Optical and microstructural properties of self-assembled InAs quantum structures in silicon

The InAs quantum structures were formed in silicon by sequential ion implantation and subsequent thermal annealing. Two kinds of crystalline InAs nanostructures were successfully synthesized: nanodots (NDs) and nanopyramids (NPs). The peaks at 215 and 235 cm^?1, corresponding to the transverse optical (TO) and longitudinal optical (LO) InAs single-phonon modes, respectively, are clearly visible in the Raman spectra. Moreover, the PL band at around 1.3 µm, due to light emission from InAs NDs with an average diameter 7±2 nm, was observed. The InAs NPs were found only in samples annealed for 20 ms at temperatures ranging from 1000 up to 1200°C. The crystallinity and pyramidal shape of InAs quantum structures were confirmed by HRTEM and XRD techniques. The average size of the NPs is 50 nm base and 50 nm height, and they are oriented parallel to the Si (001) planes. The lattice parameter of the NPs increases from 6.051 to 6.055 Å with the annealing temperature increasing from 1100 to 1200°C, due to lattice relaxation. Energy dispersive spectroscopy (EDS) shows almost stoichiometric composition of the InAs NPs.     

Large free sets in powers of universal algebras

We prove that for each universal algebra ${(A, \mathcal{A})}$ of cardinality ${|A| \geq 2}$ and infinite set X of cardinality ${|X| \geq | \mathcal{A}|}$ , the X-th power ${(A^{X}, \mathcal{A}^{X})}$ of the algebra ${(A, \mathcal{A})}$ contains a free subset ${\mathcal{F} \subset A^{X}}$ of cardinality ${|\mathcal{F}| = 2^{|X|}}$ . This generalizes the classical Fichtenholtz–Kantorovitch–Hausdorff result on the existence of an independent family ${\mathcal{I} \subset \mathcal{P}(X)}$ of cardinality ${|\mathcal{I}| = |\mathcal{P}(X)|}$ in the Boolean algebra ${\mathcal{P}(X)}$ of subsets of an infinite set X.     

Generalized Stäckel systems

We consider the generalized Stäckel systems, the broadest class of integrable Hamiltonian systems that admit separation of variables and possess separation relations affine in the Hamiltonians. For these systems we construct in a systematic fashion hierarchies of basic separable potentials. Moreover, we show how the equations of motion for the systems under study are related through appropriately chosen reciprocal transformations and how the respective constants of motion are related through generalized Stäckel transforms.     

Heat conductivity of LuAgCu4

The electrical resistivity and heat conductivity of LuAgCu₄ have been studied within the 4.2–300-K range. An additional contribution to heat conductivity, most probably due to the bipolar component, has been revealed at T≥100 K. The conclusion is drawn that LuAgCu₄ is apparently a semimetal.     

Über zwei von Hamel herrührende Extremumsätze der Funktionentheorie

Ohne Zusammenfassung     

Robust branch-cut-and-price for the Capacitated Minimum Spanning Tree problem over a large extended formulation

This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arborescence problem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. Moreover, a novel feature is introduced in such kind of algorithms: powerful new cuts expressed over a very large set of variables are added, without increasing the complexity of the pricing subproblem or the size of the LPs that are actually solved. Computational results on benchmark instances from the OR-Library show very significant improvements over previous algorithms. Several open instances could be solved to optimality.     

Beweis für die Invarianz des ebenen Gebiets

Ohne Zusammenfassung