We give sufficient conditions for the existence of a model structure on operads in an arbitrary symmetric monoidal model category. General invariance properties for homotopy algebras over operads are deduced. Mathematics Subject Classification (2000). Primary 18D50; Secondary 18G55, 55U35.

We provide a characterization of the symmetric and weighted versions of the Euclidean compromise solution for multiobjective optimization problems first proposed by P.L.Yu. These solutions minimize a measure of the distance between a feasible set and the utopia point of that set, and are closely related to solutions that have been proposed in the bargaining with claims literature. We provide ne...

In the last hundred-odd years, set theory has been studied mainly as axiomatized mathematical theory. This axiomatic approach to set theory was launched by Zermelo (1908b; see also Ebbinghaus 2007). Under Hilbert‘s influence, he presented in 1908 a set of axioms for set theory. His main objective can be said to have been to remove the uncertainties from the set-theoretical foundations of mathem...

Mutually conjugated synergetic schemes are assumed to address evolution of nonequilibrium self-organizing system. Within framework of the former, the system is parameterized by a conserving order parameter being a density, a conjugate field reducing to gradient of related flux, and control parameter, whose driven magnitude fixes stationary state. We show that so-introduced conjugate field and c...

We develop an axiomatic approach to the theory of Sobolev spaces on metric measure spaces and we show that this axiomatic construction covers the main known examples (Hajtasz Sobolev spaces, weighted Sobolev spaces, Upper-gradients, etc). We then introduce the notion of variational p-capacity and discuss its relation with the geometric properties of the metric space. The notions of p-parabolic ...

The tradeoff between fairness and throughput has been widely observed in network analysis and protocol design. Despite many existing fairness metrics (from simple ones like Jain’s index to more complex ones like α-fair utility), the meaning of fairness is largely based on problemoriented interpretations and judgments, with no well-established framework. To tackle this challenging problem, we pr...

We make a first suggestion for an axiomatic approach to string field theory in the form of what we will call a string field functor. We give a plausibility argument for the existence of a string field functor and show that it has to be unique up to a natural gauge freedom. We prove some elementary properties of string field functors and argue that such a functorial formulation is only possible ...