The name is absent



10

The geometric context of the next theorem can be easily understood in two
dimension.

Theorem 3.5 Exclusion Theorem

Let a simplex P be given in standard form with the additional condition that
ff1≠i
t¾aa holds for all i = 1,    , n. Then the Labeling Rule precludes the

possibility of the coexistence of a completely labeled simplex of type I and a com-
pletely labeled simplex of type II. If P contains an integral point, then there exists
no completely labeled simplex of type II.

Proof: We only need to consider the case in which P contains an integral point,
say æ0, i.e.,
Ax0 ≤ b. Let us suppose to the contrary that there is a completely
labeled simplex of type
II, say σ(⅛1,π) with vertices x1, ■■■, xn+1, where π =
(τr(l), ∙ ∙ ∙ ,
π(n ⅛ 1)) is a permutation of the n ⅛ 1 elments of N, and

xt+1 = xt ⅛ q(π(if), i = 1, ∙ ∙ ∙ , n;

x1 = xn+1 + q(π(n + 1)).

Now it is easy to see that there exist nonnegative integers k^, ∙ ∙ ∙, such that

x1 = x° + ∑ k⅛(i),
ieN

and

min kl = 0.
heN n

Let

I = argmin{ π 1(∕z) ∣ kjl = max: k1j

Then there exist nonnegative integers kt1, - , ktn+1 such that

xt = x0 + ∑ ktjq(f)
j
N



More intriguing information

1. Computational Batik Motif Generation Innovation of Traditi onal Heritage by Fracta l Computation
2. Popular Conceptions of Nationhood in Old and New European
3. Thresholds for Employment and Unemployment - a Spatial Analysis of German Regional Labour Markets 1992-2000
4. The name is absent
5. Commitment devices, opportunity windows, and institution building in Central Asia
6. Analyse des verbraucherorientierten Qualitätsurteils mittels assoziativer Verfahren am Beispiel von Schweinefleisch und Kartoffeln
7. The name is absent
8. The problem of anglophone squint
9. O funcionalismo de Sellars: uma pesquisa histδrica
10. The name is absent
11. A THEORETICAL FRAMEWORK FOR EVALUATING SOCIAL WELFARE EFFECTS OF NEW AGRICULTURAL TECHNOLOGY
12. Explaining Growth in Dutch Agriculture: Prices, Public R&D, and Technological Change
13. La mobilité de la main-d'œuvre en Europe : le rôle des caractéristiques individuelles et de l'hétérogénéité entre pays
14. Party Groups and Policy Positions in the European Parliament
15. Text of a letter
16. The Veblen-Gerschenkron Effect of FDI in Mezzogiorno and East Germany
17. On the job rotation problem
18. The name is absent
19. The name is absent
20. Unemployment in an Interdependent World