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A concept of a rectangular diagram of a foliation in the three-sphere is introduced. It is shown that any co-orientable finite depth foliation in the complement of a link admits a presentation by a rectangular diagram compatible with the…
Random lasers are unique systems where lasing occurs due to repetitive scattering in a disordered nanostructure. Previous descriptions of random lasing are numerous, however a full time-dependent theory that describes the introduction of…
We give the classification of solvable and splitting Lie triple system and it turn that, up to isomorphism there exist 7 non isomorphic canonical Lie triple systems and 6 non isomorphic splitting canonical Lie triple systems and find the…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
There is evidence that the distribution of suspected cosmic ray sources are associated with the spiral arm structure of galaxies. It is yet not clearly understood what effect such a cosmic ray source distribution has on the particle…
We consider a system of partial differential equations, of interest to plasma physics, and provide all its Lie point symmetries, with their respective invariant solutions. We also discuss some of its conditional and partial symmetries. We…
It is the purpose of this paper to give a characterisation of circular light rays in a plasma on an axially symmetric and stationary spacetime. We restrict to the case of an unmagnetised, pressure-free electron-ion plasma and we assume that…
We consider Lie and Strang splitting for the time integration of constrained partial differential equations with a nonlinear reaction term. Since such systems are known to be sensitive with respect to perturbations, the splitting procedure…
The dynamics of non-polar diatomic molecules interacting with a far-detuned narrow-band laser field, that only may drive rotational transitions, is studied. The rotation of the molecule is considered both classically and quantum…
This contribution describes relationship between fractions, projective representation, duality, linear algebra and geometry. Many problems lead to a system of linear equations. This paper presents equivalence of the Cross-product operation…
While modern optics is largely a physics of harmonic oscillators and two-by-two matrices, it is possible to learn about some hidden properties of the two-by-two matrix from optical systems. Since two-by-two matrices can be divided into…
A scalar integer partition problem asks for a number of nonnegative integer solutions to a linear Diophantine equation with integer positive coefficients. The manuscript discusses an algorithm of derivation of linear relations involving the…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
In this paper we consider some results on intersection between rays and a given family of convex, compact sets. These results are similar to the center point theorem, and Tverberg's theorem on partitions of a point set.
We compute the distribution of the decay rates (also referred to as residues) of the eigenstates of a disordered slab from a numerical model. From the results of the numerical simulations, we are able to find simple analytical formulae that…
We experimentally investigate the Bragg reflection of light at one-dimensionally ordered atomic structures by using cold atoms trapped in a laser standing wave. By a fine tuning of the periodicity, we reach the regime of multiple reflection…
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…
The dynamics of electrons in counter-propagating, circularly polarized laser beams are shown to exhibit attractors whose ability to trap particles depends on the ratio of the beam intensities and a single parameter describing radiation…
This work is a continuation of a previous publication {Thieberger and Spiegel,astro-ph/0204485} concerning the use of two dimensional catalogues in unraveling the large scale distribution of galaxies. Since the data in two-dimensional…
We model weak gravitational lensing of light by large-scale structure using ray tracing through N-body simulations. The method is described with particular attention paid to numerical convergence. We investigate some of the key…