Examples of area-minimizing surfaces in the sub-Riemannian Heisenberg group $${\mathbb{H}^1}$$ with low regularity

We give new examples of entire area-minimizing t-graphs in the sub-Riemannian Heisenberg group . They are locally Lipschitz in Euclidean sense. Some regular examples have prescribed singular set consisting of either a horizontal line or a finite number of horizontal halflines extending from a given point. Amongst them, a large family of area-minimizing cones is obtained. Research supported by MEC-Feder grant MTM2007-61919.     

Chaotic dynamic and control for micro-electro-mechanical systems of massive storage with harmonic base excitation

This paper explores chaotic behaviour and control of micro-electro-mechanical systems (MEMS), which consist of thousands of small read/write probe tips that access gigabytes of data stored in a non-volatile magnetic surface. The model of the system is formed by two masses connected by a nonlinear spring and a viscous damping. The paper shows that, by means of an adequate feedback law, the masses can behave as two coupled Duffing’s oscillators, which may reach chaotic behaviour when harmonic forces are applied. The chaotic motion is destroyed by applying the following control strategies: (i) static output feedback control law with constant forces and (ii) geometric nonlinear control. The aim is to drive the masses to a set point even with harmonic base excitation, by using chaotic dynamics and nonlinear control. The paper shows that it is possible to obtain a positioning time around a few ms with sub-nanometre accuracy, velocities, accelerations and forces, as it appears in the design of present MEMS devices. Numerical simulations are used to verify the mathematical discussions.     

Balance in Stable Categories

We study when the stable category ${\mathcal A}/\langle{\mathcal T}\rangleWe study when the stable category A/áT?{\mathcal A}/\langle{\mathcal T}\rangle of an abelian category A{\mathcal A} modulo a full additive subcategory T{\mathcal T} is balanced and, in case T{\mathcal T} is functorially finite in A{\mathcal A}, we study a weak version of balance for A/áT?{\mathcal A}/\langle{\mathcal T}\rangle. Precise necessary and sufficient conditions are given in case T{\mathcal T} is either a Serre class or a class consisting of projective objects. The results in this second case apply very neatly to (generalizations of) hereditary abelian categories.     

Topological representation for monadic implication algebras

In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.      

Dinuclear cyano-bridged CoIII-FeII complexes as precursors for molecular mixed-valence complexes of higher nuclearity

The preparation and characterization of a series of trinuclear mixed-valence cyano-bridged Co(III)-Fe(II)-Co(III) compounds derived from known dinuclear [[L(n)Co(III)(mu-NC)]Fe(II)(CN)(5)](-) complexes (L(n)() = N(5) or N(3)S(2) n-membered pendant amine macrocycle) are presented. All of the new trinuclear complexes were fully characterized spectroscopically (UV-vis, IR, and (13)C NMR). Complexes exhibiting a trans and cis arrangement of the Co-Fe-Co units around the [Fe(CN)(6)](4-) center are described (i.e., cis/trans-[{L(n)Co(III)(mu-NC)](2)Fe(II)(CN)(4)](2+)), and some of their structures are determined by X-ray crystallography. Electrochemical experiments revealed an expected anodic shift of the Fe(III/II) redox potential upon addition of a tripositively charged [Co(III)L(n)] moiety. The Co(III/II) redox potentials do not change greatly from the di- to the trinuclear complex, but rather behave in a fully independent and noncooperative way. In this respect, the energies and extinction coefficients of the MMCT bands agree with the formal existence of two mixed-valence Fe(II)-CN-Co(III) units per molecule. Solvatochromic experiments also indicated that the MMCT band of these compounds behaves as expected for a class II mixed-valence complex. Nevertheless, its extinction coefficient is dramatically increased upon increasing the solvent donor number.     

Optical imaging of bacterial infection in living mice using a fluorescent near-infrared molecular probe

An optical imaging probe was synthesized by attaching a near-infrared carbocyanine fluorophore to an affinity group containing two zinc(II) dipicolylamine (Zn-DPA) units. The probe has a strong and selective affinity for the surfaces of bacteria, and it was used to image infections of Gram-positive S. aureus and Gram-negative E. coli bacteria in living nude mice. After intravenous injection, the probe selectively accumulates at the sites of localized bacterial infections in the thigh muscles of the mice.     

