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28 Oct 2008: Prove that every r n Latin rectangle may be extended to an n n Latin square.7. ... Show that a graph G (with |G| > k) is k-connected ifand only if there is an a-B fan for every B V (G) with |B| = k and every vertex

21 Aug 2008: Corollary 3.4 Suppose that the left adjoint Σπ1 a π1 exists for every (first) projection π1 in B. ... 3. the right adjoint α a Πα exists for every morphism α in B.

21 Aug 2008: Corollary 3.4 Suppose that the left adjoint Σπ1 a π1 exists for every (first) projection π1 in B. ... 3. the right adjoint α a Πα exists for every morphism α in B.

23 Feb 2008: that every finitely presented group is the. ... b) If m < n, then every map Sm Sn is homotopic to a.

1 Feb 2008: U is starlike if there exists a0 U such that for every b U the line segementfrom a0 to b lies in U. ... Remark. A function f : U C is said to be analytic if for every a U, f canbe represented by a convergent power series on some B(a,r) U.

12 Mar 2008: Corollary. Every meromorphic function f : C C is the quotient a/b of two entire functions a and b. ... 1. Proof:. The theorem enables us to construct an entire function b whose zeros are poles of f.

2 Jul 2008: Lefeuvre and A. Every, Phys. Rev. B, 60 2844 (1999). 9. ... C., Every A. G. and Comins J. D, J. Opt. Soc.

6 Mar 2008: Assume that B is integral over A; thatis, every element x of B is is a zero of a monic polynomial in A[X].(i) Suppose that A, B are domains ... It is called theintegral closure of A in B.). (8) A field K is algebraically closed if every polynomial f K[x]

26 Nov 2008: 6. Show that every graph G has a partition of its vertex-set as X Y such that the numberof edges from X to Y is at least 12 e(G). ... 11. Let G be a graph in which every edge is in a unique triangle and every non-edge is adiagonal of a unique 4-cycle.

4 Feb 2008: Show that f(X b) = f(X) for every b Fp K. ... Show that. αif′(αi) = (n 1)b. (. nc. (n 1)b αi. ).