Miracle-dz/UniFAR-FTUs huggingface dataset:
Detection of velocity distribution of a flow field using sequences of Schlieren images

We present an image analysis technique for obtaining the velocity distribution from image sequences taken with a Schlieren appa- ratus. With this technique, the image sequence is considered as a series of 2-D functions that are transforming gradually through the period when the image sequence is taken. The fluid movement between the two con- secutive images is then obtained via functional analysis that gives the local function deformation at every image position. The velocity and ac- celeration of the flow field are derived. In contrast to the particle image velocimetry (PIV) techniques, the presented technique is advantageous in the situation where the tracing particles are difficult to introduce or identify. The Schlieren apparatus set up for the study is a modified positive-negative grid system. Buoyant flows produced from gas fires and gas explosion ejection are used as case studies. © 2001 Society of
Analysis of the first variation and a numerical gradient flow for integral Menger curvature

In this thesis, we consider the knot energy "integral Menger curvature" which is the triple integral over the inverse of the classic circumradius of three distinct points on the given knot to the power $p\in [2,\infty)$. We prove the existence of the first variation for a subset of a certain fractional Sobolev space if $p>3$ and for a subset of a certain H\"older space otherwise. We also discuss how fractional Sobolev and H\"older spaces can be generalised for $2\pi$-periodic, closed curves. Since this energy is not invariant under scaling, we additionally consider a rescaled version of the energy, where we take the energy to the power one over $p$ and multiply by the length of the curve to a certain power. We prove that a circle is at least a stationary point of the rescaled energy. Furthermore, we show that in general a functional with a scaling behaviour like $E(r\gamma)=r^\alpha E(\gamma)$, $\alpha\in\mathbb{R}$ cannot have stationary points unless $\alpha=0$. Consequently "integral Menger curvature" for $p\neq 3$ can be used as a subsidiary condition for a Lagrange-multiplier rule. We consider a numerical gradient flow for the rescaled energy. For this purpose we use trigonometric polynomials to approximate the knots and the trapezoidal rule for numerical integration, which is very efficient in this case. Moreover, we derive a suitable representation of the first variation. We present an algorithm for the adaptive choice of time step size and for the redistribution of the Fourier coefficients. After discussing the full discretization we present a wide collection of example flows.
Likewise theta functions of rank $r$ on $\mathbb{R}^d$: analytic properties and associated Segal-Bargmann transform

We introduce and study the Hilbert space of $(L^2,\Gamma,\chi)$-likewise theta functions on $\mathbb{R}^d$ with respect to a given discrete subgroup $\Gamma$ of arbitrary rank and a character $\chi$ of $\Gamma$. A concrete description is given and an orthonormal basis is then constructed. Its range by the classical Segal-Bargmann transform is also characterized and leads to the so-called theta-Bargmann Fock space.
The thickness of the turbulent/nonturbulent interface is equal to the radius of the large vorticity structures near the edge of the shear layer

Direct numerical simulations at Reynolds numbers ranging from Reλ=30 to 160 show that the thickness δω of the turbulent/nonturbulent (T/NT) interface in planar jets is of the order of the Taylor scale δω∼λ, while in shear free, irrotational/isotropic turbulence is of the order of the Kolmogorov microscale δω∼η. It is shown that δω is equal to the radius of the large vorticity structures (LVSs) in this region, δω≈RLVS. Thus, the mean shear and the Reynolds number affect the T/NT interface thickness insofar as they define the radial dimension of the LVS near the T/NT interface.
A perturbation analysis of stochastic matrix Riccati diffusions

Matrix differential Riccati equations are central in filtering and optimal control theory. The purpose of this article is to develop a perturbation theory for a class of stochastic matrix Riccati diffusions. Diffusions of this type arise, for example, in the analysis of ensemble Kalman-Bucy filters since they describe the flow of certain sample covariance estimates. In this context, the random perturbations come from the fluctuations of a mean field particle interpretation of a class of nonlinear diffusions equipped with an interacting sample covariance matrix functional. The main purpose of this article is to derive non-asymptotic Taylor-type expansions of stochastic matrix Riccati flows with respect to some perturbation parameter. These expansions rely on an original combination of stochastic differential analysis and nonlinear semigroup techniques on matrix spaces. The results here quantify the fluctuation of the stochastic flow around the limiting deterministic Riccati equation, at any order. The convergence of the interacting sample covariance matrices to the deterministic Riccati flow is proven as the number of particles tends to infinity. Also presented are refined moment estimates and sharp bias and variance estimates. These expansions are also used to deduce a functional central limit theorem at the level of the diffusion process in matrix spaces.
Inexact Linear Solves in Model Reduction of Bilinear Dynamical Systems

