In this paper we study various key properties for 2-microlocal Besov and Triebel–Lizorkin spaces with all exponents variable, including the lifting property, embeddings and Fourier multipliers. We also clarify and improve some statements recently published.

We prove the strong unique continuation property for the Lamé system of elastostatics in the plane, ∇· ( μ ( ∇u+∇ut )) +∇ (λ∇ · u) = 0, with variable Lamé coefficients μ, λ, when μ is Lipschitz and λ is measurable.

This paper demonstrates that the property of ‘replication invariance’, generally considered to be an innocuous requirement for the extension of fixed-population poverty comparisons to variable-population contexts, is incompatible with other plausible variableand fixed-population axioms.

Intellectual property piracy is a significant global problem and an enormous problem for U.S. companies and policymakers. This article examines why typically law-abiding people are more inclined to steal intellectual property products than more tangible, material products. The authors propose that the inclination to pay for certain types of goods and services is greater than for other types, an...

We study identiÞcation in a class of three-equation monetary models. We argue that these models are typically not identiÞed. For any given exactly identiÞed model, we provide an algorithm that generates a class of equivalent models that have the same reduced form. We use our algorithm to provide four examples of the consequences of lack of identiÞcation. In our Þrst two examples we show that it...

Consider an instance h of the Gaussian free field on a simply connected planar domain D with boundary conditions −λ on one boundary arc and λ on the complementary arc, where λ is the special constant √ π/8. We argue that even though h is defined only as a random distribution, and not as a function, it has a well-defined zero level line γ connecting the endpoints of these arcs, and the law of γ ...

Several possible implementations of variable-gain current conveyors are proposed. They can be designed with two opamps and current mirrors and exhibit constant bandwidth property. Their configuration as differential-output current amplifiers is straightforward.

This paper analyses a Chebyshev pseudospectral collocation semidiscrete (continuous in time) discretization of a variable coefficient parabolic problem. Optimal stability and convergence estimates are given. The analysis is based on an approximation property concerning the GaussLobatto-Chebyshev interpolation operator.

A new family of limited-memory variationally-derived variable metric or quasi-Newton methods for unconstrained minimization is given. The methods have quadratic termination property and use updates, invariant under linear transformations. Some encouraging numerical experience is reported.

The energy content in radiation from beyond our Galaxy is dominated by the Cosmic Microwave Background (CMB), discovered in 1965 [1]. The spectrum of the CMB is well described by a blackbody function with T = 2.725 K. This spectral form is one of the main pillars of the hot Big Bang model for the early Universe. The lack of any observed deviations from a blackbody spectrum constrains physical p...