Weak Solutions for the Motion of a Self-propelled Deformable Structure in a Viscous Incompressible Fluid

We consider the three-dimensional motion of a self-propelled deformable structure into a viscous incompressible fluid. The deformation of the solid is given whereas its position is unknown. Such a system could model the propulsion of fish-like swimmers. The equations of motion of the fluid are the Navier-Stokes equations and the equations for the structure are deduced from Newton’s laws. The corresponding system is a free boundary problem and the main result of the paper is the existence of weak solutions for this problem.     

Evaluación de la habitabilidad de edificios afectados por sismo utilizando la teoría de conjuntos difusos y las redes neuronales artificiales

The fuzzy sets theory and the artificial neural networks are computational intelligence tools which are nowadays widely used in earthquake engineering. This paper develops a method and a computer program which use these computational intelligence tools in order to support the damage and safety evaluation of buildings after strong earthquakes. The model uses an artificial neural network with three layers and a Kohonen learning algorithm; it also uses fuzzy sets in order to manage subjective information such as linguistic qualification of the damage levels in buildings and a fuzzy rule base to support the decision making process. All these techniques are incorporated in the developed computer program. The input data is the subjective and incomplete information about the building state obtained by possibly non experienced evaluators in the field of the seismic performance of buildings. The proposed method is implemented in a tool especially useful in the emergency response phase, when it supports the decision making regarding the building habitability and reparability. In order to show its effectiveness, two examples are included for two different types of buildings.     

The constrained compartmentalized knapsack problem: mathematical models and solution methods

The constrained compartmentalized knapsack problem can be seen as an extension of the constrained knapsack problem. However, the items are grouped into different classes so that the overall knapsack has to be divided into compartments, and each compartment is loaded with items from the same class. Moreover, building a compartment incurs a fixed cost and a fixed loss of the capacity in the original knapsack, and the compartments are lower and upper bounded. The objective is to maximize the total value of the items loaded in the overall knapsack minus the cost of the compartments. This problem has been formulated as an integer non-linear program, and in this paper, we reformulate the non-linear model as an integer linear master problem with a large number of variables. Some heuristics based on the solution of the restricted master problem are investigated. A new and more compact integer linear model is also presented, which can be solved by a branch-and-bound commercial solver that found most of the optimal solutions for the constrained compartmentalized knapsack problem. On the other hand, heuristics provide good solutions with low computational effort.     

A combinatorial proof of Marstrand’s theorem for products of regular Cantor sets

In a paper from 1954 Marstrand proved that if K⊂R² has a Hausdorff dimension greater than 1, then its one-dimensional projection has a positive Lebesgue measure for almost all directions. In this article, we give a combinatorial proof of this theorem when K is the product of regular Cantor sets of class C^1+α, α>0, for which the sum of their Hausdorff dimension is greater than 1.     

The Modulus of Smoothness in Metric Spaces and Related Problems

We define a general variant of the modulus of smoothness in metric spaces and show that under mild condition it is equivalent to the K-functional of a couple of Besov type spaces which in special cases coincide with spaces defined by Korevaar and Schoen. We prove various symmetrization inequalities which involve the modulus, the K-functional and the isoperimetric estimators. We also characterize the Hajłasz-type Sobolev spaces defined not necessarily on doubling measure spaces by means of generalized Poincaré inequalities. This require to study of some variants of the Fefferman–Stein sharp functions as well as the Hardy–Littlewood maximal operators.     

Insertion of Continuous Real Functions on Spaces,Bispaces, Ordered Spaces and Pointfree Spaces—A Common Root

We characterize normal and extremally disconnected biframes in terms of the insertion of a continuous real function in between given lower and upper semicontinuous real functions and show this to be the common root of several classical and new insertion results concerning topological spaces, bitopological spaces, ordered topological spaces and locales.     

Synthesis and reactivity of a phosphine-stabilized monogermanium analogue of alkynes

The synthesis of the first isolable C-phosphino-Ge-aminogermyne, stabilized by a phosphine ligand, has been achieved. X-ray diffraction analysis indicates a quite long Ge-C bond whose length is between that of a single and a double bond but consistent with the theoretically predicted values for a germyne bearing π-donating substituents. The isomerization of this germyne derivative affords a new stable N-heterocyclic germylene through migration of the original phosphine ligand from germanium to the carbon center.     

Micropollutant sorption to membrane polymers: a review of mechanisms for estrogens

Organic micropollutants such as estrogens occur in water in increasing quantities from predominantly anthropogenic sources. In water such micropollutants partition not only to surfaces such as membrane polymers but also to any other natural or treatment related surfaces. Such interactions are often observed as sorption in treatment processes and this phenomenon is exploited in activated carbon filtration, for example. Sorption is important for polymeric materials and this is used for the concentration of such micropollutants for analytical purposes in solid phase extraction. In membrane filtration the mechanism of micropollutant sorption is a relatively new discovery that was facilitated through new analytical techniques. This sorption plays an important role in micropollutant retention by membranes although mechanisms of interaction are to date not understood. This review is focused on sorption of estrogens on polymeric surfaces, specifically membrane polymers. Such sorption has been observed to a large extent with values of up to 1.2 ng/cm(2) measured. Sorption is dependent on the type of polymer, micropollutant characteristics, solution chemistry, membrane operating conditions as well as membrane morphology. Likely contributors to sorption are the surface roughness as well as the microporosity of such polymers. While retention-and/or reflection coefficient as well as solute to effective pore size ratio-controls the access of such micropollutants to the inner surface, pore size, porosity and thickness as well as morphology or shape of inner voids determines the available area for sorption. The interaction mechanisms are governed, most likely, by hydrophobic as well as solvation effects and interplay of molecular and supramolecular interactions such as hydrogen bonding, π-cation/anion interactions, π-π stacking, ion-dipole and dipole-dipole interactions, the extent of which is naturally dependent on micropollutant and polymer characteristics. Systematic investigations are required to identify and quantify both relative contributions and strength of such interactions and develop suitable surface characterisation tools. This is a difficult endeavour given the complexity of systems, the possibility of several interactions taking place simultaneously and the generally weaker forces involved.     

The speciation of vanadium in human serum

A knowledge of the speciation of vanadium in human serum is essential for an understanding of the biotransformation of antidiabetic vanadium complexes in human blood and of how vanadium is transported to the target cells. Such information may be acquired by two completely different approaches: separation techniques and modeling calculations. This review focuses on the latter.The two major metal ion binders in human serum are apotransferrin (apoTf) and human serum albumin (HSA), the interactions of which with V^IVO and V^V are discussed in detail. A partially new model for HSA–V^IVO interactions is introduced, in which the two binding sites (one for two and one for one metal ion) compete not only with each other, but also with hydrolysis of the metal ion.Focus is also placed on the possibility and importance of ternary complex formation between V^IVO, serum proteins and drug candidate ligands (maltol (mal), 1,2-dimethyl-3-hydroxy-4(1H)-pyridinone (dhp), acetylacetone (acac) and picolinic acid, (pic)): the structures and formation constants of different ternary complexes reported by the different research groups are critically reviewed.The serum speciations for V^IVO and V^V are calculated through use of the most recent stability constants; at biologically relevant concentrations (～1 μM, but definitely <10 μM) the apoTf complexes predominate for both metal ions. This has the consequences that the primary role of the drug candidate ligands of the original complexes is a carrier function until the vanadium is taken up into the serum, and the vanadium ion itself is the active metabolite responsible for the antidiabetic effect.