Variational principles for self-adjoint operator functions arising from second-order systems

Variational principles are proved for self-adjoint operator functions arising from variational evolution equations of the form $$\langle\ddot{z}(t),y \rangle + \mathfrak{d}[\dot{z} (t), y] + \mathfrak{a}_0 [z(t),y] = 0.$$ Here $\mathfrak{a}_0$ and $\mathfrak{d}$ are densely defined, symmetric and positive sesquilinear forms on a Hilbert space $H$. We associate with the variational evolution equation an equivalent Cauchy problem corresponding to a block operator matrix $\mathcal{A}$, the forms $$\mathfrak{t}(\lambda)[x,y] := \lambda^2\langle x,y\rangle + \lambda\mathfrak{d}[x,y] + \mathfrak{a}_0[x,y],$$ where $\lambda\in \mathbb C$ and $x,y$ are in the domain of the form $\mathfrak{a}_0$, and a corresponding operator family $T(\lambda)$. Using form methods we define a generalized Rayleigh functional and characterize the eigenvalues above the essential spectrum of $\mathcal{A}$ by a min-max and a max-min variational principle. The obtained results are illustrated with a damped beam equation.Comment: to appear in Operators and Matrice

Room-Temperature Activation of Hydrogen by Semi-immobilized Frustrated Lewis Pairs in Microporous Polymer Networks

Porous polymer networks based on sterically encumbered triphenylphosphine motifs, mimicking the basic sites employed in frustrated Lewis pair (FLP) chemistry, were synthesized via Yamamoto polymerization and their interactions with the strong Lewis acid B(C6F5)3 probed. The combinations yield semi-immobilized FLPs, which are able to cleave dihydrogen heterolytically at ambient temperature and low hydrogen pressure.DFG, 53182490, EXC 314: Unifying Concepts in CatalysisEC/FP7/278593/EU/Organic Zeolites/ORGZE

Copper‐Free Sonogashira Coupling for High‐Surface‐Area Conjugated Microporous Poly(aryleneethynylene) Networks

A modified one‐pot Sonogashira cross‐coupling reaction based on a copper‐free methodology has been applied for the synthesis of conjugated microporous poly(aryleneethynylene) networks (CMPs) from readily available iodoarylenes and 1,3,5‐triethynylbenzene. The polymerization reactions were carried out by using equimolar amounts of halogen and terminal alkyne moieties with extremely small loadings of palladium catalyst as low as 0.65 mol %. For the first time, CMPs with rigorously controlled structures were obtained without any indications of side reactions, as proven by FTIR and solid‐state NMR spectroscopy, while showing Brunauer–Emmett–Teller (BET) surface areas higher than any poly(aryleneethynylene) network reported before, reaching up to 2552 m2 g−1.EC/FP7/278593/EU/Organic Zeolites/ORGZEODFG, 53182490, EXC 314: Unifying Concepts in Catalysi

Spectral enclosures for a class of block operator matrices

We prove new spectral enclosures for the non-real spectrum of a class of 2x2 block operator matrices with self-adjoint operators A and D on the diagonal and operators B and -B* as off-diagonal entries. One of our main results resembles Gershgorin's circle theorem. The enclosures are applied to J-frame operators

Structure–Thermodynamic-Property Relationships in Cyanovinyl-Based Microporous Polymer Networks for the Future Design of Advanced Carbon Capture Materials

Nitrogen-rich solid absorbents, which have been immensely tested for carbon dioxide capture, seem until this date to be without decisive molecular engineering or design rules. Here, a family of cyanovinylene-based microporous polymers synthesized under metal-catalyzed conditions is reported as a promising candidate for advanced carbon capture materials. These networks reveal that isosteric heats of CO2 adsorption are directly proportional to the amount of their functional group. Motivated by this finding, polymers produced under base-catalyzed conditions with tailored quantities of cyanovinyl content confirm the systematical tuning of their sorption enthalpies to reach 40 kJ mol−1. This value is among the highest reported to date in carbonaceous networks undergoing physisorption. A six-point-plot reveals that the structure–thermodynamic-property relationship is linearly proportional and can thus be perfectly fitted to tailor-made values prior to experimental measurements. Dynamic simulations show a bowl-shaped region within which CO2 is able to sit and interact with its conjugated surrounding, while theoretical calculations confirm the increase of binding sites with the increase of PhCC(CN)Ph functionality in a network. This concept presents a distinct method for the future design of carbon dioxide capturing materials

Metal-assisted and solvent-mediated synthesis of two-dimensional triazine structures on gram scale

We thank the German Science Foundation (DFG) for financial support within the grants SFB 765 and SFB 658. M.F.G. and J.P.R. also acknowledge the support of the Cluster of Excellence “Matters of Activity. Image Space Material” funded by the DFG under Germany’s Excellence Strategy EXC 2025-390648296. Furthermore, A.T. acknowledges the DFG for funding within the project TH 1463/12-1. We thank Dr. Andreas Schäfer and Maiko Schulze for solid NMR experiments and we appreciate the effort of Vahid Ahmadi Soureshjani in MALDI-TOF experiments. We acknowledge M. Eng. Jörg M. Stockmann for operating the XPS instrument at the BAM and Prof. Stephanie Reich and Dr. Antonio Setaro for fruitful discussions. 2DTs-HRTEM and -EELS studies were conducted at the Laboratorio de Microscopias Avanzadas, Instituto de Nanociencia de Aragon, Universidad de Zaragoza, Spain. R.A. gratefully acknowledges the support from the Spanish Ministry of Economy and Competitiveness (MINECO) through project grant MAT2016-79776-P (AEI/FEDER, UE) and from the European Union H2020 programs ETN projects “Graphene Flagship” (785219 and 881603), FLAG-ERA - Graphene (MICINN) GATES (PCI2018-093137) and “ESTEEM3” (823717).Peer reviewe

Beiträge zum 28. Darmstädter Geotechnik-Kolloquium am 09. März 2022

Themenschwerpunkte: 1. Modell- und Feldversuche 2. Digitalisierung und künstliche Intelligenz in der Geotechnik 3. Nationale und internationale Großprojekte 4. Normung und Rechtliche

Beiträge zum 28. Darmstädter Geotechnik-Kolloquium am 09. März 2022

Themenschwerpunkte: 1. Modell- und Feldversuche 2. Digitalisierung und künstliche Intelligenz in der Geotechnik 3. Nationale und internationale Großprojekte 4. Normung und Rechtliche