Related papers: On the Velocity Tensors
In a coherent category, the posets of subobjects have very strong properties. We emphasize the validity of these properties, in general categories, for well-behaved classes of subobjects. As an example of application, we investigate the…
The fundamental equations of relativistic dynamics are derived from a thought experiment and from the transformation of relativistic velocity avoiding collisions and conservation laws of momentum and energy.
Covariant forms are given to a gauge theory of massive tensor field. This is accomplished by introducing another auxiliary field of scalar type to the system composed of a symmetric tensor field and an auxiliary field of vector type. The…
Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the {\it velocity-field} plays the central role. The matter (constituent…
Recurrent Neural Network, Long Short-Term Memory, and Transformer have made great progress in predicting the trajectories of moving objects. Although the trajectory element with the surrounding scene features has been merged to improve…
In this note, we provide a important considerations of a familiar topic: the gradient of a vector field. The gradient of a vector field is a common quantity represented in continuum mechanics. However, even for Cartesian coordinate systems,…
In this paper, we introduce a class of variational inequalities, where the involved function is the sum of an arbitrary given vector and a homogeneous polynomial defined by a tensor; and we call it the tensor variational inequality (TVI).…
We clarify the relation among canonical, metric and Belinfante's energy-momentum tensors for general tensor field theories. For any tensor field T, we define a new tensor field $\til {\bm T}$, in terms of which the Belinfante tensor is…
A compact expression of fourth-order statistical moments of the velocity gradient tensor in homogeneous, isotropic, incompressible turbulence is obtained as a function of its invariants and of generic components of the velocity gradient.…
The aim of the current paper is to study the multiscalar-tensor theories of gravity without derivative couplings. We construct a few basic objects that are invariant under a Weyl rescaling of the metric and transform covariantly when the…
A new class of modified theory of gravity is introduced where the volume form becomes dynamical. This approach is motivated by unimodular gravity and can also be related to Brans-Dicke theory. On the level of the action, the only change…
The displacement and deviation vectors in spaces (manifolds), the tangent bundle of which is endowed with a transport along paths, are introduced. In case these spaces are equipped with a linear connection, the deviation equations (between…
Theories proposing a varying speed of light have recently been widely promoted under the claim that they offer an alternative way of solving the standard cosmological problems. Recent observational hints that the fine structure constant may…
The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.
A new concept of the constitution of Nature is proposed. The constructed submicroscopic quantum mechanics is deterministic and is characterised by elementary excitations of the space net that is treated as the tessellation of balls, or…
Acceleration is a fundamental concept in physics which is taught in mechanics at all levels. Here, we discuss some challenges in teaching this concept effectively when the path along which the object is moving has a curvature and…
A natural two-metric formalism, generated by the world function of the space-time, is used. This circumstance admits one to localize the relative gravitational field, which is described by a tensor.
We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures…
We present some generalizations, and novel properties, of the Bel-Robinson tensor, in the context of constructing local invariants in D=11 supergravity.
It turns out that the standard application of the four-vector SR formalism does not include the concept of relative velocity. Only the absolute velocity is described by the four-vector, and even the Lorentz transformation parameters is…