The bilinear iterative rational Krylov algorithm (BIRKA) is a very popular, standard, and mathematically sound algorithm for reducing bilinear dynamical systems that arise commonly in science and engineering. This reduction process is termed as a model order reduction (MOR) and leads to a faster simulation of such systems. An efficient variant of the BIRKA, Truncated BIRKA (TBIRKA) has also been recently proposed. Like for any MOR algorithm, these two algorithms also require solving multiple linear systems as part of the model reduction process. For reducing the MOR time, these linear systems are often solved by an iterative solver, which introduces approximation errors (implying inexact solves). Hence, stability analysis of the MOR algorithms with respect to inexact linear solves is important. In our past work, we have shown that under mild conditions, the BIRKA is stable. Here, we look at the stability of the TBIRKA in the same context. Besides deriving the conditions for a stable TBIRKA, our other novel contribution is the more intuitive methodology for achieving this. The stability analysis techniques that we propose here can be extended to many other methods for doing the MOR of bilinear dynamical systems, e.g., using balanced truncation or the ADI methods.
Epidemiological study of myasthenia gravis in Japan

Myasthenia gravis (MG) is an autoimmune‐mediated neurological disorder. The relationship between MG and thymic abnormalities is well recognized, and thymectomy is one of the therapies for anti‐acetylcholine receptor antibody‐positive MG. The major pathogenic factor is anti‐acetylcholine receptor antibody followed by anti‐muscle‐specific kinase antibody, and commercial kits are available to detect these antibodies. Several decades ago, the prognosis of MG was not favorable; therefore, the Ministry of Health and Welfare (predecessor of the Ministry of Health, Labor and Welfare) organized a Taskforce for Intractable Diseases, which included MG, in 1972. The Taskforce carried out consecutive epidemiological studies for MG in 1973, 1987, 2006 and 2018. The four studies found: (i) increasing prevalence; (ii) increasing late‐ and elderly‐onset; (iii) decreasing female dominancy; (iv) decreasing infantile‐onset (onset age of 0–4 years); and (v) decreasing frequencies of crisis. The latest epidemiological study in Japan and studies from other countries suggest an increasing number of patients with anti‐acetylcholine receptor antibody‐positive MG without thymoma in the elderly. It is important to find out the causes of this phenomenon, which will improve the prevention of MG.
How Grit-S Items Work in Measuring Growth: Focusing on Item Discrimination and Sensitivity to Change

This study investigates how sensitively the current grit measure (Grit-S) is able to reflect the differences between individuals (i.e. item discrimination) and change within individuals (i.e. sensitivity to change of items) using longitudinal data. Data from the Korean Children and Youth Panel Study 2018 of elementary (fourth grade) and middle school (seventh grade) cohorts were analyzed. We compared a series of longitudinal factor models of change with an initial trait and a change in grit represented by latent traits. Results showed that the models hypothesizing two latent traits with respect to the two elements of grit (interest and effort) best fit the data. In the elementary school cohort, sensitivity to change was different from discriminating between-person differences at baseline. Meanwhile, in the middle school cohort, sensitivity to change was identical to discriminating between-person differences at baseline. The items having low discrimination and low sensitivity to change resulted in syntactical complexity and did not accurately reflect the trait that was intended to be measured. Despite the Grit-S being widely used for many years, it is suggested that researchers and educators should administer this measure at taking an individual’s change and school-level difference into account.
Gravitational dynamics for all tensorial spacetimes carrying predictive, interpretable and quantizable matter

Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations that are predictive, interpretable and quantizable. These three conditions on matter translate into three corresponding algebraic conditions on the underlying tensorial geometry, namely to be hyperbolic, time-orientable and energy-distinguishing. Lorentzian metrics, on which general relativity and the standard model of particle physics are built, present just the simplest tensorial spacetime geometry satisfying these conditions. The problem of finding gravitational dynamics—for the general tensorial spacetime geometries satisfying the above minimum requirements—is reformulated in this paper as a system of linear partial differential equations, in the sense that their solutions yield the actions governing the corresponding spacetime geometry. Thus the search for modified gravitational dynamics is reduced to a clear mathematical task.
The inverse problem of dynamics: basic facts

Finding potentials or force fields from given families of orbits is the type of inverse problem of dynamics discussed in this paper. We present the pertinent partial differential equations for various versions of the problem such as, for instance, for conservative or autonomous non-conservative fields in two or three dimensions, for inertial or relating frames, for one material point or, more, generally, for holonomic systems with n degrees of freedom. The notion of the family boundary curves is introduced. The role of the homogeneity of the given family or of the required potential, as well as the question of multitude of compatible pairs of orbits and potentials is discussed. Comments on the relation of the problem to problems of astronomical interest are made, at appropriate places, throughout the text.
Shape Preserving Piecewise Rational Interpolation

An explicit representation of a $C^1 $ piecewise rational cubic function is developed which can be used to solve the problem of shape preserving interpolation. It is shown that the interpolation method can be applied to convex and/or monotonic sets of data and an error analysis of the interpolant is given. The scheme includes, as a special case, the monotonic rational quadratic interpolant considered by the authors in [1] and [5]. However, the requirement of convexity necessitates the generalization to the rational cubic form employed here.
Book Review : Psychometric Theory (3rd ed.) by Jum Nunnally and Ira Bernstein New York: McGraw-Hill, 1994, xxiv + 752 pp

It is always sad when one of your idols turns out to have clay feet-even worse when the base substance extends higher. Unfortunately, this was my experience in reading the third edition of Nunnally’s classic work as revised by Bernstein. Because the first edition (Nunnally, 1967) came out during my graduate school career and the second (Nunnally, 1978) was useful in a decade of teaching, I looked forward to this
Demailly's conjecture on Waldschmidt constants for sufficiently many very general points in $\mathbb{P}^n$

Let $Z$ be a finite set of $s$ points in the projective space $\mathbb{P}^n$ over an algebraically closed field $F$. For each positive integer $m$, let $\alpha(mZ)$ denote the smallest degree of nonzero homogeneous polynomials in $F[x_0,\ldots,x_n]$ that vanish to order at least $m$ at every point of $Z$. The Waldschmidt constant $\widehat{\alpha}(Z)$ of $Z$ is defined by the limit \[ \widehat{\alpha}(Z)=\lim_{m \to \infty}\frac{\alpha(mZ)}{m}. \] Demailly conjectured that \[ \widehat{\alpha}(Z)\geq\frac{\alpha(mZ)+n-1}{m+n-1}. \] Recently, Malara, Szemberg, and Szpond established Demailly's conjecture when $Z$ is very general and \[ \lfloor\sqrt[n]{s}\rfloor-2\geq m-1. \] Here we improve their result and show that Demailly's conjecture holds if $Z$ is very general and \[ \lfloor\sqrt[n]{s}\rfloor-2\ge \frac{2\varepsilon}{n-1}(m-1), \] where $0\le \varepsilon<1$ is the fractional part of $\sqrt[n]{s}$. In particular, for $s$ very general points where $\sqrt[n]{s}\in\mathbb{N}$ (namely $\varepsilon=0$), Demailly's conjecture holds for all $m\in\mathbb{N}$. We also show that Demailly's conjecture holds if $Z$ is very general and \[ s\ge\max\{n+7,2^n\}, \] assuming the Nagata-Iarrobino conjecture $\widehat{\alpha}(Z)\ge\sqrt[n]{s}$.
On the cubic NLS on 3D compact domains

