Related papers: A New Kind of Uniformly Accelerated Reference Fram…
Frames normal for linear connections in vector bundles are defined and studied. In particular, such frames exist at every fixed point and/or along injective path. Inertial frames for gauge fields are introduced and on this ground the…
The non-relativistic version of the multi-temporal quantization scheme of relativistic particles in a family of non-inertial frames (see hep-th/0502194) is defined. At the classical level the description of a family of non-rigid…
Rindler's acceleration-induced partitioning of spacetime leads to a nature-given interferometer. It accomodates quantum mechanical and wave mechanical processes in spacetime which in (Euclidean) optics correspond to wave processes in a…
Vertical excursion fixed-field alternating gradient accelerators can be designed with tunes that are invariant with respect to momentum and trajectories that are scaled images of each other displaced only in the vertical direction. This is…
This paper investigates the properties of continuous frames, with a particular focus on phase retrieval and norm retrieval in the context of Hilbert spaces. We introduce the concept of continuous near-Riesz bases and prove their invariance…
Understanding transverse coupling dynamics is crucial for beam physics, accelerator design, and operations. Currently, most accelerators are designed for uncoupled beams, and coupling is treated as an error or perturbation. Many transverse…
In a stationary axisymmetric spacetime, the angular velocity of a stationary observer that Fermi-Walker transports its acceleration vector is also the angular velocity that locally extremizes the magnitude of the acceleration of such an…
We examine the problem of motion of an oscillating mass object provided no external force is applied to it. Calculations directly lead to the conclusion that the body accelerates in each system of reference except for the rest reference…
We show that Minkowski single-particle states localized beyond the horizon modify the Unruh thermal distribution in an accelerated frame. This means that, contrary to classical predictions, accelerated observers can reveal particles emitted…
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…
Finite frame theory has become a powerful tool for many applications of mathematics. In this paper we introduce a new area of research in frame theory: Integer frames. These are frames having all integer coordinates with respect to a fixed…
An inhomogeneous fluid in accelerated motion is investigated. When the velocity field $v(x)$ is not constant, the geometry viewed by a static observer is curved, as if the observer were immersed in a gravitational field. A…
Lorentz Transformation is reinterpreted. It is shown that by admitting the existence of a frame of reference with synchronized clocks, we conclude that any other frame of reference that moves related to the first has desynchronized clocks.…
The visualisation of objects moving at relativistic speeds has been a popular topic of study since Special Relativity's inception. While the standard exposition of the theory describes certain shape-changing effects, such as the…
We study how an arbitrary Gaussian state of two localized wave packets, prepared in an inertial frame of reference, is described by a pair of uniformly accelerated observers. We explicitly compute the resulting state for arbitrarily chosen…
Motions with respect to one inertial (or ``map'') frame are often described in terms of the coordinate time/velocity pair (or ``kinematic'') of the map frame itself. Since not all observers experience time in the same way, other…
In this paper, a concurrent learning based adaptive observer is developed for a class of second-order linear time-invariant systems with uncertain system matrices. The developed technique yields an exponentially convergent state estimator…
We introduce a novel type of abnormal agents that proceed in the opposite direction of that defined for the normal agents. A new order parameter, $y$, is introduced to describe the characteristic of the system. Many interesting phenomenons…
In object tracking, outlier is one of primary factors which degrade performance of image-based tracking algorithms. In this respect, therefore, most of the existing methods simply discard detected outliers and pay little or no attention to…
A new object, called the velocity tensor, is introduced. It allows to formulate a generally covariant mechanics. Some properties of the velocity tensor are derived.