Blow up in finite time and dynamics of blow up solutions for the -critical generalized KdV equation

In this paper, we describe the dynamics of blow up solutions for the critical generalized KdV equation such that the initial data is close to the soliton in and has decay in at the right. In particular, we prove that blow up occurs in finite time, and we obtain an upper bound on the blow up rate.

     

Spin-dependent electron-proton scattering in the Delta-excitation region

We report on measurements of the cross section and provide first data on spin correlation parameters A(TT') and A(TL') in inclusive scattering of longitudinally polarized electrons from nuclear-polarized hydrogen. Polarized electrons were injected into an electron storage ring operated at a beam energy of 720 MeV. Polarized hydrogen was produced by an atomic beam source and injected into an open-ended cylindrical cell, located in the electron storage ring. The four-momentum transfer squared ranged from Q2 = 0.2 GeV(2)/c(2) at the elastic scattering peak to Q2 = 0.11 GeV(2)/c(2) at the Delta(1232) resonance. The data provide a stringent test of pion electroproduction models.     

Controlled synthesis of new amphiphilic glycopolymers with liquid crystal grafts

A cholesterol‐based liquid crystal monomer, diethylene glycol cholesteryl ether acrylate (DEGCholA), has been successfully polymerized by atom transfer radical polymerization (ATRP) for the first time. Appropriate experimental conditions to control the polymerization of DEGCholA have been investigated using a model initiator (ethyl 2‐bromoisobutyrate) in tetrahydrofuran (THF) or toluene at 60 °C. Well‐controlled ATRP of DEGCholA was obtained using N,N,N′,N′,N″‐pentamethyldiethylenetriamine as ligand in THF at 60 °C. These conditions were then applied to initiate the ATRP of DEGCholA from multifunctional macroinitiators based on dextran. Using a protection/deprotection synthetic scheme, novel graft glycopolymers (Dex‐g‐PDEGCholA) have been synthesized. The mesomorphic properties of DEGCholA, PDEGCholA, and Dex‐g‐PDEGCholA have been studied by thermal polarizing optical microscopy, differential scanning calorimetry, and X‐ray scattering. PDEGCholA and Dex‐g‐PDEGCholA show an interdigitated smectic A phase (SmA_d) between T_g (～30 °C) and around 170 °C. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 3829–3839     

Protected versus unprotected dextran macroinitiators for ATRP synthesis of Dex‐g‐PMMA

The synthesis of amphiphilic dextran‐g‐poly(methyl methacrylate) glycopolymers (Dex‐g‐PMMA) is studied using “grafting from” concept and atom transfer radical polymerization. Two strategies have been examined to control the macromolecular parameters of such glycopolymers. One is involving four steps including a protection/deprotection approach and the second one only two steps. The introduction of initiators group onto a protected acetylated dextran (and directly onto dextran) was achieved resulting in protected DexAcBr (and in unprotected DexBr). These two types of polysaccharidic macroinitiators differ in term of solubility (hydrophilic DexBr vs. hydrophobic DexAcBr) and of position of the initiators groups on the glucosidic units (which are the sites of the future grafts). When evaluated as macroinitiators for ATRP of MMA, control was achieved in both cases but DexBr gave much faster polymerization and lower average grafting efficiency compared with DexAcBr or model initiator. Advantages and drawbacks of both pathways have finally been discussed. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

A study of the reaction of n-BuLi with Ti(Oi-Pr)4 as a method to generate titanacyclopropane and titanacyclopropene species

The use of the combination of reagents Ti(Oi-Pr)₄/n-BuLi, introduced by the group of J.J. Eisch in 2001, has only found a few applications so far, with sometimes conflicting observations. This article describes a study aimed at clarifying the nature, the stability and the reactivity of the active organometallic species involved. Reactions with CO₂ and other trapping reagents reveal that it is generated within a few minutes at 0 °C in THF, where it can be considered to be stable for 30 min. Most of our results are consistent with the expected titanacyclopropane nature of this reagent but some observations suggest that the chemistry at play may be more complicated.     

The Idempotents of the TL n -Module {\otimes^{n}\mathbb{C}2} in Terms of Elements of {{\rm U}_{q} \mathfrak{sl}_2}

The vector space \({\otimes^{n}\mathbb{C}^2}\) upon which the XXZ Hamiltonian with n spins acts bears the structure of a module over both the Temperley–Lieb algebra \({{\rm TL}_{n}(\beta = q + q^{-1})}\) and the quantum algebra \({{\rm U}_{q} \mathfrak{sl}_2}\) . The decomposition of \({\otimes^{n}\mathbb{C}^2}\) as a \({{\rm U}_{q} \mathfrak{sl}_2}\) -module was first described by Rosso (Commun Math Phys 117:581–593, 1988), Lusztig (Cont Math 82:58–77, 1989) and Pasquier and Saleur (Nucl Phys B 330:523–556, 1990) and that as a TL _n -module by Martin (Int J Mod Phys A 7:645–673, 1992) (see also Read and Saleur Nucl Phys B 777(3):316–351, 2007; Gainutdinov and Vasseur Nucl Phys B 868:223–270, 2013). For q generic, i.e. not a root of unity, the TL _n -module \({\otimes^{n}\mathbb{C}^2}\) is known to be a sum of irreducible modules. We construct the projectors (idempotents of the algebra of endomorphisms of \({\otimes^{n}\mathbb{C}^2}\) ) onto each of these irreducible modules as linear combinations of elements of \({{\rm U}_{q} \mathfrak{sl}_2}\) . When q = q _c is a root of unity, the TL _n -module \({\otimes^{n}\mathbb{C}^2}\) (with n large enough) can be written as a direct sum of indecomposable modules that are not all irreducible. We also give the idempotents projecting onto these indecomposable modules. Their expression now involves some new generators, whose action on \({\otimes^{n}\mathbb{C}^2}\) is that of the divided powers \({(S^{\pm})^{(r)} = \lim_{q \rightarrow q_{c}} (S^{\pm})^r/[r]!}\) .     

On the Gibbs states of the noncritical Potts model on \mathbb Z ^2

We prove that all Gibbs states of the $q$ -state nearest neighbor Potts model on $\mathbb Z ^2$ below the critical temperature are convex combinations of the $q$ pure phases; in particular, they are all translation invariant. To achieve this goal, we consider such models in large finite boxes with arbitrary boundary condition, and prove that the center of the box lies deeply inside a pure phase with high probability. Our estimate of the finite-volume error term is of essentially optimal order, which stems from the Brownian scaling of fluctuating interfaces. The results hold at any supercritical value of the inverse temperature $\beta >\beta _c (q) = \log \left(1+\sqrt{q}\right)$ .