An O(n log n) near-shortest path-planning algorithm based on the Delaunay triangulation, Ahuja-Dijkstra algorithm, and ridge points in the quadratic plane is presented. The shortest path planning is an NP-hard problem in the general 3-D space. Compared with the other O(n log n) time near-shortest path approach, the path length of the proposed method is 2.81% longer than the Kanai and Suzuki's algorithm with 29 Steiner points, but the computation is 4,261 times faster. Notably, the proposed method is ideal for being extended to solve the path-planning problem on the mission planning of cruise missile.

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.

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.

We prove that the regular N-gon minimizes the Cheeger constant among polygons with a given area and N sides.

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.

H-matrices play an important role in the theory and applications of Numerical Linear Algebra. So, it is very useful to know whether a given matrix A is an element of C(n,n), usually the coefficient of a complex linear system of algebraic equations or of a Linear Complementarity Problem (A is an element of R(n,n), with a(ii) > 0 for i = 1, 2, ... , n in this case), is an H-matrix; then, most of the classical iterative methods for the solution of the problem at hand converge. In recent years, the set of H-matrices has been extended to what is now known as the set of General H-matrices, and a partition of this set in three different classes has been made. The main objective of this work is to develop an algorithm that will determine the H-matrix character and will identify the class to which a given matrix A is an element of C(n,n) belongs; in addition, some results on the classes of general H-matrices and a partition of the non-H-matrix set are presented. (C) 2011 Elsevier Inc. All rights reserved.