Magnesium complexes incorporated by sulfonate phenoxide ligands as efficient catalysts for ring‐opening polymerization of ε‐caprolactone and trimethylene carbonate

Two novel sulfonate phenol ligands—3,3′‐di‐tert‐butyl‐2′‐hydroxy‐5,5′,6,6′‐tetramethyl‐biphenyl‐2‐yl 4‐X‐benzenesulfonate (X?CF₃, L^CF3 ‐H, and X?OCH₃, L^OMe ‐H)—were prepared through the sulfonylation of 3,3′‐di‐tert‐butyl‐5,5′,6,6′‐tetramethylbiphenyl‐2,2′‐diol with the corresponding 4‐substituted benzenesulfonyl chloride (1 equiv.) in the presence of excess triethylamine. Magnesium (Mg) complexes supported by sulfonate phenoxide ligands were synthesized and characterized structurally. The reaction of MgⁿBu₂ with L‐H (2 equiv.) produces the four‐coordinated monomeric complexes ( L^CF3 )₂Mg ( 1 ) and ( L^OMe )₂Mg ( 2 ). Complexes 1 and 2 are efficient catalysts for the ring‐opening polymerization of ε‐caprolactone (ε‐CL) and trimethylene carbonate (TMC) in the presence of 9‐anthracenemethanol; complex 1 catalyzes the polymerization of ε‐CL and TMC in a controlled manner, yielding polymers with the expected molecular weights and narrow polydispersity indices (PDIs). In ε‐CL polymerization, the activity of complex 1 is greater than that of complex 2 , likely because of the greater Lewis acidity of Mg²⁺ metal caused by the electron‐withdrawing substitute trifluoromethyl (? CF₃) at the 4‐position of the benzenesulfonate group. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3564–3572, 2010     

Generalized 1D Jörgens theorem

We study the Cauchy problem for a 1D nonlinear wave equation on R. The nonlinearity can depend on the unknown function and its first order spatial derivative. Using the fixed point theorem we prove the existence of a classical solution. Moreover, the existence of periodic and almost periodic solutions are shown.     

β‐Cyclodextrin as an Efficient and Recyclable Supramolecular Catalyst for the Synthesis of Heterocyclic Compounds

β‐Cyclodextrin (β‐CD ), a naturally occurring supramolecular structure, is an effective catalyst for the synthesis of heterocyclic compounds. Its ubiquity, high performance, nontoxicity, ease of separation, and reusability have drawn the attention of green chemists. Here we present the synthetic procedures of heterocyclic compounds catalyzed by β‐CD in water and compare them with those using organic solvents. In many cases, using water as the solvent shows better efficiency than conventional organic solvents with regard to catalytic activity and simplicity of recycling procedures. This review highlights the applications of β‐CD in catalysis covering the years 2004–2016.     

Ether drift experiments and electromagnetic momentum

Propagation of Aharonov-Bohm matter waves and light waves in moving media is characterized by the interaction electromagnetic momentum. Thus, recent models of light propagation in moving rarefied media justify and call for an optical experiment of the Mascart-Jamin type, capable of testing the modern interpretations of ether drift experiments.     

On pre-Λ-Sets and pre-v-Sets

We introduce the notions of a pre--set and a pre-V-set in a topological space. We study the fundamental properties of pre--sets and pre-V-sets and investigate the topologies defined by these families of sets.     

Multiplicity of the second Schrödinger eigenvalue on closed surfaces

We improve – roughly by a factor 2 – the known bound on the multiplicity of the second eigenvalue of Schr?dinger operators (i.e. Laplace plus potential) on closed surfaces. This gives four new topological types of surfaces for which Colin de Verdière's conjecture relating the maximal multiplicity to the chromatic number of the surface is verified. The proof goes by defining a space of "nodal splittings” of the surface, equipped with a double covering to which a Borsuk-Ulam type theorem is applied. Received: 19 June 2001; revised version: 18 March 2002 /Published online: 17 June 2002     

Small Universal Graphs for Bounded-Degree Planar Graphs

For all positive integers N and k, let denote the family of planar graphs on N or fewer vertices, and with maximum degree k. For all positive integers N and k, we construct a -universal graph of size . This construction answers with an explicit construction the previously open question of the existence of such a graph. Received July 8, 1998 RID="*" ID="*" Supported by NSF grant CCR98210-58 and ARO grant DAAH04-96-1-0013.