Related papers: Revealing how different spinors can be: the Lounes…
In this paper, we analyze some properties regarding singular spinors and how they are connected. The method employed here consists of mapping the spinorial structure and also the adjoint structure. Such a mathematical device is useful to…
We propose and develop a new method to classify orbits of the spin group ${\rm Spin}(2d)$ in the space of its semi-spinors. The idea is to consider spinors as being built as a linear combination of their pure constituents, imposing the…
Having previously identified the photon field with a (special) linear Complex, we give a brief account on identifications and reasoning so far. Then, in order to include spinorial degrees of freedom into the Lagrangean description, we…
As well as several different kinds of periodically ordered ferroic phases, there are now recognized several different examples of ferroic glassiness, although not always described as such and in material fields of study that have mostly…
The high prevalence of spinal stenosis results in a large volume of MRI imaging, yet interpretation can be time-consuming with high inter-reader variability even among the most specialized radiologists. In this paper, we develop an…
One of the possible variants of the classification of trigonometric interpolation splines is considered, depending on the chosen convergence factors, the distribution of signs of the basis functions and the interpolation factors. The…
In this survey we discuss some combinatorial aspects of higher cluster categories.
We define spinors for pairs of tangent disks in the Euclidean plane and prove a number of theorems, one of which may be interpreted as a "square root of Descartes Theorem". In any Apollonian disk packing, spinors form a network. In the…
The article consists of the Russian and English variants of Ph.D. Thesis in which the answers is given on the following questions: 1. how to construct the spinor formalism for n=6; 2. how to construct the spinor formalism for n=8; 3. how to…
It is shown how one can apply the classification of the holonomy algebras of Lorentzian manifolds to solve some problems. In particular, a new proof to the classification of Lorentzian manifolds with recurrent curvature tensor is given; the…
Quaternionic and octonionic realizations of Clifford algebras and spinors are classified and explicitly constructed in terms of recursive formulas. The most general free dynamics in arbitrary signature space-times for both quaternionic and…
Segmentation and labeling of vertebrae in MRI images of the spine are critical for the diagnosis of illnesses and abnormalities. These steps are indispensable as MRI technology provides detailed information about the tissue structure of the…
Spinors are mathematical objects susceptible to the spacetime characteristics upon which they are defined. Not all spacetimes admit spinor structure; when it does, it may have more than one spinor structure, depending on topological…
Motivated by the relationship between orthogonal complex structures and spure spinors, we define twisted partially pure spinors in order to characterize spinorially subspaces of Euclidean space endowed with a complex structure.
We present here definitions and constructions basic for the theory of monoidal and tensor categories. We provide references to the original sources, whenever possible. Group-theoretical categories are used as examples
This is an expository paper which presents the holomorphic classification of rational complex surfaces from a simple and intuitive point of view, which is not found in the literature. Our approach is to compare this classification with the…
This present work is based on our previous publications, which all together trigger our "Killing spinor programme". Other significant spinor fields are injected into the scheme and the intricate relations between them and their bilinears…
We show that differential calculus (in its usual form, or in the general form of topological differential calculus) can be fully imdedded into a functor category (functors from a small category of anchord tangent algebras to anchored sets).…
The relationship between spinors and Clifford (or geometric) algebra has long been studied, but little consistency may be found between the various approaches. However, when spinors are defined to be elements of the even subalgebra of some…
In this paper, we explore the field propagator with a structure that is general enough to encompass both the case of newly-defined mass-dimension $1$ fermions and spin-$1/2$ bosons. The method we employ is to define a map between spinors of…