相关论文: Curves and The Photon

We give a geometric approach to the relation between the irreducible components of the characteristic varieties of local systems on a plane curve arrangement complement and the associated pencils of plane curves discovered recently by M.…

Near a singular point of a surface or a curve, geometric invariants diverge in general, and the orders of diverge, in particular the boundedness about these invariants represent geometry of the surface and the curve. In this paper, we study…

It was first pointed out by Weil that we can use classical invariant theory to compute the Jacobian of a genus one curve. The invariants required for curves of degree n = 2,3,4 were already known to the nineteenth centuary invariant…

For description of the quantum dynamics on a curved group manifold the path integrals in a space of the group parameters is offered. The formalism is illustrated by the $H$-atom problem.

We consider a class of "harmonic variations" for nonsingular curves, obtained as asymptotic degenerations along bitangents. On a geometric level, we obtain an attractive relationship between the class and the genus of $C$. The distribution…

The main aim of this paper is to investigate the nature of invariancy of rectifying curve under conformal transformation and obtain a sufficient condition for which such a curve remains conformally invariant. It is shown that the normal…

Classification of curves up to affine transformation in a finite dimensional space was studied by some different methods. In this paper, we achieve the exact formulas of affine invariants via the equivalence problem and in the view of…

We explore several variations on the recently discovered phenomena of murmurations for elliptic curves and modular forms.

The possibility of reversion of the inequality in the Second Main Theorem of Cartan in the theory of holomorphic curves in projective space is discussed. A new version of this theorem is proved that becomes an asymptotic equality for a…

In this Chapter, we give a brief review of the state of the art of theoretical and experimental studies of quantum fluids of light. Such systems consist of ensembles of photons that acquire a finite mass from spatial confinement or…

We establish sharp lower and upper bounds for the number of integral points near dilations of a space curve with nowhere vanishing torsion.

We consider the connection of functional decompositions of rational functions over the real and complex numbers, and a question about curves on a Riemann sphere which are invariant under a rational function.

We define the type of a plane curve as the initial degree of the corresponding Bourbaki ideal. Then we show that this invariant behaves well with respect to the union of curves. Curves of type $0$ are precisely the free curves, while curves…

The increasing precision of the measurements on the proton structure and an improved treatment of the correlated systematic experimental errors constitute a major step forward in our understanding of the flavour decomposition of the proton…

We give effective upper bounds for the number of purely inseparable points on non isotrivial curves over function fields of positive characteristic and of transcendence degree one. These bounds depend on the genus of the curve, the genus of…

In this paper, we investigate the geometric invariant properties of a normal curve on a smooth immersed surface under conformal transformation. We obtain an invariant-sufficient condition for the conformal image of a normal curve. We also…

Photon statistics is one of the key properties of the photon state for the study of quantum coherence and quantum information techniques. Here, we discuss the photon indistinguishability induced bunching effect which can significantly…

In this work, we give some new characterizations for inclined curves and slant helices in n-dimensional Euclidean space E^{n}. Morever, we consider the pre-characterizations about inclined curves and slant helices and reconfigure them.

The structure of the photon is probed in photon-photon interactions at LEP and in photon-proton interactions at HERA.

Many classical results in algebraic geometry arise from investigating some extremal behaviors that appear among projective varieties not lying on any hypersurface of fixed degree. We study two numerical invariants attached to such…