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The zigzag product was introduced by Reingold, Vadhan & Wigderson (2000). When the zig-zag product was first introduced, it was used for the explicit construction of constant degree expanders and extractors. Later on, the zig-zag product was used in computational complexity theory to prove that symmetric logspace and logspace are equal ...
Upper and Lower Jaw Functional Expanders. This is a comprehensive list of functional appliances that are used in the field of orthodontics. The functional appliances can be divided into fixed and removable. The fixed functional appliances have to be bonded to the teeth by an orthodontist.
Tooth supported expanders allow the forces to be applied directly to the teeth of maxillary arch instead of the tissue. The most common tooth-borne expander is known as the Hyrax (hygienic rapid expander) or Biedermann appliance. This appliance was developed by Bidermann.
A palatal expander Upper and lower jaw functional expanders. A palatal expander is a device in the field of orthodontics which is used to widen the upper jaw [1] so that the bottom and upper teeth will fit together better. [2] [3] This is a common orthodontic procedure. The use of an expander is most common in children and adolescents 8–18 ...
Therefore, a zig-zag product can also be used to construct families of expander graphs. If G is a ( n , d , λ 1 ) -graph and H is an ( m , d , λ 2 ) -graph, then the zig-zag product G H is a ( nm , d 2 , φ ( λ 1 , λ 2 )) -graph where φ has the following properties.
Salil Vadhan is an American computer scientist. He is Vicky Joseph Professor of Computer Science and Applied Mathematics at Harvard University. [1] After completing his undergraduate degree in Mathematics and Computer Science at Harvard in 1995, he obtained his PhD in Applied Mathematics from Massachusetts Institute of Technology in 1999, where his advisor was Shafi Goldwasser. [2]
They involve attaching the orthodontic brackets on the inner (lingual vs. buccal) sides of the teeth. The main advantage of lingual braces is their near invisibility [1] compared to the standard braces, which are attached on the buccal (cheek) sides of the tooth. [2] Lingual braces were invented by Craven Kurz in 1976. [3]
This is done by using a palate expander which can stretch the patients jaw as to better fit the teeth in a patient's mouth. To counter the tooth crowding as a result of macrodontia, an orthodontist may suggest braces and a retainer to help straighten the teeth to minimize additional misalignment and thus make the teeth appear smaller. This is ...