Related papers: A vectorlike representation of multilayers

We introduce a higher dimensional quasiregular map analogous to the trigonometric functions and we use the dynamics of this map to define, for d>1, a partition of d-dimensional Euclidean space into curves tending to infinity such that two…

We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…

It turns out that complex geodesics in Teichm\"uller spaces with respect to their invariant metrics are intrinsically connected with variational calculus for univalent functions. We describe this connection and show how geometric features…

We use some fundamental ideas from complex analysis to create symmetric images and animations. Using a domain coloring algorithm, we generate mappings to the entire complex plane or the hyperbolic upper half-plane. The resulting designs can…

We study the tomography of propagators for spin systems in the context of finite-dimensional Wigner representations, which completely characterize and visualize operators using shapes assembled from linear combinations of spherical…

We start developing a formalism which allows to construct supersymmetric theories systematically across space-time signatures. Our construction uses a complex form of the supersymmetry algebra, which is obtained by doubling the spinor…

We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for…

Wigner's "unreasonable effectiveness of mathematics" in physics can be understood as a reflection of a deep and unexpected unity between the fundamental structures of mathematics and of physics. Some of the history of evidence for this is…

Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will…

We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…

We present the extension of the Lagrangian loop gauge invariant representation in such a way to include matter fields. The partition function of lattice compact U(1)-Higgs model is expressed as a sum over closed as much as open surfaces. We…

We theoretically describe the optical computation of the divergence of a two-dimensional vector field, which is composed by the transverse electric field components of an incident light beam. The divergence is computed in reflection at…

We describe gravitational lensing by a gravitational wave, in the regime in which multiple images of a light source are created. We adapt the vector formalism employed for ordinary gravitational lenses to the case of a non-stationary…

We provide a one-to-one map between the spin correlations and certain three-dimensional shapes, analogous to the map between single spins and Bloch vectors, and demonstrate its utility. Much as one can reason geometrically about dynamics…

We provide a proof of the Alpern multi-tower theorem for Z^d actions. We reformulate the theorem as a problem of measurably tiling orbits of a Z^d action by a collection of rectangles whose corresponding sides have no non-trivial common…

A monoid structure on families of representations of a quiver is introduced by taking extensions of representations in families, i.e. subvarieties of the varieties of representations. The study of this monoid leads to interesting…

We present a brief overview of some key concepts in the theory of generalised complex manifolds. This new geometry interpolates, so to speak, between symplectic geometry and complex geometry. As such it provides an ideal framework to…

A group-theoretical approach to the construction of quasiperiodic tilings of a Euclidean plane, possessing five-fold symmetry, is applied. Of the infinitely many of variants of quasiperiodic partitions of the plane, possessing the dihedral…

In this paper, a generalization of the concept of electrical power for periodic current and voltage waveforms based on a new generalized complex geometric algebra (GCGA) is proposed. This powerful tool permits, in n-sinusoidal/nonlinear…

This article describes a natural piecewise Euclidean bi-simplicial cell structure for the space of $n$-element multisets in a fixed Euclidean rectangle. In particular, we highlight some connections with spaces of complex polynomials and…