Urine : Albumin +. No sugar or casts. Widal.?Negative 1 in 25 for B. typhosus, and para A, B and and C. Weil-Felix reaction.?OXK 25, OX2 -f100, 0X19 + 200. Progress.?The temperature became normal on the morning of the 14th day of illness. He had slight rise of temperature in the evening for the next 3 days, and it settled down to normal on the 18th day. The hiccough continued till the 16th day....

It seems so obvious that cheating is wrong that providing a justification is not a main concern: most of the research is empirical and focuses on quantification and correlations. I look at a number of reasons why cheating may be wrong: it provides an unfair advantage over other students, it hinders learning, and it is dishonest. They are unexpectedly weak (often not proving that cheating is wro...

In this paper we solve some problems posed by Kolchin about differential algebraic groups. The main result (from which the others follow) is the embeddability of any differential algebraic group in an algebraic group. A crucial intermediate result, and one of independent interest, is a generalisation of Weil’s theorem on recovering an algebraic group from birational data, to pro-algebraic groups.

It is proved that on any bounded domain in the complex Euclidean space C(n) the Bergman metric is always greater than or equal to the Carathéodory distance. This leads to a number of interesting consequences. Here two such consequences are given. (i) The Bergman metric is complete whenever the Carathéodory distance is complete on a bounded domain. (ii) The Weil-Petersson metric is not uniformly...

1. January 21, 2010 2 1.1. Why define a curve to be f rather than V (f) ⊂ P(k)? 3 1.2. Cubic plane curves 3 2. January 26, 2010 4 2.1. A little bit about smoothness 4 2.2. Weierstrass form 5 3. January 28, 2010 6 3.1. An algebro-geometric description of the group law in terms of divisors 6 3.2. Why are the two group laws the same? 7 4. February 2, 2010 7 4.1. Overview 7 4.2. Uniqueness of Weier...

τ(n)e(nz). The two equations were proven for τ(n) by Mordell, using what are now known as the Hecke operators. The inequality was proven by Deligne as a consequence of his proof of the Weil conjectures. Those results determine everything about af (n) except for the distribution of the af (p) ∈ [−2, 2]. Define θf (p) ∈ [0, π] by af (p) = 2 cos θf (p). It is conjectured that for each f the θf (p)...

In this talk the definition of polarization of abelian variety and Weil paring will be given. After introducing some proposition of Weil pairing, we will show the Zarhin’s trick about principal polarization.

In this paper, we study the Mordell-Weil group of an elliptic curve as a Galois module. We consider an elliptic curve E defined over a number field K whose Mordell-Weil rank over a Galois extension F is 1, 2 or 3. We show that E acquires a point (points) of infinite order over a field whose Galois group is one of Cn×Cm (n = 1, 2, 3, 4, 6, m = 1, 2), Dn×Cm (n = 2, 3, 4, 6, m = 1, 2), A4×Cm (m = ...

In this article we would like to address the following situation. Let f : X → C be an elliptic surface with section S0. We further assume that X is relatively minimal and smooth, and that all singular fibers are semistable, that is, are cycles of P’s (type “Im” in Kodaira’s notation, see [K]). Given a section S of f , it will meet one and only one component in every singular fiber. The fundamen...

In this paper, we construct a quantization functor, associating a complex vector space H(V ) to a finite dimensional symplectic vector space V over a finite field of odd characteristic. As a result, we obtain a canonical model for the Weil representation of the symplectic group Sp (V ). The main new technical result is a proof of a stronger form of the Stone-von Neumann property for the Heisenb...