On Nested Chain Decompositions of Normalized Matching Posets of Rank 3

In 1975, J. Griggs conjectured that a normalized matching rank-unimodal poset possesses a nested chain decomposition. This elegant conjecture remains open even for posets of rank 3. Recently, Hsu, Logan, and Shahriari have made progress by developing techniques that produce nested chain decompositions for posets with certain rank numbers. As a demonstration of their methods, they prove that the conjecture is true for all rank 3 posets of width at most 7. In this paper, we present new general techniques for creating nested chain decompositions, and, as a corollary, we demonstrate the validity of the conjecture for all rank 3 posets of width at most 11.     

Inclusion relations for the spaces L(ℝ), \mathcal{H}\mathcal{K} (ℝ) ∩ \mathcal{B}\mathcal{V} (ℝ), and L 2(ℝ)

The inclusion relations for the spaces $ \mathcal{H}\mathcal{K} $ (I), L(I), $ \mathcal{H}\mathcal{K} $ (I) ∩ $ \mathcal{B}\mathcal{V} $ (I), and L ²(I) are found. On unbounded intervals, functions in $ \mathcal{H}\mathcal{K} $ (I) ∩ $ \mathcal{B}\mathcal{V} $ (I) need not be Lebesgue integrable.     

Kinetic study of the nitrosation of 1,3‐dialkylureas in aqueous‐perchloric acid medium

The kinetics of the nitrosation of 1,3‐dimethyl (DMU), 1,3‐diethyl (DEU), 1,3‐dipropylurea (DPU), 1,3‐dibuthyl (DBU), and 1,3‐diallylurea (DAU) were studied in a conventional UV/vis spectrophotometer in aqueous‐perchloric acid media. The kinetic study was carried out using the initial rate method. The reaction rate observed was where K_a is the acidity constant of nitrous acid. The diureas exhibited the reactivity order DMU ? DEU > DPU > DAU, which can be interpreted as a function of the steric impediment generated by the R alkyl group in the rate controlling step. A probable relationship between both the chemical reactivity and structure of the nitrosable substrate with the biological activity of the N‐nitroso compounds generated is proposed. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 273–279, 2004     

Development of an Amperometric Immunosensor for the Quantification of Staphylococcus aureus Using Self‐Assembled Monolayer‐Modified Electrodes as Immobilization Platforms

Amperometric immunosensors for the detection and quantification of S. aureus using MPA self‐assembled monolayer modified electrodes for the immobilization of the immunoreagents are reported. Two different immunosensor configurations were compared. A competitive mode, in which protein A‐bearing S. aureus cells and antiRbIgG labeled with horseradish peroxidase (HRP) compete for the binding sites of RbIgG immobilized onto the 3‐mercaptopropionic acid (MPA) modified electrode, was evaluated. Moreover, a sandwich configuration in which S. aureus cells were immobilized onto the MPA SAM, and RbIgG and antiRbIgG labeled with HRP were further linked to the electrode surface, was also tested. In both cases, TTF was used as the redox mediator of the HRP reaction with H₂O₂, and it was co‐immobilized onto the MPA‐modified gold electrode. After optimization of the working variables for both configurations, the analytical performance of the amperometric measurements carried out at 0.00 V (vs. Ag/AgCl) showed that the competitive immunosensor exhibited a lower limit of detection (1.6×10⁵ S. aureus cells mL^?1), as well as a better repeatability and reproducibility of the measurements.     

High-Pressure Synthesis of SeCu 1− x Zn x O 3 Perovskites

The SeCu 1 m x Zn x O 3 solid solution, with a distorted perovskite-type structure, has been synthesized under high pressures and temperatures. X-ray diffraction analysis indicates that the zinc ions occupy the copper sites, a solid solution being formed. It seems that high-pressure stabilises a small cation such as Se 4+ in the A site of the perovskite structure ABO 3 although the material is better described as formed by selenite anions \rm{SeO}_{3}^{-} and Cu 2+ /Zn 2+ cations.     

Near‐IR BODIPY Dyes à la Carte—Programmed Orthogonal Functionalization of Rationally Designed Building Blocks

Herein, we report the synthesis of polyfunctional BODIPY building blocks suitable to be subjected to several reaction sequences with complete chemoselectivity, thereby allowing the preparation of complex BODIPY derivatives in a versatile and programmable manner. The reactions included the Liebeskind–Srogl cross‐coupling reaction (LSCC), nucleophilic aromatic substitution (S_NAr), Suzuki, Sonogashira, and Stille couplings, and a desulfitative reduction of the MeS group. This novel synthetic protocol is a powerful route to design a library of compounds with tailored photophysical properties for advanced applications. In this context, it is noteworthy that it offers a straightforward and cost‐effective strategy to shift the BODIPY emission deep into the near‐infrared spectral region while retaining high fluorescence quantum yields as well as highly efficient and stable laser action. These new dyes outperform the lasing behaviour of dyes considered as benchmarks over the red spectral region, overcoming the important drawbacks associated with these commercial laser dyes, namely low absorption at the standard pump wavelengths (355 and 532 nm) and/or poor photostability.     

Elastic properties,Debye temperature,density of states and electron–phonon coupling of ZrB12 under pressure

The structural parameters, elastic constants and the electronic density of states of ZrB₁₂ under pressure are determined using first-principles calculations with plane-wave pseudopotential density functional theory, within the generalized gradient approximation. From the elastic constants the elastic parameters and Debye temperature were calculated. They increase as the pressure is increased. The density of states at the Fermi level decreases as pressure is increased, changing from 0.576 to 0.515. Using the Debye temperature and the McMillan equation, the electron–phonon coupling constant was obtained as a function of pressure. It is found that the electron–phonon coupling constant is proportional to the logarithm of the ratio between the value of the Debye temperature and the value of the superconducting critical temperature.     

Mössbauer study of the (Ru1-xFex)Sr2GdCu2O8-δ system and two of its possible impurities: SrRuO3 and Gd2CuO4

Mössbauer spectra of a series of samples of the weak ferromagnetic $ {\left( {Ru_{{1 - x}} Fe_{x} } \right)}Sr_{2} GdCu_{2} O_{{8 - \delta }} M?ssbauer spectra of a series of samples of the weak ferromagnetic system reveal the existence of three dissimilar sites where the Fe atoms can go into the structure. The M?ssbauer parameters of the three observed quadrupole doublets, together with the relative population on each site, allow the following site assignment for the iron atoms: Fe³⁺ in four-fold planar coordination at Ru sites; Fe³⁺ in five-fold pyramidal coordination also at Ru sites and Fe²⁺ or Fe³⁺ in five-fold coordination at Cu sites. This assignment implies the formation of oxygen-vacancies at the charge reservoir (the RuO₂ planes) that affect the structure and the superconducting and magnetic properties of the undoped system. Moreover, a close correlation between the oxygen content, calculated through the M?ssbauer data, and the measured cell volume is established. We also report the M?ssbauer spectra of two compounds (SrRu_0.95Fe_0.05O₃ and Gd₂Cu_0.95Fe_0.05O₄) that could be formed as impurities during the synthesis of our samples.