Miracle-dz/UniFAR-FTUs huggingface dataset:
Cluster algebras and continued fractions

We establish a combinatorial realization of continued fractions as quotients of cardinalities of sets. These sets are sets of perfect matchings of certain graphs, the snake graphs, that appear naturally in the theory of cluster algebras. To a continued fraction $[a_{1},a_{2},\ldots ,a_{n}]$ we associate a snake graph ${\mathcal{G}}[a_{1},a_{2},\ldots ,a_{n}]$ such that the continued fraction is the quotient of the number of perfect matchings of ${\mathcal{G}}[a_{1},a_{2},\ldots ,a_{n}]$ and ${\mathcal{G}}[a_{2},\ldots ,a_{n}]$ . We also show that snake graphs are in bijection with continued fractions. We then apply this connection between cluster algebras and continued fractions in two directions. First we use results from snake graph calculus to obtain new identities for the continuants of continued fractions. Then we apply the machinery of continued fractions to cluster algebras and obtain explicit direct formulas for quotients of elements of the cluster algebra as continued fractions of Laurent polynomials in the initial variables. Building on this formula, and using classical methods for infinite periodic continued fractions, we also study the asymptotic behavior of quotients of elements of the cluster algebra.
Entropy of partially hyperbolic flows with center dimension two

In this article we study the regularity of the topological and metric entropy of partially hyperbolic flows with two-dimensional center direction. We show that the topological entropy is upper semicontinuous with respect to the flow, and we give an example where the lower semicontinuity fails. We also show that if such a flow has no fixed points, then it is entropy expansive, and consequentely the metric entropy function is upper semicontinuous, there exist equilibrium states (and measures of maximal entropy), and principal symbolic extensions.
Regularity of monotone transport maps between unbounded domains

The regularity of monotone transport maps plays an important role in several applications to PDE and geometry. Unfortunately, the classical statements on this subject are restricted to the case when the measures are compactly supported. In this note we show that, in several situations of interest, one can to ensure the regularity of monotone maps even if the measures may have unbounded supports.
The Effetiveness of Training and Development on Employee Perfomance to Enhance Competitive Advantage: A Case Study of Social Enterprise Development Sierra Leone (Send-SI)

This study aimed to examine the effect of Human Resources development and training on performance. Data were collected using questionnaires from 71 workers who were selected at random. The collected data were analyzed using Structural Equation Modeling (SEM), which employed Smart-PLS3. The analysis results show that on-the-job training measured by (Job-rotation, Job-instruction, orientation and workshop) had no significant direct effect on Employee Performance but a significant direct effect on Employee Competitive Advantage. While Off-the-job training measured by (exchange learning, short courses, self-development, and simulation) had a significant direct impact on employee performance but had no significant immediate effection employee competitive advantage. Also, employee performance was found to have a significant direct impact on employee competitive advantage. The result further revealed that through the mediation of employee performance, on-the-job training had no significant indirect effect on employee competitive advantage, while off-the-job training had a substantial indirect impact on employee competitive advantage.
Left-handed chiral isotropic metamaterials: analysis and detailed numerical study

Chiral isotropic metamaterials with a negative index of refraction design consisting of arrays of a sole structure are proposed. The Cn point group is selected based on its chiral and isotropic properties. A circuit analysis model is obtained for the double negative NIR passband design. The structure’s orientation provides flexibility to adjust the properties. Structure modification, based on the capacitance and inductance value, controls the locations of the structure’s effective material parameters and the double negative NIR passband. These proposed designs give the highest possible rank of isotropy. The negative index of refraction is also validated.
Down‐tail mass loss by plasmoids in Jupiter's and Saturn's magnetospheres

