Novel Symmetries in Christ-Lee Model

We demonstrate that the gauge-fixed Lagrangian of the Christ-Lee model respects four fermionic symmetries, namely; (anti-)BRST symmetries, (anti-)co-BRST symmetries within the framework of BRST formalism. The appropriate anticommutators amongst the fermionic symmetries lead to a unique bosonic symmetry. It turns out that the algebra obeyed by the symmetry transformations (and their corresponding conserved charges) is reminiscent of the algebra satisfied by the de Rham cohomological operators of differential geometry. We also provide the physical realizations of the cohomological operators in terms of the symmetry properties. Thus, the present model provides a simple model for the Hodge theory.Comment: LaTeX File, 12 Pages, Text Modified, Typos Fixed, Refences Added, No Figure

Analysis of the Web Graph Aggregated by Host and Pay-Level Domain

In this paper the web is analyzed as a graph aggregated by host and pay-level domain (PLD). The web graph datasets, publicly available, have been released by the Common Crawl Foundation and are based on a web crawl performed during the period May-June-July 2017. The host graph has $\sim$1.3 billion nodes and $\sim$5.3 billion arcs. The PLD graph has $\sim$91 million nodes and $\sim$1.1 billion arcs. We study the distributions of degree and sizes of strongly/weakly connected components (SCC/WCC) focusing on power laws detection using statistical methods. The statistical plausibility of the power law model is compared with that of several alternative distributions. While there is no evidence of power law tails on host level, they emerge on PLD aggregation for indegree, SCC and WCC size distributions. Finally, we analyze distance-related features by studying the cumulative distributions of the shortest path lengths, and give an estimation of the diameters of the graphs

The Livelihoods concept integrated into the DPSIR analytical tool

DPSIR stands for Drivers, Pressures, State, Impact, and Responses. DPSIR is an analytical tool used to understand the causes of environmental change and the subsequent socio-economic impacts in order to formulate the most adequate responses (R). It is a linear cause-effect model. It assumes natural and human-made factors of change (Drivers) that cause Pressures, which in turn lead to a change in the State of the environment. Changes in State lead to socio-economic Impacts and this triggers Reponses, either by governments or other players. The DPSIR analytical tool was originally proposed by the European Environmental Agency and adopted by many national and European institutions, EEA, and Eurostat among other

User's guide for the computer code COLTS for calculating the coupled laminar and turbulent flow over a Jovian entry probe

A user's guide for a computer code 'COLTS' (Coupled Laminar and Turbulent Solutions) is provided which calculates the laminar and turbulent hypersonic flows with radiation and coupled ablation injection past a Jovian entry probe. Time-dependent viscous-shock-layer equations are used to describe the flow field. These equations are solved by an explicit, two-step, time-asymptotic finite-difference method. Eddy viscosity in the turbulent flow is approximated by a two-layer model. In all, 19 chemical species are used to describe the injection of carbon-phenolic ablator in the hydrogen-helium gas mixture. The equilibrium composition of the mixture is determined by a free-energy minimization technique. A detailed frequency dependence of the absorption coefficient for various species is considered to obtain the radiative flux. The code is written for a CDC-CYBER-203 computer and is capable of providing solutions for ablated probe shapes also