Second Order Optimality Conditions for Problems with Continuously Differentiable Data

In this note, by making use of the concept of unbounded approximate Hessian matrices, we present second order optimality conditions for a constrained mathematical programming problem with data whose gradient map is continuous, but not necessarily locally Lipschitz.     

Optimal error estimates of a decoupled scheme based on two-grid finite element for mixed Stokes–Darcy model

Although the numerical results suggest the optimal convergence order of the two-grid finite element decoupled scheme for mixed Stokes–Darcy model with Beavers–Joseph–Saffman interface condition in literatures, the numerical analysis only gets the optimal error order for porous media flow and a non-optimal error order that is half order lower than the optimal one in fluid flow. The purpose of this paper is to fill in the gap between the numerical results and the theoretical analysis.     

LARGE SCALE,EFFICIENT SYNTHESIS OF 9-UNSUBSTITUTED DIPYRRINONE

ABSTRACT

9-Unsubstituted dipyrrinone 8, the useful precursor for the synthesis of biliverdins, bilirubins, and other bile pigments, was synthesized in large scale and high yield starting from acetaldehyde and nitroethane in eight steps with overall yield 10%. The key intermediate 3,4-dimethyl-2-ethoxycarbonylpyrrole 3 was synthesized via Zard–Barton's method in high yield.     

Metal‐ and solvent‐free,clickable synthesis and postpolymerization functionalization of poly(triazole)s

In this study, a series of linear poly(triazole)s (PTAs) were successfully synthesized by the metal‐ and solvent‐free, thermal click polymerization of diazide and dialkyne (A₂ + B₂) monomers. All click polymerizations proceeded smoothly at 80 °C in an open atmosphere without protection from oxygen and moisture. After being polymerized for 36 h, the crude polymer was further fractionated into three fractions using a multistep precipitation method. By selectively choosing precipitating agents, this process produced poly(triazole) fractions with low polydispersity index (<1.30). The resulting PTAs are soluble in common organic solvents and stable at a temperature up to 320 °C. Furthermore, the methyl benzoate moieties in the main chain can serve as useful building blocks for further postpolymerization functionalization, yielding 1,2,4‐triazole derivatives. This functionalization strategy offers potential for the development of novel triazole‐based materials. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Microwave‐assisted synthesis and characterization of biodegradable block copolyesters based on poly(3‐hydroxyalkanoate)s and poly(D,L‐lactide)

Microwave (MW)‐assisted ring‐opening polymerization (ROP) provides a rapid and straightforward method for engineering a wide array of well‐defined poly(3‐hydroxyalkanoate)‐b‐poly(D,L ‐lactide) (PHA‐b‐PLA) diblock copolymers. On MW irradiation, the bulk ROP of D,L ‐lactide (LA) could be efficiently triggered by a series of monohydroxylated PHA‐based macroinitiators previously produced via acid‐catalyzed methanolysis of corresponding native PHAs, thus affording diblock copolyesters with tunable compositions. The dependence of LA polymerization on temperature, macroinitiator structure, irradiation time, and [LA]₀/[PHA]₀ molar ratio was carefully investigated. It turned out that initiator efficiency values close to 1 associated with conversions ranging from 50 to 85% were obtained only after 5 min at 115 °C. A kinetic investigation of the MW‐assisted ROP of LA gave evidence of its “living”/controlled character under the experimental conditions selected. Structural analyses and thermal properties of biodegradable diblock copolyesters were also performed. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Crime and punishment: Does it pay to punish?

Crime is the result of a rational distinctive balance between the benefits and costs of an illegal act. This idea was proposed by Becker more than forty years ago (Becker (1968) [1]). In this paper, we simulate a simple artificial society, in which agents earn fixed wages and can augment (or lose) wealth as a result of a successful (or not) act of crime. The probability of apprehension depends on the gravity of the crime, and the punishment takes the form of imprisonment and fines. We study the costs of the law enforcement system required for keeping crime within acceptable limits, and compare it with the harm produced by crime. A sharp phase transition is observed as a function of the probability of punishment, and this transition exhibits a clear hysteresis effect, suggesting that the cost of reversing a deteriorated situation might be much higher than that of maintaining a relatively low level of delinquency. Besides, we analyze economic consequences that arise from crimes under different scenarios of criminal activity and probabilities of apprehension.     

