Renormalization Group¶and the Melnikov Problem for PDE's

We give a new proof of persistence of quasi-periodic, low dimensional elliptic tori in infinite dimensional systems. The proof is based on a renormalization group iteration that was developed recently in [BGK] to address the standard KAM problem, namely, persistence of invariant tori of maximal dimension in finite dimensional, near integrable systems. Our result covers situations in which the so called normal frequencies are multiple. In particular, it provides a new proof of the existence of small-amplitude, quasi-periodic solutions of nonlinear wave equations with periodic boundary conditions. Received: 29 January 2001 / Accepted: 8 March 2001     

Preparation of amino acid nanoparticles at varying saturation conditions in an aerosol flow reactor

In this article, we describe the synthesis of new and ion-selective nanofiltration (NF) membranes using polyvinylidene fluoride (PVDF) nanofibers and hyperbranched polyethylenimine (PEI) as building blocks. These new nanofibrous composite (NFC) membranes consist of crosslinked hyperbranched PEI networks supported by PVDF nanofibrous scaffolds that are electrospun onto commercial PVDF microfiltration (MF) membranes. A major objective of our study was to fabricate positively charged NF membranes that can be operated at low pressure with high water flux and improved rejection for monovalent cations. To achieve this, we investigated the effects of crosslinker chemistry on membrane properties (morphology, composition, hydrophobicity, and zeta potential) and membrane performance (salt rejection and permeate flux) in aqueous solutions (2,000?mg/L) of four salts (NaCl, MgCl₂, Na₂SO₄, and MgSO₄) at pH 4, 6, and 8. We found that an NFC?CPVDF membrane with a network of PEI macromolecules crosslinked with trimesoyl chloride has a high water flux (~30?L?m^?2?h^?1) and high rejections for MgCl₂ (~88 %) and NaCl (~65 %) at pH 6 using a pressure of 7?bar. The overall results of our study suggest that PVDF nanofibers and hyperbranched PEI are promising building blocks for the fabrication of high performance NF membranes for water purification.     

The Altshuler–Shklovskii Formulas for Random Band Matrices I: the Unimodular Case

Communications in Mathematical Physics - We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We show that the correlation function of the local eigenvalue...     

Baseline value specification and sensitivity analysis in multiattribute project portfolio selection

A key issue in applying multi-attribute project portfolio models is specifying the baseline value – a parameter which defines how valuable not implementing a project is relative to the range of possible project values. In this paper we present novel baseline value specification techniques which admit incomplete preference statements and, unlike existing techniques, make it possible to model problems where the decision maker would prefer to implement a project with the least preferred performance level in each attribute. Furthermore, we develop computational methods for identifying the optimal portfolios and the value-to-cost -based project rankings for all baseline values. We also show how these results can be used to (i) analyze how sensitive project and portfolio decision recommendations are to variations in the baseline value and (ii) provide project decision recommendations in a situation where only incomplete information about the baseline value is available.     

Ethyl Pyrogall[6]arene and Pyrogall[4]arene: Synthesis,Structural Analysis and Derivatization

In the acid-catalyzed synthesis of ethyl pyrogallarene, a novel hexamer, ethyl pyrogall arene, is obtained as a readily isolable minor product. Pyrogallarene can be isolated from the reaction mixture in three different ways yielding the hexamer in different forms and stabilities. Crystallization from DMSO and then recrystallization from acetone gives a stable crystalline solid, recrystallization directly from acetone yields an unstable white powder, while direct recrystallization from THF gives a stable white powder. Both pyrogallarene and pyrogallarene crystallize readily with DMSO filling the voids in the crystal lattice. Co-crystallization studies of the hexamer isolated by recrystallization from acetone resulted in a novel directly hydrogen-bonded capsule formed by two pyrogallarenes and an included TMA cation, while the DMSO/acetone isolated product yielded the intact hexamer with clathrate-type TMA inclusion.     

Structural Principles and Thermoelectric Properties of Polytypic Group 14 Clathrate‐II Frameworks

We have investigated the structural principles and thermoelectric properties of polytypic group 14 clathrate‐II frameworks using quantum chemical methods. The experimentally known cubic 3C polytype was found to be the energetically most favorable framework, but the studied hexagonal polytypes (2 H, 4 H, 6 H, 8 H, 10 H) lie energetically close to it. In the case of germanium, the energy difference between the 3C and 6H clathrate‐II polytypes is ten times smaller than the difference between the experimentally known 3C‐Ge (α‐Ge) and 4H‐Ge polytypes. The thermoelectric properties of guest‐occupied clathrate‐II structures were investigated for compositions Na–Rb–Ga–Ge and Ge–As–I. The clathrate‐II structures show promising thermoelectric properties and the highest Seebeck coefficients and thermoelectric power factors were predicted for the 3C polytype. The structural anisotropy of the largest studied hexagonal polytypes affects their thermoelectric power factors by over a factor of two.     

Triplet harvesting in poly(9‐vinylcarbazole) and poly(9‐(2,3‐epoxypropyl)carbazole) doped with CdSe/ZnS quantum dots encapsulated with 16‐(N‐carbazolyl) hexadecanoic acid ligands

Semiconductor quantum dots (QDs) can be used as alternative for transition metal complexes to harvest the nonemissive triplet excitons in organic light‐emitting diodes (OLEDs). In search for a QD‐based OLED material generating blue emission, poly(9‐vinylcarbazole) (PVK) and poly(9‐(2,3‐epoxypropyl) carbazole) (PEPK) are chosen as host for blue‐emitting CdSe/ZnS core/shell QDs. The QDs are encapsulated with 16‐(N‐carbazolyl) hexadecanoic acid (C16), a ligand terminated by a carbazole moiety. As alternative for PVK, PEPK, where the lower molecular weight and less extensive excimer formation could promise a better film formation and more extensive exciton hopping, is explored. The efficiencies of singlet ( ) and triplet ( ) energy transfer to the C16 capped QDs are estimated by combining stationary photoluminescence spectra and fluorescence decays of pristine polymer films with those of polymer films doped with the QDs. At a loading of 30 wt % of the QDs, increases from 12 ± 1% in PVK to 41 ± 2% in PEPK while increases from 37 ± 22% in PVK to 72 ± 48% in PEPK. The investigation of the film morphology by atomic force microscopy confirms that the main factor limiting the triplet transfer efficiency in the PVK matrix is the clustering of the C16 capped QDs. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 539–551