Miracle-dz/UniFAR-FTUs huggingface dataset:
Wetting Characteristics of Nanosilica-Poly (acrylic acid) Transparent Anti-Fog Coatings

The effect of particle loading on the wetting properties of coatings was investigated by modifying a coating formulation based on hydrophilic silica nanoparticles and poly (acrylic acid) (PAA). Water contact angle (WCA) measurements were conducted for all coatings to characterize the surface wetting properties. Wettability was improved with an increase in particle loading. The resulting coatings showed superhydrophilic (SH) behavior when the particle loading was above 53 vol. %. No new peaks were detected by attenuated total reflection (ATR-FTIR). The surface topography of the coatings was studied by atomic force microscopy (AFM) and scanning electron microscopy (SEM). The presence of hydrophilic functional groups and nano-scale roughness were found to be responsible for superhydrophilic behavior. The surface chemistry was found to be a primary factor determining the wetting properties of the coatings. Adhesion of the coatings to the substrate was tested by tape test and found to be durable. The antifogging properties of the coatings were evaluated by exposing the films under different environmental conditions. The SH coatings showed anti-fogging behavior. The transparency of the coatings was significantly improved with the increase in particle loading. The coatings showed good transparency (>85% transmission) when the particle loading was above 84 vol. %.
Quadro-Quadric Special Birational Transformations of Projective Spaces

Special birational transformations Φ : P99KZ defined by quadric hypersurfaces are studied by means of the variety of lines Lz ⊂ P passing through a general point z ∈ Z. Classification results are obtained when Z is either a Grassmannian of lines, or the 10-dimensional spinor variety, or the E6variety. In the particular case of quadro-quadric transformations, we extend the well-known classification of Ein and Shepherd-Barron coming from Zak’s classification of Severi varieties to a wider class of prime Fano manifolds Z. Combining both results, we get a classification of special birational transformations Φ : P99KZ defined by quadric hypersurfaces onto (a linear setion of) a rational homogeneous variety different from a projective space and a quadric hypersurface.
Extreme value theory for random walks on homogeneous spaces

In this paper we study extreme events for random walks on homogeneous spaces. We consider the following three cases. On the torus we study closest returns of a random walk to a fixed point in the space. For a random walk on the space of unimod- ular lattices we study extreme values for lengths of the shortest vector in a lattice. For a random walk on a homogeneous space we study the maximal distance a random walk gets away from an arbitrary fixed point in the space. We prove an exact limiting distribution on the torus and upper and lower bounds for sparse subsequences of random walks in the two other cases. In all three settings we obtain a logarithm law.
A multiplier algebra functional calculus

This paper generalizes the classical Sz. -Nagy--Foias $H^{\infty}(\mathbb{D})$ functional calculus for Hilbert space contractions. In particular, we replace the single contraction $T$ with a tuple $T=(T_1, \dots, T_d)$ of commuting bounded operators on a Hilbert space and replace $H^{\infty}(\mathbb{D})$ with a large class of multiplier algebras of Hilbert function spaces on the unit ball in $\mathbb C^d$.
Group incentives and rational voting 1

Our model describes competition between groups driven by the choices of self-interested voters within groups. Within a Poisson voting environment, parties observe aggregate support from groups and can allocate prizes or punishments to them. In a tournament style analysis, the model characterizes how contingent allocation of prizes based on relative levels of support affects equilibrium voting behavior. In addition to standard notions of pivotality, voters influence the distribution of prizes across groups. Such prize pivotality supports positive voter turnout even in non-competitive electoral settings. The analysis shows that competition for a prize awarded to the most supportive group is only stable when two groups actively support a party. However, competition among groups to avoid punishment is stable in environments with any number of groups. We conclude by examining implications for endogenous group formation and how politicians structure the allocation of rewards and punishments.
Exponential divisor functions

Consider the operator $E$ on arithmetic functions such that $Ef$ is the multiplicative arithmetic function defined by $(Ef)(p^a) = f(a)$ for every prime power $p^a$. We investigate the behaviour of $E^m\tau_k$, where $\tau_k$ is a $k$-dimensional divisor function and $E^m$ stands for the $m$-fold iterate of $E$. We estimate the error terms of $\sum_{n\le x} E^m\tau_k(n)$ for various combinations of $m$ and $k$. We also study properties of $E^mf$ for arbitrary $f$ and sufficiently large $m$. Our study provides a unified approach to functions with exponential divisors. We improve special cases of the Dirichlet asymmetric divisor problem and several results on the exponential divisor and totient functions.
Stand and Tree Characteristics Influence Damage Severity after a Catastrophic Hurricane Disturbance

