This paper is a study of fuzzy type theory (FTT) with partial functions. Out of several possibilities we decided tointroduce a special value ”∗” that represents ”undefined”. In the interpretation of FTT, this value lays outside of thecorresponding domain. In the syntax it can be naturally represented by the description operator acting on the empty(fuzzy) set, because choosing an element from it...

For an integer ρ such that 1≤ρ≤v∕3, define β(ρ,v) to be the maximum number of blocks in any partial Steiner triple system on v points which parallel class has size ρ. We obtain lower bounds by giving explicit constructions, and upper result from counting arguments. show β(ρ,v)∈Θ(v) if is a constant, β(ρ,v)∈Θ(v2) ρ=v∕c, where c constant. When our differ constant depends Finally, we apply results...

Objective: To determine the pattern of partial edentulism and cast removable dental prosthesis design in relation to Classes recorded.
 Study Design: Cross-sectional study.
 Place Duration Study: Department Prosthodontics, Armed Forces Institute Dentistry (AFID), Rawalpindi Pakistan, from Apr Sep 2021.
 Methodology: A total 67 partially dentate male female patients presenting Pro...

an airlift-type activated sludge reactor using a sponge support medium was fed with wastewater containing 500 mg-n/l of nh4 +-n. in order to establish partial nitrification, the reactor was kept at 35°c. moreover, the reactor was started up with the nahco3 solution as an alkali agent to supply inorganic carbon for enhancement of partial nitrification. the partial nitrification was established d...