On the locus formed by the maximum heights of projectile motion with air resistance

We present an analysis on the geometrical place formed by the set of maxima of the trajectories of a projectile launched in a media with linear drag. Such a place, the locus of apexes, is written in term of the Lambert $W$ function in polar coordinates, confirming the special role played by this function in the problem. In order to characterize the locus, a study of its curvature is presented in two parameterizations, in terms of the launch angle and in the polar one. The angles of maximum curvature are compared with other important angles in the projectile problem. As an addendum, we find that the synchronous curve in this problem is a circle as in the drag-free case.Comment: 7 pages, 6 color eps figures. Synchronous curve added. Typos and style corrected

Online, interactive user guidance for high-dimensional, constrained motion planning

We consider the problem of planning a collision-free path for a high-dimensional robot. Specifically, we suggest a planning framework where a motion-planning algorithm can obtain guidance from a user. In contrast to existing approaches that try to speed up planning by incorporating experiences or demonstrations ahead of planning, we suggest to seek user guidance only when the planner identifies that it ceases to make significant progress towards the goal. Guidance is provided in the form of an intermediate configuration $\hat{q}$, which is used to bias the planner to go through $\hat{q}$. We demonstrate our approach for the case where the planning algorithm is Multi-Heuristic A* (MHA*) and the robot is a 34-DOF humanoid. We show that our approach allows to compute highly-constrained paths with little domain knowledge. Without our approach, solving such problems requires carefully-crafting domain-dependent heuristics

Lower and Middle Famennian (Upper Devonian) rugose corals from southern Belgium and northern France

After the late Frasnian extinctions, the rugose corals slowly recovered during the Lower and Middle Famennian (crepida to marginifera conodont zones) in southern Belgium and northern France (Avesnois) (Namur–Dinant Basin). Six genera represented by seven species are recognized and described here; one species (Breviphrentis superstes) is new. The rugose coral fauna described herein includes small solitary forms belonging to the so-called Cyathaxonia fauna and is similar or very close to those previously described within the same stratigraphic interval in Australia, China and Germany. It also contains a large species belonging to the genus Breviphrentis which was considered as extinct since the end of the Givetian (Middle Devonian) (“Lazarus taxon”). The tabulate corals from the Lower and Middle Famennian of this area, mainly represented by auloporids, are also briefly discussed. Rugosa only constituted a minor part of the fauna after the end-Frasnian crisis in the Namur–Dinant Basin contrary to the brachiopods, which were abundant and relatively diversified, and no rugose corals have been recovered from the early Lower Famennian (triangularis Zone). The first important Famennian coral radiation only took place during the Latest Famennian (Strunian)

A survey of services for the speech and hearing handicapped in New England

Thesis (Ed. M.)--Boston University, 195

A survey of services for the speech and hearing handicapped in New England

Thesis (Ed. M.)--Boston University, 195

Visualizing the logistic map with a microcontroller

The logistic map is one of the simplest nonlinear dynamical systems that clearly exhibit the route to chaos. In this paper, we explored the evolution of the logistic map using an open-source microcontroller connected to an array of light emitting diodes (LEDs). We divided the one-dimensional interval $[0,1]$ into ten equal parts, and associated and LED to each segment. Every time an iteration took place a corresponding LED turned on indicating the value returned by the logistic map. By changing some initial conditions of the system, we observed the transition from order to chaos exhibited by the map.Comment: LaTeX, 6 pages, 3 figures, 1 listin

Poynting's theorem for planes waves at an interface: a scattering matrix approach

We apply the Poynting theorem to the scattering of monochromatic electromagnetic planes waves with normal incidence to the interface of two different media. We write this energy conservation theorem to introduce a natural definition of the scattering matrix S. For the dielectric-dielectric interface the balance equation lead us to the energy flux conservation which express one of the properties of S: it is a unitary matrix. For the dielectric-conductor interface the scattering matrix is no longer unitary due to the presence of losses at the conductor. However, the dissipative term appearing in the Poynting theorem can be interpreted as a single absorbing mode at the conductor such that a whole S, satisfying flux conservation and containing this absorbing mode, can be defined. This is a simplest version of a model introduced in the current literature to describe losses in more complex systems.Comment: 5 pages, 3 figures, submitted to Am. J. Phy

An Experimental Examination of Activist Type and Effort on Brand Image and Purchase Intentions

In 2016, several prominent athletes kneeled or sat during the national anthem of their games to protest social injustice in America. For their activism, these athletes inconsistently experienced both positive and negative consequences from their sponsors and fans. Therefore, the purpose of this study was to investigate this phenomenon more closely by examining the effect of activism type and activism effort on a sponsor’s brand image and purchase intention of a product the athlete endorses, when controlling for brand familiarity. Participants (N = 384) were randomly assigned into groups in a 2 (activism type: safe, risky) x 2 (activism effort: low, high) experimental study. Results indicated brand image and purchase intention were negatively impacted by risky activism compared to safe activism, but activism effort had no effect on the two variables. Further implications and future research are expanded upon in the discussion

Dust from Mars-Analog Plains (Iceland): Physico-Compositional Properties as a Function of Grain-Size Fraction

Dust is a key component of the geological and climatic systems of Earth and Mars. On Mars, dust is ubiquitous. It coats rocks and soils, and, in the atmosphere, it interacts strongly with solar and thermal radiation. Yet, key questions remain about the genesis and fate of martian dust, as well as its sources, composition, and properties. We collected wind-blown dust from basaltic plains in SW Iceland at Skjaldbreiauhraun that represent a geologic Mars-analog environment. Icelandic dust differs from the typical continental sources (e.g. Sahara, Asia) because of its basaltic volcanogenic origin, which is similar to Mars. Dust collection took place in July of 2019 as a complementary project to the SAND-E: Semi-Autonomous Navigation for Detrital Environments project. Here we report preliminary analyses of this Mars-analog dust material, with the goal of understanding the processes that control the physico-chemical proper-ties of the different grain-size fractions

Sequences of globally regular and black hole solutions in SU(4) Einstein-Yang-Mills theory

SU(4) Einstein-Yang-Mills theory possesses sequences of static spherically symmetric globally regular and black hole solutions. Considering solutions with a purely magnetic gauge field, based on the 4-dimensional embedding of $su(2)$ in $su(4)$, these solutions are labelled by the node numbers $(n_1,n_2,n_3)$ of the three gauge field functions $u_1$, $u_2$ and $u_3$. We classify the various types of solutions in sequences and determine their limiting solutions. The limiting solutions of the sequences of neutral solutions carry charge, and the limiting solutions of the sequences of charged solutions carry higher charge. For sequences of black hole solutions with node structure $(n,j,n)$ and $(n,n,n)$, several distinct branches of solutions exist up to critical values of the horizon radius. We determine the critical behaviour for these sequences of solutions. We also consider SU(4) Einstein-Yang-Mills-dilaton theory and show that these sequences of solutions are analogous in most respects to the corresponding SU(4) Einstein-Yang-Mills sequences of solutions.Comment: 40 pages, 5 tables, 19 Postscript figures, use revtex.st