Hudnall, Todd W.
Tennyson, Andrew G.
Bielawski, Christopher W.

Condensation of N,N'-dimesitylformamidine with phthaloyl chloride afforded 1 center dot HCl, which, upon treatment with base, afforded 2,4-dimesitylbenzo[e][1,3]diazepin-1,5-dione-2-ylidene (1), a seven-membered N,N'-diamidocarbene (DAC), in high yield (85%). The free DAC was used to synthesize four new, late transition metal complexes: [Rh(cod)(1)Cl] (2a) (cod = 1,5-cyclooctadiene), [Ir(cod)(1)Cl] (2b), [Rh(CO)(2)(1)Cl] (3a), and [1-AuCl] (5). The Tolman electronic parameter (TEP) of 1 was calculated to be 2047 cm(-1) from the IR spectrum of 3a. This TEP value is approximately 10 cm(-1) than known DACs and 5 cm(-1) lower than known imidazol-2-ylidenes, indicating that DAC 1 is a relatively strong electron donor. Additionally, electrochemical analyses of 2a and 2b corroborated the IR data obtained on 3a and revealed E(1/2) values that were shifted cathodically by ca. 0.16 V when compared to analogous complexes supported by N-heterocyclic carbenes. The gold complex 5 was found to catalyze the hydration of phenylacetylene, affording acetophenone in yields up to 78% after 12 h at 80 C at a catalyst loading of 2 mol %. Treatment of 1 with 2,6-dimethylphenylisocyanide afforded N, N'-diamidoketenimine 4 as a thermally robust, crystalline solid.

An n- poised node set X in the plane is called GCn set if the ( bivariate) fundamental polynomial of each node is a product of n linear factors. A line is called k- node line if it passes through exactly k- nodes of X. An ( n + 1)- node line is called a maximal line. In 1982, Gasca and Maeztu conjectured that every GCn set has a maximal line. Until now the conjecture has been proved only for n =3D 5. We say that a node uses a line if the line is a factor of the fundamental polynomial of this node. It is a simple fact that any maximal line. is used by all n+ 12 nodes in X \.. We consider the main result of the paper- Bayramyan and Hakopian ( Adv. Comput. Math. 43, 607- 626, 2017) stating that any n- node line of GCn set is used either by exactly n2 nodes or by exactly n- 12 nodes, provided that the Gasca- Maeztu conjecture is true. Here, we show that this result is not correct in the case n =3D 3. Namely, we bring an example of a GC3 set and a 3- node line there which is not used at all. Fortunately, then we were able to establish that this is the only possible counterexample, i. e., the abovementioned result is true for all n =3D 4. We also characterize the exclusive case n =3D 3 and present some new results on the maximal lines and the usage of n- node lines in GCn sets.

In this paper, we first prove that, for a non-zero function faD(a"e (n) ), its multi-Hilbert transform Hnf is bounded and does not have compact support. In addition, a new distribution space D' (H) (a"e (n) ) is constructed and the definition of the multi-Hilbert transform is extended to it. It is shown that D' (H) (a"e (n) ) is the biggest subspace of D'(a"e (n) ) on which the extended multi-Hilbert transform is a homeomorphism.

Chandrika, Nishad Thamban
Dennis, Emily K.
Shrestha, Sanjib K.
Ngo, Huy X.
Green, Keith D.
Kwiatkowski, Stefan
Deaciuc, Agripina Gabriela
Dwoskin, Linda P.
Watt, David S.
Garneau-Tsodikova, Sylvie

N,N'-Diaryl-bishydrazones of [1,1'-biphenyl]-3,4'-dicarboxaldehyde, [1,1'-biphenyl]-4,4'-dicarboxaldehyde, and 4,4'-bisacety1-1,1-biphenyl exhibited excellent antifungal activity against a broad spectrum of filamentous and non-filamentous fungi. These N,N'-diaryl-bishydrazones displayed no antibacterial activity in contrast to previously reported N,N'-diamidino-bishydrazones and N-amidino-N'-aryl-bishydrazones. The leading candidate, 4,4'-bis((E)-1-(2-(4-fluorophenyl)hydrazono)ethyl)-1,1'-biphenyl, displayed less hemolysis of murine red blood cells at concentrations at or below that of a control antifungal agent (voriconazole), was fungistatic in a time-kill study, and possessed no mammalian cytotoxicity and no toxicity with respect to hERG inhibition. (C) 2018 Elsevier Masson SAS. All rights reserved.

