Coagulum formation and elimination in emulsion copolymerization of tribromostyrene with styrene

Coagulum formation in emulsion polymerization of tribromostyrene and also in its copolymerization with styrene has been shown to be due to thermal polymerization. The latter takes place in the monomer reservoirs, even in the absence of radical generating initiators, converting them into sticky particles which then form the undesired coagulum. The coagulum formation phenomenon can thus be remedied by reducing the thermal initiation level through a semi-batch emulsion polymerization method, by lowering the polymerization temperature, and reduction of the collision frequency of monomer/polymer particles.     

The Dual‐Stereocontrol Mechanism: Heteroselective Polymerization of rac‐Lactide and Syndioselective Polymerization of meso‐Lactide by Chiral Aluminum Salan Catalysts

We describe alkoxo‐aluminum catalysts of chiral bipyrrolidine‐based salan ligands that follow the dual‐stereocontrol mechanism wherein a given combination of stereogeneities at the metal site and the proximal center of the last inserted lactidyl (“match”) is active towards lactide having a proximal stereogenic center of the opposite configuration, while the diastereomeric combination of stereogeneities (“mismatch”) is inactive towards any lactide. Polymerization of rac‐LA by the enantiomerically pure catalysts was sluggish and gave stereoirregular poly(lactic acid) (PLA) because selective insertion to a match diastereomer gives a mismatch diastereomer. The racemic catalysts showed higher activity and led to highly heterotactic PLA following polymeryl exchange between two mismatched catalyst enantiomers. A succession of match diastereomers in selective meso‐LA insertions led to syndiotactic PLAs reaching a syndiotacticity degree of α=0.96. This polymer featured a T_m of 153 °C matching the highest reported value, and the highest crystallinity (ΔH_m=56 J g^?1) ever reported for syndiotactic PLA.     

Estimates of Green and Martin kernels for Schrödinger operators with singular potential in Lipschitz domains

Consider operators of the form $L^{\gamma V}:=\mathrm{\Delta }+\gamma V$ in a bounded Lipschitz domain $\mathrm{\Omega }?{\mathbb{R}}^N$. Assume that $V\in C^1(\mathrm{\Omega })$ satisfies $|V(x)|\le \overline{a}\mathrm{dist}{(x,?\mathrm{\Omega })}^{?2}$ for every $x\in \mathrm{\Omega }$ and γ is a number in a range $({\gamma }_{?},{\gamma }_{+})$ described in the introduction. The model case is $V(x)=\mathrm{dist}{(x,F)}^{?2}$ where F is a closed subset of ?Ω and $\gamma <c_H(V)=$ Hardy constant for V. We provide sharp two sided estimates of the Green and Martin kernel for $L^{\gamma V}$ in Ω. In addition we establish a pointwise version of the 3G inequality.     

On the Aqueous Chemistry of the UIV–DOTA Complex

The 1,4,7,10-tetrazacyclodecane-1,4,7,10-tetraacetic acid (DOTA) aqueous complex of U^IV with H₂O, OH⁻, and F⁻ as axial ligands was studied by using UV/Vis spectrophotometry, ESI-MS, NMR spectroscopy, X-ray crystallography, and electrochemistry. The U^IV–DOTA complex with either water or fluoride as axial ligands was found to be inert to oxidation by molecular oxygen, whereas the complex with hydroxide as an axial ligand slowly hydrolyzed and was oxidized by dioxygen to a diuranate precipitate. The combined data set acquired shows that, although axial substitution of fluoride and hydroxide ligands instead of water does not seem to significantly change the aqueous DOTA complex structure, it has an important effect on the electronic configuration of the complex. The U^IV/U^III redox couple was found to be quasi-reversible for the complex with both axially bonded H₂O and hydroxide, but irreversible for the complex with axially bonded fluoride. Intriguingly, binding of the axial fluoride renders the irreversible one-electron U^V/U^IV oxidation of the [U^IV(DOTA)(H₂O)] complex quasi-reversible, which suggests the formation of the short-lived pentavalent form of the complex, an aqueous non-uranyl chelated U^V cation.     

