Related papers: Unit Vectors for Similar Oblate Spheroidal Coordin…
Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is…
We propose a new embedding method for a single vector and for a pair of vectors. This embedding method enables: a) efficient classification and regression of functions of single vectors; b) efficient approximation of distance functions; and…
Retrieval of classical behaviour in quantum cosmology is usually discussed in the framework of minisuperspace models in the presence of scalar fields together with the inhomogeneous modes of gravitational or scalar fields. In this work we…
Symmetry is present in many tasks in computer vision, where the same class of objects can appear transformed, e.g. rotated due to different camera orientations, or scaled due to perspective. The knowledge of such symmetries in data coupled…
Commuting and noncommuting space-time coordinates in a class of deformed special relativity theories are investigated. Their momentum space representation, transformation behaviour, space-time algebra, invariants and the corresponding field…
(This short article is a continuation of a longer, review work, in the same volume of Proceedings, by Ashtekar, Marolf and Mour\~ao [gr-qc/9403042]. All the details and other results are to be found in joint papers of the author with Abhay…
Phase transitions with spontaneous symmetry breaking and vector order parameter are considered in multidimensional theory of general relativity. Covariant equations, describing the gravitational properties of topological defects, are…
A special approach to examine spinor structure of 3-space is proposed. It is based on the use of the concept of a spatial spinor defined through taking the square root of a real-valued 3-vector. Two sorts of spatial spinor according to…
To represent real $m$-dimensional vectors, a positional vector system given by a non-singular matrix $M \in \mathbb{Z}^{m \times m}$ and a digit set $\mathcal{D} \subset \mathbb{Z}^m$ is used. If $m = 1$, the system coincides with the well…
We study $N=2$ supersymmetric $SU(2)/U(1)$ and $SL(2,R)/U(1)$ gauged Wess-Zumino-Witten models. It is shown that the vector gauged model is transformed to the axial gauged model by a mirror transformation. Therefore the vector gauged model…
Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave…
We consider planar noncommutative theories such that the coordinates verify a space-dependent commutation relation. We show that, in some special cases, new coordinates may be introduced that have a constant commutator, and as a consequence…
Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement.
The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry…
Convex or concave sequences of $n$ positive terms, viewed as vectors in $n$-space, constitute convex cones with $2n-2$ and $n$ extreme rays, respectively. Explicit description is given of vectors spanning these extreme rays, as well as of…
The BSSN and standard gauge equations are written in covariant form with respect to spatial coordinate transformations. The BSSN variables are defined as tensors with no density weights. This allows us to evolve a given set of initial data…
Meta-conformal transformations are constructed as dynamical symmetries of the linear transport equation in $d$ spatial dimensions. In one and two dimensions, the associated Lie algebras are infinite-dimensional and isomorphic to the direct…
In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.
The covariant derivative capable of differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent quantum state is introduced. It is proved to be covariant under gauge and coordinate…
A transformation optics approach was used to derive a general method for designing electromagnetic devices able to manipulate the wave vectors in the specific manner required by the functionality of the device. While the wave paths inside…