Recent estimates of the plasma mass‐loss rates by the formation and down‐tail propagation of plasmoids observed in the plasma sheet in Jupiter's and Saturn's magnetosphere fall short of inner moon source rates by at least an order of magnitude. Here we argue that on the time scale between large‐scale disconnection events, ~15 h at Jupiter and ~45 h at Saturn, mass‐loaded closed flux tubes will typically have stretched out a few hundred planetary radii down tail at speeds ~100–200 km s−1. Consequently, the “plasmoids” of order ~10 planetary radii in length observed at closer planetary distances represent only a small planetward portion of the overall structure that is disconnected and lost down tail. Plasmoid mass‐loss estimates are then revised upward by around an order of magnitude, becoming comparable to the moon source values. Additional “hidden,” e.g., small‐scale, mass‐loss processes of comparable strength may not then be required. The essentially continuous azimuthally flowing source plasma in the dusk sector is shown to correspond to a plasma sheet layer adjacent to the magnetopause of width typically ~10% of the distance to the magnetopause in that local time sector. This physical picture also provides a simple explanation for the asymmetry in the plasmoid bipolar field signature observed at both Jupiter and Saturn and predicts that the apparent plasmoid length will increase with distance down tail to a limit beyond a few hundred planetary radii where the full ~100–200 planetary radii structures will be observed.
Quantitative stratification of $F$-subharmonic functions

In this paper, we study the singular sets of $F$-subharmonic functions $u: B_{2}(0^{n})\rightarrow\mathbf{R}$, where $F$ is a subequation. The singular set $\mathcal{S}(u)\subset B_{2}(0^{n})$ has a stratification $\mathcal{S}^{0}(u)\subset\mathcal{S}^{1}(u)\subset\cdots\subset\mathcal{S}^{k}(u)\subset\cdots\subset\mathcal{S}(u)$, where $x\in\mathcal{S}^{k}(u)$ if no tangent function to $u$ at $x$ is $(k+1)$-homogeneous. We define the quantitative stratification $\mathcal{S}_{\eta,r}^{k}(u)$ and $\mathcal{S}_{\eta}^{k}(u)=\cap_{r}\mathcal{S}_{\eta,r}^{k}(u)$. When homogeneity of tangents holds for $F$, we prove that $dim_{H}\mathcal{S}^{k}(u)\leq k$ and $\mathcal{S}(u)=\mathcal{S}^{n-p}(u)$, where $p$ is the Riesz characteristic of $F$. And for the top quantitative stratification $\mathcal{S}_{\eta}^{n-p}(u)$, we have the Minkowski estimate $\text{Vol}(B_{r}(\mathcal{S}_{\eta}^{n-p}(u)\cap B_{1}(0^{n})))\leq C\eta^{-1}(\int_{B_{1+r}(0^{n})}\Delta u)r^{p}$. When uniqueness of tangents holds for $F$, we show that $S_{\eta}^{k}(u)$ is $k$-rectifiable, which implies $\mathcal{S}^{k}(u)$ is $k$-rectifiable. When strong uniqueness of tangents holds for $F$, we introduce the monotonicity condition and the notion of $F$-energy. By using refined covering argument, we obtain a definite upper bound on the number of $\{\Theta(u,x)\geq c\}$ for $c>0$, where $\Theta(u,x)$ is the density of $F$-subharmonic function $u$ at $x$. Geometrically determined subequations $F(\mathbb{G})$ is a very important kind of subequation (when $p=2$, homogeneity of tangents holds for $F(\mathbb{G})$; when $p>2$, uniqueness of tangents holds for $F(\mathbb{G})$). By introducing the notion of $\mathbb{G}$-energy and using quantitative differentation argument, we obtain the Minkowski estimate of quantitative stratification $\text{Vol}(B_{r}(\mathcal{S}_{\eta,r}^{k}(u))\cap B_{1}(0^{n}))\leq Cr^{n-k-\eta}$.
On protostellar evolution

An investigation of the evolution of spherically symmetric protostars with initial masses in the range 0.1less than or equal toM/M/sub sun/less than or equal to50 has been carried out. In order to perform the calculations, a numerical technique has been developed in which rapid dynamical motions in one region of the star and quasi-static evolution in another region can be simultaneously computed. The general evolutionary features are similar to those found by other workers: an initial free-fall collapse is followed by the creation of a core in hydrostatic equilibrium, and the core's subsequent accretion of the surrounding envelope. However, our final hydrostatic-equilibrium configurations have radii large compared with those of the protostellar models of Larson (but in reasonable agreement with those of conventional pre-main-sequence models). For low-mass protostars (Mless than or equal toM/sub sun/) the luminosity remains relatively small until late evolutionary times and the evolution is very sensitive to the treatment of convective energy transport. For large-mass protostars (Mgreater than or equal to3M/sub sun/) a convective phase never exists, and a fraction (increasing with mass) of the initial mass is ejected by the combined effects of heating and radiation pressure in the envelope.
Strong measure zero and meager-additive sets through the prism of fractal measures

