Idempotency of linear combinations of three idempotent matrices, two of which are commuting

The considerations of the present paper were inspired by Baksalary [O.M. Baksalary, Idempotency of linear combinations of three idempotent matrices, two of which are disjoint, Linear Algebra Appl. 388 (2004) 67-78] who characterized all situations in which a linear combination P=c₁P₁+c₂P₂+c₃P₃, with c_i, i=1,2,3, being nonzero complex scalars and P_i, i=1,2,3, being nonzero complex idempotent matrices such that two of them, P₁ and P₂ say, are disjoint, i.e., satisfy condition P₁P₂=0=P₂P₁, is an idempotent matrix. In the present paper, by utilizing different formalism than the one used by Baksalary, the results given in the above mentioned paper are generalized by weakening the assumption expressing the disjointness of P₁ and P₂ to the commutativity condition P₁P₂=P₂P₁.     

Über einen Satz des Herrn Helge von Koch über die Integrale linearer Differentialgleichungen

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Das Verhalten von Chrom zu o-Oxyehinolin

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Set characterizations and convex extensions for geometric convex-hull proofs

Mathematical Programming - In the present work, we consider Zuckerberg’s method for geometric convex-hull proofs introduced in Zuckerberg (Oper Res Lett 44(5):625–629, 2016). It has...     

Superoxide-assisted electrochemical deposition of semiconductor polyhydroxyphenylporphyrin films

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On a common generalization of Koszul duality and tilting equivalence

We propose a new definition of Koszulity for graded algebras where the degree zero part has finite global dimension, but is not necessarily semi-simple. The standard Koszul duality theorems hold in this setting.     

Theoretical rovibrational spectroscopy beyond fc-CCSD(T): the cation CNC+

An accurate near-equilibrium potential energy surface (PES) for CNC⁺ is constructed based on a high-level composite ab initio method. By combining explicitly correlated all-electron CCSD(T)-F12b with scalar relativistic effects and higher order correlation up to coupled cluster theory with singles, doubles, triples and quadruples (CCSDTQ) we achieve convergence in the wavenumbers of the fundamentals to ca. 1 cm^?1. Rovibrational energies are calculated in a variational approach and vibrational term energies and rotational constants are in excellent agreement with available experimental data. Accurate values for centrifugal distortion constants of CNC⁺ in different vibrational states are predicted. Especially the centrifugal distortion constants in the vibrational ground state of D₀ = 0.563 · 10^?6 cm^?1 and H₀ = 0.188 · 10^?10 cm^?1 should be superior to experimentally derived values. Reassignments of some experimentally observed transitions are suggested based on a comparison of experimental and calculated term differences. The bending part of the PES appears to be almost quartic and the band origin of the bending vibration is predicted at 94.2 cm^?1. Absolute line intensities are calculated for various transitions in CNC⁺. For the bending vibration, an intensity is predicted that is three orders of magnitude smaller than for the antisymmetric stretching vibration.     

Properties of superhydrophobic paper treated with rapid expansion of supercritical CO<Subscript>2</Subscript> containing a crystallizing wax

Paper samples were rendered superhydrophobic with Alkyl Ketene Dimer using (1) Airblasting with cryo ground micro particles, (2) crystallizing from organic solvents and (3) spraying with Rapid Expansion of Supercritical Solutions (RESS) technique. The papers were characterized using Scanning Electron Microscopy, contact angle to water measurements and X-ray Photoelectron Spectroscopy (XPS). Advancing contact angles were in the region of 150°–160° and receding contact angles were in the region of 110°–130°. Diagrams showing the drop base diameter vs. the contact angle when water is pumped into, and then withdrawn from, a sessile drop show that a stick slip pattern is present in the advancing phase for a non coated internally sized paper. Papers rendered superhydrophobic with the RESS technique showed a much less pronounced stick slip pattern in the advancing phase but still a stick slip pattern in the receding phase.     

Über diophantische Approximationen

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