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.     

Isolated tin fluoride molecules in a copper lattice

A Mössbauer absorber was made by simultaneous evaporation of copper and implantation of¹¹⁹Sn, and postimplantation of F. A large fraction of Sn⁴⁺ was formed, assigned to the formation of SnF₄.     

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     

Effect of non-associated electrolyte solutions on the behaviour of poly(vinyl alcohol)-based hydrogels

The aim of this paper is to present the behaviour of the poly(vinyl alcohol) hydrogels [PVA-HG] in sodium and potassium chlorides aqueous solutions, due to their interactions. The tested [PVA-HG]-s have been obtained by repeated freezing and thawing cycles. White, heterogeneous hydrogels have been obtained. These hydrogels exhibit a mechanical active behaviour at their contact with electrolytes aqueous solutions, manifested by important changing in mass, volume and density of the hydrogel samples. These modifications could be explained by water elimination from the hydrogels that initially reached the equilibrium of swelling. The kinetic of the water desorption and the reversibility of this process, have been studied and some of the factors that influence this behaviour have been evidenced. The sensitivity of PVA hydrogels to electrolyte nature and concentration could be used in sensors design and also could explain some aspects of electrolytes diffusion through PVA membranes and targeted drugs delivery.