Neurofibrillary tangles and plaques are not accompanied by white matter pathology in aged triple transgenic-Alzheimer disease mice

Alzheimer's disease (AD) is a progressive neurodegenerative disorder that is the most common cause of dementia in aging populations. Although senile plaques and neurofibrillary tangles are well-established hallmarks of AD, changes in cerebral white matter correlate with cognitive decline and may increase the risk of the development of dementia. We used the triple transgenic (3xTg)-AD mouse model of AD, previously used to show that white matter changes precede plaque formation, to test the hypothesis that MRI detectable changes occur in the corpus callosum, external capsule and the fornix. T₂-weighted and diffusion tensor magnetic resonance imaging and histological stains were employed to assess white matter in older (11–17 months) 3xTg-AD mice and controls. We found no statistically significant changes in white matter between 3xTg-AD mice and controls, despite well-developed neurofibrillary tangles and beta amyloid immunoreactive plaques. Myelin staining was normal in affected mice. These data suggest that the 3xTg-AD mouse model does not develop MRI detectable white matter changes at the ages we examined.     

Formation of a crosslinked POSS network by an unusual hydrosilylation: Thermo‐oxidative stabilization of the α‐cristobalite phase in its amorphous regions

A semicrystalline inorganic–organic hybrid crosslinked network containing polyhedral oligomeric silsesquioxane (POSS) cores was constructed by the unusual hydrosilylation of the terminal vinyl groups of an internal acetylene‐containing silane linker by a POSS monomer. Products from the thermal treatments of this network in either argon or air at 250, 550, and 1000 °C, respectively, were characterized by Fourier transform infrared, Solid‐state ¹³C and ²⁹Si magic angle spinning NMR, X‐ray diffraction and XPS analyses. The highly symmetrically functionalized POSS silica clusters, in the fluorite silica phase, in the network were found to remain unchanged on thermal treatment possibly due to the shielding of the silica core by the functionalities and a cancellation of thermal stresses on the silica core. Stabilization of the metastable α‐cristobalite phase, which is typically formed on cooling by a β‐ to α‐transition of the β‐cristobalite phase formed above 1400 °C, was observed in the amorphous regions in the network sample treated only to 1000 °C in air. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Synthesis and characterization of polymethacrylates containing conjugated oligo(phenylene ethynylene)s as side chains

In order to form suitable systems designed for resonance energy transfer, a series of monodisperse methacrylate‐based monomers containing rigid π‐conjugated oligo(phenylene ethynylenes) with different sizes of the conjugated systems ( M1 – M3 ), and therefore different optoelectronic properties, were synthesized and subsequently polymerized using the reversible addition–fragmentation chain transfer polymerization technique ( P1 – P3 ). In addition, these oligomers were also copolymerized with methyl methacrylate. The obtained polymers were characterized by ¹H NMR spectroscopy, size exclusion chromatography, and analytical ultracentrifugation. The photophysical properties of the polymers were studied by UV–vis absorption and emission spectroscopy in diluted solutions as well as in thin films and compared to the photophysics of the corresponding monomers. Thereby, changes going from monomeric to polymeric systems could be detected in fluorescence quantum yields and lifetimes pointing to energy trapping, e.g., energy transfer. Donor–acceptor copolymers containing different numbers of monomeric units within the side chain exhibit differences in the emission spectra, indicating that energy trapping in polymers is very sensitive to structural properties such as the chain length. UV–vis absorption spectroscopy as well as time‐resolved lifetime studies indicate intrapolymer and interpolymer energy transfer. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012