Scroll codes

We study algebraic geometric codes obtained from rational normal scrolls. We determine the complete weight hierarchy and spectrum of these codes.      

Perimidine-based synthetic receptors for determination of copper(II) in water solution

Perimidine-based chelators 1 and 2 were prepared, and their structures were confirmed by ¹H and ¹³C NMR, MS spectroscopy and elemental analysis. These compounds were studied as specific synthetic receptors for the recognition of transition metal ions. They exhibited high affinity and selectivity towards Cu(II) ions. The conditional binding constants, linear dynamic range and detection limit were determined by UV–vis spectroscopy. These parameters demonstrated high potential of the prepared synthetic receptors for the recognition and determination of Cu(II) ions. The minimum detectable concentrations of Cu(II) ions for the synthetic receptors 1 and 2 were 270 and 75 nM (R ² = 0.9915 and 0.9964) in aqueous medium (water/DMSO; 99:1 (v/v)), respectively.     

Riordan group involutions

We study involutions in the Riordan group, especially those with combinatorial meaning. We give a new determinantal criterion for a matrix to be a Riordan involution and examine several classes of examples. A complete characterization of involutions in the Appell subgroup is developed. In another direction we find several examples that generalize the RNA matrix but are of independent interest.     

Simple proofs of open problems about the structure of involutions in the Riordan group

We prove that if D=(g(x),f(x)) is an element of order 2 in the Riordan group then g(x)=±exp[Φ(x,xf(x)] for some antisymmetric function Φ(x,z). Also we prove that every element of order 2 in the Riordan group can be written as BMB^-1 for some element B and M=(1,-1) in the Riordan group. These proofs provide solutions to two open problems presented by L. Shapiro [L.W. Shapiro, Some open questions about random walks, involutions, limiting distributions and generating functions, Adv. Appl. Math. 27 (2001) 585-596].     

Reaction of 3-chloroquinoline-2,4-diones with ethanolamine and rearrangement of the reaction products

The reaction of tertiary α-chloroketones with ethanolamine has not been hitherto described in the literature. Herein, we describe the reaction of tertiary 3-chloroquinoline-2,4-diones with ethanolamine to give novel 3-(2-hydroxyethylamino)quinoline-2,4-diones. These compounds provide 3-(2-oxooxazolidin-3-yl)quinoline-2,4(1H,3H)-diones and new compounds with dimeric character after reaction with triphosgene. Molecular rearrangement proceeds during the reaction of 3-(2-hydroxyethylamino)quinoline-2,4-diones with isocyanic acid. Three types of reaction products arise: 2-(2-hydroxyethyl)imidazo[1,5-c]quinazoline-3,5-diones, 3-(2-hydroxyethyl)-3,3a-dihydro-2H-imidazo[4,5-]quinoline-4(5H)diones and primarily 5-hydroxy-1-(hydroxyethyl)-1′H-spiro[imidazolidine-5,3′-indole]-2,2′-diones. The reaction mechanism and product stereochemistry are discussed. The ¹H, ¹³C and ¹⁵N NMR spectra of the prepared compounds were measured, and all resonances were assigned from appropriate two-dimensional experiments.     

Influence of HPAM on W/O emulsion separation properties

The present study reports on the influence of partially hydrolyzed polyacrylamide (HPAM) on essential w/o emulsion properties. The characterization has been undertaken with low field NMR to follow droplet sizes and distributions, sedimentation and coalescence kinetic, bench-scale electrocoalescence (E_crit) experiments to follow emulsion stability changes, and electrorheology to detect changes in the viscosity upon applying an external electric field. The result is that HPAM does not basically influence the droplet size distribution (DSD) and the stability level of the emulsions as can be expected of bulk polymers. However, there seems to be an interaction between added demulsifiers either through direct molecular interaction or via an interfacial complexation.     

Self‐Assembly of Coiled Coils in Synthetic Biology: Inspiration and Progress

Biological self‐assembly is very complex and results in highly functional materials. In effect, it takes a bottom‐up approach using biomolecular building blocks of precisely defined shape, size, hydrophobicity, and spatial distribution of functionality. Inspired by, and drawing lessons from self‐assembly processes in nature, scientists are learning how to control the balance of many small forces to increase the complexity and functionality of self‐assembled nanomaterials. The coiled‐coil motif, a multipurpose building block commonly found in nature, has great potential in synthetic biology. In this review we examine the roles that the coiled‐coil peptide motif plays in self‐assembly in nature, and then summarize the advances that this has inspired in the creation of functional units, assemblies, and systems.