Interpolation inequality and some applications

We introduce a new interpolation inequality which will be more relevant than the standard weighted one \cite{GT, H1, FH, RW} in providing integral estimate to solutions of PDE's. Consequently, we establish explicit universal estimate of finite Morse index solutions to polyharmonic equation. Differently to previous works \cite{DDF, fa, H1, WY}, we propose here a direct proof under large superlinear and subcritical growth conditions to show that the universal constant evolves as a polynomial function of the Morse index. We also improve previous nonexistence results \cite{H1, FH} concerning stable at infinity weak solutions to the $p$-polyharmonic equation in the subcritical range.Comment: This paper is origina

Low-Temperature Solution-Processed Electron Transport Layers for Inverted Polymer Solar Cells

© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimProcessing temperature is highlighted as a convenient means of controlling the optical and charge transport properties of solution processed electron transport layers (ETLs) in inverted polymer solar cells. Using the well-studied active layer – poly(3-hexylthiophene-2,5-diyl):indene-C60 bisadduct – the influence of ETL processing temperatures from 25 to 450 °C is shown, reporting the role of crystallinity, structure, charge transport, and Fermi level (EF) on numerous device performance characteristics. It has been determined that an exceptionally low temperature processed ETL (110 °C) increases device power conversion efficiency by a factor greater than 50% compared with a high temperature (450 °C) processed ETL. Modulations in device series and shunt resistance, induced by changes in the ETL transport properties, are observed in parallel to significant changes in device open circuit voltage attributed to changes on the EF of the ETLs. This work highlights the importance of interlayer control in multilayer photovoltaic devices and presents a convenient material compatible with future flexible and roll-to-roll processes

The Lane–Emden equation in strips

International audienceWe study the Lane-Emden equation in strips

Finite Morse index solutions of the Hénon Lane–Emden equation

Abstract In this paper, we are concerned with Liouville-type theorems of the Hénon Lane–Emden triharmonic equations in whole space. We prove Liouville-type theorems for solutions belonging to one of the following classes: stable solutions and finite Morse index solutions (whether positive or sign-changing). Our proof is based on a combination of the Pohozaev-type identity, monotonicity formula of solutions and a blowing down sequence

Decoherence of flux qubits due to 1/f flux noise

We have investigated decoherence in Josephson-junction flux qubits. Based on the measurements of decoherence at various bias conditions, we discriminate contributions of different noise sources. In particular, we present a Gaussian decay function of the echo signal as evidence of dephasing due to $1/f$ flux noise whose spectral density is evaluated to be about $(10^{-6} \Phi_0)^2$/Hz at 1 Hz. We also demonstrate that at an optimal bias condition where the noise sources are well decoupled the coherence observed in the echo measurement is mainly limited by energy relaxation of the qubit.Comment: 4 pages, error in Fig.4 corrected, to appear in PR