— The purpose of this article is to give formulas for Bloch-Kato’s exponential map and its dual for an absolutely crystalline p-adic representation V , in terms of the (φ,Γ)module associated to that representation. As a corollary of these computations, we can give a very simple (and slightly improved) description of Perrin-Riou’s exponential map (which interpolates Bloch-Kato’s exponentials for...

We consider the class of linear programs with infinitely many variables and constraints having the property that every constraint contains at most finitely many variables while every variable appears in at most finitely many constraints. Examples include production planning and equipment replacement over an infinite horizon. We form the natural dual linear programming problem and prove strong d...

This paper describes a method for rendering search coordinate system independent, Adaptive Encoding. Adaptive Encoding is applicable to any iterative search algorithm and employs incremental changes of the representation of solutions. One attractive way to change the representation in the continuous domain is derived from Covariance Matrix Adaptation (CMA). In this case, adaptive encoding recov...

We describe an N = 2 heterotic superstring model of rank-3 which is dual to the type-II string compactified on a Calabi-Yau manifold with Betti numbers b 1,1 = 2 and b 1,2 = 86. We show that the exact duality symmetry found from the type II realization contains the per-turbative duality group of the heterotic model, as well as the exact quantum monodromies of the rigid SU(2) super-Yang-Mills th...

Excursions from a fixed point b are studied in the framework of a general Borel right process X, with a fixed excessive measure m serving as background measure; such a measure always exists if b is accessible from every point of the state space of X. In this context the left-continuous moderate Markov dual process b X arises naturally and plays an important role. This allows the basic quantitie...

Lattice Definition. (Lattice) Given n linearly independent vectors b1, , bn ∈ R, the lattice generated by them · · · is defined as L(b1, b2, · · · bn) = { xibi|xi ∈ Z}. We refer to b1, · · · , bn as a basis of the lattice. Equivalently, if we define B as the m × n matrix whose columns are b1, , bn, then the lattice generated by B is · · · L(B) = L(b1, b2, · · · , bn) = {Bx|x ∈ Z}. We say that t...

A Fibonacci expansion of a nonnegative integer n is an expression of n as a sum of Fibonacci numbers Fk with k > 2. It may be thought of as a partition of n into Fibonacci parts. The most commonly studied such expansion is the unique one in which the parts are all distinct and no two consecutive Fibonacci numbers appear. C. G. Lekkerkerker first showed this expansion was unique in 1952 [5]. The...

We discuss general properties and possible types of magnetic vortices in non-Abelian gauge theories (we consider here G = SU(N), SO(N), USp(2N)) in the Higgs phase. The sources of such vortices carry “fractional” quantum numbers such as Zn charge (for SU(N)), but also full non-Abelian charges of the dual gauge group. If such a model is re-interpreted as an effective dual magnetic theory of the ...

At high energies, elastic hadronic cross sections, such as pp, pp, πp, are dominated by vacuum exchange, which in leading order of the 1/Nc expansion has been identified as the BFKL Pomeron or its strong AdS dual the closed string Reggeized graviton [1]. However the difference of particle anti-particle cross sections are given by a so-called Odderon, carrying C = -1 vacuum quantum numbers ident...

The following theorem is due to Dilworth [12]: Let P be a partially ordered set. If the maximal number of elements in an independent subset (anti-chain) of P is k, then P is the union of k chains (cliques). In this article we formalize an elegant proof of the above theorem for finite posets by Perles [17]. The result is then used in proving the case of infinite posets following the original pro...