On Minimal Defining Sets of Full Designs and Self-Complementary Designs, and a New Algorithm for Finding Defining Sets of t-Designs

A defining set of a t-(v, k, λ) design is a partial design which is contained in a unique t-design with the given parameters. A minimal defining set is a defining set, none of whose proper partial designs is a defining set. This paper proposes a new and more efficient algorithm that finds all non-isomorphic minimal defining sets of a given t-design. The complete list of minimal defining sets of 2-(6, 3, 6) designs, 2-(7, 3, 4) designs, the full 2-(7, 3, 5) design, a 2-(10, 4, 4) design, 2-(10, 5, 4) designs, 2-(13, 3, 1) designs, 2-(15, 3, 1) designs, the 2-(25, 5, 1) design, 3-(8, 4, 2) designs, the 3-(12, 6, 2) design, and 3-(16, 8, 3) designs are given to illustrate the efficiency of the algorithm. Also, corrections to the literature are made for the minimal defining sets of four 2-(7, 3, 3) designs, two 2-(6, 3, 4) designs and the 2-(21, 5, 1) design. Moreover, an infinite class of minimal defining sets for 2-((v) || 3){v\choose3} designs, where v ≥ 5, has been constructed which helped to show that the difference between the sizes of the largest and the smallest minimal defining sets of 2-((v) || 3){v\choose3} designs gets arbitrarily large as v → ∞. Some results in the literature for the smallest defining sets of t-designs have been generalized to all minimal defining sets of these designs. We have also shown that all minimal defining sets of t-(2n, n, λ) designs can be constructed from the minimal defining sets of their restrictions when t is odd and all t-(2n, n, λ) designs are self-complementary. This theorem can be applied to 3-(8, 4, 3) designs, 3-(8, 4, 4) designs and the full 3-(8 || 4)3-{8 \choose 4} design using the previous results on minimal defining sets of their restrictions. Furthermore we proved that when n is even all (n − 1)-(2n, n, λ) designs are self-complementary.     

Unitals in Topological Affine Translation Planes Need Not Be Strictly Convex

We study the relationship of two incidence geometric convexity notions, namely, ovoids in real affine spaces and compact unitals of codimension 1 in topological affine translation planes. In [3] we showed that every ovoid in a translation plane is a unital, and we asked if the converse is true. Here we introduce the notion of a shell, which is distinctly weaker than that of an ovoid and still implies the unital property if the translation plane is properly chosen (and the shell is not too degenerate). We give an explicit example of a shell that is not an ovoid. The question remains whether or not conversely, every compact unital of codimension 1 in a translation plane is a shell.     

An Investigation into Domino‐Heck Reactions of N‐Acylamino‐Substituted Tricyclic Imides: Synthesis of New Prospective Pharmaceuticals

Heck and domino‐Heck reactions of unsaturated N‐acylamino‐substituted tricyclic imides with aryl(heteroaryl) iodides and phenyl‐ or (trimethylsilyl)acetylene were either carried out in the presence of formate or phenyl‐ and (trimethylsilyl)acetylene, respectively. The C? C coupling reactions appeared to be completely diastereoselective, giving the corresponding N‐acylamino‐5‐exo‐aryl (heteroaryl)‐ ( 5a – c, 6a , b ), N‐(benzoylamino)‐5‐exo‐phenyl‐6‐exo‐[(trimethylsilyl)ethynyl]‐ ( 5d ), or 5‐exo‐(4‐chlorophenyl)‐N‐(2,2‐dimethylpropanoylamino)‐6‐exo‐(phenylethynyl)bicyclo[2.2.1]heptane‐2‐endo,3‐endo‐dicarboximide ( 6c ) (Schemes 3 and 4).     

Spectrophotometric multicomponent determination of sunset yellow, tartrazine and allura red in soft drink powder by double divisor-ratio spectra derivative, inverse least-squares and principal component regression methods

Double divisor-ratio spectra derivative (graphical method), classical least-squares and principal component regression (two numerical methods) methods were developed for the spectrophotometric multicomponent analysis of soft drink powders and synthetic mixtures containing three colorants without any chemical separation. The graphical method is based on the use of derivative signals of the ratio spectra using double divisor. In this method, the linear determination ranges were 2-8 mug ml(-1) sunset yellow, 4-18 mug ml(-1) tartrazine and 2-8 mug ml(-1) allura red in 0.1 M HCl. In the numerical methods, a training set was randomly prepared by using 18 samples containing between 0 and 8 mug ml(-1) of sunset yellow, 0-18 mug ml(-1) of tartrazine and 0-8 mug ml(-1) of allura red. The chemometric calibrations were calculated by using the prepared training set and its absorbances at seven points (from 375.0 to 550.0 nm) in the spectral region 325-584 nm. The proposed methods were validated by using synthetic ternary mixtures and applied to the simultaneous determination of three colorants in soft drink powders. The obtained results were statistically compared with each other.     