Catastrophic wind disturbances can greatly impact the economic and ecological values of working forests worldwide. For example, Hurricane Michael caused severe economic damage in 2018 to commercial loblolly (Pinus taeda L.) and slash ( Pinus elliotti Engelm.) planted pine stands in the southeastern U.S. This project examined the relative importance of prior management activities, stand characteristics, and soil and terrain attributes in predicting stand damage from a catastrophic hurricane event. We assembled data from land managers in coastal Alabama, the Florida panhandle, and South Georgia, on percent loss of trees after Hurricane Michael in over 400 stands, along with stand management history, and stand characteristics. Digital elevation models were utilized to determine terrain and hydrological characteristics of the landscape including aspect, channel distance, elevation, LS factor (slope and length steepness factor), slope angle, slope position, terrain ruggedness index, topographic wetness index, and wind exposition index. Random forest models were used to determine the relative accuracy of windspeed, management history, stand characteristics, and soil and terrain attributes in predicting stand damage. From the variables evaluated, stand density (as described by trees per acre), and tree height (as described by the average height of dominant and co-dominant trees) were among the most influential characteristics in predicting damage severity along with windspeed and linear distance from the coast. Stands with dominant heights > 14 m, trees per acre < 600 (trees per hectare < 1,483), and within 50 km of the coast were the most likely to experience severe damage. Topographic wetness index was the most influential terrain characteristic, with sands in wetter soils more likely to experience more severe damage. Recently thinned stands were slightly more vulnerable to severe damage. Results from this study can be used to develop vulnerability profiles for commercial pine stands in the coastal plain region in the southern U.S. region.
The area preserving curve shortening flow with Neumann free boundary conditions

κ ds L ≕ κ̄ is the average of the curvature. For simple closed curves ̄ κ = 2π L holds. Gage pointed out that this evolution equation arises as the “ L2-gradient flow” of the length functional under the constant enclosed area constraint. The term ̄ κ is the suitable Lagrange parameter for this variational problem. Gage proved that a strictly convex simple closed cu rve which evolves according to (1) remains strictly convex and converges to a circle in the C∞ metric ast → ∞, see [15, Theorem 4.1]. Note that there is a connection to another problem i n geometric analysis, namely the isoperimetric problem inR2, i.e. finding the shortest curve under all closed curves that enclose a certain fixed area. The area preserving curve shortening flo w deforms a given convex, simple closed curve with enclosed area A0 to the solution of the isoperimetric problem in R2: the circle with enclosed area A0. The same result was proven by Huisken in [20] for n ≥ 2. In this case, the evolution equation is as follows: Let Mn be a compact n-dimensional manifold without boundary andF0 : Mn → Rn+1 a smooth immersion. A familyF : Mn × [0,T) → Rn+1 with T > 0 is a solution to thevolume preserving mean curvature flow if it is a smooth family of
Management of postoperative respiratory complication in a child with severe obstructive sleep apnoea syndrome during Covid-19

Coronavirus disease (Covid-19) was first discovered in December 2019 with no signs of conceding to date. Many operations which are regarded as not lifesaving are postponed indefinitely owing to hospital bed shortage as well as to reduce the spread of infection among patients and staff. However, healthcare professionals are thrown down a huge challenge when deciding the timing of treatment for non-life-threatening conditions like severe paediatric obstructive sleep apnoea syndrome (OSAS) with a substantial impact on the development of very young children.To outline management of postoperative respiratory complication in a child with severe obstructive sleep anoea syndrome during Covid-19.We present a case of a major respiratory event requiring reintubation that developed post-adenotonsillectomy in a 3-year-old child with severe OSAS.The child was given close monitoring for 6 h in the post-anaesthetic care unit (PACU) before he was transferred to the general paediatric ward, without PICU admission during his stay in the hospital.Postoperative monitoring at the step-down unit with a high nurse-to-patient ratio appears to be beneficial as it does not compromise the need for close postoperative observation, meanwhile saving costs.
Rigged configurations and cylindric loop Schur functions

