Regularity and uniqueness in quasilinear parabolic systems

Inspired by a problem in steel metallurgy, we prove the existence, regularity, uniqueness, and continuous data dependence of solutions to a coupled parabolic system in a smooth bounded 3D domain, with nonlinear and nonhomogeneous boundary conditions. The nonlinear coupling takes place in the diffusion coefficient. The proofs are based on anisotropic estimates in tangential and normal directions, and on a refined variant of the Gronwall lemma.     

Geometry of tropical moduli spaces and linkage of graphs

We prove the following “linkage” theorem: two p-regular graphs of the same genus can be obtained from one another by a finite alternating sequence of one-edge-contractions; moreover this preserves 3-edge-connectivity. We use the linkage theorem to prove that various moduli spaces of tropical curves are connected through codimension one.     

Synthesis and structural characterization of syndiotactic trans‐1,2 and cis‐1,2 polyhexadienes

The (E) isomer in mixtures of (E) and (Z) 1,3‐hexadiene was polymerized with the system CoCl₂(PⁱPrPh₂)₂‐MAO, a highly active and stereospecific catalyst for the preparation of 1,2 syndiotactic polybutadiene. A new crystalline polymer with a melting point of 109 °C was obtained. The polymer was characterized by IR, NMR (¹³C, ¹H in solution and ¹³C in the solid‐state), X‐ray diffraction, DSC, GPC and it was found to have a trans‐1,2 syndiotactic structure with a 5.18 ± 0.04 Å fiber periodicity. Since only the (E) isomer was polymerized, at the end of the reaction we were able to separate the (Z) isomer, which was ultimately polymerized with CpTiCl₃‐MAO at low temperature, obtaining a low molecular weight, stereoregular polymer that, characterized by IR and NMR methods, was found to exhibit a cis‐1,2 syndiotactic structure, never reported before. Molecular mechanics calculations were carried out on the trans‐1,2 syndiotactic polymer and structural models consistent with the X‐ray diffraction data are proposed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5339–5353, 2007     

Origin of the optical contrast in phase-change materials

Several chalcogenide alloys exhibit a pronounced contrast between the optical absorption in the metastable rocksalt and in the amorphous phase. This phenomenon is the basis for their application in optical data storage. Here we present ab initio calculations of the optical properties of GeTe and Ge1Sb2Te4 in the two phases. The analysis of our computations and experimental data reveal the correlation between local structural changes and optical properties as well as the origin of the optical contrast in these materials. We find that the change in optical properties cannot be attributed to a smearing of transition energies as commonly assumed for amorphous semiconductors: the optical contrast between the two phases can only be explained by significant changes in the transition matrix elements.     

Gompertz zero-inflated cure rate regression models applied to credit risk data

In the financial market, it is important to consider that there is a proportion of customers that have settled their debt in time zero, immediately recovering their ability to pay. In this context, in this paper, we propose a survival analysis methodology that allows the insertion of times equal to zero in scenarios where credit risk is observed. The proposed model addresses the survival analysis model of the zero-inflated cure rate which incorporates the heterogeneity of three subgroups (individuals having events in the initial time, and individuals not susceptible and susceptible to the event). In our proposal, all available survival data of customers are modeled considering that the number of competitive causes follows a Poisson distribution and the baseline risk function follows a Gompertz distribution. The model parameter estimation is obtained by the maximum likelihood estimation procedure and simulation studies are conducted to evaluate the estimators' performance. The studied methodology will be applied to a credit database provided by a financial institution in Brazil.     

Effect of defect energy on strain-gradient predictions of confined single-crystal plasticity

Gurtin recently proposed a strain-gradient theory for crystal plasticity in which the gradient effect originates from a defect energy that characterizes energy storage due to the presence of a net Burgers vector. Here we consider a number of different possibilities for this energy: specifically, working within a simple two-dimensional framework, we compare predictions of the theory with results of discrete-dislocation simulations of stress relaxation in thin films. Our objective is to investigate which specific defect energies are capable of capturing the size-dependent response of such systems for different crystal orientations.     