Synthesis, characterization and thermoreversible behaviours of poly(dimethyl siloxane)/poly(N-isopropyl acrylamide) semi-interpenetrating networks

Simultaneous and sequential poly(N-isopropyl acrylamide) (PNIPAAm)/poly(dimethyl siloxane) (PDMS) semi-interpenetrating polymer networks (IPNs) with different linear PDMS contents were prepared by free radical polymerization method. Their phase morphologies have been characterized by FTIR, DSC and SEM. The simultaneous semi-IPNs exhibited phase transition temperatures (T_pt) shifted higher temperature from glass transition temperatures (T_g) of their respective homopolymers, suggesting a heterophase morphology and only physical entanglement between the PNIPAAm network and linear PDMS with high molecular weight (Mn≈9000 g/mol). For sequential semi-IPNs, the shift of T_pts towards lower temperature suggested that the chemical interaction between the constituents of the IPNs increased with increasing PDMS content in the network. In addition, these semi-IPNs were characterized for their thermo-sensitive behaviour by equilibrium swelling studies. The results showed that incorporation of hydrophobic PDMS polymer into the thermo- and pH-sensitive PNIPAAm and P(NIPAAm-co-IA) (itaconic acid) hydrogels by semi-IPN formation decreased swelling degrees of IPNs without affecting their LCSTs whereas addition of acrylated PDMS (Tegomer V-Si 2250) as crosslinker instead of N,N^′-methylenebisacrylamide (BIS) into the structures of these hydrogels changed their LCSTs along with their swelling degrees.     

Inkjet Printing of Functional Polymers and Materials: 2nd International Workshop in Eindhoven

This section contains reports on topical conferences. Reports are usually written at the request of the editorial office, but unsolicited contributions are also welcome. Suggestions should be sent to the editorial office of the Macromolecular journals, preferably by E‐mail to macromol@wiley‐vch.de.     

Synthesis of palladium complexes derived from imidazolidin‐2‐ylidene ligands and used for catalytic amination reactions

N‐Aryl amination and the Buchwald–Hartwig reaction are of great synthetic and industrial interest and scientists accept their usefulness and versatility for obtaining arylamines. In this study Ag–N‐heterocyclic carbene complexes were used as transmetallation reagents for the synthesis of Pd–N‐heterocyclic carbene complexes. The new Pd–N‐heterocyclic carbene complexes were characterized using elemental analysis and ¹H NMR, ¹³C NMR and infrared spectroscopies. The crystal structure of one, namely dichlorobis[1,3‐bis(2‐methylbenzyl)imidazolidin‐2‐yliden]palladium(II), is presented. The activity of the Pd(II) complexes in the coupling reaction of anilines or amines with bromobenzene was investigated. These complexes exhibited high catalytic activities in the direct synthesis of triarylamines and secondary amines in a single step. Copyright © 2016 John Wiley & Sons, Ltd.     

Synthesis,Spectroscopic, and Dyeing Properties of New Azo and Bisazo Dyes Derived from 5‐Pyrazolones

This study is in continuation of our work related to 5‐pyrazolones aimed at synthesizing new heterocycles with dyeing and anticipated biological properties. Compounds 1 and 2 ; 1‐methyl‐ or 1‐(2,4‐dimethylphenyl)‐3‐phenyl‐1H‐pyrazol‐5(4H)‐one, 3 ; 1‐methyl‐5‐oxo‐3‐phenyl‐4,5‐dihydro‐1H‐pyrazole‐4‐carbaldehyde and 4 ; 2‐(1‐methyl‐5‐oxo‐3‐phenyl‐1H‐pyrazol‐4(5H)‐ylidene)‐3‐phenylthiazolidin‐5‐one were prepared and subjected to diazotation with aromatic amines and diamines. New azo ( 1a – c , 2a, b , 3a , b , 4a , c ) and bisazo dyes ( 2c , d , 4b ) were obtained, and their structures were confirmed by spectroscopic and analytical methods. In addition, UV–vis measurements, dyeing performance, and fastness tests were carried out for all compounds.