A new electrochemical cell adapted to quartz crystal microbalance measurements

As the resonance frequency of an oscillating quartz changes upon the deposition of a given mass to the crystal surface, it can be used as a very sensitive mass measuring device. Despite a growing interest in the use of electrochemical quartz crystal microbalance (EQCM), there is still no commercial available measurement cell which can satisfy all the conditions needed in electrochemical investigations. The design and characteristics of a new electrochemical cell adapted to EQCM measurements are presented. The sensitivity of the microbalance, which is determined by several calibration runs of silver electrodeposition is (183.2±2.9) Hz μg⁻¹ cm². This value, which is close to the theoretical one, confirms the validity of the system we have developed. The calibration procedure and the EQCM using range are then discussed.     

Neutral bis­(ethyl­enedi­thio)­tetra­thia­fulvalene at 100 K

The low‐temperature crystal structure of bis­(ethyl­enedi­thio)­tetra­thia­fulvalene (BEDT‐TTF), C₁₀H₈S₈, is similar to its high‐temperature structure. The room‐temperature central bond lengths of this mol­ecule are often used as reference in empirical methods to estimate the charge carried by the (BEDT‐TTF)_xⁿ⁺ cations in the BEDT‐TTF mol­ecule‐based organic conductors. We show that the method we previously reported can still be used with low‐temperature BEDT‐TTF salts data. Moreover, we confirm the purely thermal origin of the ordering of the ethyl­ene group.     

L1 Continuous Dependence Property¶for Systems of Conservation Laws

This paper is concerned with the uniqueness and L¹ continuous dependence of entropy solutions for nonlinear hyperbolic systems of conservation laws. We study first a class of linear hyperbolic systems with discontinuous coefficients: Each propagating shock wave may be a Lax shock, or a slow or fast undercompressive shock, or else a rarefaction shock. We establish a result of L¹ continuous dependence upon initial data in the case where the system does not contain rarefaction shocks. In the general case our estimate takes into account the total strength of rarefaction shocks. In the proof, a new time-decreasing, weighted L¹ functional is obtained via a step-by-step algorithm. To treat nonlinear systems, we introduce the concept of admissible averaging matrices which are shown to exist for solutions with small amplitude of genuinely nonlinear systems. Interestingly, for many systems of continuum mechanics, they also exist for solutions with arbitrary large amplitude. The key point is that an admissible averaging matrix does not exhibit rarefaction shocks. As a consequence, the L¹ continuous dependence estimate for linear systems can be extended to nonlinear hyperbolic systems using a wave-front tracking technique.     

A Sobolev mapping property of the Bergman kernel

We prove that if D is a pseudoconvex domain with Lipschitz boundary having an exhaustion function such that is plurisubharmonic, then the Bergman projection maps the Sobolev space boundedly to itself for any . Received March 10, 1999 / Published online May 8, 2000     

Multianalytical Study of Patina Formed on Archaeological Metal Objects from Bliesbruck-Reinheim

 Patinas naturally formed on archaeological bronze alloys were characterized using light microscopy (LM), micro energy dispersive X-ray fluorescence analysis (μ-EDXRF), time of flight secondary ion mass spectrometry (TOF-SIMS) and scanning electron microscopy in combination with energy dispersive X-ray microanalysis (SEM/EDX). The examinations carried out on cross-sections of samples have shown that in all samples the copper content in the corrosion layer is lower than in the bulk, while an increase of tin and lead could be observed. Two different types of corrosion were found: first type, a corrosion formation leading to a three layer structure was observed on lead bronze. The outer layer consists mainly of Cu(II) compounds and soil material, followed by a fragmented layer of cuprous oxide and the surface layer of the alloy, where a depletion of copper and an enrichment of tin and high amounts of Cl could be detected. The second type of corrosion is characterized by a two layer structure on the tin bronze sample consisting of an outer layer with copper containing corrosion products and a layer with cracks, which reveals a depletion of copper whereas tin and lead are enriched. Also high amounts of Si were detected in this surface layer.     