Working in the geometric approach, we construct the lagrangians of N = 1 and N = 2 pure supergravity in four dimensions with negative cosmological constant, in the presence of a non trivial boundary of space-time. We find that the supersymmetry invariance of the action requires the addition of topological terms which generalize at the supersymmetric level the Gauss-Bonnet term. Supersymmetry invariance is achieved without requiring Dirichlet boundary conditions on the fields at the boundary, rather we find that the boundary values of the fieldstrengths are dynamically fixed to constant values in terms of the cosmological constant Lambda. From a group-theoretical point of view this means in particular the vanishing of the OSp (N vertical bar 4)-supercurvatures at the boundary.

Recently, we have identified a randomized quartet phylogeny algorithm that has O(n log n) runtime with high probability, which is asymptotically optimal. Our algorithm has high probability of returning the correct phylogeny when quartet errors are independent and occur with known probability, and when the algorithm uses a guide tree on O(log log n) taxa that is correct with high probability. In practice, none of these assumptions is correct: quartet errors are positively correlated and occur with unknown probability, and the guide tree is often error prone. Here, we bring our work out of the purely theoretical setting. We present a variety of extensions which, while only slowing the algorithm down by a constant factor, make its performance nearly comparable to that of Neighbour Joining, which requires Theta (n(3)) runtime in existing implementations. Our results suggest a new direction for quartet-based phylogenetic reconstruction that may yield striking speed improvements at minimal accuracy cost. An early prototype implementation of our software is available at http://www.cs.uwaterloo.ca/similar to jmtruszk/qtree.tar.gz.

We prove that, for every n >=3D 5, the Hasse norm principle holds for a degree n extension K/k of number fields with normal closure N such that Gal(N/k) congruent to A(n). We also show the validity of weak approximation for the associated norm one tori. (C) 2019 Elsevier Inc. All rights reserved.

For a finite group G, let K(G) denote the field generated over Q by its character values. For alternating groups, G.R. Robinson and J.G. Thompson [6] determined K(A(n)) as an explicit multiquadratic field. Confirming a speculation of Thompson [7], we show that arbitrary suitable multiquadratic fields are similarly generated by the values of A(n)-characters restricted to elements whose orders are only divisible by ramified primes. (C) 2019 Elsevier Inc. All rights reserved.

Recently, a shift-independent information measure known as generalized cumulative entropy of order n (GCE(n)) was proposed by Kayal (2016). In this communication, we propose a shift-dependent version of GCE(n). Various properties including the effect of transformations, bounds etc. have been discussed. Several relationships of the shift-dependent GCE(n) with some well-known reliability measures are studied. Few characterization results are obtained. We derive an estimator for the proposed measure via empirical distribution function approach. Large sample properties of the estimator are studied when independent observations are taken from a Weibull distribution.

Let S-k denote a maximal torus in the complex Lie group G =3D SLn (C)/C-k and let T-k denote a maximal torus in its compact real form SUn (C)/C-k, where k divides n. Let W denote the Weyl group of G, namely the symmetric group S-n. We elucidate the structure of the extended quotient S-k // W as an algebraic variety and of T-k // W as a topological space, in both cases describing them as bundles over unions of tori. Corresponding to the invariance of K-theory under Langlands duality, this calculation provides a homotopy equivalence between T-k // W and its dual T-n/k // W. Hence there is an isomorphism in cohomology for the extended quotients. Moreover this is stratified as a direct sum over conjugacy classes of the Weyl group. We derive a formula for the periodic cyclic homology of the group ring of an extended affine Weyl group in terms of these extended quotients and use our formulae to compute a number of examples of homology, cohomology and K-theory.

We show that a certain moduli space of minimal A(infinity)-structures coincides with the modular compactification (M) over bar (1),(n) (n - 1) of M-1,n constructed by Smyth in [26]. In addition, we describe these moduli spaces and the universal curves over them by explicit equations, prove that they are normal and Gorenstein, show that their Picard groups have no torsion and that they have rational singularities if and only if n <=3D 11.

Mechsner, Bastian
Boese, Dietrich
Hogenkamp, Fabian
Ledermann, Nadia
Hartmann, Rudolf
Bochinsky, Kevin
Frey, Wolfgang
Pietruszka, Joerg

The development of the first enantioselective total synthesis of altersolanol N is reported. The decisive step of the synthesis is the enantioselective formation of the tetrahydroanthraquinone nucleus by a [4+ 2]-cycloaddition in high yield and with excellent diastereo-and enantioselectivity (> 95: 5 dr and 95: 5 er). In addition, a demanding selective monoacetylation of the OH group at the C-2 position was achieved: an epoxide ring opening with the participation of a neighbouring acetyl group could be established. The route proved to be an efficient alternative to also access enantiomerically pure altersolanol A.