A ring R is uniquely (nil) clean in case for any $a in R$ there exists a uniquely idempotent $ein R$ such that $a-e$ is invertible (nilpotent). Let $C =(A V W B)$ be the Morita Context ring. We determine conditions under which the rings $A,B$ are uniquely (nil) clean. Moreover we show that the center of a uniquely (nil) clean ring is uniquely (nil) clean.

Abstract Every year, hundreds of people go missing in the wilderness Saudi Arabia. There is an urgent need to examine modern geographic techniques for finding such people. Geographical information systems, example, play a crucial role search and rescue (WiSAR), not only mapping probability areas but also applying further analysis modeling methods reduce time effort guide life-saving task forces...

It is shown that a commutative reduced ring R is a Baer ring if and only if it is a CS-ring; if and only if every dense subset of Spec (R) containing Max (R) is an extremally disconnected space; if and only if every non-zero ideal of R is essential in a principal ideal generated by an idempotent.

here, we propose an add-drop and a channel drop filter based on two-dimensional photonic crystal all circular ring resonators. these structures are made of a square lattice of silicon rods with the refractive index n1=3.464 surrounded by air (with refractive index n2=1). the broadest photonic band gap occurs at the filling ratio of r/a = 0.17. two linear defect w1 waveguides couple to the ring....

A model for missing data in mixed binary and continuous responses, which can be used on cross-sectional data, is presented. In this model response indicator for the binary response can be dependent on the continuous response. A closed form for the likelihood is found. For data with a complicated pattern of missing responses some new residuals are also proposed. The model of multiplicative heter...