Calculus can show that the variables must be equal for maximizing over the reals, see Lagrange multiplier, but from that point to apply the conditions of integrality and distinctness needs a more combinatorial argument.
22.
His major contributions include an algorithm for approximating the weight of the Euclidean minimum spanning tree in sublinear time, and finding a tight integrality gap for the vertex cover problem using the Frankl R�dl graphs.
23.
For " p "-adic curves the analogue of complex conjugation is the Frobenius endomorphism, and the analogue of the quasi-Fuchsian condition is an integrality condition on the indigenous line bundle.
24.
A limitation of the original Gilmore and Gomory method is that it does not handle integrality, so the solution may contain fractions, e . g . a particular pattern should be produced 3.67 times.
25.
The Japanese government in the 1980s granted after-work entertainment such as hostess clubs tax-deductible expense status as a result of the idea that its integrality to corporate culture would help Japan's economic success.
26.
For the set cover problem, Lov�sz proved that the integrality gap for an instance with " n " elements is " H n ", the " n " th harmonic number.
27.
The index theorem can also be run " in reverse " : the index is obviously an integer, so the formula for it must also give an integer, which sometimes gives subtle integrality conditions on invariants of manifolds.
28.
The use of the word integral puts a consistent emphasis on the common desire of being integral, and with this aim in view, the systemic and transdisciplinary approaches are also considered as part of the same quest for integrality.
29.
In the case of a nilpotent group " G " the correspondence involves all orbits, but for a general " G " additional restrictions on the orbit are necessary ( polarizability, integrality, Pukanszky condition ).
30.
Aspirants were provided with typescript lectures ( " sutras " ) on metaphysical topics, using idiosyncratic terms like " integrality " and " partitivity . " A system of alms provided for funds to be remitted back up the same chain down which these instructions descended.
