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used. Balanced truncation (BT) and singular perturbation approximation (SPA) are well-known projection techniques in the deterministic framework which reduce the order of a control system and hence reduce computational complexity. This work considers both methods when the control is replaced by a noise term. We provide theoretical tools such as stochastic concepts for reachability and observability, which are necessary for balancing related model order reduction of linear stochastic differential equations with additive Levy noise. Moreover, we derive error bounds for both BT and SPA and provide numerical results for a specific example which support the theory.
Real quadrics in $\Bbb C^n$, complex manifolds and convex polytopes

In this paper, we investigate the topology of a class of non-K\"ahler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics in $\Bbb C^n$ which are invariant with respect to the natural action of the real torus $(\Bbb S^1)^n$ onto $\Bbb C^n$. The quotient space is a simple convex polytope. The problem reduces thus to the study of the topology of certain real algebraic sets and can be handled using combinatorial results on convex polytopes. We prove that the homology groups of these compact complex manifolds can have arbitrary amount of torsion so that their topology is extremely rich. We also resolve an associated wall-crossing problem by introducing holomorphic equivariant elementary surgeries related to some transformations of the simple convex polytope. Finally, as a nice consequence, we obtain that affine non K\"ahler compact complex manifolds can have arbitrary amount of torsion in their homology groups, contrasting with the K\"ahler situation.
Wilson RG of Noncommutative $\Phi_{4}^4$

We present a study of phi-four theory on noncommutative spaces using a combination of the Wilson renormalization group recursion formula and the solution to the zero dimensional vector/matrix models at large N. Three fixed points are identified. The matrix model θ = ∞ fixed point which describes the disordered-to-nonuniform-ordered transition. The Wilson–Fisher fixed point at θ = 0 which describes the disordered-to-uniform-ordered transition, and a noncommutative Wilson–Fisher fixed point at a maximum value of θ which is associated with the transition between nonuniform-order and uniform-order phases.
The Work Intervention Network (WIN): Foundations of a Holistic Vocational Intervention

The aim of the current study was to examine whether the key constructs targeted in the Work Intervention Network (WIN) intervention uniquely predicted well-being outcomes and mediated relations between un/underemployment and these outcomes. Using data from a sample of 462 adults in the U.S., we positioned employment status as a predictor of life satisfaction, well-being, and psychological distress. We also tested four mediators of these relations that operationalized targets in the WIN intervention – career engagement, social support, self-care, and self-blame. Employment status indirectly predicted life satisfaction, life meaning, and psychological distress via self-care and self-blame. Career engagement mediated the relation between employment status and psychological distress but in an unexpected direction. Social support was not directly predicted by employment status but predicted life satisfaction and life meaning. Results provided initial support for the WIN intervention and corroborate the contention that employment status is an important predictor of well-being.
A characterization of equivalent martingale measures in a renewal risk model with applications to premium calculation principles

Generalizing earlier work of Delbaen and Haezendonck for given compound renewal process $S$ under a probability measure $P$ we characterize all probability measures $Q$ on the domain of $P$ such that $Q$ and $P$ are progressively equivalent and $S$ remains a compound renewal process under $Q$. As a consequence, we prove that any compound renewal process can be converted into a compound Poisson process through a change of measures and we show how this approach is related to premium calculation principles.
Dynamic Sharing Through the ADMM

In this paper, we study a dynamic version of the sharing problem, in which a dynamic system cost function composed of time-variant local costs of subsystems and a shared time-variant cost of the whole system is minimized. A dynamic alternating direction method of multipliers (ADMM) is proposed to track the varying optimal points of the dynamic optimization problem in an online manner. We analyze the convergence properties of the dynamic ADMM and show that, under several standard technical assumptions, the iterations of the dynamic ADMM converge linearly to some neighborhoods of the time-varying optimal points. The sizes of these neighborhoods depend on the drifts of the dynamic objective functions: the more drastically the dynamic objective function evolves across time, the larger the sizes of these neighborhoods. We also upper bound the limiting optimality gaps of the dynamic ADMM explicitly, and analyze its regret and constraint violation. Finally, two numerical examples are presented to corroborate the effectiveness of the proposed dynamic ADMM.
Super-easy quantum groups: definition and examples

We investigate the "two-parameter" quantum symmetry groups that we previously constructed with Skalski, with the conclusion that some of these quantum groups, namely those without singletons, are "super-easy" in a suitable sense, that we axiomatize here. Our formalism covers as well the symplectic group $Sp_n$ and its free version $Sp_n^+$, and some other interesting examples. Finally, we address the general problem of classifying the super-easy quantum groups, and we make a few comments on it.