Solving the spectroscopic phase: imaging excited wave packets and extracting excited state potentials from fluorescence data

We develop an inversion scheme for obtaining the signs of transition-dipole amplitudes from fluorescence line intensities. Using the amplitudes thus obtained we show how to extract highly accurate excited state potential(s) and the transition-dipole(s) as a function of inter-nuclear displacements. The same dipole amplitudes can also be used to extract the phase and amplitude of unknown time-evolving wave packets, in essentially a quantum non-demolition manner. The procedure, which is demonstrated for the A((1)∑) and B((1)Π(u)) states of the Na(2) molecule, is shown to yield reliable results even when we are given incomplete or uncertain data. We also demonstrate the success of our approach in extracting double minimum potentials. The inversion scheme is in principle applicable to any polyatomic molecule.     

Scale-free human migration and the geography of social networks

The “gravitational law of social interaction”, by which the probability of a social link decreases inversely with the square of the geographic distance, has been recently documented. The source of this spatial property of social networks, however, is yet unknown. The formation of social links is related to human dynamics both on the day-to-day, typically small scale, level of mobility, and on larger scale migration (or reallocation) movements. In this study we analyze human migration patterns by investigating the migration of 46.8 million individuals across the US during 1995-2000. We find that the probability of migration decreases as a power law of the distance, with exponent −1. We show that this finding offers an explanation for the gravitational law of social interaction. Possible explanations and implications of the scale-free migration pattern are discussed.     

An Apparatus for Production of Isotopically and Spin-Enriched Hydrogen for Induced Polarization Studies

An apparatus for the production of hydrogen for hydrogenation-induced polarization studies was developed. The apparatus provides hydrogen gas from a solid source, thereby simplifying the requirement for siting of the apparatus. The produced hydrogen can be either isotopically enriched (with deuterium) or spin-enriched (with parahydrogen). These specialty gases were produced at small predetermined quantities and ambient pressure. The properties of the hydrogen mixtures were characterized by gas-phase nuclear magnetic resonance. The T ₁ of the hydrogen mixtures (3.7 ms) was not affected by para-enrichment. The line width of the hydrogen signal in the para-enriched mixture was 34% larger. The reaction of ethyl propiolate hydrogenation served to evaluate the performance in terms of the ability to create hyperpolarized states. In this reaction, a polarization of 11.2% was measured for protons. Consecutive alkene hydrogenations as well as hydrogenations of the catalyst ligand resulted in additional hyperpolarized signals which were systematically assigned.     

Lanchester model for three-way combat

Lanchester (1960) modeled combat situations between two opponents, where mutual attrition occurs continuously in time, by a pair of simple ordinary (linear) differential equations. The aim of the present paper is to extend the model to a conflict consisting of three parties. In particular, Lanchester’s main result, i.e. his Square Law, is adapted to a triple fight. However, here a central factor – besides the initial strengths of the forces – determining the long run outcome is the allocation of each opponent’s efforts between the other two parties. Depending on initial strengths, (the) solution paths are calculated and visualized in appropriate phase portraits. We are able identify regions in the state space where, independent of the force allocation of the opponents, always the same combatant wins, regions, where a combatant can win if its force allocation is wisely chosen, and regions where a combatant cannot win itself but determine the winner by its forces allocation. As such, the present model can be seen as a forerunner of a dynamic game between three opponents.     

The effectiveness of ‘what if not’ strategy coupled with dynamic geometry software in an inquiry-based geometry classroom

In this paper we present the results of a study which was carried out in an inquiry-based teaching and learning environment with the use of ‘what if not’ methodology coupled with the integration of dynamic geometry software. The vast majority of the students reported that they perceived themselves as participants rather than spectators. Most of the prospective teachers came to the conclusion that the implementation of the findings of this study in their future teachings was a good idea and that it will raise the students’ motivation and enhance and deepen the knowledge pool of the learners.     

Maximum Conditional Probability Stochastic Controller for Linear Systems with Additive Cauchy Noises

Journal of Optimization Theory and Applications - Motivated by the sliding mode control approach, a stochastic controller design methodology is developed for discrete-time, vector-state linear...