Synthesis of Fréchet-type dendritic homotriptycenes

A rapid and efficient synthesis of novel dendrimer homotriptycenes is presented. The dendronized 9,10-dihydroanthracen-9-ols 4, having high electron densities in the benzene rings of the Fréchet-type dendrons, exhibited in the presence of acid a quantitative transannular ring closure to the corresponding dendritic homotriptycenes. The electron-donating Fréchet-type dendrons enabled the intramolecular FC alkylation by a regioselective 1,7-elimination of H2O.     

Comparative analysis of shape memory-based self-healing coatings

Self-healing materials exhibit the ability to repair and to recover their functionality upon damage. Here, we report on an investigation into preparation and characterization of shape memory assisted self-healing coatings. We built on past work in which poly(ε-caprolactone) electrospun fibers were infiltrated with a shape memory epoxy matrix and delve into fabricating and characterizing a coating with the same materials, but employing a blending approach, polymerization induced phase separation. After applying controlled damage, the ability of both coatings to self-heal upon heating was investigated. In both methods, coatings showed excellent thermally induced crack closure and protection against corrosion, with the blend approach being more suitable for large-scale applications given its process simplicity. Two different approaches to the preparation of shape memory-based self-healing coatings were compared for their ability to heal structurally and functionally by heating. These two approaches, electrospinning versus polymerization-induced phase separation were found to feature comparable and quite complete healing, with the latter system offering the advantage of facile processing. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1415–1426     

Electron impact induced fragmentation of aromatic N-alkoxy-imines I. Ring closure in (M-CH2O)+• ions by intramolecular aromatic substitution

Summary N-Butoxy- and N-propoxy-imines derived fromo-,m-, andp-substituted benzaldehydes (X = F, Cl, Br, I) decompose upon electron impact to the respective aldoximes by loss of C _n H_2n and competitivelyvia 1,5-distonic radical cations by loss of CH₂O to 1,3-distonic ions which eliminate H and/or a halogen atom in the course of homolytic aromatic substitution, giving rise to cyclic (M-CH₂O-H)⁺ or (M-CH₂O-X )⁺ ions.Dedicated with warm regards to Prof. Dr.D. Seebach, Zürich, on the occasion of his 60^th birthday     

Hindman spaces

A topological space is Hindman if for every sequence in there exists an infinite so that the sequence , indexed by all finite sums over , is IP-converging in . Not all sequentially compact spaces are Hindman. The product of two Hindman spaces is Hindman.

Furstenberg and Weiss proved that all compact metric spaces are Hindman. We show that every Hausdorff space that satisfies the following condition is Hindman:

Consequently, there exist nonmetrizable and noncompact Hindman spaces. The following is a particular consequence of the main result: every bounded sequence of monotone (not necessarily continuous) real functions on has an IP-converging subsequences.

     

New Wavelet Bases and Isometric Between Symbolic Operators Spaces $$ {\text{OP}}S^{m}_{{1,\delta }} $$ and Kernel Distributions Spaces

In the fifties, Calderón established a formal relation between symbol and kernel distribution, but it is difficult to establish an intrinsic relation. The Calderón-Zygmund (C-Z) school studied the C-Z operators, and Hörmander, Kohn and Nirenberg, et al. studied the symbolic operators. Here we apply a refinement of the Littlewood-Paley (L-P) decomposition, analyse under new wavelet bases, to characterize both symbolic operators spaces \({\text{OP}}S^{m}_{{1,\delta }} \) and kernel distributions spaces with other spaces composed of some almost diagonal matrices, then get an isometric between \({\text{OP}}S^{m}_{{1,\delta }} \) and kernel distribution spaces     

Trace Functionals on Noncommutative Deformations of Moduli Spaces of Flat Connections

We describe an efficient construction of a canonical noncommutative deformation of the algebraic functions on the moduli spaces of flat connections on a Riemann surface. The resulting algebra is a variant of the quantum moduli algebra introduced by Alekseev, Grosse, and Schomerus and Buffenoir and Roche. We construct a natural trace functional on this algebra and show that it is related to the canonical trace in the formal index theory of Fedosov and Nest and Tsygan via Verlinde's formula.     

The Wiener transform on the Besicovitch spaces

In his fundamental research on generalized harmonic analysis, Wiener proved that the integrated Fourier transform defined by is an isometry from a nonlinear space of functions of bounded average quadratic power into a nonlinear space of functions of bounded quadratic variation. We consider this Wiener transform on the larger, linear, Besicovitch spaces defined by the norm . We prove that maps continuously into the homogeneous Besov space for and , and is a topological isomorphism when .

     

On the dimension of almost -dimensional spaces

Oversteegen and Tymchatyn proved that homeomorphism groups of positive dimensional Menger compacta are -dimensional by proving that almost -dimensional spaces are at most -dimensional. These homeomorphism groups are almost -dimensional and at least -dimensional by classical results of Brechner and Bestvina. In this note we prove that almost -dimensional spaces for are -dimensional. As a corollary we answer in the affirmative an old question of R. Duda by proving that every hereditarily locally connected, non-degenerate, separable, metric space is -dimensional.