We develop a theory of \emph{sharp measure zero} sets that parallels Borel's \emph{strong measure zero}, and prove a theorem analogous to Galvin-Myscielski-Solovay Theorem, namely that a set of reals has sharp measure zero if and only if it is meager-additive. Some consequences: A subset of $2^\omega$ is meager-additive if and only if it is $\mathcal E$-additive; if $f:2^\omega\to2^\omega$ is continuous and $X$ is meager-additive, then so is $f(X)$.
Vortices, Generators and Heat Transfer

Longitudinal vortices are more efficient for heat transfer enhancement than transverse vortices.A survey is given on triangular and rectangular protrusions from a heat transfer surface which generate mainly longitudinal vortex systems. Wings and winglets are considered in boundary layer and channel flow, either by themselves, or in a single row transverse to the flow direction, or in a two dimensional array. Local and global heat transfer are studied as a function of the major parameters. For channel flows also the pressure losses are given. Winglets are superior to wings, but winglet form is of minor importance. In laminar flow, heat transfer enhancement increases with Reynolds number. Heat transfer enhancement increases for constant winglet aspect ratio with angle of attack up to a maximum angle of attack. But it increases also up to limiting values with winglet height relative to transverse and streamwise winglet spacing and relative to channel height or boundary layer thickness. The nonlinear character of fluid mechanics does not allow simple predictions.
Topological Hochschild homology of X(n)

We show that Ravenel's spectrum $X(2)$ is the versal $E_1$-$S$-algebra of characteristic $\eta$. This implies that every $E_1$-$S$-algebra $R$ of characteristic $\eta$ admits an $E_1$-ring map $X(2)\to R$, i.e. an $\mathbb{A}_\infty$ complex orientation of degree 2. This implies that $R^\ast(\mathbb{C}P^2)\cong R_\ast[x]/x^3$. Additionally, if $R$ is an $\mathbb{E}_2$-ring Thom spectrum admitting a map (of homotopy ring spectra) from $X(2)$, e.g. $X(n)$, its topological Hochschild homology has a simple description.
Electron microscopy study of interfacial reaction between eutectic SnPb and Cu/Ni(V)/Al thin film metallization

The wetting reaction between molten eutectic SnPb solder and a sputtered trilayer Cu/Ni(V)/Al thin film metallization was studied using cross-sectional transmission electron microscopy and scanning electron microscopy. Reaction temperatures were from 200 to 240 °C and reaction times ranged from 1 to 40 min. The initial reaction products were Cu6Sn5 and Cu3Sn. The latter transforms to the former after an annealing greater than 1 min at 220 °C. The Cu6Sn5 grains adhere well to the Ni(V) surface and no spalling of them was observed, even after 40 min at 220 °C. This surprising result indicates that the Cu/Ni(V)/Al or Cu6Sn5/Ni(V)/Al is a stable thin film metallization for low temperature eutectic SnPb solder direct chip attachment to organic substrates. Additionally, Kirkendall voids accompanied Cu3Sn formation, yet the voids disappear when the Cu3Sn transforms to Cu6Sn5.
A family of isospectral Euler–Bernoulli beams

In this paper we consider the class of Euler–Bernoulli beams such that the product between the bending stiffness and the linear mass density is constant. Under the assumption that the end conditions are any combination of pinned and sliding, we obtain closed-form expressions for beams isospectral to a given one. The analysis is based on the fact that this special class of beams is, in a certain sense, equivalent to a string, and uses a Darboux lemma after reduction of the string equation to Sturm–Liouville canonical form.
Total variation superiorized conjugate gradient method for image reconstruction

