Optimal Control of Second Order Systems with Infinite Time Horizon: Existence of Solutions

We investigate an optimal control problem described by a second-order ordinary differential equation on the interval ]0,∞[ and an integral cost functional. The study of this problem is based on a variational approach.     

Study of phase equilibria established up to the solidus line in the system Fe2V4O13−WO3

The phase equilibria established up to the solidus line in the system Fe₂V₄O₁₃−WO₃, one of the intersections of the three-component system Fe₂O₃−V₂O₅−WO₃, have been studied. The system appears not to be a real two-component system.

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Zusammenfassung Es wurde eine Untersuchung des Phasengleichgewichtes durchgeführt, welches bezüglich der Solidus-Linie im System Fe₂V₄O₁₃−WO₃, einer der Zwischenbereiche im Dreikomponentensystem Fe₂O₃−V₂O₅−WO₃, nachgewiesen wurde. Dieses System scheint kein echtes Zweikomponentensystem zu sein.

     

A search for new phases in the system Fe2O3-V2O5-WO3

Studies on the three-component system Fe₂O₃-V₂O₅-WO₃ have shown the occurrence of a new, compound with molecular formula FeVW₂O₁₀. Its X-ray characteristics and its melting temperature, 865±10 °C, have been established.

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Zusammenfassung Einleitende Untersuchungen am Dreikomponentensystem Fe₂O₃-V₂ O₅-WO₃ zeigten das Auftreten einer neuen, noch nicht publizierten Verbindung der Formel FeVW₂O₁₀. Die Verbindung wurde röntgenographisch beschrieben, ihr Schmelzpunkt beträgt 865 ±10°C.

     

Phase Equilibria in the Fe8V10W16O85-Fe2O3 and Fe8V10W16O85-Fe2WO6 Systems

Using DTA and X-ray phase diffraction methods, a diagram of phase equilibria established in two sections of a tricomponent oxide triangle Fe₂O₃-V₂O₅-WO₃was constructed, that is, in the sections: Fe₈V₁₀W₁₆O₈₅-Fe₂O₃and Fe₈V₁₀W₁₆O₈₅-Fe₂WO₆. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of metallosupramolecular polymer concentration on the synthesis of poly[n]catenanes

Poly[n]catenanes are a class of polymers that are composed entirely of interlocked rings. One synthetic route to these polymers involves the formation of a metallosupramolecular polymer (MSP) that consists of alternating units of macrocyclic and linear thread components. Ring closure of the thread components has been shown to yield a mixture of cyclic, linear, and branched poly[n]catenanes. Reported herein are investigations into this synthetic methodology, with a focus on a more detailed understanding of the crude product distribution and how the concentration of the MSP during the ring closing reaction impacts the resulting poly[n]catenanes. In addition to a better understanding of the molecular products obtained in these reactions, the results show that the concentration of the reaction can be used to tune the size and type of poly[n]catenanes accessed. At low concentrations the interlocked product distribution is limited to primarily oligomeric and small cyclic catenanes . However, the same reaction at increased concentration can yield branched poly[n]catenanes with an ca. 21 kg mol⁻¹, with evidence of structures containing as many as 640 interlocked rings (1000 kg mol⁻¹).

Concentration of the metallosupramolecular polymer precursors have a significant effect on the architecture and size of the resulting poly[n]catenanes formed via a ring closing metathesis step.     

Serendipity and design in the generation of new coordination polymers: an extensive series of highly symmetrical guanidinium-templated, carbonate-based networks with the sodalite topology

