The discrete-time preemptive repeat identical priority queue

Priority queueing systems come natural when customers with diversified delay requirements have to wait to get service. The customers that cannot tolerate but small delays get service priority over customers which are less delay-sensitive. In this contribution, we analyze a discrete-time two-class preemptive repeat identical priority queue with infinite buffer space and generally distributed service times. Newly arriving high-priority customers interrupt the on-going service of a low-priority customer. After all high-priority customers have left the system, the interrupted service of the low-priority customer has to be repeated completely. By means of a probability generating functions approach, we analyze the system content and the delay of both types of customers. Performance measures (such as means and variances) are calculated and the impact of the priority scheduling is discussed by means of some numerical examples.     

Matchings in graphs of odd regularity and girth

We establish lower bounds on the matching number of graphs of given odd regularity d$d$ and odd girth g$g$, which are sharp for many values of d$d$ and g$g$. For d=g=5$d=g=5$, we characterize all extremal graphs.     

Preparation of Cr2O3-Al2O3 Solid Solutions by Reactive Magnetron Sputtering

 (Al,Cr)₂O₃ layers were deposited on cemented carbide insert tips at a substrate temperature of 500 °C by means of reactive magnetron sputtering. An Al target was sputtered in RF mode and a Cr target in DC mode simultaneously in an oxygen/argon plasma. The influence of the Al and Cr sputter power and of the oxygen partial pressure on composition and structure of the (Al,Cr)₂O₃ layers as well as on the binding states of their components were investigated. Special attention was paid to the interpretation of the O ls and O-KLL fine structure and peak shifts. For the binary phases γ-Al₂O₃ and Cr₂O₃, a good agreement with literature values was observed in each case. In case of the ternary phases a continuous shift of the energetic position of the O1s peak, the O-KL₂₃L₂₃ transition and the modified Auger parameter α ′ of oxygen between the two binary phases γ-Al₂O₃ and Cr₂O₃ could be detected, indicating a wide range of solid solubility between Al₂O₃ and Cr₂O₃. As revealed by grazing incidence X-ray diffraction, the crystallinity of the ternary phases is less pronounced as compared to the binaries and increases with increasing oxygen flow rate.     

Sandwich-type tetranuclear lanthanide complexes with cucurbit[6]uril: from molecular compounds to coordination polymers

Sandwich-type lanthanide complexes with macrocyclic ligand cucurbit[6]uril (C 36H 36N 24O 12, CB[6]) were synthesized under hydrothermal conditions from aqueous solutions of lanthanide(III) bromides, CB[6], and 4-cyanopyridine. According to X-ray analysis (Ln = La, Pr, Dy, Ho, Er, and Yb), the compounds with different structural types of lanthanide cores have a common fragment where the tetranuclear hydroxo complex is sandwiched between two macrocycles {(IN@CB[6])Ln 4(mu 3-OH) 4(IN@CB[6])} (6+) (IN = isonicotinate). The photoluminescence (for Ln = Eu) and Fourier transform ion cyclotron resonance mass spectra (for Ln = Pr, Dy, and Er) were studied. The compounds are used for the first time as precursors for the synthesis of lanthanide-silver heterometallic coordination polymers. The chainlike crystal structure of polymers (Ln = La, Pr, and Dy) is constituted by the sandwich complexes linked via the coordination of IN nitrogen atoms to the silver atoms.     

Biopolymere in textilen Anwendungen. Polylactid,Polyhydroxyalkanoate

Biopolymers represent an interesting class of polymers whose potential is not yet been fully realised. However, more recently, biopolymers are gaining impetus in the market. Among the biopolymers, polylactic acid (PLA) is being used successfully and is widely accepted because it is produced from natural raw material and is degradable. Furthermore, it has comparable properties to standard thermoplastic polymers and can also be processed using similar process channels as conventional thermoplastic synthetic materials. Biopolymer applications are manifold and range from foils, fruit and vegetable packaging to hygiene and medical products. It can be expected that in future the application spectrum of biopolymers will increase even further.     

The coordinative properties of the ligands Ph2ECH2EPh2 (E = P,As, Sb) in carbonylvanadium complexes,and the molecular structure of η5-C5H5V(CO)3As2Ph4

Photo-reaction between the ligands Ph₂ECH₂EPh₂ (E = P: dppm, E = As: dpam, E = Sb: dpsm), L, and the vanadium complexes η⁵-C₅H₅V(CO)₄ and [Et₄N][V(CO)₆] yields monosubstituted mononuclear (dpsm) and dinuclear, ligand-bridged complexes (dpam, dpsm). With dppm, the final products are disubstituted chelate complexes, but monosubstituted mono- and dinuclear species are formed as intermediates.The shielding of the ⁵¹V nucleus decreases in the series dpsm > dppm > dpam and {M(CO)_n} > {M(CO)_n?1} L > {M(CO)_n?1}₂μ-L > {M(CO)_n?2}dppm ({M(CO)_n}[V(CO)₆]^?, η⁵-C₅H₅V(CO)₄). The half-widths of the NMR signals are greater for dinuclear than for mononuclear complexes.The crystal and molecular structures of η⁵-C₅H₅V(CO)₃As₂Ph₄ have been determined. The compound crystallizes in the space group P2₁/c with a = 1347.8, b = 1020.0, c = 2085.2 pm and β = 82.3°. Due to steric crowding, the ⁵¹V shielding is low composed to that of {η⁵-C₅H₅V(CO)₃}₂μ-dpam.     

Tetrameric Cubic Structures of Two Solvated Lithium Enolates

The structures of the crystalline lithium enolates derived from 3, 3-dimethyl-2-butanone and from cyclopentanone have been determined by X-ray analysis. Both structures are tetrameric aggregates based on a Li₄O₄-cube, each Li⁺-ion being additionally bonded to the O-atom of a tetrahydrofuran solvent molecule.