Two infinite families of terminating binomial sums

We present a family of identities including both binomial coefficients and a power of a natural number \(m \ge 2\). We find a combinatorial interpretation of these identities, which provides bijective proof. Dual alternating sign identities are also presented.     

Simulated Gastric and Intestinal Fluid Electrolyte Solutions as an Environment for the Adsorption of Apple Polyphenols onto β-Glucan

Interactions with dietary fibers in the gastrointestinal tract might affect the potential bioactivities of phenolic compounds. In this study, the interactions between apple phenolic compounds and β-glucan (a dietary fiber) were studied by studying the adsorption process in simulated gastric and intestinal fluid electrolyte solutions. Phenolic compounds were extracted from apples, adsorbed onto β-glucan (2 h, 37 °C, in gastric or intestinal fluid electrolyte solutions), and determined using high performance liquid chromatography. Phenolic compounds (flavan-3-ols, flavonols, phenolic acids, and dihydrochalcone) were stable in the gastric fluid (pH 3). In the intestinal fluid (pH 7), flavan-3-ols were not found and chlorogenic acid isomerized. Polyphenols from the apple peel (up to 182 and 897 mg g⁻¹) and flesh (up to 28 and 7 mg g⁻¹) were adsorbed onto β-glucan in the gastric and intestinal fluids, respectively. The adsorption was affected by the initial concentration of the polyphenols and β-glucan and by the environment (either gastric or intestinal fluid electrolyte solution). By increasing the initial polyphenol amount, the quantity of adsorbed polyphenols increased. Increasing the amount of β-glucan decreased the amount adsorbed. The results can be helpful in explaining the fate of phenolic compounds in the gastrointestinal tract.     

Cation assisted binding and cleavage of dinitrogen by uranium complexes

The role of alkali promoters in N₂ cleavage by metal complexes remains poorly understood despite its relevance to the industrial production of ammonia from N₂. Here we report a series of alkali bound-oxo-bridged diuranium(iii) complexes that provide a unique example of decreasing N₂ binding affinity with increasing cation size (from K to Cs). N₂ binding was found to be irreversible in the presence of K. A N₂ complex could be isolated in the solid state in the presence of the Rb cation and crystallographically characterized, but N₂ binding was found to be reversible under vacuum. In the presence of the Cs cation N₂ binding could not be detected at 1 atm. Electrochemical and Computational studies suggest that the decrease in N₂ binding affinity is due to steric rather than electronic effects. We also find that weak N₂ binding in ambient conditions does not prevent alkali assisted N₂ cleavage to nitride from occurring. More importantly, we present the first example of cesium assisted N₂ cleavage leading to the isolation of a N₂ derived multimetallic U/Cs bis-nitride. The nitrides readily react with protons and CO to yield ammonia, cyanate and cyanide.

N₂ binding affinity decreases markedly in a series of isostructural U(iii)–alkali ions complexes with increasing cation size. N₂ binding is undetectable in the Cs analogue, but the first example of cesium-assisted N₂ cleavage to bis-nitride was observed at ambient condition.     

Characterisation of the thermo-oxidative degradation of polyethylene pipes by chromatographical,rheological and thermo-analytical methods

In this work the influence of three different stabiliser systems on the stress rupture behaviour of high density polyethylene (PE-HD) pipes under constant internal pressure was examined at 60 and 80°C with special consideration of the quasi-brittle failure by growth of a single crack in the failure regime preceding the global chemical degradation of the pipes. It could be proven that the pipes of the three formulations did not show global molecular and morphological differences in this failure regime and that the stabilisation was still intact. Therefore, the differences in failure times observed for the three formulations are believed to be a result of local ageing around the crack tip related to the combined influence of time, the elevated temperature, the presence of oxygen and water, and the high mechanical stresses in the immediate crack tip region.     

EPMA and GDOES in Functional-Gradient Hardmetal Systems

 WDS-EPMA and GDOES measurements were applied for the characterization of the in-situ surface modification process of (Ti, W)C-based hardmetals by in-diffusion of carbon and nitrogen leading to complicated microstructures composed by layers and/or gradients. The calibration of the analytical techniques was performed with chemically characterized specimens prepared by diffusional techniques or hot-pressing. In addition, for the GDOES method, certified reference materials (CRMs) have been used. The work was started from a re-investigation of the W-C and Mo-C systems in order to measure homogeneity regions of the various phases prepared by use of diffusion couples. Subsequently, the metal and non-metal contents of various sequences of layers and/or gradients in functional-gradient hardmetals (FGHs) were measured. Both methods were employed as complementary tools to get information about the element-concentration distribution in FGHs so that a better understanding of the influence of process parameters for fabrication of special hardmetals is possible.     

