Local analytic regularity in the linearized Calder\'on problem

We consider the linearization of the Dirichlet-to-Neumann (DN) map as a function of the potential. We show that it is injective at a real analytic potential for measurements made at an open subset of analyticity of the boundary. More generally, we relate the analyticity up to the boundary of the variations of the potential to the analyticity of the symbols of the corresponding variations of the DN-map.Comment: A gap in the proof of Lemma 1.2 in v1 prompted us to remove that lemma, causing a superficial change in the formulation of the main resul

Psychosemantic analyticity

It is widely agreed that the content of a logical concept such as and is constituted by the inferences it enters into. I argue that it is impossible to draw a principled distinction between logical and non-logical concepts, and hence that the content of non-logical concepts can also be constituted by certain of their inferential relations. The traditional problem with such a view has been that, given Quine’s arguments against the analytic-synthetic distinction, there does not seem to be any way to distinguish between those inferences that are content constitutive and those that are not. I propose that such a distinction can be drawn by appealing to a notion of ‘psychosemantic analyticity’. This approach is immune to Quine’s arguments, since ‘psychosemantic analyticity’ is a psychological property, and it is thus an empirical question which inferences have this property

Analyticity of the closures of some Hodge theoretic subspaces

In this paper, we prove a general theorem concerning the analyticity of the closure of a subspace defined by a family of variations of mixed Hodge structures, which includes the analyticity of the zero loci of degenerating normal functions. For the proof, we use a moduli of the valuative version of log mixed Hodge structures

Non-Analytic Vertex Renormalization of a Bose Gas at Finite Temperature

We derive the flow equations for the symmetry unbroken phase of a dilute 3-dimensional Bose gas. We point out that the flow equation for the interaction contains parts which are non-analytic at the origin of the frequency-momentum space. We examine the way this non-analyticity affects the fixed point of the system of the flow equations and shifts the value of the critical exponent for the correlation length closer to the experimental result in comparison with previous work where the non-analyticity was neglected. Finally, we emphasize the purely thermal nature of this non-analytic behaviour comparing our approach to a previous work where non-analyticity was studied in the context of renormalization at zero temperature.Comment: 21 pages, 4 figure