Related papers: Curves and The Photon
Chains are vector-valued signals sampling a curve. They are important to motion signal processing and to many scientific applications including location sensors. We propose a novel measure of smoothness for chains curves by generalizing the…
Controlling the photon statistics of light is paramount for quantum science and technologies. Recently, we demonstrated that transmitting resonant laser light past an ensemble of two-level emitters can result in a stream of single photons…
Topology is revolutionizing photonics, bringing with it new theoretical discoveries and a wealth of potential applications. This field was inspired by the discovery of topological insulators, in which interfacial electrons transport without…
This is a survey on recent results on counting of curves over finite fields. It reviews various results on the maximum number of points on a curve of genus g over a finite field of cardinality q, but the main emphasis is on results on the…
After years of experimental and theoretical efforts, direct photons become a strong and reliable tool to establish the basic characteristics of a hot and dense matter produced in heavy ion collisions. The recent direct photon measurements…
The ability to approach a physical phenomenon and grasp its major importance is a remarkable quality of understanding. This paper presents a rather elegant and novel way of looking at the resonance phenomenon, which among others shares a…
Structure of the space of photonic states is discussed in the context of a working hypothesis of existence of a preferred frame for photons. Two polarisation experiments are proposed to test the preferred frame scenario.
We study Gromov-Witten invariants on the blow-up of P^n at a point, which is probably the simplest example of a variety whose moduli spaces of stable maps do not have the expected dimension. It is shown that many of these invariants can be…
This paper examines the relationship between the knotting of an embedded surface in $\R^3$ and the knotting of its fold curves, formed by the singular set of projection to a plane. The first result shows that every surface, no matter how…
While quantum mechanics precludes the perfect knowledge of so-called "conjugate" variables, such as time and frequency, we discuss the importance of compromising to retain a fair knowledge of their combined values. In the case of light, we…
Invariant functions and metrics are studied on various classes of domains in $\Bbb C^n.$
In this paper, we focus on some characterizations for curves in the Galilean and Pseudo-Galilean space.
Within the Hamiltonian formulation of diffeomorphism invariant theories we address the problem of how to determine and how to reduce diffeomorphisms outside the identity component.
The relation of the Weierstrass semigroup with several invariants of a curve is studied. For Galois covers of curves with group $G$ we introduce a new filtration of the group decomposition subgroup of $G$. The relation to the ramification…
The kernel method is an essential tool for the study of generating series of walks in the quarter plane. This method involves equating to zero a certain polynomial, the kernel polynomial, and using properties of the curve, the kernel curve,…
It is shown that the description of light beams in terms of the corresponding photon quantum numbers elucidates the properties of these beams. In particular, this description shows that the helicity quantum number plays the fundamental…
We quantitatively investigate the non-classicality and non-locality of a whole new class of mixed disparate quantum and semiquantum photon sources at the quantum-classical boundary. The latter include photon added thermal and photon added…
The phenomenon of quantum number fractionalization is explained. The relevance of non-trivial phonon field topology is emphasized.
This article describes the mean curvature flow, some of the discoveries that have been made about it, and some unresolved questions.
Properties of the recently reported homogeneous Hilbert curves are deduced and reported. The nature of the affine transformations involved in the construction of the Hilbert curves is explored. The analytical representation of proper and…