Permutations avoiding 4321 and 3241 have an algebraic generating function

We show that permutations avoiding both of the (classical) patterns 4321 and 3241 have the algebraic generating function conjectured by Vladimir Kruchinin.Comment: 12 pages, 6 figure

A Definitive Optical Detection of a Supercluster at z = 0.91

We present the results from a multi-band optical imaging program which has definitively confirmed the existence of a supercluster at z = 0.91. Two massive clusters of galaxies, CL1604+4304 at z = 0.897 and CL1604+4321 at z = 0.924, were originally observed in the high-redshift cluster survey of Oke, Postman & Lubin (1998). They are separated by 4300 km/s in radial velocity and 17 arcminutes on the plane of the sky. Their physical and redshift proximity suggested a promising supercluster candidate. Deep BRi imaging of the region between the two clusters indicates a large population of red galaxies. This population forms a tight, red sequence in the color--magnitude diagram at (R-i) = 1.4. The characteristic color is identical to that of the spectroscopically-confirmed early-type galaxies in the two member clusters. The red galaxies are spread throughout the 5 Mpc region between CL1604+4304 and CL1604+4321. Their spatial distribution delineates the entire large scale structure with high concentrations at the cluster centers. In addition, we detect a significant overdensity of red galaxies directly between CL1604+4304 and CL1604+4321 which is the signature of a third, rich cluster associated with this system. The strong sequence of red galaxies and their spatial distribution clearly indicate that we have discovered a supercluster at z = 0.91.Comment: Accepted for publication in Astrophysical Journal Letters. 13 pages, including 5 figure

How explicit are the barriers to failure in safety arguments?

Safety cases embody arguments that demonstrate how safety properties of a system are upheld. Such cases implicitly document the barriers that must exist between hazards and vulnerable components of a system. For safety certification, it is the analysis of these barriers that provide confidence in the safety of the system. The explicit representation of hazard barriers can provide additional insight for the design and evaluation of system safety. They can be identified in a hazard analysis to allow analysts to reflect on particular design choices. Barrier existence in a live system can be mapped to abstract barrier representations to provide both verification of barrier existence and a basis for quantitative measures between the predicted barrier behaviour and performance of the actual barrier. This paper explores the first stage of this process, the binding between explicit mitigation arguments in hazard analysis and the barrier concept. Examples from the domains of computer-assisted detection in mammography and free route airspace feasibility are examined and the implications for system certification are considered

Tax Revenue Stability of Replacing the Property Tax with a Sales Tax - Brief

This policy brief discusses the implications for tax revenue stability of proposals that would replace the property tax with an increased sales tax. FRC Brief 16

Albuquerque Evening Citizen, 06-29-1906

https://digitalrepository.unm.edu/abq_citizen_news/4321/thumbnail.jp

Inside AICPA, November 21, 1994

https://egrove.olemiss.edu/aicpa_news/4321/thumbnail.jp