Synthesis and structural characterization of functionalized dimeric aluminophosphonates and a monomeric gallophosphonate anion

Reaction of t-BuP(O)(OSiMe(3))(OH) with Me(3)Al leads to the formation of [Me(2)Al(mu-O)(2)P(OSiMe(3))(t-Bu)](2) (1) whereas Me(2)AlCl reacts with Ph(2)P(O)(OH) to yield [(Cl)(Me)Al(mu-O)(2)PPh(2)](2) (2). These compounds represent the first examples of functionalized dimeric four-ring type aluminophosphonate systems. The double four-ring type gallophosphonate, namely, [t-BuPO(3)GaMe](4), reacts with n-Bu(4)NHF(2) under ambient conditions, resulting in the formation of a monomeric gallophosphonate [n-Bu(4)N][MeGa[t-BuPO(2)(OH)](3)] (3). These derivatives have been adequately characterized using various spectroscopic techniques and X-ray diffraction studies.     

Oxidative cleavage of a cyclobutane pyrimidine dimer by photochemically generated nitrate radicals (no(3)*)

[reaction: see text] Photochemically generated nitrate radicals (NO(3)(*)) cleave the stereoisomeric N,N-dimethyl-substituted uracil cyclobutane dimers 1a-d into the monomeric uracil derivative 2 as the major reaction pathway. A preferred splitting of the syn dimers 1a,b was observed. The reaction is expected to proceed through initial one-electron oxidation with formation of an intermediate cyclobutane radical cation 11. In addition to cycloreversion, competing reaction steps of 11, which lead to the observed byproducts, are suggested.     

Interview with Ludwig Reich

On the occasion of his 80th birthday, Ludwig Reich, editor-in-chief of Aequationes Mathematicae from 1996 to 2008, gave an interview conducted via Zoom. This paper presents his answers to several questions regarding his education and academic life.

     

Robust Identification of Parametric Radiation Force Models via Impulse Response Fitting

This paper presents a new identification method for obtaining parametric state-space models for radiation force computation. These state-space models can substitute the convolution integral in the equations of motion based on the impulse response function method. Thus, the method converts the integro-differential equation to an ordinary differential equation which reduces the computational effort of radiation force computation significantly. The identification is performed in time-domain which means that the retardation function is subject to fit. The method is verified by the application to a floating cylinder. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non‐rainbow colorings of 3‐, 4‐ and 5‐connected plane graphs

We study vertex‐colorings of plane graphs that do not contain a rainbow face, i.e., a face with vertices of mutually distinct colors. If G is a 3 ‐connected plane graph with n vertices, then the number of colors in such a coloring does not exceed . If G is 4 ‐connected, then the number of colors is at most , and for n≡3(mod8), it is at most . Finally, if G is 5 ‐connected, then the number of colors is at most . The bounds for 3 ‐connected and 4 ‐connected plane graphs are the best possible as we exhibit constructions of graphs with colorings matching the bounds. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 129–145, 2010     

Coloring plane graphs with independent crossings

We show that every plane graph with maximum face size four in which all faces of size four are vertex‐disjoint is cyclically 5‐colorable. This answers a question of Albertson whether graphs drawn in the plane with all crossings independent are 5‐colorable. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 184–205, 2010     

Lattice Points in Three-Dimensional Convex Bodies with Points of Gaussian Curvature Zero at the Boundary

 In this article we investigate the number of lattice points in a three-dimensional convex body which contains non-isolated points with Gaussian curvature zero but a finite number of flat points at the boundary. Especially, in case of rational tangential planes in these points we investigate not only the influence of the flat points but also of the other points with Gaussian curvature zero on the estimation of the lattice rest. Received 19 June 2001; in revised form 17 January 2002 RID="a" ID="a" Dedicated to Professor Edmund Hlawka on the occasion of his 85th birthday     

Colorings Of Plane Graphs With No Rainbow Faces

We prove that each n-vertex plane graph with girth g≥4 admits a vertex coloring with at least ⌈n/2⌉+1 colors with no rainbow face, i.e., a face in which all vertices receive distinct colors. This proves a conjecture of Ramamurthi and West. Moreover, we prove for plane graph with girth g≥5 that there is a vertex coloring with at least if g is odd and if g is even. The bounds are tight for all pairs of n and g with g≥4 and n≥5g/2−3. * Supported in part by the Ministry of Science and Technology of Slovenia, Research Project Z1-3129 and by a postdoctoral fellowship of PIMS. ** Institute for Theoretical Computer Science is supported by Ministry of Education of CzechR epublic as project LN00A056.     

Material parameter identification using model reduction to uniaxial tensile test

Material parameter identification is the necessary link between constitutive modeling and application of material models in complex simulations of real world problems. We present an approach to make use of already developed stress algorithms for three-dimensional finite-element computations in terms of a reduction to uniaxial tensile tests for material parameter identification. Strain-driven stress algorithms lead to the approach of solving differential-algebraic equations. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)