Continuous reaction system to investigate the dispersion polymerization of vinyl monomers in supercritical carbon dioxide

A laboratory‐scale continuous reaction system using a stirred tank reactor was assembled in our laboratory to study the dispersion polymerization of vinyl monomers in supercritical carbon dioxide (scCO₂). The apparatus was equipped with a suitable downstream separation section to collect solid particles entrained in the effluent stream from the reactor, whose monomer concentration could be measured online with a gas chromatograph. The dispersion polymerization of methyl methacrylate in scCO₂ was selected as a model process to be investigated in the apparatus. The experiments were performed at 65 °C and 25 MPa with 2,2′‐azobisisobutyronitrile as the initiator and a reactive polysiloxane macromonomer as a surfactant to investigate the effect of the mean residence time of the reaction mixture on the monomer conversion, polymerization rate, polymer molecular weight, and particle size distribution. The results were compared with those obtained in batch polymerizations carried out under similar operative conditions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4122–4135, 2006     

Diff (S 1) and the Teichmüller spaces

Precisely two of the homogeneous spaces that appear as coadjoint orbits of the group of string reparametrizations, , carry in a natural way the structure of infinite dimensional, holomorphically homogeneous complex analytic Kähler manifolds. These areN=Diff(S ¹)/Rot(S ¹) andM=Diff(S ¹)/Möb(S ¹). Note thatN is a holomorphic disc fiber space overM. Now,M can be naturally considered as embedded in the classical universal Teichmüller spaceT(1), simply by noting that a diffeomorphism ofS ¹ is a quasisymmetric homeomorphism.T(1) is itself a homomorphically homogeneous complex Banach manifold. We prove in the first part of the paper that the inclusion ofM inT(1) iscomplex analytic.In the latter portion of this paper it is shown that theunique homogeneous Kähler metric carried byM = Diff (S ¹/SL(2, ) induces preciselythe Weil-Petersson metric on the Teichmüller space. This is via our identification ofM as a holomorphic submanifold of universal Teichmüller space. Now recall that every Teichmüller spaceT(G) of finite or infinite dimension is contained canonically and holomorphically withinT(1). Our computations allow us also to prove that everyT(G), G any infinite Fuchsian group, projects out ofM transversely. This last assertion is related to the fractal nature ofG-invariant quasicircles, and to Mostow rigidity on the line.Our results thus connect the loop space approach to bosonic string theory with the sum-over-moduli (Polyakov path integral) approach.     

Existence of standing waves for dirac fields with singular nonlinearities

We prove the existence of stationary states for nonlinear Dirac equations of the form (E) $$i\sum\limits_{\mu = 0}^3 {\gamma ^\mu \partial _\mu \psi - M\psi + F\left( {\bar \psi \psi } \right)\psi = 0,} $$ whereM>0 andF is a singular self-interaction. In particular, in the model case whereF(s)=?s ^?α, for some 0<α<1, and for every ω>M, there exists a solution of (E) of the form ψ(t, x)=e ^iωt?(x), wherex ₀=t andx=(x ₁,x ₂,x ₃), such that ? has compact support. IF 0<α<1/3, then ? is of classC ¹. If 1/3<α<1, then ? is continuously differentiable, except on some sphere {|x|=R}, where |??| is infinite.     

Bounded speed of propagation for solutions to radiative transfer equations

The Radiative Transfer Equation is the nonlinear transport equation

Generalized solutions of a class of nuclear-space-valued stochastic evolution equations

Generalized solutions are defined for stochastic evolution equations of the formdY _t =A ^* Y _t dt + dZ _t on the nuclear triplel(R ^d ) L²(R ^d ) l(R ^d ), whereA does not mapl(R ^d ) into itself. One case which is treated in detail involvesA = –(–) ^/2 ,0 < < 2. This example arises as the Langevin equation for the fluctuation limit of a system of particles migrating according to a symmetric stable process and undergoing critical branching in a random medium.The research of D. A. Dawson was supported by the Natural Sciences and Engineering Research Council of Canada. L. G. Gorostiza's research was supported in part by CONACyT Grants PCEXCNA-040319 and 140102 G203-006, Mexico.     

Divisible modules and space of divisibility of an integral domain

Sunto Se A è un modulo divisibile su un dominio d'integrità R e Q è il campo delle frazioni di R, sia R_A Q il massimo sopraanello di R tale che A possa essere dotato della struttura di R_A-modulo. La struttura di R_A riflette quella di A. Se A è un modulo divisibile semplice di torsione, cioè è divisibile di torsione e non ha sottomoduli divisibili propri non nulli, R_A è analiticamente irriducibile. Se C e D sono due moduli divisibili semplici, diciamo C equivalente a D se R_C=R_D. Se d-Space (R) è un insieme di rappresentanti delle classi di equivalenza degli R-moduli divisibili semplici, d-Space (R) puó essere dotato di una struttura di spazio di Hausdorff zero-dimensionale; lo spazio topologico d-Space (R) (da noi chiamato lo spazio di divisibilità di R) contiene un sottospazio chiuso omeomorfo alla superficie di Riemann astratta di R dotata della patch topology.

---

---

Lavoro eseguito con il contribute del Ministero délia Pubblica Istruzione     

Self-assembled peptide tubelets with 7 A pores

Here we report the preparation and structural characteristics of self-assembling peptide tubelets composed of 32-membered rings formed of alternating alpha-amino acids and cis-3-aminocyclohexanecarboxylic acids. The tubelets possess a partial hydrophobic core environment, provided by the projection of the cyclohexane C2 methylene moiety into the lumen, and a Van der Waals pore diameter of about 7 A.     

A comparative study of several HPLC methods for determining free amino acid profiles in honey

A study of the viability of three derivatizing reagents for obtaining amino acid profiles in honey through high performance liquid chromatography (HPLC) is presented. A method using diode array detection based on a reaction with diethyl ethoxymethylene malonate (DEMM) and two other methods using fluorescence detection based on derivatization with fluorenylmethyl chloroformate (FMOC-Cl) and 6-aminoquinolyl-N-hydroxysuccinimidyl carbamate (AQC) have been developed. The three methods yield detection limits close to the ppb level, but vary in relation to other analytical characteristics. The use of methyl chloroformate derivatives allows the profile to be obtained with the greatest sensitivity within a short time frame. On applying such methods to honey samples of diverse botanical origin, we observe that the proline values obtained are always lower than those found using the official spectrophotometric method, thereby underlining the advisability of using HPLC methods to reduce uncertainty in these results.