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21 Jun 2007: Vortex Moduli Space. Suppose we have an Abelian vortex solution ,. We can trivially embed this in the non-Abelian theory. B =B?0.(. ... BPS Vortex Equations in this theory are FB12 = e2(|B|2 |B̃|2 v2).

20 Sep 2007: B. B. WARDY. Plato Republic 473–535 (12L, weeks 1–6). Tu. Th. ... 5.15–6.45. DR R. B. B. WARDY, MR N. C. DENYER AND DR J.

22 Nov 2007: The Lipschitz condition is in turn impliedby the existence and boundedness of the gradient b = b/x, which is usually easy tocheck. ... A diffusion process is a generalization of the differential equation ẋt = b(xt).

16 Nov 2007: B.2 Wall Street Journal 139. List of Figures. 1.1 General speech recognition system 2. ... The probability for a given state sequence & 3 :B and observations / is givenby the product of the transition and output probabilities:. / &

11 Jul 2007: a-a and b-b are parallel to the x- and y- axes respectively, while u-u and v-v are at 45. ... To these must be added the moments from a-a and b-b to give the total moment field, which must be compared with the moment capacity described above.

11 Jul 2007: At corners b will span round concave corners in circular arcs all of radius, r. ... It is straight forward to show that A=a 1.5.ω.r 2 and that B= b 3.ω.r.

3 Jun 2007: It corresponds to the Möbius transformation C C ; z 7 (az b)/(cz d). ... Exercises. Let T : z 7 (az b)/(cz d) be a Möbius transformation.7.

21 Nov 2007: Show that f = gR f gLand hence, or otherwise, show that f is differentiable at B. ... Show that f is differentiable at (a, b). (b) Suppose instead that D1f exists and is bounded on some open ball around (a, b), and that for fixed x.

18 Jan 2007: wherelimB!1 g(B)=B = 0, and where I can becomputed as the solution to an optimal control problemposed in terms of rate functions Ii, i = 1; : : : ;M forthe M trac ... A switch with dedicated output buersA single output buer per output link:B.

3 Jun 2007: Proof:. The theorem enables us to construct an entire function b whose zeros are poles of f. ... Thus G is a subgroup of the groupof translations: {z 7 z b : b C}.