Related papers: The defect
The problem of error growth due to the incomplete knowledge of the evolution law which rules the dynamics of a given physical system is addressed. Major interest is devoted to the analysis of error amplification in systems with many…
We give a necessary and sufficient condition for the existence of a local solution of the inverse problem of calculus of variations in terms of the identical vanishing of the variation of a functional on an extended space (with the number…
We study the deformation theory of nonsigular projective curves defined over algebraic closed fields of positive characteristic. We show that under some assumptions the local deformation problem for automorphisms of powerseries can be…
The goal of this paper is to explain how basic properties of perverse sheaves sometimes translate via Riemann-Hilbert correspondences (in both characteristic $0$ and characteristic $p$) to highly non-trivial properties of singularities,…
Recent work in psychology and experimental philosophy has shown that judgments of actual causation are often influenced by consideration of defaults, typicality, and normality. A number of philosophers and computer scientists have also…
In this paper we examine the natural interpretation of a ramified type hierarchy into Martin-L\"of type theory with an infinite sequence of universes. It is shown that under this predicative interpretation some useful special cases of…
This is a revised version of gr-qc/9304033
We introduce a method to obtain deformed defects starting from a given scalar field theory which possesses defect solutions. The procedure allows the construction of infinitely many new theories that support defect solutions, analytically…
It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.
The classical Artin--Whaples approximation theorem allows to simultaneously approximate finitely many different elements of a field with respect to finitely many pairwise inequivalent absolute values. Several variants and generalizations…
We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in $d \geq 3$ dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model…
In the present paper, several properties concerning generalized derivatives of multifunctions implicitly defined by set-valued inclusions are studied by techniques of variational analysis. Set-valued inclusions are problems formalizing the…
We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross-Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen…
We define the universal exponential extension of an algebraically closed differential field and investigate its properties in the presence of a nice valuation and in connection with linear differential equations. Next we prove normalization…
Let F be a field complete for a real valuation. It is a standard result in valuation theory that a finite extension of F admits a valuation basis if and only if it is without defect. We show that even otherwise, one can construct bases in…
We investigate distality and existence of distal expansions in valued fields and related structures. In particular, we characterize distality in a large class of ordered abelian groups, provide an AKE-style characterization for henselian…
The algebraic approach to quantum field theory focuses on the properties of local algebras, whereas the study of (possibly non-invertible) global symmetries emphasizes global aspects of the theory and spacetime. We study connections between…
Let k be a field of characteristic zero, K an algebraic function field over k, and V a k-valuation ring of K. Zariski's theorem of local uniformization shows that there exist algebraic regular local rings R_i with quotient field K which are…
Topological defects and smooth excitations determine the properties of systems showing collective order. We introduce a generic non-singular field theory that comprehensively describes defects and excitations in systems with $O(n)$ broken…
The Fundamental Theorem of Algebra can be thought of as a statement about the real numbers as a space, considered as an algebraic set over the real numbers as a field. This paper introduces what it means for an algebraic set or affine…