On the monodromy action on Milnor fibers of graphic arrangements

We analyze the monodromy action, over the rationals, on the first homology group of the Milnor fiber, for arbitrary subarrangements of Coxeter arrangements. We propose a combinatorial formula for the monodromy action, involving Aomoto complexes in positive characteristic. We verify the formula, in cases A, B and D.     

Persistent phosphinyl radicals featuring a bulky amino substituent and the 2,6-bis(trifluoromethyl)phenyl group

Persistent phosphinyl radicals featuring the 2,6-bis(trifluoromethyl)phenyl group were prepared and characterized. Their electronic structure was theoretically investigated, and their low-temperature dimerization into the corresponding diphosphines was found to be strongly inhibited when the sterically very demanding (tert-butyl)(trimethylsilyl)amino substituent was used.     

On the planarity of bicolored digraph grammar systems

D. Wood has asked in [2] whether there exists an inherently non-planar bicolored digraph-grammar language. We shall give below a negative answer to this question.     

Finite element modeling of welding processes

This work deals with the simulation of fusion welding by the Finite Element Method. The implemented models include a moving heat source, temperature dependence of thermo-physical properties, elasto-plasticity, non-steady state heat transfer, and mechanical analysis. The thermal problem is assumed to be uncoupled from the mechanical one, so the thermal analysis is performed separately and previously to the mechanical analysis at each time step. The mechanical problem is based on the thermal history. A special treatment is performed on mechanical elements during the liquid/solid and solid/liquid phase changes to account for stress states. The three-dimensional stress state of a butt-welded joint is obtained as an example of an application.     

Arnowitt–Deser–Misner representation and Hamiltonian analysis of covariant renormalizable gravity

We study the recently proposed Covariant Renormalizable Gravity (CRG), which aims to provide a generally covariant ultraviolet completion of general relativity. We obtain a spacetime decomposed form—an Arnowitt–Deser–Misner (ADM) representation—of the CRG action. The action is found to contain time derivatives of the gravitational fields up to fourth order. Some ways to reduce the order of these time derivatives are considered. The resulting action is analyzed using the Hamiltonian formalism, which was originally adapted for constrained theories by Dirac. It is shown that the theory has a consistent set of constraints. It is, however, found that the theory exhibits four propagating physical degrees of freedom. This is one degree of freedom more than in Hořava–Lifshitz (HL) gravity and two more propagating modes than in general relativity. One extra physical degree of freedom has its origin in the higher order nature of the CRG action. The other extra propagating mode is a consequence of a projectability condition similarly as in HL gravity. Some additional gauge symmetry may need to be introduced in order to get rid of the extra gravitational degrees of freedom.     

Crystal structure of tetra(μ-acetato)-bis{[1-ethyl-3-(pyridine-2-yl)carbamide]copper}

The crystal structure of tetra(μ-acetato)-bis{[1-ethyl-3-(pyridine-2-yl)carbamide]copper} Cu₂(L)₂(CH₃COO)₄ (I), where L is 1-ethyl-3-(pyridine-2-yl)carbamide, is determined. The asymmetric unit cell of the crystal structure of I contains a copper complex with two acetate ions and a monodentate molecule of 1-ethyl-3-(pyridine-2-yl)carbamide, which is coordinated via the pyridine nitrogen atom. Due to the symmetry center, binuclear complexes form in the crystal, in which the acetate ions act as bridges between the metal atoms. In them, the coordination polyhedron of the central copper atoms represents an almost ideal tetragonal pyramid. Its base is formed from the oxygen atoms of acetate ions. In the crystal of the binuclear complex, hydrogen bonds form between the acetate ions and the L ligand along with an intramolecular hydrogen bond, which stabilize the conformation of the organic L molecule. Between the neighboring complexes in the crystal, the van der Waals interaction occurs.     

Rational synthesis of multicyclic bis[2]catenanes

Bis-loop tetraurea calix[4]arene 6 has been prepared by acylation of the wide-rim calix[4]arene tetraamine 1 with the activated bis(urethane) 8 under dilution conditions. Similarly the bis(Boc-protected) tetraamine 2 is converted into the mono-loop derivative 3 which after deprotection and acylation gives the bisalkenyl derivative 5. In apolar solvents this tetraurea calix[4]arene 5 forms regioselectively a single hydrogen-bonded homodimer, from which the bis[2]catenane 10a is formed in 49% by a metathesis reaction followed by hydrogenation. Bis-loop derivative 6 forms no homodimers for steric reasons, but a stoichiometric mixture with the open-chain tetraalkenyl derivative 7a contains exclusively the heterodimer. Metathesis and subsequent hydrogenation now yields 65 % of the pure bis[2]catenane 10a which could not be isolated from the complex reaction mixture obtained from the homodimer 7a.7a. The chirality of 10a (D(2) symmetry) has been verified by optical resolution using HPLC on a chiral stationary phase.     

Quantifying brain tumor tissue abundance in HR‐MAS spectra using non‐negative blind source separation techniques

Given high‐resolution magic angle spinning (HR‐MAS) spectra from several glial tumor subjects, our goal is to differentiate between tumor tissue types by separating the different sources that contribute to the profile of each spectrum. Blind source separation techniques are applied for obtaining characteristic profiles for necrosis, highly cellular tumor and border tumor tissue and providing the contribution (abundance) of each of these tumor tissue types to the profile of each spectrum. The problem is formulated as a non‐negative source separation problem. Non‐negative matrix factorization, convex analysis of non‐negative sources and non‐negative independent component analysis methods are considered. The results are in agreement with the pathology obtained by the histopathological examination that succeeded the HR‐MAS measurements. Furthermore, an analysis to verify to which extent the dimension of the input space, the input features and the number of sources to be extracted from the HR‐MAS data could influence the performance of the source separation is presented. Copyright © 2012 John Wiley & Sons, Ltd.