Related papers: First-order definitions in function fields over an…

In this paper we extend our recent results (hep-th/0304067) on the first order formulation for the massless mixed symmetry tensor fields to the case of massive fields both in Minkowski as well as in (Anti) de Sitter spaces (including all…

The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and…

In [2], an exhaustive construction is achieved for the class of all 4-dimensional unital division algebras over finite fields of odd order, whose left nucleus is not minimal and whose automorphism group contains Klein's four-group. We…

Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with…

We prove that there exists, up to isomorphism, exactly one function field over the finite field of two elements of class number one and genus four. This result, together with the ones of MacRae, Madan, Leitzel, Queen and Stirpe, establishes…

Let $n\in\mathbb{N}$ and let $K$ be a field with a henselian discrete valuation of rank $n$ with hereditarily euclidean residue field. Let $F/K$ be an algebraic function field in one variable. We show that the Pythagoras number of $F$ is…

One of the main themes in this thesis is the description of the signature of both the infinite place and the finite places in cubic function fields of any characteristic and quartic function fields of characteristic at least 5. For these…

We provide Sobolev estimates for solutions of first order Hamilton-Jacobi equations with Hamiltonians which are superlinear in the gradient variable. We also show that the solutions are differentiable almost everywhere. The proof relies on…

Given a digraph D, the minimum semi-degree of D is the minimum of its minimum indegree and its minimum outdegree. D is k-ordered Hamiltonian if for every ordered sequence of k distinct vertices there is a directed Hamilton cycle which…

We show that the presence and the location of first order phase transitions in a thermodynamic system can be deduced by the study of the topology of the potential energy function, V(q), without introducing any thermodynamic measure. In…

We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…

We define a notion of formal quantum field theory and associate a formal quantum field theory to K-theoretical intersection theories on Hilbert schemes of points on algebraic surfaces. This enables us to find an effective way to compute…

First-order logic is the basis for many knowledge representation formalisms and methods. Providing technological support for learning to write first-order formulas for natural language specifications requires methods to test formulas for…

A complete first-order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition.…

Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…

Notions of k-asimulation and asimulation are introduced as asymmetric counterparts to k-bisimulation and bisimulation, respectively. It is proved that a first-order formula is equivalent to a standard translation of an intuitionistic…

We prove, assuming resolution of singularities in positive characteristic, an analogue of Siegel's theorem on sum of squares in positive characteristic. The method of proof combines techniques from central simple algebras with model theory…

We consider first-order definability and decidability questions over rings of integers of algebraic extensions of $\Q$, paying attention to the uniformity of definitions. The uniformity follows from the simplicity of our first-order…

In contrast with QFT, classical field theory can be formulated in a strict mathematical way if one defines even classical fields as sections of smooth fiber bundles. Formalism of jet manifolds provides the conventional language of dynamic…

In this article we obtain a complete description of the congruences of lines in $\p^4$ of order one provided that the fundamental surface $F$ is non-reduced (and possibly reducible) at one of its generic points, and their classification…