Remarks about fields of high intensity

Remarks about Uniform Boundedness of Rational Points over Function Fields

We prove certain uniform versions of the Mordell Conjecture and of the Shafarevich Conjecture for curves over function fields and their rational points.

Remarks about Euclidean Domains

We will call (1) the d-inequality. Sometimes it is expressed in a different way: for nonzero a and b, if a|b then d(a) ≤ d(b). This is equivalent to the d-inequality, taking into account of course the different roles of a and b in the two descriptions. Examples of Euclidean domains are Z (with d(n) = |n|), F [T ] for any field F (with d(f) = deg f ; this example is the reason that one doesn’t a...

Remarks about Schlumprecht space

Let S denote the Schlumprecht space. We prove that 1. l∞ is finitely disjointly respresentable in S; 2. S contains an l1-spreading model; 3. for any sequence (nk) of natural numbers, S is isomorphic to the space ( ∑∞ k=1⊕ lnk ∞ ) S . Let (ei) ∞ i=1 be the standard basis of the linear space c00, the set of all finitely supported sequences. For x = ∞ ∑ i=1 aiei ∈ c00, suppx denotes the set {i ∈ N...

Remarks about metastability

Transverse spreading of electrons in high-intensity laser fields.

We show that for collisions of electrons with a high-intensity laser, discrete photon emissions introduce a transverse beam spread that is distinct from that due to classical (or beam shape) effects. Via numerical simulations, we show that this quantum induced transverse momentum gain of the electron is manifest in collisions with a realistic laser pulse of intensity within reach of current tec...