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We say that a specialization (gamma :V{setminus }{sinks}rightarrow E) is a frame specialization if the set of all special paths (p=e_1ldots e_n) with (s(e_1),ldots, s(e_n)notin mathop {cup }limits _{ige 1}^k W_i) is finite.
We claim that with the specialization (gamma ) defined above there are finitely many special paths in (Gamma.) If not, then (Gamma ) contains a special cycle.
By Lemma 11 there exist a specialization (gamma ':V'{setminus }{w}rightarrow E') such that the set of all special paths in (Gamma ') is finite.
Let (Gamma = V,E)) be a finite graph with a sink v which is a descendant of every vertex in V. Then there exists a specialization (gamma : V{setminus }{v}rightarrow E,) such that the set of all special paths in (Gamma ) is finite.
Under Mali's recently ousted president, who is a Peul, the herders were allowed to cross Dogon territory on special paths.
(Puerto Ricans have the vote automatically, as their island is American territory. Cubans have enjoyed special paths to citizenship since the cold war).
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Historians refer to its 19th-century version as the Sonderweg (special path).
The immigrants take their name from the Dream Act, legislation that would open a special path to citizenship for young people here illegally.
Then they would be sent to the back of the line in the existing system to apply to become permanent residents, without any special path to citizenship.
When German historians tried to discover why Germany went down its disastrous "special path", its Sonderweg, in the late 19th and early 20th centuries, they contrasted it with Britain.
For more than 70 years after it, the country is developing on its own, absolutely unique "special path" (as they say now).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com