Rigged configurations are known to provide action-angle variables for remarkable discrete dynamical systems known as box-ball systems. We conjecture an explicit piecewise-linear formula to obtain the shapes of a rigged configuration from a tensor product of one-row crystals. We introduce cylindric loop Schur functions and show that they are invariants of the geometric R-matrix. Our piecewise-linear formula is obtained as the tropicalization of ratios of cylindric loop Schur functions. We prove our conjecture for the first shape of a rigged configuration, thus giving a piecewise-linear formula for the lengths of the solitons of a box-ball system.
The inducibility of small oriented graphs

We use Razborov's flag algebra method to show an asymptotic upper bound for the maximal induced density $i(\vec P_3)$ of the orgraph $\vec P_3$ in an arbitrary orgraph. A conjecture of Thomass\'e states that $i(\vec P_3)=2/5$. The hitherto best known upper bound $i(\vec P_3)\leq12/25$ was given by Bondy. We can show that $i(\vec P_3)\leq 0.4446$. Further, we consider such a maximal density for some other small orgraphs. With easy arguments one can see that $i(\vec C_3)=1/4$, $i(\vec K_2 \cup \vec E_1)=3/4$ and $2/21\leq i(\vec C_4)$. We show that $i(\vec C_4)\leq 0.1104$ and conjecture that the extremal orgraphs of $\vec P_3$ and $\vec C_4$ are the same. Furthermore we show that $6-4\sqrt{2}\leq i(\vec K_{1,2})\leq 0.4644$.
Optimal sweepouts of a Riemannian 2-sphere

Given a sweepout of a Riemannian 2-sphere which is composed of curves of length less than L, we construct a second sweepout composed of curves of length less than L which are either constant curves or simple curves. This result, and the methods used to prove it, have several consequences; we answer a question of M. Freedman concerning the existence of min-max embedded geodesics, we partially answer a question due to N. Hingston and H. -B. Rademacher, and we also extend the results of [CL] concerning converting homotopies to isotopies in an effective way.
Product Markovian quantization of an R^d -valued Euler scheme of a diffusion process with applications to finance

We introduce a new approach to quantize the Euler scheme of an $\mathbb R^d$-valued diffusion process. This method is based on a Markovian and componentwise product quantization and allows us, from a numerical point of view, to speak of {\em fast online quantization} in dimension greater than one since the product quantization of the Euler scheme of the diffusion process and its companion weights and transition probabilities may be computed quite instantaneously. We show that the resulting quantization process is a Markov chain, then, we compute the associated companion weights and transition probabilities from (semi-) closed formulas. From the analytical point of view, we show that the induced quantization errors at the $k$-th discretization step $t_k$ is a cumulative of the marginal quantization error up to time $t_k$. Numerical experiments are performed for the pricing of a Basket call option, for the pricing of a European call option in a Heston model and for the approximation of the solution of backward stochastic differential equations to show the performances of the method.
Understanding X‐ray reflection emissivity profiles in AGN: locating the X‐ray source

The illumination pattern (or emissivity profile) of the accretion disc due to the reflection of X-rays in active galactic nucleus can be understood in terms of relativistic effects on the rays propagating from a source in a corona surrounding the central black hole, both on their trajectories and on the accretion disc itself. Theoretical emissivity profiles due to isotropic point sources as well as simple extended geometries are computed in general relativistic ray-tracing simulations performed on graphics processing units (GPUs). Such simulations assuming only general relativity naturally explain the accretion disc emissivity profiles determined from relativistically broadened emission lines which fall off steeply (with power-law indices of between 6 and 8) over the inner regions of the disc, then flattening off to almost a constant before tending to a constant power law of index 3 over the outer disc. Simulations for a variety of source locations, extents and geometries show how the emissivity profiles depend on these properties, and when combined with reverberation time lags allow the location and extent of the primary X-ray source to be constrained. Comparing the emissivity profile determined from the broadened iron K emission line in spectra of 1H 0707−495 obtained in 2008 January to theoretical emissivity profiles and applying constraints from reverberation lags suggest that there exists an extended region of primary X-ray emission located as low as 2rg above the accretion disc, extending outwards to a radius of around 30rg.
On the heritability of the Hall property $D_\pi$ by overgroups of $\pi$-Hall subgroups

Let $\pi$ be a set of primes. We say that a finite group $G$ is a $D_\pi$-group if all its maximal $\pi$-subgroups are conjugate. In this paper, we give an affirmative answer to the problem 17.44(b) from "The Kourovka notebook": we prove that in a $D_\pi$-group an overgroup of a $\pi$-Hall subgroup is always a $D_\pi$-group.
Some remarks on the Gromov width of homogeneous Hodge manifolds

