Related papers: The Hyperbolic Tangent as an Educational Tool for …
Here I present a summarised description of the general behavior of waves near turning points. I show that when asymptotic matching to a prescribed incident wavefield is performed, the solution changes from being the Airy function to being…
A real-time motion training system for skydiving is proposed. Aerial maneuvers are performed by changing the body posture and thus deflecting the surrounding airflow. The natural learning process is extremely slow due to unfamiliar…
In this paper, we develop a systematical approach in applying an asymptotic method of moving planes to investigate qualitative properties of positive solutions for fractional parabolic equations. We first obtain a series of needed key…
Modern advances in transformation optics and electromagnetic metamaterials made possible experimental demonstrations of highly unusual curvilinear optical spaces, such as various geometries necessary for electromagnetic cloaking. Recently…
The paper proposes an alternative to the Foucault pendulum for detecting various movements of rotation of the Earth. Calculations suggest that if the duration of a "free" fall becomes longer the eastward deflection will be amplified in…
The paper is devoted to the development of the theory of inverse problems for evolution equations with terms rapidly oscillating in time. A new approach to setting such problems is developed for the case in which additional constraints are…
Hamilton-Jacobi theory provides a natural starting point for a covariant description of the gravitational field. Using a spatial gradient expansion, one may solve for the phase of the wavefunction by using a line-integral in superspace.…
The paper introduces a method to solve inverse problems for hyperbolic systems where the leading order terms are non-linear. We apply the method to the coupled Einstein-scalar field equations and study the question whether the structure of…
We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for…
This paper tackles the challenge of enabling real-world humanoid robots to perform expressive and dynamic whole-body motions while maintaining overall stability and robustness. We propose Advanced Expressive Whole-Body Control (Exbody2), a…
Understanding physical phenomena is a key competence that enables humans and animals to act and interact under uncertain perception in previously unseen environments containing novel objects and their configurations. In this work, we…
Spatio-temporal grounding describes the task of localizing events in space and time, e.g., in video data, based on verbal descriptions only. Models for this task are usually trained with human-annotated sentences and bounding box…
We define finite-time hyperbolic coordinates, describe their geometry, and prove various results on both their convergence as the time scale increases, and on their variation in the state space. Hyperbolic coordinates reframe the classical…
Nonlinear dynamics of a bouncing ball moving vertically in a gravitational field and colliding with a moving limiter is considered and the Poincare map, describing evolution from an impact to the next impact, is described. Displacement of…
Hyperbolic space is a geometry that is known to be well-suited for representation learning of data with an underlying hierarchical structure. In this paper, we present a novel hyperbolic distribution called \textit{pseudo-hyperbolic…
Stable dynamical systems are a flexible tool to plan robotic motions in real-time. In the robotic literature, dynamical system motions are typically planned without considering possible limitations in the robot's workspace. This work…
This paper introduces a method of navigation in a large family of tilings of the hyperbolic plane and looks at the question of possible applications in the light of the few ones which were already obtained.
We propose a numerical method to solve general hyperbolic systems in any space dimension using forward Euler time stepping and continuous finite elements on non-uniform grids. The properties of the method are based on the introduction of an…
It is difficult for the common sense to admit that an object dropped from the top of the mast of a ship moving at a constant velocity falls down at the bottom of the mast because it keeps inside the horizontal movement of the ship. This…
Present bias, the tendency to overvalue immediate rewards while undervaluing future ones, is a well-known barrier to achieving long-term goals. As artificial intelligence and behavioral economics increasingly focus on this phenomenon, the…