In this paper, we extend the classical Lie symmetry analysis from partial differential equations to integro-differential equations with functional derivatives. We continue the work of Oberlack and Wacławczyk (2006, Arch. Mech. 58, 597), (2013, J. Math. Phys. 54, 072901), where the extended Lie symmetry analysis is performed in the Fourier space. Here, we introduce a method to perform the extend...

For the H1 and ZEUS Collaborations Recent results of real and virtual photon structure from the H1 and ZEUS collaborations are discussed. Jet cross-sections in photoproduction processes provide new constraints on the real photon parton densities. Measurements of dijet cross-sections in deep-inelastic scattering show clear evidence for a resolved component to the virtual photon which is suppress...

On behalf of the H1 Collaboration. ABSTRACT A review of recent jet measurements of the photon structure from the H1 experiment at HERA is presented. A manifestation of the photon structure in single-jet and di-jet cross sections is shown. From di-jet cross sections the effective parton distribution function is extracted and its dependence on the scale as well as the photon virtuality is discussed.

Within the hard pomeron approach it is shown that the triple pomeron interaction gives no contribution to the cross-section for a projectile with large enough virtuality g 2 ln Q 2 ∼ 1. For small virtualities g 2 ln Q 2 << 1 its contribution is essential.

Continuum modeling of many physical systems typically assumes that the spatial extent of an atom is small compared to the quantities of interest and can therefore be neglected. We show that this is valid only asymptotically. For many applications of practical interest, the spatial extent of a discrete atom cannot be neglected. We have developed a model for the description of epitaxial growth ba...

Navigating a Changing Continuum of Care With Heart

A simple closed curve is the simplest example of a compact, nondegenerate, homogeneous continuum. If a bounded, nondegenerate, homogeneous plane continuum has any local connectedness property, even of the weakest sort, it is known to be a simple closed curve [l, 2, 3].1 The recent discovery of a bounded, nondegenerate, homogenous plane continuum which does not separate the plane [4, 5] has give...

The objective of this paper is to show that the structure of the spatiotemporal continuum has important implications in practical stochastic hydrology (e.g., geostatistical analysis of hydrologic sites) and is not merely an abstract mathematical concept. We propose that the concept of physical geometry as a spatiotemporal continuum with properties that are empirically de®ned is important in hyd...

on behalf of the ZEUS collaboration We present results from recent investigations of diffractive vector meson production using the ZEUS detector at HERA. These consist of measurements of ρ 0 production in the region of photon virtuality 0.25 < Q 2 < 0.85 GeV 2 , of ρ 0 , φ, and J/ψ production for values of the momentum transfer to the proton 0.3 < |t| < 4.0 GeV 2 , and of elastic J/ψ production...