The serendipitous discovery of a 3D [Cu(CO(3))(2)(2-)](n) network with the topology of the 4(2)6(4) sodalite net in [Cu(6)(CO(3))(12)(CH(6)N(3))(8)].K(4).8H(2)O paved the way for the deliberate engineering of an extensive series of structurally related guanidinium-templated metal carbonates of composition [M(6)(CO(3))(12)(CH(6)N(3))(8)]Na(3-)[N(CH(3))(4)].xH(2)O, where the divalent metal M in the framework may be Mg, Mn, Fe, Co, Ni, Cu, Zn, or Cd. A closely related crystalline material with a [Ca(CO(3))(2)(2-)](n) sodalite-like framework, but containing K(+) rather than Na(+), of composition [Ca(6)(CO(3))(12)(CH(6)N(3))(8)]K(3)[N(CH(3))(4)].3H(2)O was also isolated. All of these compounds were obtained under the simplest possible conditions from aqueous solution at room temperature, and their structures were determined by single-crystal X-ray diffraction. Pairs of guanidinium cations are associated with the hexagonal windows of the sodalite cages, alkali-metal cations are associated with their square windows, and N(CH(3))(4)(+) ions are located at their centers. Structures fall into two classes depending on the metal, M(II), in the framework. One type, the BC type (Im3m), comprising the compounds for which M(2+) = Ca(2+), Mn(2+), Cu(2+), and Cd(2+), has a body-centered cubic unit cell, while the second type, the FC type (Fd3c), for which M(2+) = Mg(2+), Fe(2+), Co(2+), Ni(2+), and Zn(2+), has a face-centered cubic unit cell with edges on the order of twice those of the BC structural type. The metal M in the BC structures has four close carbonate oxygen donors and four other more distant ones, while M in the FC structures has an octahedral environment consisting of two bidentate chelating carbonate ligands and two cis monodentate carbonate ligands.     

Phase equilibria in the FeVO4-Fe2(MoO4)3 system

Phase équilibria have been investigated in the FeVO₄-Fe₂(MoO₄)₃ system for the whole concentration range of the components. In this system there is one compound which melts incongruently: Fe₄V₂Mo₃O₂₀. The results are presented in the form of a phase diagram.

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Zusammenfassung Phasengleichgewichte im System FeVO₄-Fe₂(MoO₄)₃ wurden über den ganzen Konzentrationsbereich der Komponenten hinweg untersucht. Eine Verbindung des Systems, Fe₄V₂Mo₃O₂₀, schmilzt inkongruent. Die Ergebnisse sind in Form eines Phasendiagramms angegeben.

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FeVO₄-Fe₂(MoO₄)₃ . Fe₄V₂Mo₃O₂₀, . .

     

Phase equilibria up to the solidus line in the V2O5−Cr2(MoO4)3 system

Phase equilibria being established in the subsolidus area of the V₂O₅?Cr₂(MoO₄)₃ system at the whole component concentration range have been studied basing on DTA and X-ray phase powder diffraction. It has been established that the system is not a real two-component system in the subsolidus area. The fact has been proved by the presence of fields in that area, where three solid phases remain in mutual equilibrium.     

Reaction Mechanism of Fe8W10W16O85 Synthesis

The reaction mechanism of the synthesis of Fe₈V₁₀W₁₆O₈₅ was studied by means of XRD, IR spectroscopy and DTA techniques. It was found that the intermediate in the reaction may be either FeVO₄ or FeVO₄ admixed with an unidentified phase X, depending on the reaction temperature. The IR spectrum of the phase Fe₈V₁₀W₁₆O₈₅ is reported for the first time. This revised version was published online in July 2006 with corrections to the Cover Date.     

EPR study of the Ag6S3O4 compound prepared by two methods

The temperature dependence of the EPR spectra of the recently discovered Ag₆S₃O₄ phase in the Ag-O-S system prepared by two methods, the known method of co-precipitation from aqueous solution and a new method depending on the interaction of Ag₂S and Ag₂SO₄ solid reagents, has been investigated. No EPR spectra were observed at room temperature, while at liquid helium temperature a number of EPR spectra have been recorded, which disappeared upon increasing temperature up to liquid nitrogen temperature. The sample obtained by the co-precipitation method revealed an intense, rich EPR spectrum that has been tentatively interpreted assuming the presence of at least two different Ag²⁺ ion complexes, one monomer resulting in an intense anisotropic, rhombic EPR powder pattern with g₁ = 1.93(1), g₂ = 2.025(3), g₃ = 2.094(5), hyperfine constants A₁ = = A₂ = 60(5) · 10^?4 cm^?1,A ₃ = 90(5) · 10^?4 cm^?1 and one dimer EPR pattern presumably involving a pair of Ag²⁺ ions with internuclear separation of 4.3 Å. However, the presence of larger clusters could not be excluded. On the other hand, the sample obtained by a solid state reaction method has given rise to two rather weak EPR lines centered at g_eff = 2.105(3) and g_eff = 4.213(3), respectively.