The conjugate gradient (CG) method is commonly used for the relatively-rapid solution of least squares problems. In image reconstruction, the problem can be ill-posed and also contaminated by noise; due to this, approaches such as regularization should be utilized. Total variation (TV) is a useful regularization penalty, frequently utilized in image reconstruction for generating images with sharp edges. When a non-quadratic norm is selected for regularization, as is the case for TV, then it is no longer possible to use CG. Non-linear CG is an alternative, but it does not share the efficiency that CG shows with least squares and methods such as fast iterative shrinkage-thresholding algorithms (FISTA) are preferred for problems with TV norm. A different approach to including prior information is superiorization. In this paper it is shown that the conjugate gradient method can be superiorized. Five different CG variants are proposed, including preconditioned CG. The CG methods superiorized by the total variation norm are presented and their performance in image reconstruction is demonstrated. It is illustrated that some of the proposed variants of the superiorized CG method can produce reconstructions of superior quality to those produced by FISTA and in less computational time, due to the speed of the original CG for least squares problems. In the Appendix we examine the behavior of one of the superiorized CG methods (we call it S-CG); one of its input parameters is a positive number ε. It is proved that, for any given ε that is greater than the half-squared-residual for the least squares solution, S-CG terminates in a finite number of steps with an output for which the half-squared-residual is less than or equal to ε. Importantly, it is also the case that the output will have a lower value of TV than what would be provided by unsuperiorized CG for the same value ε of the half-squared residual.
On existence and curvature estimates of Ricci flow

In this work, using the method by He, we prove a short time existence for Ricci flow on a complete noncompact Riemannian manifold with the following properties: (i) there is $r_0>0$ such that the volume of any geodesic balls of radius $r\le r_0$ is close to the volume of the geodesic ball in the Euclidean space with the same radius; (ii) the Ricci curvature is bounded below; (iii) the sectional curvature is bounded below by $-Cd^2(x,x_0)$ where $d(x,x_0)$ is the distance from a fixed point. An application to the uniformization for complete noncompact Kahler manifolds with nonnegative bisectional curvature and maximal volume growth is given. The result is related to the results of He and Liu. We prove if $g(t)$ is a complete solution to the Kahler-Ricci flow on a complete noncompact Kahler manifold so that $g(0)$ has nonnegative bisectional curvature and the curvature of $g(t)$ is bounded by $at^{-b}$ for some $a>0, 2>b>0$, then $g(t)$ also has nonnegative bisectional curvature. This generalizes a previous result. Under the assumption that $g(0)$ is noncollapsing, with additional assumption that the curvature of $g(t)$ is uniformly bounded away from $t>0$, we prove that the curvature of $g(t)$ is in fact bounded by $at^{-1}$ for some $a>0$. This result is proved using the method by Simon and Topping.
Geometrical Structures for Classical and Quantum Probability Spaces

On the affine space containing the space $\mathcal{S}$ of quantum states of finite-dimensional systems there are contravariant tensor fields by means of which it is possible to define Hamiltonian and gradient vector fields encoding relevant geometrical properties of $\mathcal{S}$. Guided by Dirac's analogy principle, we will use them as inspiration to define contravariant tensor fields, Hamiltonian and gradient vector fields on the affine space containing the space of fair probability distributions on a finite sample space and analyse their geometrical properties. Most of our considerations will be dealt with for the simple example of a three-level system.
Conductor and discriminant of Picard curves

We describe normal forms and minimal models of Picard curves, discussing various arithmetic aspects of these. We determine all so‐called special Picard curves over Q with good reduction outside 2 and 3, and use this to determine the smallest possible conductor a special Picard curve may have. We also collect a database of Picard curves over Q of small conductor.
Electrons in the ionosphere of Titan

A theoretical model of the spatial and energy distribution of electrons in the ionosphere of Titan has been constructed using the two-stream electron transport method and the electron energy equation. The calculated electron spectra show abrupt decreases that can contribute to the “bite-out” signature observed by the Voyager 1 plasma science instrument. Energy deposition rates in the exosphere of Titan by photoelectrons and magnetospheric electrons are calculated. Calculated N2 EUV airglow emission rates lead to the conclusion that airglow emission due to photoelectron impact is much more important than airglow emission due to magnetospheric electron interactions. Thermal electron temperatures at Titan are calculated for the first time. The electron gas remains well thermalized with the neutral atmosphere for radial distances from the center of Titan less than 3500 km. For radial distances beyond about 4000 km, energy transport dominates the energetics, and the electrons are almost isothermal along magnetic field lines.
Two-point generating function of the free energy for a directed polymer in a random medium

