The Flattening Metallicity Gradient in the Milky Way’s Thin Disk

We calculate the ages, orbits and phase-space coordinates for a sample of ∼4 million LAMOST and Gaia stars. The ages are cross-matched and compared with values from two other popular age catalogs, which derive the ages using different methods. Of these ∼4 million stars, we select a sample of 1.3 million stars and investigate their radial metallicity gradients (as determined by orbital radii) as a function of their ages. This analysis is performed on various subsets of the data split by chemistry and orbital parameters. We find that commonly used selections for “thin disk” stars (such as low-α chemistry or vertically thin orbits) yield radial metallicity gradients that generally grow shallower for the oldest stars. We interpret this as a hallmark feature of radial migration (churning). Constraining our sample to very small orbital Z max (the maximal height of a star’s integrated orbit) makes this trend most pronounced. A chemistry-based “thin disk” selection of α-poor stars displays the same trend, but to a lesser extent. Intriguingly, we find that “thick disk” selections in chemistry and Z max reveal slightly positive radial metallicity gradients, which seem similar in magnitude at all ages. This may imply that the thick disk population is well mixed in age, but not in radius. This finding could help constrain conditions during the early epochs of Milky Way formation and shed light on processes such as the accretion and reaccretion of gases of different metallicities.

TAKE-OFF HIP EXTENSION ANGLE INFLUENCE ON THE TUCKED BACK SOMERSAULT PERFORMANCE

Back somersault is a basic element of gymnastics; its performance is strongly influenced by the take-off phase. The present work aimed to study how hip extension in the take-off of the tucked back somersault influences the velocity of rotation and the height of the somersault. To this end, we recorded a total of 60 somersaults by 4 gymnasts (i.e., 15 somersaults each). There were three groups of somersaults based on the instructions that were given to the gymnasts: no specific instruction, somersault as high as possible and rotate as fast as possible. The records were then analyzed in order to quantify the following variables: maximal height of the mass center and maximal body angular velocity during somersault, the hip angle and the knee angle at the take-off. Gymnasts seemed to be inclined to bend their knees rather than extend their hips in order to carry out the instruction.

Bijections Between Walks Inside a Triangular Domain and Motzkin Paths of Bounded Amplitude

This paper solves an open question of Mortimer and Prellberg asking for an explicit bijection between two families of walks. The first family is formed by what we name triangular walks, which are two-dimensional walks moving in six directions (0°, 60°, 120°, 180°, 240°, 300°) and confined within a triangle. The other family is comprised of two-colored Motzkin paths with bounded height, in which the horizontal steps may be forbidden at maximal height. We provide several new bijections. The first one is derived from a simple inductive proof, taking advantage of a 2n-to-one function from generic triangular walks to triangular walks only using directions 0°, 120°, 240°. The second is based on an extension of Mortimer and Prellberg's results to triangular walks starting not only at a corner of the triangle, but at any point inside it. It has a linear-time complexity and is in fact adjustable: by changing some set of parameters called a scaffolding, we obtain a wide range of different bijections. Finally, we extend our results to higher dimensions. In particular, by adapting the previous proofs, we discover an unexpected bijection between three-dimensional walks in a pyramid and two-dimensional simple walks confined in a bounded domain shaped like a waffle.

Waves of maximal height for a class of nonlocal equations with inhomogeneous symbols

In this paper, we consider a class of nonlocal equations where the convolution kernel is given by a Bessel potential symbol of order α for α > 1. Based on the properties of the convolution operator, we apply a global bifurcation technique to show the existence of a highest, even, 2 π-periodic traveling-wave solution. The regularity of this wave is proved to be exactly Lipschitz.

The Rating of Perceived Exertion Predicts Performance Loss and Physiological Demand in Vertical Jump Session Until Voluntary Failure

The aims of this study were (a) to assess the ability of the rating of perceived exertion (RPE) to predict performance loss (i.e. percent of drop in height relative to maximal height) of vertical jump session until voluntary failure, and (b) to determine the ability of RPE to describe the physiological demand of this session via heart rate monitor. Ten healthy men performed vertical jumps (counter-movement jump) until voluntary failure. Before session start maximal jump height for every subject was determined. Heart rate and RPE, separately for legs (RPE legs) and for breath (RPE breath), were recorded every ten jumps throughout the sessions. Results have shoved that RPE legs and performance loss have about 99% of same variance ( =0,9899; p<0,000), and RPE breath explains about 98% heart rate variance ( =0,9789; p<0,000) in vertical jump session until voluntary failure.

Efficient Computation of the Large Inductive Dimension Using Order- and Graph-theoretic Means

Finite topological spaces and their dimensions have many applications in computer science, e.g., in digital topology, computer graphics and the analysis and synthesis of digital images. Georgiou et. al. [11] provided a polynomial algorithm for computing the covering dimension dim(X; 𝒯) of a finite topological space (X; 𝒯). In addition, they asked whether algorithms of the same complexity for computing the small inductive dimension ind(X; 𝒯) and the large inductive dimension Ind(X; 𝒯) can be developed. The first problem was solved in a previous paper [4]. Using results of the that paper, we also solve the second problem in this paper. We present a polynomial algorithm for Ind(X; 𝒯), so that there are now efficient algorithms for the three most important notions of a dimension in topology. Our solution reduces the computation of Ind(X; 𝒯), where the specialisation pre-order of (X; 𝒯) is taken as input, to the computation of the maximal height of a specific class of directed binary trees within the partially ordered set. For the latter an efficient algorithm is presented that is based on order- and graph-theoretic ideas. Also refinements and variants of the algorithm are discussed.

Comparative Kinematic Analysis of Hurdle Clearance Technique in Dogs: A Preliminary Report

Although the jumping characteristics of agility dogs have been examined in recent years, there is currently a lack of data related to the suspension phase. The purpose of the present study was to investigate the biomechanics of the suspension phase of the agility jump and to analyze the kinematic differences in dogs with different jumping abilities. Two groups of dogs of the same height category (large dogs) competing at different skill levels and assessed as excellent jumpers (n = 4) and less-skilled jumpers (n = 3), respectively, were analyzed and statistically compared. Excellent jumpers showed longer and faster jumps with flatter jump trajectories than less-skilled jumpers. In less-skilled jumpers, the distance in front of the hurdle was notably greater than the distance behind it, while the difference between these two distances was less in excellent jumpers. Length and duration of the jump, maximal height of the jumping trajectory, take-off and landing distances to the hurdle, time of occurrence of maximal jump height, and time of change in back orientation essentially defines the suspension phase of the agility jump. This study presents preliminary evidence that the kinematic characteristics of hurdle clearance are different in excellent jumper dogs and in less-skilled jumper dogs.