The Euclidean Steiner tree problem in Rn: A mathematical programming formulation

A nonconvex mixed-integer programming formulation for the Euclidean Steiner Tree Problem (ESTP) in Rⁿ is presented. After obtaining separability between integer and continuous variables in the objective function, a Lagrange dual program is proposed. To solve this dual problem (and obtaining a lower bound for ESTP) we use subgradient techniques. In order to evaluate a subgradient at each iteration we have to solve three optimization problems, two in polynomial time, and one is a special convex nondifferentiable programming problem. This revised version was published online in June 2006 with corrections to the Cover Date.     

Fast algorithm for solving the Hankel/Toeplitz Structured Total Least Squares problem

The Structured Total Least Squares (STLS) problem is a natural extension of the Total Least Squares (TLS) problem when constraints on the matrix structure need to be imposed. Similar to the ordinary TLS approach, the STLS approach can be used to determine the parameter vector of a linear model, given some noisy measurements. In many signal processing applications, the imposition of this matrix structure constraint is necessary for obtaining Maximum Likelihood (ML) estimates of the parameter vector. In this paper we consider the Toeplitz (Hankel) STLS problem (i.e., an STLS problem in which the Toeplitz (Hankel) structure needs to be preserved). A fast implementation of an algorithm for solving this frequently occurring STLS problem is proposed. The increased efficiency is obtained by exploiting the low displacement rank of the involved matrices and the sparsity of the associated generators. The fast implementation is compared to two other implementations of algorithms for solving the Toeplitz (Hankel) STLS problem. The comparison is carried out on a recently proposed speech compression scheme. The numerical results confirm the high efficiency of the newly proposed fast implementation: the straightforward implementations have a complexity of O((m+n)³) and O(m³) whereas the proposed implementation has a complexity of O(mn+n²). This revised version was published online in June 2006 with corrections to the Cover Date.     

Estimation of a Bivariate Extreme Value Distribution

Several threshold methods have been proposed for the purpose of estimating a bivariate extreme value distribution from a sample of data whose distribution is only in its domain of attraction. An integrated view of these methods is presented which leads to the introduction of a new asymptotically consistent estimator of the dependence function characterizing the extreme dependence structure. Through Monte Carlo simulations, the new estimator is also shown to do as well as its competitors and to outperform them in cases of weak dependence. To the authors' knowledge, this is the first time that the small-sample behavior of nonparametric bivariate threshold methods has ever been investigated.     

Inviscid Limits¶of the Complex Ginzburg–Landau Equation

In the inviscid limit the generalized complex Ginzburg–Landau equation reduces to the nonlinear Schr?dinger equation. This limit is proved rigorously with H ¹ data in the whole space for the Cauchy problem and in the torus with periodic boundary conditions. The results are valid for nonlinearities with an arbitrary growth exponent in the defocusing case and with a subcritical or critical growth exponent at the level of L ² in the focusing case, in any spatial dimension. Furthermore, optimal convergence rates are proved. The proofs are based on estimates of the Schr?dinger energy functional and on Gagliardo–Nirenberg inequalities. Received: 2 April 1999 / Accepted: 29 March 2000     

Preparation of Well‐Defined Poly[(ethylene oxide)‐block‐(sodium 2‐acrylamido‐2‐methyl‐1‐propane sulfonate)] Diblock Copolymers by Water‐Based Atom Transfer Radical Polymerization

Summary: Well‐defined poly[(ethylene oxide)‐block‐(sodium 2‐acrylamido‐2‐methyl‐1‐propane sulfonate)] diblock copolymers [P(EO_m‐b‐AMPS_n)], have been obtained by water‐based ATRP using α‐methoxy‐ω‐(2‐methylbromoisobutyrate) poly(ethylene oxide)s (MeO‐P[EO]_m‐BrⁱB with m ranging from 12 to 113) and CuBr · 2Bpy (Bpy for 2,2′‐bipyridyl) as macroinitiator and catalytic complex, respectively. Compared to direct polymerization in water, it has been demonstrated that the water/methanol (3:1, v/v) mixture is better suited for predicting the final number‐average molar mass from the initial monomer‐to‐macroinitiator molar ratio and achieving a quite narrow polydispersity, even at high monomer conversion ( ≈ 1.4 at 80% conversion). The effect of temperature, solvent mixture composition and addition of NaCl salt on the polymerization rate and extent of control over the copolymer molecular parameters have been highlighted as well.