Backward running has long been used in sports conditioning programs and has recently been incorporated into rehabilitative settings as a method of increasing quadriceps strength while decreasing the joint compressive forces about the knee. Although backward locomotion has been studied kinetically, the metabolic cost of backward walking and/or running has not to our knowledge been previously cha...

the paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. motivated by an open question of s. e. rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of l. a. zadeh. on the next step, w...