On numerical integration of perturbed linear oscillating systems

Zusammenfassung Es wird ein Schrittverfahren zur numerischen Integration von gestörten linearen Differentialgleichungssystemen aufgestellt. Die Grundlage dazu bildet die Definition einer Folge von ganzen Funktionen, die keine Polynome sind, aber eine einfache Potenzreihendarstellung besitzen. Im Gegensatz zu den üblichen Potenzreihenverfahren, wird nicht nach Potenzen der unabhängigen Variabeln, sondern nach diesen Funktionen entwickelt. Das Integrationsverfahren hat die Eigenschaft, dass die ungestörten Differentialgleichungen ohne Diskretisationsfehler integriert werden, und dass die Eigenwerte der Koeffizientenmatrix nicht berechnet werden müssen. Die Verbesserung gegenüber der gewöhnlichen Potenzreihenmethode wird durch asymptotische Formeln für die Residuen und durch numerische Beispiele belegt.Nach einer Einleitung über Ziel und Zweck der Arbeit wird die Methode anhand eine: gestörten linearen Differentialgleichung zweiter Ordnung illustriert. Anschliessend wird das Integrationsverfahren auf beliebige gestörte lineare Systeme verallgemeinert.     

Selected Nitrocarbamates of Glycerine & Co. and the First Acetylene Derivative

A simple two step synthesis route for the preparation of several energetic multivalent nitrocarbamates of easily available alcohols is presented. The carbamates were obtained by the reaction of the alcohols and the reactive reagent chlorosulfonyl isocyanate (CSI) with subsequent aqueous work‐up. The nitration of the carbamates was performed with mixed acid (nitric and sulfuric acid). The thermal stabilities were explored by using differential scanning calorimetry and the energies of formation were calculated on the CBS‐4M level of theory, as well as several detonation and propulsion parameters for the application as energetic materials. All compounds were fully characterized and discussed in addition with single X‐ray diffraction.     

A new type of nano-sized silicon/carbon composite electrode for reversible lithium insertion

A new type of nano-sized silicon/carbon composite was developed. It shows superior electrochemical cycling properties as negative electrode material for possible use in lithium-ion batteries with respect to high reversible and low irreversible capacity, and low fading.     

Synthesis of Trisubstituted Ureas by a Multistep Sequence Utilizing Recyclable Magnetic Reagents and Scavengers

Unprecedented magnetic borohydride exchange (mBER), magnetic Wang aldehyde (mWang) and magnetic amine resins were prepared from highly magnetic polymer‐coated cobalt or iron nanoparticles. Microwave irradiation was used to obtain excellent degrees of functionalization (>95 %) and loadings (up to 3.0 mmol g^?1) in short reaction times of 15 min or less. A small library of ureas and thioureas was synthesized by the exclusive application of these magnetic resins. As a first step, a reductive amination of aromatic and aliphatic aldehydes was carried out with mBER. The excess of primary amine needed to complete the reaction was subsequently scavenged selectively by mWang. Simple magnetic decantation from the resins resulted in secondary amines in good to excellent yields and purities. The used magnetic resins were efficiently regenerated and reused for the next run. In a second step, the secondary amines were converted to trisubstituted (thio)ureas in excellent yields and purities by stirring with an excess of iso(thio)cyanate, which was scavenged by addition of the magnetic amine resin after completion of the reaction. The whole reaction sequence is carried out without any purification apart from magnetic decantation; moreover, conventional magnetic stirring can be used as opposed to the vortexing required for polystyrene resins.     

Large Deviations of the Range of the Planar Random Walk on the Scale of the Mean

Journal of Theoretical Probability - We prove an upper large deviation bound on the scale of the mean for a symmetric random walk in the plane satisfying certain moment conditions. This result...     

Efficient Synthesis of Primary Nitrocarbamates of Sugar Alcohols: From Food to Energetic Materials

The synthesis of various new polyvalent nitrocarbamates derived from sugar alcohols was accomplished by an economically benign two‐step synthesis. The precursor carbamates were synthesized with the reagent chlorosulfonyl isocyanate (CSI) and further nitrated using mixed acid. The starting materials, sugar alcohols, are renewable biomass, mainly used in food and cosmetic industry. The structures of one carbamate and one nitrocarbamate were exemplary described by single‐crystal X‐ray‐analysis. The heat of formation is calculated by the use of isodesmic reactions and the energetic performance data were estimated. All compounds were fully characterized by elemental analysis, vibrational spectroscopy, ¹H, ¹³C, and ^14/15N NMR spectroscopy and thermal analysis (DSC). The nitrocarbamates exhibit good detonation performance and have significantly lower sensitivities compared to the commonly used nitrate ester explosive PETN.     

Intramolecular monomer-on-monomer (MoM) Mitsunobu cyclization for the synthesis of benzofused thiadiazepine-dioxides

The utilization of a monomer-on-monomer (MoM) intramolecular Mitsunobu cyclization reaction employing norbornenyl-tagged (Nb-tagged) reagents is reported for the synthesis of benzofused thiadiazepine-dioxides. Facile purification was achieved via ring-opening metathesis (ROM) polymerization initiated by one of three metathesis catalyst methods: (i) free metathesis catalyst, (ii) surface-initiated catalyst-armed silica, or (iii) surface-initiated catalyst-armed Co/C magnetic nanoparticles.     

Ultrafast photovoltaic response in ferroelectric nanolayers

We show that light drives large-amplitude structural changes in thin films of the prototypical ferroelectric PbTiO3 via direct coupling to its intrinsic photovoltaic response. Using time-resolved x-ray scattering to visualize atomic displacements on femtosecond time scales, photoinduced changes in the unit-cell tetragonality are observed. These are driven by the motion of photogenerated free charges within the ferroelectric and can be simply explained by a model including both shift and screening currents, associated with the displacement of electrons first antiparallel to and then parallel to the ferroelectric polarization direction.