Supplementary Figure S1: Antenna enhancement for another antenna-particle pair: Same graph as in Fig.4 of the main text, but for another antenna-nanoparticle pair. The black curve shows the differential pump-probe spectrum of a single nanoparticle with 50 nm in diameter. As predicted this signal is stronger and also red shifted by about ∆λ = 20 nm compared to the single 40 nm nanoparticle shown...

We investigate the infra-red stable fixed points of the Yukawa couplings in the minimal version of the supersymmetric standard model with R-parity violation. Retaining only the R-parity violating couplings of higher generations, we analytically study the solutions of the renormalization group equations of these couplings together with the topand b-quark Yukawa couplings. We show that only the B...

We embed the standard λ-calculus, denoted Λ, into two larger λ-calculi, denoted Λ∧ and &Λ∧. The standard notion of β-reduction for Λ corresponds to two new notions of reduction, β∧ for Λ∧ and &β∧ for &Λ∧. A distinctive feature of our new calculus Λ∧ (resp., &Λ∧) is that, in every function application, an argument is used at most once (resp., exactly once) in the body of the function. We establi...

2 Homotopy λ-calculus 16 1 Type systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 Homotopy λ-calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3 Basic layer syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4 Basic layer semantics in Top . . . . . . . . . . . . . . . . . . . . . . . . ...

In this paper we investigate the λ-calculus, a λ-calculus enriched with resource control. Explicit control of resources is enabled by the presence of erasure and duplication operators, which correspond to thinning and contraction rules in the type assignment system. We introduce directly the class of λ-terms and we provide a new treatment of substitution by its decomposition into atomic steps. ...

We study the growth of perturbations in a uniformly collapsing cloud of self-gravitating Brownian particles. This problem shares analogies with the formation of large-scale structures in a universe experiencing a "big-crunch" or with the formation of stars in a molecular cloud experiencing gravitational collapse. Starting from the barotropic Smoluchowski-Poisson system, we derive a new equation...

We establish the existence of a nontrivial solution of system:  −∆pu = λ a(x)u|u|p−2 + λ′c(x)u|u|α−1|v|β+1 + f in Ω −∆qv = μ b(x)v|v|q−2 + λ′c(x)|u|α+1v|v|β−1 + g in Ω (u, v) ∈W 1,p 0 (Ω)×W 1,q 0 (Ω) under some restrictions on λ, μ, λ′, α, β, f and g. We show this result by a local minimization.

Let L be a finite-dimensional, semisimple Lie algebra over an algebraically closed field k of characteristic 0. Let H be a fixed Cartan subalgebra of L, and Φ be the root system. Fix a base ∆ = {α1, · · · , αl} of Φ. Let Λ denote the set of dominant, integral linear functions on H. Theorem 0.1. There is a one-to-one correspondence Λ ∼ −→ {isomorphism classes of finite-dimensional irreducible L-...

This paper gives a characterisation, via intersection types, of the strongly normalising proof-terms of an intuitionistic sequent calculus (where LJ easily embeds). The soundness of the typing system is reduced to that of a well known typing system with intersection types for the ordinary λ-calculus. The completeness of the typing system is obtained from subject expansion at root position. Next...

In this paper, we present Λ∧, a fully typed λ-calculus based on the intersection-type system discipline, which is a counterpart à la Church of the type assignment system as invented by Coppo and Dezani. The relationship between Λ∧ and the intersection type assignment system is the standard isomorphism between typed and type assignment system, and so the typed language inherits from the untyped ...