Darboux operators for linear first-order multi-component equations in arbitrary dimensions

We construct Darboux operators for linear, multi-component partial differential equations of first order. The number of variables and the dimension of the matrix coefficients in our equations are arbitrary. The Darboux operator and the transformed equation are worked out explicitly. We present an application of our formalism to the (1+2)-dimensional Weyl equation.     

Stereoselective photoinduced electrocyclic ring closure of aromatic enehydrazides. Asymmetric synthesis of 3-aryl dihydroisoquinolones and tetrahydroisoquinolines

A flexible route for the stereoselective synthesis of a variety of 3-aryl dihydroisoquinolones and tetrahydroisoquinolines has been developed. The key step is a diastereoselective photoinduced 6π-electrocyclic ring closure of enantiopure aromatic enehydrazides via a 1,4-remote asymmetric induction. N–N bond cleavage to release the chiral appendage from the preliminary annulated compounds and/or concomitant reduction of the lactam carbonyl group completed the synthesis of the title compounds.     

Protein-Polysaccharide Interactions for Stabilization of Food Emulsions

Proteins, polysaccharides and their blends, as examples of natural biopolymers, are surface active materials. Biopolymers may be considered as amphiphilic macromolecules that play an essential role in stabilizing food formulations (foams, emulsions and dispersions). Under specific conditions (such as protein-to-polysaccharide ratio, pH, ionic strength, temperature, mixing processing), it has been stated that proteins and polysaccharides form hybrids (complexes) with enhanced functional properties in comparison to the proteins and polysaccharides alone. Different protein-polysaccharide pairs are reviewed with particular attention to the emulsification capability of their mixtures. In the case of uncomplexed blends of biopolymers, competitive adsorption onto hydrophobic surfaces is generally reported. Conversely, electrostatic complexation between oppositely charged proteins and polysaccharides allows better anchoring of the new-formed macro-molecular amphiphile onto oil-water interfaces. Moreover, improved thermal stability and increased resistance to external treatment (high pressure) involved in food processing are obtained. This review presents basic and applied knowledge on protein-polysaccharide interactions in aqueous medium and at the oil-water interface in food emulsion systems. Electrostatic interactions and thermodynamic incompatibility in mixed biopolymer solutions are correlated to the functional properties (rheology, surface hydrophobiciry, emulsification power) of these interesting blends. Basic and industrial selected systems of different families of hydrocolloids (as gum Arabic, galactomannans, pectins) and protein (caseins, whey, soya, gelatin) mixtures are reviewed.     

Ionization by pH and Anionic Surfactant Binding Gives the Same Thickening Effects of Crosslinked Polyacrylic Acid Derivatives

Physical properties of aqueous solutions of hydrophobically modified crosslinked polyacrylic acids change quite extensively as the polymer is charged up. A study is carried out concerning the similarities between two polymer ionization processes, that is, by pH increment and anionic surfactant addition. The two processes charge the polymer by distinctly different mechanisms. At sufficiently high pH the carboxylic groups of the polymer are virtually all ionized and the polymer is, therefore, fully charged. The effective repulsion among the charged groups due to the entropy of the counterions promotes an increased stiffness as well as an expansion of the polymer particles. We investigate here how the ionization and swelling will be if, instead of high pH, the polymer is at low pH conditions but associated to ionic surfactants. Surfactants associate to the polymer both in a noncooperative way by the binding of individual surfactant molecules and in a cooperative way as micelles since the polymer promotes surfactant self-assembly. This binding leads to a highly charged polymer-surfactant complex and leads to an osmotic swelling as well. The swelling and the gelation were monitored by rheology and dynamic light scattering, of polymer solutions by varying the pHs and adding ionic surfactants at low pH. The results show that ionization by surfactants and by pH lead to approximately the same gelation degree, as can be seen by similar viscosity values. Both processes result in dramatic viscosity increases, up to 8 orders of magnitude. More hydrophobic surfactants, with longer alkyl chain, are shown to be more efficient as enhancers of swelling and gelation. The network that is formed at high pH or at sufficiently high concentration of surfactant can be weakened or even disrupted if monovalent or divalent salts are added, demonstrating the role of counterion entropy.     

Complexes of N-Phosphorylated Thioureas RNHC(S)NHP(O)(OiPr)2 (R = 2-MeC6H4, 2,6-Me2C6H3, 2,4,6-Me3C6H2) With Nickel(II)

The reaction of O,O′-diisopropylphosphoric acid isothiocyanate (iPrO)₂P(O)NCS with 2-methylaniline 2-MeC₆H₄NH₂, 2,6-dimethylaniline 2,6-Me₂C₆H₃NH₂, or 2,4,6-trimethylaniline 2,4,6-Me₃C₆H₂NH₂ leads to the N-phosphorylated thioureas RNHC(S)NHP(O)(OiPr)₂ (R = 2-MeC₆H₄?, HL^I ; 2,6-Me₂C₆H₃?, HL^II ; 2,4,6-Me₃C₆H₂?, HL^III ). Reaction of the potassium salts of HL^{I –III} with Ni(II) in aqueous EtOH leads to [Ni(L^I–III-N,S)₂] ([NiL^I–III ₂ ]) chelate complexes. The compounds obtained were investigated by ¹H, ³¹P{¹H} NMR spectroscopy and microanalysis. The molecular structure of the thiourea HL^III was elucidated by single crystal X-ray diffraction analysis. Single crystal X-ray diffraction studies showed that HL^III forms both intra- and intermolecular hydrogen bonds, which in turn leads to the formation of polymeric chains. One of the intermolecular hydrogen bonds is of the type N?H…S. Moreover, the formation of intermolecular C?H…η⁶-phenyl interactions was established.

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