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8 Dec 2015: jk by deforming the embedding ei does not create new intersection points.

15 Oct 2015: Show that G is a tree if and only if theaddition of any edge to G produces exactly 1 new cycle.

7 Mar 2015: Itherefore find a new pair of primes and announce that I shall be using the Rabin code with modulusN′ > N. ... Alice uses the Elgamal signature scheme to sign a sequence of messages, incrementing the value ofk by 2 for each new message.

22 Jan 2015: Find an injective function h on (0,) such that, writ-ing ψ = h(θ), the maximum likelihood estimator ψ̂ of the new parameter ψ isunbiased.

23 Dec 2015: 3. The action of diffeomorphisms. If f : M M is a diffeomorphism and ξ isa stable framing, we obtain a new stable framing fξ by. ... Similarly, if ζ = (E,b) is a stable almost complex structure, we obtain a new onefζ = (fE,fb) where fb is given by.

25 Feb 2015: A new code is formed by adding a single parity check bit to the end of the Hamming code, showthat this is linear and repeat the exercise above for this code.

19 Feb 2015: A new code is formed by adding a single parity check bit to the end of the Hamming code, showthat this is linear and repeat the exercise above for this code.

12 Feb 2015: fn gn = hn. Use unique factorisation in C[X] to construct a new solution tothis equation involving polynomials of smaller degree.

21 Oct 2015: Illinois J. Math 46, 885-891 2002. [Gor68] D. Gorenstein. Finite Groups Harper and Row, New York, 1968.

9 Jan 2015: Finally, we fix an isomorphism ι : Ql = C. For each irreducible algebraic representation ξ of the semi-simplegroup G, we can define a new lisse sheaf F0,ξ on U0, which

2 Jun 2015: 1)2, respectively 1, 3. , ( 3. )2. We. then eliminate t, and homogenise (introducing a new variable s) to give. ... Silverman. and G. Stevens (eds.), Springer-Verlag, New York, (1997), 447–461. University of Cambridge, DPMMS, Centre for Mathematical

15 Sep 2015: In particular, we obtain a new recursive proof of the well-known factthat every n-ary quadratic form over Qp is isotropic when n 5. ... We note that our general argument shows in particular thatquadratic forms in n 5 variables over Qp are always isotropic

11 Sep 2015: Lemma 4.2 shows that thereexists ξ S satisfying the condition on line 14, and that after modifying αk online 15, the new αk satisfies (6) with j = k. ... We also found 10 new examples of ellipticcurves E/Q with E(Q) = Z/2ZZ/8ZZ3, including one where

7 Aug 2015: In this paper we attempt to initiatea new theory of D-modules for rigid analytic spaces in the sense of Tate [30]. ... In this new programme we extend that work in twodirections. In the base direction, by working on the rigid analytic flag variety

10 Dec 2015: HSBT10]. Therefore the new content of ourwork is the existence of Π itself, on its proper ground field. ... In contrast to the situation of [CT15], although this argument does produce a new automorphicrepresentation that is ‘more ramified’ than the

3 Apr 2015: 1 Introduction. In this paper, we prove a new automorphy theorem for 2-dimensional Galois representations, and applyit to the problem of modularity of elliptic curves. ... Theorem 1.2 is new even when F = Q, and can be viewed as a special case of the

10 Mar 2015: Consider the new code we obtain by changing thesingle code word c(aK) to w. ... The construction ofthe Huffman code shows that there is a Huffman code h̃ on the new alphabet.