Abstract We prove bilinear estimates for the Schrödinger equation on 3D domains, with Dirichlet boundary conditions. On non-trapping domains, they match the ${ \mathbb{R} }^{3} $ case, while on bounded domains they match the generic boundaryless manifold case. We obtain, as an application, global well-posedness for the defocusing cubic NLS for data in ${ H}_{0}^{s} (\Omega )$, $1\lt s\leq 3$, with $\Omega $ any bounded domain with smooth boundary. Résumé On démontre des estimations bilinéaires pour l’équation de Schrödinger sur des domaines tridimensionnels, avec condition de Dirichlet au bord. Dans le cas non-captant, on retrouve les estimations connues dans ${ \mathbb{R} }^{3} $, et sur un domaine borné on obtient des estimations similaires à celles du cas d’une variété compacte générique sans bord. Une application est donnée à l’existence de solutions globales dans ${ H}_{0}^{s} (\Omega )$, $1\lt s\leq 3$, avec $\Omega $ un domaine borné régulier.
The convergence of a sequence of polynomials and the distribution of their zeros

Suppose that $\langle f_n \rangle$ is a sequence of polynomials, $\langle f_n^{(k)}(0)\rangle$ converges for every non-negative integer $k$, and that the limit is not $0$ for some $k$. It is shown that if all the zeros of $f_1, f_2, \dots$ lie in the closed upper half plane $\rm{Im}\ z\geq 0$, or if $f_1, f_2, \dots$ are real polynomials and the numbers of their non-real zeros are uniformly bounded, then the sequence converges uniformly on compact sets in the complex plane. The results imply a theorem of Benz and a conjecture of P\'olya.
The Response of Different-Levels Public Hospitals to Regional Global Budget with a Floating Payment System: Evidence from China

Background: Regional Global Budget with a Floating Payment System (RGB-FPS) is a global budget widely used in medical insurance payments. However, existing studies on hospitals’ responses to RGB-FPS have limitations. First, existing studies have paid little attention to RGB-FPS’s macro effects. Theoretical studies did not analyze differences between different levels of hospitals. Secondly, studies did not reveal whether RGB-FPS has the same impact on the public-hospital-dominated market. Methods: First, we refine the research hypotheses through theoretical analysis. We then test the hypotheses empirically through interrupted time series analysis. Results: Theoretical analysis found that small hospitals were easier to transfer costs. The empirical analysis found that after RGB-FPS, the proportion of inpatients (PI)and the average times of inpatients in large hospitals increased (p < 0.001), and the proportion of non-reimbursable expenses (PNE) remained stable (p > 0.05). PI in secondary hospitals decreased (p < 0.01), and PNE increased (p < 0.01). PI in the primary hospital decreased (p < 0.05), and PNE increased (p < 0.001). Conclusion: This study verifies theoretically and empirically that large hospitals are easier to increase service volume and small hospitals are easier to transfer costs under the influence of RGB-FPS. Chinese public hospitals’ response to RGB-FPS is similar to that of private hospitals.
Putting whanaungatanga at the heart of students’ online learning experiences

This paper explores the role of relationships in students’ experiences of online learning during the COVID-19 pandemic in Aotearoa| New Zealand. Students’ voices are foregrounded through narratives and the analysis of four discrete stories of these specific circumstances. Using a conceptual framing of whanaungatanga, a M? ori view of the process of establishing and maintaining relationships, we move beyond who is involved in the relationship to explore how relationships are developed and what counts from the students’ perspectives. Sharing, an ethic of care, a sense of belonging, collaboration, scaffolding of learning, and feedback acknowledging students’ efforts were all considered important aspects of relationships between students and faculty which were enacted online. The importance of broader institutional relationships, such as those with the library and student support services, were also foregrounded.
Examining the mediating role of peer antisocial behavior on the relationship between parenting and bullying behaviors

