Automorphisms and Homotopies of Groupoids and Crossed Modules

This paper is concerned with the algebraic structure of groupoids and crossed modules of groupoids. We describe the group structure of the automorphism group of a finite connected groupoid C as a quotient of a semidirect product. We pay particular attention to the conjugation automorphisms of C, and use these to define a new notion of groupoid action. We then show that the automorphism group of a crossed module of groupoids C\mathcal{C}, in the case when the range groupoid is connected and the source group totally disconnected, may be determined from that of the crossed module of groups C_u\mathcal{C}_u formed by restricting to a single object u. Finally, we show that the group of homotopies of C\mathcal{C} may be determined once the group of regular derivations of C_u\mathcal{C}_u is known.     

A spectral collocation algorithm for two-point boundary value problem in fiber Raman amplifier equations

A novel algorithm implementing Chebyshev spectral collocation (pseudospectral) method in combination with Newton’s method is proposed for the nonlinear two-point boundary value problem (BVP) arising in solving propagation equations in fiber Raman amplifier. Moreover, an algorithm to train the known linear solution for use as a starting solution for the Newton iteration is proposed and successfully implemented. The exponential accuracy obtained by the proposed Chebyshev pseudospectral method is demonstrated on a case of the Raman propagation equations with strong nonlinearities. This is in contrast to algebraic accuracy obtained by typical solvers used in the literature. The resolving power and the efficiency of the underlying Chebyshev grid are demonstrated in comparison to a known BVP solver.     

Synthesis and Spectroscopic Studies of 3,6-Diphenyl-2,5-Dihydropyrrolo[3,4-C]Pyrrole-1,4-Dion’s N,N’-Dialkyl Derivatives

3,6-diaryl-2,5-dihydro-1,4-diketopyrrolo[3,4-c]pyrrole-1,4-dione (DPPD) derivatives are used commercially as red pigments, because of their color strength, brightness, and very low solubility in most common solvents. These products, although highly colored, appear to be of limited value as dyes, since they show a tendency to form an aggregate when incorporated into a solvent. Monoalkyl and dialkyl derivatives of DPPD were synthesized and then characterized with IR, ¹HNMR, UV-Vis absorption and emission spectroscopy. Molar absorption coefficient, singlet energy level and Stokes’ shift values of DPPD derivatives were declared. Monoalkyl and dialkyl derivatives of DPPD’s solubilities were measured from saturated solutions of dimethylformamide (DMF), tetrahydrofuran (THF), dichloromethane (DCM), acetonitrile (ACN) and toluene and they are compared with each other.     

Polymer grafting onto polyurethane backbone via Diels–Alder reaction

The aliphatic polyurethane with pendant anthracene moieties (PU‐anthracene) was prepared from polycondensation of anthracen‐9‐yl methyl 3‐hydroxy‐2‐(hydroxymethyl)‐2‐methylpropanoate (anthracene diol), 1 with hexamethylenediisocyanate in the presence of dibutyltindilaurate in CH₂Cl₂ at room temperature for 10 days. Thereafter, the PU‐anthracene (M_n,GPC = 12,900 g/mol, M_w/M_n = 1.87, relative to PS standards) was clicked with a linear α‐furan protected‐maleimide terminated‐poly(methyl methacrylate) (PMMA‐MI) (M_n,GPC = 2500 g/mol, M_w/M_n = 1.33), or ‐poly(ethylene glycol) (PEG‐MI) (M_n,GPC = 550 g/mol, M_w/M_n = 1.09), to result in well‐defined PU‐graft copolymers, PU‐g‐PMMA (M_n,GPC = 23800 g/mol, M_w/M_n = 1.65, relative to PS standards) or PU‐g‐PEG (M_n,GPC = 11,600 g/mol, M_w/M_n = 1.45, relative to PS standards) using Diels–Alder reaction in dioxane/toluene at 105 °C. The Diels–Alder grafting efficiencies were found to be over 93–99% using UV spectroscopy. Moreover, the structural analyses and the thermal transitions of all copolymers were determined via ¹H NMR and DSC, respectively. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 521–527     

Catalytic activity of Ru/tetrahydropyrimidinium salts system for transfer hydrogenation reactions

New 1,3‐dialkyltetrahydropyrimidinium salts as NHC precursors have been synthesized and characterized. The in situ prepared three‐component 1,3‐dialkyltetrahydropyrimidinium salts/[RuCl₂(p‐cymene)]₂ and KOH catalyzes quantitatively the transfer hydrogenation of ketones under mild reaction conditions in 2‐propanol. Also, the molecular structure of 1,3‐bis(2‐methylbenzyl)‐3,4,5,6‐tetrahydropyrimidinium was determined using single‐crystal X‐ray diffraction. Ions of the title compound are linked by C? H…Cl and O? H…Cl hydrogen bonding interactions. The N? C? N bond angle (124.3(2)°) and C? N bond lengths (1.316(3) and 1.314(3) Å) confirm the existence of strong resonance in this part of the molecule. Copyright © 2015 John Wiley & Sons, Ltd.     

3‐miktoarm star terpolymers using triple click reactions: Diels–Alder,copper‐catalyzed azide‐alkyne cycloaddition,and nitroxide radical coupling reactions

Well‐defined linear furan‐protected maleimide‐terminated poly(ethylene glycol) (PEG‐MI), tetramethylpiperidine‐1‐oxyl‐terminated poly(ε‐caprolactone) (PCL‐TEMPO), and azide‐terminated polystyrene (PS‐N₃) or ‐poly(N‐butyl oxanorbornene imide) (PONB‐N₃) were ligated to an orthogonally functionalized core ( 1 ) in a two‐step reaction mode through triple click reactions. In a first step, Diels–Alder click reaction of PEG‐MI with 1 was performed in toluene at 110 °C for 24 h to afford α‐alkyne‐α‐bromide‐terminated PEG (PEG‐alkyne/Br). As a second step, this precursor was subsequently ligated with the PCL‐TEMPO and PS‐N₃ or PONB‐N₃ in N,N‐dimethylformamide at room temperature for 12 h catalyzed by Cu(0)/Cu(I) through copper‐catalyzed azide‐alkyne cycloaddition and nitroxide radical coupling click reactions, yield resulting ABC miktoarm star polymers in a one‐pot mode. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Various brush polymers through ring opening metathesis polymerization and nitroxide radical coupling reaction

A 2,2,6,6‐tetramethylpiperidine‐1‐oxyl (TEMPO)‐terminated poly(ethylene glycol) (PEG) or ‐poly(ε‐caprolactone) (PCL) (PEG₁₁‐TEMPO or PCL₂₃‐TEMPO) is grafted as a side chain onto a ROMP‐generated polyoxanorbornene (PONB) main backbone with bromide pendant groups (PONB₂₀‐Br) using the NRC click reaction to yield related the brush copolymers, PONB₂₀‐g‐PEG₁₁ or PONB₂₀‐g‐PCL₂₃ catalyzed by Cu(I), Cu(0), and N,N,N′,N″,N″‐pentamethyldiethylenetriamine in N,N‐dimethylformamide at room temperature. Additionally, a ROMP‐generated brush copolymer PONB₉‐g‐poly(methyl methacrylate)₂₄ (PMMA)₂₄‐Cl was reacted with a PEG₁₁‐TEMPO or a PCL₂₃‐TEMPO precursor via the NRC click reaction to yield a corresponding brush terpolymer, PONB₉‐g‐(PMMA₂₄‐b‐PEG₁₁) or PONB₉‐g‐(PMMA₂₄‐b‐PCL₂₃) under a similar reaction condition described above. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011