相关论文: A vectorlike representation of multilayers

It is proved that the set of geodesic circles in two dimensions may be given a variational description and the explicit form of it is presented. In the limit case of the Euclidean geometry a certain claim of uniqueness of such description…

In this paper we construct a geometric analogue of the Weil representation over a finite field. Our construction is principally invariant, not choosing any specific realization. This eliminates most of the unpleasant formulas that appear in…

We show that the optical properties of an oblique layered system with two kinds of isotropic materials can be described using the concept of transformation media as long as the thickness of the layers is much smaller than the wavelength.…

It is known that quaternions represent rotations in 3D Euclidean and Minkowski spaces. However, product by a quaternion gives rotation in two independent planes at once and to obtain single-plane rotations one has to apply by half-angle…

The paper presents a generalized Weierstrass representation for pseudospherical surfaces in terms of 3x3 matrices, using moving frames and loop group decompositions. The construction of all such surfaces, starting from a given…

We revisit the gravitational lensing phenomenon using a new visualization technique. It consists in projecting the observers sky into the source plane, what gives rise to a folded and stretched surface. This provides a clear graphical tool…

Given a compact Kaehler manifold, we consider the complement U of a divisor with normal crossings. We study the variety of unitary representations of the fundamental group of U with certain restrictions related to the divisor. We show that…

In classical differential geometry, a central question has been whether abstract surfaces with given geometric features can be realized as surfaces in Euclidean space. Inspired by the rich theory of embedded triply periodic minimal…

Starting from fundamental multiple scattering theory it is shown that negative refraction indices are feasible for matter waves passing a well-defined ensemble of scatterers. A simple approach to this topic is presented and explicit…

We determine the range of thicknesses and refractive indices for which omnidirectional reflection from quasiperiodic multilayers occurs. By resorting to the notion of area under the transmittance curve, we assess in a systematic way the…

We study the lightlike foliations that appear on Lorentzian manifolds with weakly irreducible not irreducible holonomy algebra. We give global structure equations for the foliation that generalize the Gauss and Weingarten equations for one…

We observe a property of orthogonality of the Mellin-Barnes transformation of the triangle one-loop diagrams, which follows from our previous papers [JHEP {\bf 0808} (2008) 106, JHEP {\bf 1003} (2010) 051, JMP {\bf 51} (2010) 052304]. In…

Multipole expansion of an incident radiation field - that is, representation of the fields as sums of vector spherical wavefunctions - is essential for theoretical light scattering methods such as the T-matrix method and generalised…

A periodic layer of resonant scatterers is considered in the dipolar approximation. An asymptotic expression for the field diffracted is given in terms of an impedance operator. It is shown that surface Bloch modes appear as a collective…

For any knot, the following are equivalent. (1) The infinite cyclic cover has uncountably many finite covers; (2) there exists a finite-image representation of the knot group for which the twisted Alexander polynomial vanishes; (3) the knot…

Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized "step" represents a distinct topological state. Here, we seek a counterpart for "visualizing" quantum geometry, which is a broader…

We present a unitary approach to the construction of representations and intertwining operators. We apply it to the $C^*$-algebras, groups, Gabor type unitary systems and wavelets. We give an application of our method to the theory of…

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency…

Two-, three- and four-dimensional representations of Penrose tilings of the plane are described. The vertices that occur in these representations lie on lattices. Symmetries and methods of visualizing these representations are discussed.…

The study of quadric surfaces of revolution is a cornerstone of classical Euclidean geometry, but its extension to the three-dimensional sphere $\mathbb{S}^3$ has not been sufficiently explored. This article addresses this important gap by…