ABSTRACT Although prior research has established the influence of parents and peers on adolescents’ bullying behaviors, there is a void in the literature of the potential mediating effect of negative peer influence in the relationship between parenting practices and bullying behaviors among a United States sample. Using data from the Pathways to Desistance study, the present study examines the mediating role of peer antisocial behavior in the association between parenting (i.e., parental monitoring and maternal warmth) and adolescents’ bullying behaviors (i.e., bully perpetration, bully victimization, bully-victim, and non-involved). Results indicate that the effect of parental monitoring on youth who engaged in bully perpetration (vs. non-involved) was mediated by peer antisocial behavior. That is, poor parental monitoring increased delinquent peer association, which in turn predicted a high risk of engaging in bully perpetration. However, peer antisocial behavior did not mediate the relationship between parental monitoring and bully victimization (vs. non-involved) nor bully-victim (vs. non-involved). The findings have important implications for adolescents’ bullying behavior and possible intervention programs by informing researchers and practitioners about the mechanisms surrounding multiple types of bullying behaviors.
A Markov model for Selmer ranks in families of twists

Abstract We study the distribution of 2-Selmer ranks in the family of quadratic twists of an elliptic curve $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}E$ over an arbitrary number field $K$. Under the assumption that ${\rm Gal}(K(E[2])/K) \ {\cong }\ S_3$, we show that the density (counted in a nonstandard way) of twists with Selmer rank $r$ exists for all positive integers $r$, and is given via an equilibrium distribution, depending only on a single parameter (the ‘disparity’), of a certain Markov process that is itself independent of $E$ and $K$. More generally, our results also apply to $p$-Selmer ranks of twists of two-dimensional self-dual ${\bf F}_p$-representations of the absolute Galois group of $K$ by characters of order $p$.
Measuring deformations with deflectometry

Phase-measuring deflectometry is a powerful method to measure reflective surfaces. It is relatively easy to extract slope and curvature information from the measured phase maps; however, retrieving shape information depends very sensitively on the calibration of the camera and the geometry of the measurement system. Whereas we have previously demonstrated shape uncertainties below 1 μm, the range below 100 nm is currently inaccessible to deflectometric shape measurement. On the other hand, the astounding sensitivity of deflectometry can be put to good use for deformation measurements. The evaluation of corresponding shape differences rather than absolute shapes is much less susceptible to system calibration errors and its resolution is given mostly by the measurement system’s sensitivity. We give an overview of recent progress in difference deflectometry. Firstly we show results from solar mirror substrates under load to detect flaws with high sensitivity. Secondly we present a preliminary simulation study of achievable deformation-measurement uncertainties to assess the feasibility of deflectometric characterisation of actuator performance and gravity sag for the mirror segments of the European Extremely Large Telescope (E-ELT). Results for the relevant Zernike terms show reliable detection of Zernike coefficients at the 25 nm level. Random artefacts related to noise in the phase measurements are seen to translate into bogus Zernike terms, and we discuss possible mitigation techniques to enhance the sensitivity and accuracy further.
Variational formulations of sound‐proof models

We derive a family of ideal (non‐dissipative) three‐dimensional (3D) sound‐proof fluid models that includes both the Lipps–Hemler anelastic approximation (AA) and the Durran pseudo‐incompressible approximation (PIA). This family of models arises in the Euler–Poincaré framework involving a constrained Hamilton's principle expressed in the Eulerian fluid description. The derivation in this framework establishes the following properties of each member of the entire family: the Kelvin–Noether circulation theorem, conservation of potential vorticity on fluid parcels, a Lie–Poisson Hamiltonian formulation possessing conserved Casimirs, a conserved domain‐integrated energy and an associated variational principle satisfied by the equilibrium solutions.
Dopa-Responsive Dystonia: An Early Presentation of Ataxia-Telangiectasia

Ataxia-telangiectasia (AT) is a complex genetic neurodegenerative disease with autosomal recessive inheritance. The typical initial features of ataxia telangiectasia include ataxia, cutaneous telangiectasia, and immune deficiency with recurrent infections. Usually, movement disorder occurs late in the course of the disease. A diagnosis of variant or atypical ataxia-telangiectasia (variant AT) is considered in case of any deviation from the normal course of illness giving rise to variable presentations of the disease. Only a few cases of variant AT with predominant movement disorder have been reported worldwide. A knowledge of atypical presentations helps in early diagnosis and thus to initiate management and counselling of the family at the earliest. Here, we report a case of genetically confirmed ataxia-telangiectasia with an initial presentation of dopamine responsive dystonia.