We consider a (1 + 1)-dimensional directed continuum polymer in a Gaussian delta-correlated spacetime random potential. For this model the moments (= replica) of the partition function, Z(x, t), can be expressed in terms of the attractive δ-Bose gas on the line. Based on a recent study of the structure of the eigenfunctions, we compute the generating function for Z(x1, t), Z(x2, t) under a particular decoupling assumption and thereby extend recent results on the one-point generating function of the free energy to two points. It is established that in the long-time limit the fluctuations of the free energy are governed by the two-point distribution of the Airy process, which further supports that the long-time behavior of the KPZ equation is the same as derived previously for lattice growth models.
Photoionization modeling of Magellanic Cloud planetary nebulae. I

The results of self-consistent photoionization modeling of 38 Magellanic Cloud PNe are presented and used to construct an H-R diagram for the central stars and to obtain both the nebular chemical abundances and the physical parameters of the nebulae. T(eff)s derived from nebular excitation analysis are in agreement with temperatures derived by the classical Zanstra method. There is a linear correlation between log T(eff) and the excitation class. The majority of the central stars in the sample with optically thick nebulae have masses between 0.55 and 0.7 solar mass and are observed during their hydrogen-burning excursion toward high temperatures. Optically thin objects are found scattered throughout the H-R diagram, but tend to have a somewhat smaller mean mass. Type I PN are found to have high core masses and to lie on the descending branch of the evolutionary tracks. The nebular mass of the optically thick objects is closely related to the nebular radius, and PN with nebular masses over one solar are observed. 62 refs.
Inverse Nodal Problems for Dirac-Type Integro-Differential Operators with Linear Functions in the Boundary Condition

Abstract In this article, Dirac-type integro-differential operator with linear functions in the boundary condition is considered. We obtain asymptotic expressions for the solution of the differential system and derive the large eigenvalues and nodal points. We also give a constructive procedure for solving an inverse nodal problem. We prove that a dense subset of the nodes determines the coefficients of the differential part of the operator and gives partial information for the integral part of it.
Multiple Solutions for a Flow between Two Concentric Spheres with Different Temperatures and Their Stability

Finite amplitude steady solutions for convections between two concentric spheres under the effects of differential rotation and temperature difference between the spheres are obtained and their linear stability is investigated numerically. Under the assumption of axisymmetry about the axis of rotation, the solutions are classified into the s y m m e t r i c solution and the a s y m m e t r i c solution with respect to the equator. It is found that the symmetric solution consists of the u p w a r d solution and the d o w n w a r d solution which have different flow profiles, rates of heat transfer between two spheres. A perfect pitchfork bifurcation is observed for the asymmetric solution, whereas an imperfect pitchfork bifurcation is observed for the symmetric solution, as the rate of the differential rotation is increased.
Long paths in first passage percolation on the complete graph I. Local PWIT dynamics

We study the random geometry of first passage percolation on the complete graph equipped with independent and identically distributed edge weights, continuing the program initiated by Bhamidi and van der Hofstad [9]. We describe our results in terms of a sequence of parameters $(s_n)_{n\geq 1}$ that quantifies the extreme-value behavior of small weights, and that describes different universality classes for first passage percolation on the complete graph. We consider both $n$-independent as well as $n$-dependent edge weights. The simplest example consists of edge weights of the form $E^{s_n}$, where $E$ is an exponential random variable with mean 1. In this paper, we investigate the case where $s_n\rightarrow \infty$, and focus on the local neighborhood of a vertex. We establish that the smallest-weight tree of a vertex locally converges to the invasion percolation cluster on the Poisson weighted infinite tree. In addition, we identify the scaling limit of the weight of the smallest-weight path between two uniform vertices.
The Complete Classification of Large-Amplitude Geostrophic Flows in a Two-Layer Fluid

Abstract We examine two-layer geostrophic flows over a flat bottom on the β-plane. If the displacement of the interface is of the order of the depth of the upper layer, the dynamics of the flow depends on the following non-dimensional parameters: (i) the Rossby number ∊, (ii) the ratio δ of the depth of the upper layer to the total depth of the fluid, (iii) the “β-effect number” α = Ro/Re cot θ, where Ro is the deformation radius, Re, is the earth's radius and θ is the latitude. In this paper We derive four sets of asymptotic equations which cover the parameter space (∊ ≪ 1,α,δ). In order to find out, which asymptotic regimes are relevant to the real ocean, we estimate ∊, δ and α a number of frontal flows in the Northern Pacific and Southern oceans We also discuss the stability properties of large-amplitude geostrophic flows and classify them in the (∊, α, δ)