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The article is devoted to linear quasigroups and some of their generalizations. In the first part main definitions and notions of the theory of quasigroups are given. In the second part some elementary properties of linear quasigroups and…
1 Generalities 2 Empirical diagnostics based on emission lines 3 Photoionization modelling 4 Pending questions 5 Appendix: Lists of useful lines and how to deal with them
In this lecture the basic concepts of electromagnetic waves in accelerating structures are discussed. After a short introduction on the propagation of electromagnetic waves and on the concept of travelling wave and standing wave structures,…
The definitions and some basic properties of the linear transports along paths in vector bundles and the normal frames for them are recalled. The formalism is specified on line bundles and applied to a geometrical description of the…
We give an elementary introduction to the structure of supergravity theories. This leads to a table with an overview of supergravity and supersymmetry theories in dimensions 4 to 11. The basic steps in constructing supergravity theories are…
Electromagnetic (EM) composites have stimulated tremendous fundamental and practical interests owing to their flexible electromagnetic properties and extensive potential engineering applications. Hence, it is necessary to systematically…
The present understanding of nuclear electromagnetic properties including electromagnetic moments, form factors and transitions in nuclei with A $\le$ 10 is reviewed. Emphasis is on calculations based on nuclear Hamiltonians that include…
After a self-contained introduction to Lie algebra cohomology, we present some recent applications in mathematics and in physics. Contents: 1. Preliminaries: L_X, i_X, d 2. Elementary differential geometry on Lie groups 3. Lie algebra…
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…
In this scientific preface to the first issue of International Journal of Geometric Methods in Modern Physics, we briefly survey some peculiarities of geometric techniques in quantum models.
We review basic computational techniques for simulations of various magnetic properties of solids. Several applications to compute magnetic anisotropy energy, spin wave spectra, magnetic susceptibilities and temperature dependent…
A complete geometric unification of gravity and electromagnetism is proposed by considering two aspects of torsion: its relation to spin established in Einstein--Cartan theory and the possible interpretation of the torsion trace as the…
A core level of basic information for physics is identified, based on an analysis of the characteristics of the parameters space, time, mass and charge. At this level, it is found that certain symmetries operate, which can be used to…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
We give a self-contained exposition of some mathematical aspects of the Mueller-Stokes formalism. In the first part we review some basic notions of linear algebra and establish a proper notation. In the second part we introduce the…
We present a concise definition of an electromagnetic curve on a Riemannian manifold and illustrate the explicit case of the motion of a charged particle on the unit sphere under the influence of a uniform magnetic field.
We briefly sketch the noncommutative geometry approach to the Standard Model, with attention to what can be inferred about particle masses.
This article shows the relations between the electricity, magnetism, gravity and mechanics by presenting an existing hidden structure in the Maxwell equations. This hidden structure allows to discover the classical physic from a new point…