We provide an upper bound for the Gromov width of compact homogeneous Hodge manifolds (M, ω) with b2(M) = 1. As an application we obtain an upper bound on the Seshadri constant ϵ(L) where L is the ample line bundle on M such that .
The prescribed Ricci curvature problem on three‐dimensional unimodular Lie groups

Let G be a three‐dimensional unimodular Lie group, and let T be a left‐invariant symmetric (0,2)‐tensor field on G. We provide the necessary and sufficient conditions on T for the existence of a pair (g,c) consisting of a left‐invariant Riemannian metric g and a positive constant c such that Ric(g)=cT , where Ric(g) is the Ricci curvature of g. We also discuss the uniqueness of such pairs and show that, in most cases, there exists at most one positive constant c such that Ric(g)=cT is solvable for some left‐invariant Riemannian metric g.
Spontaneous Neurological Recovery of Patients with Acute Traumatic Spinal Cord Injuries (ATSCI) without Intervention the Injured Cord”

Acute traumatic spinal cord injuries (ATSCI) are life threatening and life changing events. With good Active Physiological Conservative Management (APCM) of the injured spine and the systemic effects of cord damage to prevent further mechanical and non-mechanical damage of the cord the majority of patients make some spontaneous neurological recovery (SNR). The magnitude and extent of this recovery depends on the initial degree and topographical sparing of sensory and sensory-motor tracts functions at and below the Zone of Partial Preservation (ZPP).
Appraisals of Social Trauma and Their Role in the Development of Post-Traumatic Stress Disorder and Social Anxiety Disorder

Cognitive theories of post-traumatic stress disorder (PTSD) feature appraisal of trauma as a critical factor in the development and maintenance of the disorder. Here we explored appraisals of social trauma (severe rejection or humiliation). Participants were outpatients with social anxiety disorder (SAD) and clinically significant PTSD symptoms (PTSS) after social trauma (n = 15); two clinical control groups of either SAD (n = 32) or obsessive-compulsive disorder (OCD; n = 13); and a control group with no diagnoses (n = 38). Measures included a clinical interview to assess social trauma and related open-ended appraisals and the Posttraumatic Cognitions Inventory (PTCI). Raters blind to group assignment performed content analyses of appraisals. Results showed that the PTSS group scored significantly higher than either clinical group on the PTCI SELF subscale. Only the SELF subscale predicted a diagnosis of both PTSS and SAD. All but one PTSS participant reported primarily negative beliefs about their social trauma, and the most common categories were flawed self and others are critical or cruel. Post-traumatic appraisals implicated in the course of PTSD are significant in how individuals respond to social trauma, with negative self-cognitions linked to both PTSS and SAD.
Extensions of bounded holomorphic functions on the tridisk

We study sets $V$ in the tridisc that are relatively polynomially convex and have the polynomial extension property. If $V$ is one-dimensional, and is either algebraic, or has polynomially convex projections, we show that it is a retract. If $V$ is two-dimensional, we show that either it is a retract, or, for any choice of the coordinate functions, it is the graph of a function of two variables.
The double of representations of Cohomological Hall Algebra for $A_1$-quiver

We compute two representations of COHA for $A_1$-quiver. The two untwisted representations can be combined into a representation of $D_{n+1}$ Lie algebra. The untwisted increasing representation and the twisted decreasing representation can be combined into a representation of a finite Clifford algebra.
Fermi's Golden Rule and $H^1$ Scattering for Nonlinear Klein-Gordon Equations with Metastable States

In this paper, we explore the metastable states of nonlinear Klein-Gordon equations with potentials. These states come from the instability of a bound state under a nonlinear Fermi's golden rule. In [16], Soffer and Weinstein studied the instability mechanism and obtained an anomalously slow-decaying rate $1/(1+t)^{\frac{1}{4}}$. Here we develop a new method to study the $L^2_x$ norm of solutions to Klein-Gordon equations. With this method, we prove the first $H^1$ scattering result for Klein-Gordon equations with metastable states. By exploring the oscillations, we also give another more robust and more intuitive approach to derive the sharp decay rate $1/(1+t)^{\frac{1}{4}}$.
Smallest bases of expansions with multiple digits