Anion-templated supramolecular C3 assembly for efficient inclusion of charge-dispersed anions into hydrogen-bonded networks

The binding properties and conformational adaptability of a known nitrate/sulfate receptor N,N'-3-azapentane-1,5-bis[3-(1-aminoethylidene)-6-methyl-3H-pyran-2,4-dione] (L) toward various charge-dispersed monoanions (HSO(3)(-), ClO(4)(-), IO(4)(-), PF(6)(-), and SbF(6)(-)) are considered. These anions template the folding of three HL(+) species through a self-assembly process into a new hollow supramolecular trication. During the self-assembly, all strong hydrogen-bond donors of the podand become coordinatively saturated by interactions with the oxo functionalities from other HL(+) molecules. In that way, only the weak hydrogen-bond-donating groups in the exterior part of the receptor are accessible for anion binding. The investigated anions are accommodated in the hydrophobic pockets of the isomorphous hydrogen-bonded frameworks, which serve as a basis for selective crystallization from the highly competitive anion/solvent systems. This behavior is discussed in terms of size and geometry of the anions as well as the receptor's coordination capabilities to provide the most favorable surroundings for guest inclusion both in solution and in the solid state.     

Morpholine adducts of Co, Ni, and Mn benzoylacetonates: isostructurality and C–H···O hydrogen bonding

Morpholine adducts of nickel(II), cobalt(II), and manganese(II) benzoylacetonates, as well as a morpholine solvate of manganese(II) benzoylacetonate, were prepared and characterized by X-ray diffraction and thermal analysis. All four compounds crystallize in the P2₁/c space group with two complex molecules per unit cell. The morpholine solvate, along with the two adduct molecules, also contains four solvent morpholine molecules in the unit cell. The non-solvate compounds are isostructural, with crystal structures comprising 2D networks formed by C–H···O hydrogen bonding between phenyl rings and morpholine oxygen atoms. The topology of these networks can be described as intersecting C₂²(24) chains forming R₄⁴(48) rings. Networks with the same topology are also present in the solvate, but they are heavily distorted due to the presence of solvent morpholine molecules. Thermogravimetric analysis shows similar behavior of the non-solvate compounds upon thermal decomposition, with three degradation steps which can be related to gradual loss of morpholine molecules and subsequent overall decomposition. Decomposition of the solvate also proceeds in several steps, the first of which can be related to loss of solvent morpholine molecules and the further steps are analogous to those in the non-solvate compounds.     

Nonlinear mixture‐wise expansion approach to underdetermined blind separation of nonnegative dependent sources

Underdetermined blind separation of nonnegative dependent sources consists in decomposing a set of observed mixed signals into greater number of original nonnegative and dependent component (source) signals. That is an important problem for which very few algorithms exist. It is also practically relevant for contemporary metabolic profiling of biological samples, such as biomarker identification studies, where sources (a.k.a. pure components or analytes) are aimed to be extracted from mass spectra of complex multicomponent mixtures. This paper presents a method for underdetermined blind separation of nonnegative dependent sources. The method performs nonlinear mixture‐wise mapping of observed data in high‐dimensional reproducible kernel Hilbert space (RKHS) of functions and sparseness‐constrained nonnegative matrix factorization (NMF) therein. Thus, the original problem is converted into new one with increased number of mixtures, increased number of dependent sources, and higher‐order (error) terms generated by nonlinear mapping. Provided that amplitudes of original components are sparsely distributed, which is the case for mass spectra of analytes, sparseness‐constrained NMF in RKHS yields, with significant probability, improved accuracy relative to the case when the same NMF algorithm is performed on the original problem. The method is exemplified on numerical and experimental examples related respectively to extraction of 10 dependent components from five mixtures and to extraction of 10 dependent analytes from mass spectra of two to five mixtures. Thereby, analytes mimic complexity of components expected to be found in biological samples. Copyright © 2013 John Wiley & Sons, Ltd.     

Synthesis and polymerization reactions of cyclic imino ethers. 5: naphthalene unit‐containing poly(ether amide)s

Poly(ether amide)s containing naphthalene unit were prepared either by the polyaddition reaction of aromatic bis(2‐oxazoline)s with the different dihydroxynaphthalenes or by the homopolyaddition of a monomer containing an oxazoline, a hydroxy, and naphthalene moieties. First, polymerization method represents AA + BB mode where 1,4‐phenylene‐2,2′‐bis(2‐oxazoline) (A) and 1,3‐phenylene‐2,2′‐bis(2‐oxazoline) (B) were used as AA monomers and four different dihydroxynaphthalenes 1–4 were used as BB monomers. In the second case, 2‐(6‐hydroxynaphthalene‐2‐yl)‐2‐oxazoline (5) was used as AB‐type monomer in thermally induced polymerizations. The time dependences of polyadditions in bulk as well as in the solution were examined. The reduction of molar mass was observed after the initial fast increase of molar mass. This can be explained by the presence of side and degradation reactions. In both cases, polyadditions resulted in the linear poly(ether amide)s, which were characterized by ¹H and ¹³C NMR spectroscopy. Thermal properties of the prepared polymers were studied by differential scanning calorimetry (DSC) measurements. Comparison of the temperatures of glass transition for polymers prepared in AA + BB mode shows the strong dependence of thermal properties on the structure of the polymers. The values were in the range of 136–171°C. The glass‐transition temperature (T_g) of poly[2‐(6‐hydroxynaphthalene‐2‐yl)‐2‐oxazoline] prepared by AB‐type polyaddition is 183°C, which corresponds to the higher contents of hard aromatic segments in the latter type of polymers compared to the polymers prepared in the AA + BB‐type polyadditions. The described polymers represent novel naphthalene unit‐containing poly(ether amide)s for different applications in material science. Copyright © 2011 John Wiley & Sons, Ltd.