This paper studies the Ratliff-Rush closure and the integral closure of an ideal in a valuation and Prüfer domains. By definition, the RatliffRush closure (respectively the integral closure) of an ideal I of a domain R is the ideal Given by Ĩ := S (I :R I ) (respectively I := {x ∈ R|x satisfies an equation of the form x + a1x + · · ·+ ak = 0, where ai ∈ I i for each i ∈ {1, . . . , k}}). An ide...

This paper studies the Ratliff-Rush closure and the integral closure of an ideal in a valuation and Prüfer domains. By definition, the RatliffRush closure (respectively the integral closure) of an ideal I of a domain R is the ideal given by Ĩ := S (I :R I ) (respectively I := {x ∈ R|x satisfies an equation of the form x + a1x + · · ·+ ak = 0, where ai ∈ I i for each i ∈ {1, . . . , k}}). An ide...

Fiber cones of 0-dimensional ideals with almost minimal multiplicity in CohenMacaulay local rings are studied. Ratliff-Rush closure of filtration of ideals with respect to another ideal is introduced. This is used to find a bound on the reduction number with respect to an ideal. Rossi’s bound on reduction number in terms of Hilbert coefficients is obtained as a consequence. Sufficient condition...

OF DISSERTATION Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Engineering The University of New Mexico Albuquerque, New Mexico December, 2004 A Generalized Algebraic Scene-based Nonuniformity Correction Algorithm for Infrared Focal Plane Arrays by Bradley Michael Ratliff B.S., Computer Engineering, University of Dayton, 2000 M.S., Electrical Enginee...

Mach bands are illusory bright am! da.rk bands seen where a lumin<lnce plateau meets <I ramp, as in half-shadows or penumbras. Ra.tliff, Milkman, and Kaufman (1983) showed that Mach bands are attenmtted by placing stimuli, such as bars, nemby. An experiment comparing Mach band attenuation for bar a.ncl Craik-O'Brien stimuli shows that they are equally effective in attenuating Mach bands. 'J'he ...