Given two positive integers $M$ and $k$, let $\B_k$ be the set of bases $q>1$ such that there exists a real number $x$ having exactly $k$ different $q$-expansions over the alphabet $\{0,1,\cdots,M\}$. In this paper we investigate the smallest base $q_2$ of $\B_2$, and show that if $M=2m$ the smallest base $$q_2 =\frac{m+1+\sqrt{m^2+2m+5}}{2},$$ and if $M=2m-1$ the smallest base $q_2$ is the appropriate root of $$ x^4=(m-1)\,x^3+2 m\, x^2+m \,x+1. $$ Moreover, for $M=2$ we show that $q_2$ is also the smallest base of $\B_k$ for all $k\ge 3$. This turns out to be different from that for $M=1$.
Atmospheric parameters of 82 red giants in the Kepler field

Context. Accurate fundamental parameters of stars are essential for the asteroseismic analysis of data from the NASA Kepler mission. Aims. We aim at determining accurate atmospheric parameters and the abundance pattern for a sample of 82 red giants that are targets for the Kepler mission. Methods. We have used high-resolution, high signal-to-noise spectra from three different spectrographs. We used the iterative spectral synthesis method VWA to derive the fundamental parameters from carefully selected high-quality iron lines. After determination of the fundamental parameters, abundances of 13 elements were measured using equivalent widths of the spectral lines. Results. We identify discrepancies in log g and [Fe/H], compared to the parameters based on photometric indices in the Kepler Input Catalogue (larger than 2.0 dex for log g and [Fe/H] for individual stars). The Teff found from spectroscopy and photometry shows good agreement within the uncertainties. We find good agreement between the spectroscopic log g and the log g derived from asteroseismology. Also, we see indications of a potential metallicity effect on the stellar oscillations. Conclusions. We have determined the fundamental parameters and element abundances of 82 red giants. The large discrepancies between the spectroscopic log g and [Fe/H] and values in the Kepler Input Catalogue emphasize the need for further detailed spectroscopic follow-up of the Kepler targets in order to produce reliable results from the asteroseismic analysis.
The classification of CMC foliations of $\mathbb{R}^3$ and $\mathbb{S}^3$ with countably many singularities

In this paper we generalize the Local Removable Singularity Theorem in [16] for minimal laminations to the case of weak $H$-laminations (with $H\in \mathbb{R}$ constant) in a punctured ball of a Riemannian three-manifold. We also obtain a curvature estimate for any weak CMC foliation (with possibly varying constant mean curvature from leaf to leaf) of a compact Riemannian three-manifold $N$ with boundary solely in terms of a bound of the absolute sectional curvature of $N$ and of the distance to the boundary of $N$. We then apply these results to classify weak CMC foliations of $\mathbb{R}^3$ and $\mathbb{S}^3$ with a closed countable set of singularities.
On $k$-stellated and $k$-stacked spheres

We introduce the class $\Sigma_k(d)$ of $k$-stellated (combinatorial) spheres of dimension $d$ ($0 \leq k \leq d + 1$) and compare and contrast it with the class ${\cal S}_k(d)$ ($0 \leq k \leq d$) of $k$-stacked homology $d$-spheres. We have $\Sigma_1(d) = {\cal S}_1(d)$, and $\Sigma_k(d) \subseteq {\cal S}_k(d)$ for $d \geq 2k - 1$. However, for each $k \geq 2$ there are $k$-stacked spheres which are not $k$-stellated. The existence of $k$-stellated spheres which are not $k$-stacked remains an open question. We also consider the class ${\cal W}_k(d)$ (and ${\cal K}_k(d)$) of simplicial complexes all whose vertex-links belong to $\Sigma_k(d - 1)$ (respectively, ${\cal S}_k(d - 1)$). Thus, ${\cal W}_k(d) \subseteq {\cal K}_k(d)$ for $d \geq 2k$, while ${\cal W}_1(d) = {\cal K}_1(d)$. Let $\bar{{\cal K}}_k(d)$ denote the class of $d$-dimensional complexes all whose vertex-links are $k$-stacked balls. We show that for $d\geq 2k + 2$, there is a natural bijection $M \mapsto \bar{M}$ from ${\cal K}_k(d)$ onto $\bar{{\cal K}}_k(d + 1)$ which is the inverse to the boundary map $\partial \colon \bar{{\cal K}}_k(d + 1) \to {\cal K}_k(d)$.