If P has at least two linear factors, say [[alpha].sub.1], [[alpha].sub.2] [member of] Q are two distinct roots
of P, then the condition of the theorem implies that [[lambda].sub.3] - [[lambda].sub.4] [member of] Q for any [[lambda].sub.3], [[lambda].sub.4] [member of] Z(P).
with the distinct roots
[z.sub.k] that are interpreted as the wave function nodes and can be determined by the Bethe ansatz equations.
Rafflesia flowers are unique in that they are entirely parasitic on the roots and stems of specific Tetrastigma vines in the forests and have no distinct roots
, stems, or leaves of their own, explained coauthor, professor Edwino S.
"In academic sense, the Dictionary bridges two languages with distinct roots
and traditions and different syntax and grammar and in social and political sense, it strengthens linkages between peoples of Pakistan and China, who are like "iron brothers", the President said.
The root may appear as a single, fused root or as two distinct roots
with a communication.
where [[alpha].sub.1] and [[alpha].sub.2] are two distinct roots
Root perimeter (P) was determined in four fragments (1cm in length) in ten distinct roots
It is clear that 1, [epsilon], [[epsilon].sup.2], ..., [[epsilon].sup.n-1] are exactly n distinct roots
Let f and g be two non-constant meromorphic functions sharing (oo, 0) and suppose a1 and a2 are two distinct roots
of the equation
The original source is Franz Boas [who said in 1911 only that Eskimo uses four apparently distinct roots
for snow on the ground, falling snow, drifting snow, and a snow drift].
The difference in number of sign changes is the number of distinct roots
between a and b.
It seems less likely that the secondary tooth is the result of gemination because it has distinct roots
and a relatively distinct crown, indicating that it has its own pulp cavity.