Related papers: Frames of Reference and Some of its Applications
Frames play significant role in various areas of science and engineering. In this paper, we introduce the concepts of frames for $End_{\mathcal{A}}^{\ast}(\mathcal{H, K})$ and their generalizations. Moreover, we obtain some new results for…
Reference systems and frames are crucial for high precision absolute astrometric work, and their foundations must be well-defined. The current frame, the International Celestial Reference Frame, will be discussed: its history, the use of…
Multimodal referring segmentation aims to segment target objects in visual scenes, such as images, videos, and 3D scenes, based on referring expressions in text or audio format. This task plays a crucial role in practical applications…
We develop a transitional geometry, that is, a family of geometries of constant curvatures which makes a continuous connec-tion between the hyperbolic, Euclidean and spherical geometries. In this transitional setting, several geometric…
As shown by the development of Special Relativity the simultaneity concept should be related to that of reference frame. Poincare' proposed to define the simultaneity of two events by means of light signals following what is nowadays known…
We give a convenient representation for any map that is covariant with respect to an irreducible representation of SU(2), and use this representation to analyze the evolution of a quantum directional reference frame when it is exploited as…
It is mandatory to know how to operationally define and translate a reference frame into mathematics, in order that a physical interpretation of theory calculations in terms of observational data is possible. The situation is particularly…
The vorticity of a congruence is often considered to be the rate of rotation for the precession of a gyroscope moving along a world-line belonging to that congruence. Our aim here was to determine the evolution equation for the angular…
The high accuracy of modern space astrometry requires the use of General Relativity to model the propagation of stellar light through the gravitational field encountered from a source to a given observer inside the Solar System. In this…
We develop a rigidity theory for bar-joint frameworks in Euclidean $d$-space in which specified classes of edges are allowed to change length in a coordinated fashion that requires differences of lengths to be preserved within each class.…
Classical non-relativistic mechanics in a general setting of time-dependent transformations and reference frame changes is formulated in the terms of fibre bundles over the time-axis R. Connections on fibre bundles are the main ingredient…
Lenses, optics and dependent lenses (or equivalently morphisms of containers, or equivalently natural transformations of polynomial functors) are all widely used in applied category theory as models of bidirectional processes. From the…
As a subject, an observer is fundamentally at rest in a reference frame, and this being at rest allows for measuring the motion of physical objects. Exploring the experience of centrifugal force brings to the fore the natural inclination to…
We give an elementary proof of the fact that any orientable 3-manifold admits a framing (i.e. is parallelizable) and any non-orientable 3-manifold admits a projective framing. The proof uses only basic facts about immersions of surfaces in…
This paper addresses the natural question: ``How should frames be compared?'' We answer this question by quantifying the overcompleteness of all frames with the same index set. We introduce the concept of a frame measure function: a…
From a communications perspective, a frame defines the packaging of the language used in such a way as to encourage certain interpretations and to discourage others. For example, a news article can frame immigration as either a boost or a…
Scalable frames are frames with the property that the frame vectors can be rescaled resulting in tight frames. However, if a frame is not scalable, one has to aim for an approximate procedure. For this, in this paper we introduce three…
Embedding fields provide a way of coupling a background structure to a theory while preserving diffeomorphism-invariance. Examples of such background structures include embedded submanifolds, such as branes; boundaries of local subregions,…
We focus on three distinct lines of recent developments: edge modes and boundary charges in gravitational physics, relational dynamics in classical and quantum gravity, and quantum reference frames. We argue that these research directions…
Structure from Motion (SfM) refers to the problem of recovering both structure (i.e., 3D coordinates of points in the scene) and motion (i.e., camera matrices) starting from point correspondences in multiple images. It has attracted…