Moduli Spaces and Formal Operads

Let overline{M}_{g,n} be the moduli space of stable algebraic curves of genus g with n marked points. With the operations which relate the different moduli spaces identifying marked points, the family (overline{M}_{g,n})_{g,n} is a modular operad of projective smooth Deligne-Mumford stacks, overline{M}. In this paper we prove that the modular operad of singular chains C_*(overline{M};Q) is formal; so it is weakly equivalent to the modular operad of its homology H_*(overline{M};Q). As a consequence, the "up to homotopy" algebras of these two operads are the same. To obtain this result we prove a formality theorem for operads analogous to Deligne-Griffiths-Morgan-Sullivan formality theorem, the existence of minimal models of modular operads, and a characterization of formality for operads which shows that formality is independent of the ground field.Comment: 36 pages (v3: some typographical corrections

A Cartan-Eilenberg approach to Homotopical Algebra

In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects by an extension property analogous to the classical lifting property of projective modules. We define a Cartan-Eilenberg category as a category with strong and weak equivalences such that there is an equivalence between its localization with respect to weak equivalences and the localised category of cofibrant objets with respect to strong equivalences. This equivalence allows us to extend the classical theory of derived additive functors to this non additive setting. The main examples include Quillen model categories and functor categories with a triple, in the last case we find examples in which the class of strong equivalences is not determined by a homotopy relation. Among other applications, we prove the existence of filtered minimal models for \emph{cdg} algebras over a zero-characteristic field and we formulate an acyclic models theorem for non additive functors

Property (gb) through local spectral theory

Property (gb) for a bounded linear operator T on a Banach space X means that the points c of the approximate point spectrum for which c I-T is upper semi B-Weyl are exactly the poles of the resolvent. In this paper we shall give several characterizations of property (gb). These characterizations are obtained by using typical tools from local spectral theory. We also show that property (gb) holds for large classes of operators and prove the stability of property (gb) under some commuting perturbations

Asymmetrical Noncomplementary Modulation Strategies for Independent Power Control in Multioutput Resonant Inverters

Domestic induction heating (IH) design trends aim at improving user experience by increasing the cooking surface flexibility while maintaining a cost-effective implementation. The design of multioutput topologies is a key development for this purpose. However, due to their complexity, output power control usually relies on low-frequency pulse density modulations that, in addition to the slow response due to significant power averaging times, present severe restrictions as a consequence of power pulsation regulations. This article proposes two different noncomplementary asymmetrical modulation strategies that allow continuous operation avoiding both flicker and heating performance issues and obtaining a fast-response load power control. In order to prove the feasibility of the proposed modulations, a prototype featuring 12 IH loads of 2000-W maximum rated power has been built, and both strategies have been tested

Asymmetrical Modulation Strategies for Partially Covered Inductors in Flexible Induction Heating Appliances

Cost-effective multi-output resonant inverter topologies are a key enabling technology for the development of flexible surfaces for induction heating appliances. These topologies present several challenges when applied to a wide range of IH-loads simultaneously. In this paper, two asymmetrical modulations are proposed as an alternative solution to control output power. The proposed approach has been verified using an experimental prototype featuring 2 induction heating loads up to 3.6 kW with output power control in the whole operating range

Multi-Output Resonant Power Converters for Domestic Induction Heating

Induction heating has become the most relevant domestic heating technology due to its accurate power control, clean operation and high efficiency. Current design tendencies aim to reduce limitations in pot positioning to increase the cooktop versatility and to improve the user experience. These desired flexible surfaces are implemented by means of multi-coil structures which require the design of new multi-output power converters. This paper reviews and classifies the different inverters proposed in the literature to power multi-coil structures, and analyzes them in terms of versatility, performance, and component count