It is a family of surfaces with one planar end and one Enneper surface-like self-intersecting end.
2.
In a generic family of surfaces umbilics can be created, or destroyed, in pairs : the " birth of umbilics " transition.
3.
As " a " varies the locus of these characteristic curves defines a surface called the "'envelope "'of the family of surfaces.
4.
Because they are members of the same associate family of surfaces, one can bend a catenoid into a portion of a helicoid without stretching.
5.
Because they are members of the same associate family of surfaces, a catenoid can be bent into a portion of a helicoid, and vice versa.
6.
I'm not even totally sure about the'family of surfaces'- would it be as the constant varies or as some paramater in f ( x ) varies?
7.
Both rOmpA and rOmpB are members of a family of surface cell antigens ( Sca ) which are autotransporter proteins; they act as ligands for the Omp proteins and are found throughout the " rickettsiae ".
8.
These included systems for a new family of surface-to-air missiles being developed jointly by France and Italy and other missile-related orders for Korea and Britain, while other orders came in from Turkey, Malaysia, Greece, Norway and France for air, naval and ground systems.
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