Organocatalytic,Asymmetric Eliminative [4+2] Cycloaddition of Allylidene Malononitriles with Enals: Rapid Entry to Cyclohexadiene‐Embedding Linear and Angular Polycycles

A direct aminocatalytic synthesis has been developed for the chemo‐, regio‐, diastereo‐, and enantioselective construction of densely substituted polycyclic carbaldehydes containing fused cyclohexadiene rings. The chemistry utilizes, for the first time, remotely enolizable π‐extended allylidenemalononitriles as electron‐rich 1,3‐diene precursors in a direct eliminative [4+2] cycloaddition with both aromatic and aliphatic α,β‐unsaturated aldehydes. The generality of the process is demonstrated by approaching 6,6‐, 5,6‐, 7,6‐, 6,6,6‐, and 6,5,6‐fused ring systems, as well as biorelevant steroid‐like 6,6,6,6,5‐ and 6,6,6,5,6‐rings. A stepwise reaction mechanism for the key [4+2] addition is proposed as a domino bis‐vinylogous Michael/Michael/retro‐Michael reaction cascade. The utility of the malononitrile moiety as traceless activating group of the dicyano nucleophilic substrates is demonstrated.     

Diketopyrrolopyrrole‐Porphyrin Conjugates with High Two‐Photon Absorption and Singlet Oxygen Generation for Two‐Photon Photodynamic Therapy

Two‐photon photodynamic therapy is a promising therapeutic method which requires the development of sensitizers with efficient two‐photon absorption and singlet‐oxygen generation. Reported here are two new diketopyrrolopyrrole‐porphyrin conjugates as robust two‐photon absorbing dyes with high two‐photon absorption cross‐sections within the therapeutic window. Furthermore, for the first time the singlet‐oxygen generation efficiency of diketopyrrolopyrrole‐containing systems is investigated. A preliminary study on cell culture showed efficient two‐photon induced phototoxicity.     

Using controlled radical polymerization to confirm the lower critical solution temperature of an N‐(alkoxyalkyl) acrylamide polymer in aqueous solution

N‐(3‐Methoxypropyl) acrylamide (MPAM) was polymerized by controlled radical polymerization (CRP) methods such as nitroxide‐mediated polymerization (NMP) and reversible addition–fragmentation chain‐transfer polymerization (RAFT). CRP was expected to yield well‐defined polymers with sharp lower critical solution temperature (LCST) transitions. NMP with the BlocBuilder (2‐([tert‐butyl[1‐(diethoxyphosphoryl)‐2,2‐dimethylpropyl]amino]oxy)‐2‐methylpropanoic acid) and SG1 ([tert‐butyl[1‐(diethoxyphosphoryl)‐2,2‐dimethylpropyl]amino] oxidanyl) initiating system revealed low yields and lack of control (high dispersity, ? ～ 1.5–1.6, and inhibition of chain growth). However, RAFT was far more effective, with linear number average molecular weight, , versus conversion, X, plots, low ? ～ 1.2–1.4 and the ability to form block copolymers using N,N‐diethylacrylamide (DEAAM) as the second monomer. Poly(MPAM) (with = 13.7–25.3 kg mol^?1) thermoresponsive behavior in aqueous media revealed cloud point temperatures (CPT)s between 73 and 92 °C depending on solution concentration (ranging from 1 to 3 wt %). The and the molecular weight distribution were the key factors determining the CPT and the sharpness of the response, respectively. Poly(MPAM)‐b‐poly(DEAAM) block copolymer ( = 22.3 kg mol^?1, ? = 1.41, molar composition F_DEAAM = 0.38) revealed dual LCSTs with both segments revealing distinctive CPTs (at 75 and 37 °C for poly(MPAM) and poly(DEAAM) blocks, respectively) by both UV–Vis and dynamic light scattering. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 59–67