Let R be an associative ring with unity. An element a in R is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von Neumann) element in R. If every element of R is r-clean, then R is called an r-clean ring. In this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. Further we prove that if 0 and 1 are the only idempotents...

One-loop off-shell contributions to the three-gluon vertex are calculated, in arbitrary covariant gauge and in arbitrary space-time dimension, including quark-loop contributions (with massless quarks). It is shown how one can get the results for all on-shell limits of interest directly from the general off-shell expression. The corresponding general expressions for the one-loop ghost-gluon vert...

Content Analysis of Elementary School Textbooks in Terms of Covering Renewable Energy Sources     E. Saalehi Omraan, Ph.D.* M. Aabedini Beltork, Ph.D.** G. Mehralitabaar Firoozjaa’i***   The world is facing an energy crisis brought about by the ever increasing consumption of fossil fuels that leads to pollution and health problems. The renewable clean energies must b...

let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...

let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...

How much should governments subsidize the development of new clean technologies? We use patent citation data to investigate the relative intensity of knowledge spillovers in clean and dirty technologies in four technological fields: energy production, automobiles, fuel and lighting. We find that clean patents receive on average 43% more citations than dirty patents. Clean patents are also cited...

The main features of the lazy functional language Concurrent Clean and of its semantics based on Term Graph Rewriting are presented. 1 History The pure, lazy functional language Concurrent Clean (version 1.0) is a major upgrade of the previous release (0.84b) of Clean ((3,10,11]). Clean was originally designed as an experimental intermediate language and deliberately kept syntactically as poor ...

The growing concern for global warming caused by the increased atmospheric concentration of carbon dioxide (CO2) has a significant effect on environmental and energy policies and economic activities, due to the ever-increasing use of fossil fuels such as coal, oil and natural gas throughout the world. A variety of complexities and uncertainties exist in CO2-emission-related processes and variou...