Complexes between lithium cation and diphenylalkanes in the gas phase: the pincer effect

The gas-phase lithium cation basicities (LCB values, Gibbs free energies of binding) of alpha,omega-diphenylalkanes Ph-(CH(2))(n)-Ph (n=2, 3, or 7) and 1,1-diphenylethane Ph-CH(Me)-Ph were investigated by means of Fourier-transform ion cyclotron resonance (FTICR) mass spectrometry. Their structures, and those of the corresponding Li(+) complexes were optimized at the B3LYP/6-31G(d) level and their relative stabilities calculated at the B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d) level. Whereas the most stable conformers of the free diphenylalkanes were found to adopt a completely stretched aliphatic chain connecting the two benzene rings, the most stable Li(+) complexes correspond to conformers in which the alkali metal cation interacts simultaneously with both benzene rings through the folding of the aliphatic chain ("pincer effect"). This chelation brings about a significant enhancement of the Li(+) binding enthalpies (LBE values), which were calculated to be approximately 75 kJ mol(-1) higher than those evaluated for conventional (singly coordinated) pi complexes in which the metal cation interacts with only one of the benzene rings. The increase of the corresponding lithium cation basicities, however, (Gibbs free energies of Li(+) binding, LCB values) was calculated to be smaller by approximately 15 kJ mol(-1) as the pincer effect is entropically disfavored. The good agreement between the calculated LCB values, assuming a statistical distribution of the different conformers present in the gas phase, and the experimental LCB values measured by means of FTICR mass spectrometry are considered indirect evidence of the existence of the pincer effect.     

Simultaneous determination of the herbicides diquat and paraquat in water

A method based on solid-phase extraction (on silica cartridges) and high-performance liquid chromatography (HPLC) followed by diode array UV detection is presented as an analytical tool for screening diquat (DQ) and paraquat (PQ) in drinking waters. The method is useful for quality control laboratories of water companies and beverage industries. Absolute recoveries of DQ and PQ from drinking water (25 mL in all cases), spiked at levels between 0.1, 1.0, and 5.0 microg/L, range from 91% to 103%. Relative standard deviation percentages are between 3% and 11%. Quantitation and detection limits are 70 and 40 ng/L for DQ and 90 and 60 ng/L for PQ, respectively; therefore, these herbicides can be detected and quantitated at levels below the limits established by the European Union.     

Rapid tool for distinction of wines based on the global volatile signature

A new methodology capable of performing the simultaneous analysis of the main surfactants--linear alkylbenzene sulfonates (LAS), alkyl ethoxysulfates (AES), alkyl sulfates (AS), nonylphenol polyethoxylates (NPEOs) and alcohol polyethoxylates (AEOs)--and their carboxylated metabolites--sulfophenyl carboxylic acids (SPCs) and alkylphenol ethoxycarboxylates (APECs)--in environmental samples has been developed for the first time. Extraction is carried out by solid-phase extraction (SPE) and pressurized liquid extraction (PLE) from water and sediment, respectively. Identification and quantification of the target compounds is performed using a liquid chromatography-mass spectrometry (LC-MS) system equipped with an electrospray interface (ESI) operating in mixed-mode. Optimization of parameters such as pH, ionic strength, temperature and solvents has been carried out in order to obtain recoveries in the range from 70 to 107% for most homologs, while the limits of detection are 0.05-0.5 ng mL(-1) in water and 1-10 ng g(-1) in sediment. The proposed methodology has been applied for the simultaneous determination of all the target compounds in samples taken from aquatic ecosystems in the SW of Spain. Values for LAS, AS, AES, NPEOs and AEOs are up to 38.7, 3.0, 2.9, 5.0 and 1.2 microg L(-1) in waters, and in the ranges of 1.73-12.80, 0.11-0.24, 0.02-0.59, 1.94-2.70 and 0.64-3.64 mg kg(-1) in sediments, respectively. The highest concentrations of metabolites found in water are 149.6 microg L(-1) of SPCs and 3.9 microg L(-1) of APECs.