Proof of Theorem 3.2 for the mixed class
A Proof of Theorem 1.2
... prove Theorem 3.2 Proof of Theorem ...y 2 . To show consistency, assume x 1 = y 1 , x 2 = y 2 , so OPT = ...job 2 cannot finish before job 1 in this stage: since λ < ...
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3 Proof of theorem
... (−1/(r 2 + 1)), for some r > ...≥ 3) in Euclidean space R n+1 with constant scalar curvature and with two distinct principal curvatures one of which is ...
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3 Proof of Theorem 3
... contained in G [V (P ∪ L)] , such that they are independent. If S is a set of subgraphs of G, we write G ⊇ S. For an integer k ≥ 1 and a graph G , we use kG to denote k independent graphs isomorphic to G . If G 1 , ...
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3 Proof of the Theorem 3
... In this paper we obtain existence results for the positive solution of a singular elliptic boundary value problem.. Our study is motivated by the works of Shu [17], Arcoya, Carmona, Leon[r] ...
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3 Proof of Theorem 1.8
... a 2 , . . . , a k and n are positive integers such that n = a 1 +a 2 +· · ·+a k , then the sum a 1 + a 2 + · · · + a k is said to be a partition of n of length k, and a 1 , a 2 , ...
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3 Proof of Theorem 6
... from 3 to ...a 2-connected graph to be ...= 2 implies max{d(u), d(v)} ≥ (n + ...P 3 and a 2-connected claw-f 1 -heavy graph G which is not a cycle, G being S-f 1 -heavy implies G is ...
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3 Proof of Theorem 2.7
... (4) Extension theorems are often used for optimal linear codes problem, especially to prove the nonexistence of linear codes with certain parameters.. Moreover, the extended matrix of G [r] ...
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3 Proof of the main theorem
... Claim 3 G is the union of stars and at most one double star. Moreover, if H has no double stars, then G also has no double stars. We may assume that k ≥ 4 since otherwise H ∈ F ∞ ∪ {P 4 }. Assume that G has a path ...
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3 Proof of Theorem 1.2
... A vector ~y ∈ S is called an optimal vector of λ(G) if λ(G, ~y) = λ(G). The following fact is easily implied by the definition of the Lagrange function. Fact 2.1 Let G 1 , G 2 be r-uniform graphs and G 1 ⊂ G ...
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3. Proof of Theorem 2.11
... Both categories Top of topological spaces and SSets of simplicial sets are right (and left) proper [Hi, Theorems 13.1.11, 13.1.13]. Therefore, in both categories the fibrations are h-fibrations, and thus the h-fibrations ...
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3 The proof of Theorem 1
... ON SQUARE VALUES OF THE PRODUCT OF THE EULER TOTIENT AND SUM OF DIVISORS FUNCTIONS KEVIN BROUGHAN, KEVIN FORD, AND FLORIAN LUCA Abstract. If n is a positive integer such that φ(n)σ(n) = m 2 for some positive ...
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2 Proof of Theorem 1.15
... {1, 2, ...≥ 3 and k ≥ 2, let G i = P 2i+3 be a path on 2i + 3 vertices for all i ∈ {0, 1, ...− 2} and G n−1 ∈ {C 2n , P 2n+1 ...
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2 Proof of Theorem 1
... combinatorial proof of the rank-unimodality of the poset of order ideals of a product of chains of lengths 2, n, and m, and find a symmetric chain decomposition in the case where n = ...
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2 Proof of the main theorem
... Furthermore, we show that if N (k) is the number of n values for which k = dlog 3 ne and B(n) > k, then N (k) is an unbounded function of k. 1 Introduction Coin-weighing puzzles have been abundantly discussed ...
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2 Proof of Theorem 1
... extend Theorem 1 to higher dimensions and/or to trees with weighted ...the class of the considered metric ...R 2 would require distortion larger than about ...
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3 The Compactness Theorem (1st proof)
... say 2 ⌃ / # and ¬ / 2 ⌃ # ...S 2 ✓ ⌃ # such that neither { } [ S 1 nor {¬ } [ S 2 is ...S 2 ✓ ⌃ # , finite, so has a model, A ...S 2 , a ...
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2 Proof of Theorem 5 — the upper bound for kites
... Compact 2-manifolds are called surfaces for short throughout the ...a 2-cell embedding. If each vertex has degree ≥ 3 and each vertex of degree h is incident with h different faces then G is called a ...
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4. Proof of the theorem
... 22 (1, 1) rr r ! = ∞ whenever p 6= r. The reasoning in the previous lemmas will not help us now, since in Lemma 4.2 we needed c < ∞. As we shall see in Proposition 5.1, the proof for c = ∞ must use lower ...
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A. Proof of Theorem 1
... To end case 1, we have to ensure that the first sequence element is greater than zero: s n 1 ≥ s 1 > 0. This is not the case if the first N matrices have two orthogonal columns, s 1 = ... = s N = 0. We can then skip ...
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M PROOF OF THE DIVERGENCE THEOREM AND STOKES THEOREM
... Divergence Theorem, we use the same approach as we used for Green’s Theorem; first prove the theorem for rectangular regions, then use the change of variables formula to prove it for regions ...
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