x ,   y ) ▁= ▁min ( x ,   y ) ▁is ▁one ▁possible ▁friend ▁of ▁the ▁logical ▁conj unction ▁( AND ). ▁R - functions ▁are ▁used ▁in ▁computer ▁graphics ▁and ▁geometric ▁model ing ▁in ▁the ▁context ▁of ▁implicit ▁surfaces ▁and ▁the ▁function ▁representation . ▁They ▁also ▁appear ▁in ▁certain ▁boundary - value ▁problems , ▁and ▁are ▁also ▁popular ▁in ▁certain ▁artificial ▁intelligence ▁applications , ▁where ▁they ▁are ▁used ▁in ▁pattern ▁recognition . ▁ ▁R - functions ▁were ▁first ▁proposed ▁by ▁ ▁() ▁in ▁ 1 9 6 3 , ▁though ▁the ▁name , ▁" R - functions ", ▁was ▁given ▁later ▁on ▁by ▁Ek ater ina ▁L . ▁R v ache va - Y ush chen ko , ▁in ▁memory ▁of ▁their ▁father , ▁Log vin ▁Fed or ov ich ▁R v ache v ▁( ). ▁ ▁See ▁also ▁▁ ▁Function ▁representation ▁S les aren ko ▁function ▁( S - function ) ▁ ▁Notes ▁ ▁References ▁▁ ▁M esh free ▁Model ing ▁and ▁Analysis , ▁R - Function s ▁( Univers ity ▁of ▁Wisconsin ) ▁ ▁Pattern ▁Rec ogn ition ▁Method s ▁Based ▁on ▁R v ache v ▁Function s ▁( P urd ue ▁University ) ▁ ▁Sh ape ▁Model ing ▁and ▁Computer ▁Graphics ▁with ▁Real ▁Function s ▁ ▁Category : Non - class ical ▁logic ▁Category : Real ▁analysis ▁Category : Types ▁of ▁functions <0x0A> </s> ▁Fen zy ▁is ▁a ▁sc uba ▁div ing ▁and ▁industrial ▁breath ing ▁equipment ▁design ▁and ▁manufact uring ▁firm . ▁It ▁started ▁in