A family of skew Hadamard difference sets

In 1933 a family of skew Hadamard difference sets was described by Paley using matrix language and was called the Paley-Hadamard difference sets in the literature. During the last 70 years, no new skew Hadamard difference sets were found. It was conjectured that there are no further examples of skew Hadamard difference sets. This conjecture was proved to be true for the cyclic case in 1954, and further progress in favor of this conjecture was made in the past 50 years. However, the conjecture remains open until today. In this paper, we present a family of new perfect nonlinear (also called planar) functions, and construct a family of skew Hadamard difference sets using these perfect nonlinear functions. We show that some of the skew Hadamard difference sets presented in this paper are inequivalent to the Paley-Hadamard difference sets. These new examples of skew Hadamard difference sets discovered 70 years after the Paley construction disprove the longstanding conjecture on skew Hadamard difference sets. The class of new perfect nonlinear functions has applications in cryptography, coding theory, and combinatorics.     

A complete set of numerical invariants for a subfactor

We show that certain numerical invariants associated naturally to a subfactor planar algebra constitute a complete family in the sense of determining the isomorphism class of the subfactor planar algebra.In the course of the proof, we show also that planar algebra isomorphisms of subfactor planar algebras can always be chosen to be ∗-preserving. This latter statement generalises the fact that ‘Hopf algebra isomorphisms of finite-dimensional Kac algebras can be chosen to be ∗-preserving’.     

Design and synthesis of novel imidazolium-based ionic liquids with a pseudo crown-ether moiety: diastereomeric interaction of a racemic ionic liquid with enantiopure europium complexes

A planar-chiral imidazolium salt with a tris(oxoethylene) bridge was synthesized, and its potential application as a room temperature ionic liquid with a molecular-recognition ability was demonstrated.     

The design of molecules containing planar tetracoordinate carbon

A novel preference for planar tetracoordination was observed over the conventional tetrahedral arrangement in a new series of C₅H₂, C₅H₄, C₅H₄^1+/2+ and related compounds. The stability of these molecules is assessed with the ring-opening barriers, HOMO-LUMO gap, singlet-triplet energy differences and nucleus independent chemical shift values.     

Miniaturization of separation techniques using planar chip technology

Miniaturization of separation columns implies equally reduced vol- umes of injectors, detectors, and the connecting channels. Planar chip technology provides a powerful means for the fabrication of micron-sized structures such as channels. This is demonstrated by two examples. An optical absorbance detector chip exhibits the expected behavior of a 1 mm optical path length cell despite its volume of 1 nL. A capillary electrophoresis device allows integrated injections of 100 pL samples, efficiencies of 70,000 to 160,000 theoretical plates in 10 to 20 seconds, and external laser-induced fluorescence detection at any capillary length of choice between 5 and 50 mm.     

Is planarity of pyridin-2-yl- and pyrazin-2-yl-formamide thiosemicarbazones related to their tuberculostatic activity? X-ray structures of two pyrazine-2-carboxamide-N′-carbonothioyl-hydrazones

Crystal structures of two title compounds and several their relatives known earlier reveal conservative and characteristic features, which may be related to their tuberculostatic activity. The molecules are predominantly planar due to conjugation through five successive bonds in the zwitterionic fragment S⁻–C(sp²)–N–NH⁺–C(sp²)–NH₂ and intramolecular hydrogen bonds, which prevent rotation of the adjacent pyrazine (or pyridine) ring. It has been suggested that in spatial sense such planar molecules resemble acridines intercalating with nucleic acids and that similar process may be responsible for tuberculostatic activity of the title pyrazine-2-carboxamide-N′-carbonothioyl-hydrazones.     

Introduction of a planar chirality onto steroid substrates: synthesis of (S) and (R)-2′-formylcymantrenyl-17α-ethynylestradiols using (S) and (R)-1-formyl-2-iodo-cymantrenes

We report the synthesis and characterisation of (S) and (R)-2′-formylcymantrenyl-17α-ethynylestradiol synthesized using the Sonogashira cross-coupling reaction between optically pure (S) and (R) 1-formyl-2-iodo cymantrenes and ethynylestradiol. (S) and (R) 1-formyl-2-iodo cymantrenes were obtained from the same precursor: (2R,4R)-4-(methoxymethyl)-2-cymantrenyl-1,3-dioxane.     

Microfabricated ISEs: critical comparison of inherently conducting polymer and hydrogel based inner contacts

A rigorous side by side comparison of miniature planar potassium-selective electrodes with hydrogel and potassium hexacyanoferrate(II)/(III) doped polypyrrole (PPy/FeCN) based inner contacts is presented. The planar electrodes were manufactured by screen printing as four- and five-site arrays on ceramic substrates. These electrode arrays were incorporated into a flow-through cell, which could accommodate nine electrode sites. Two identical flow cells were connected in series and the effect of the inner contacts on the analytical performance of the respective electrodes has been critically evaluated. The time necessary to reach steady state conditions has been determined and the effect of experimental parameters (temperature, ambient light intensity, CO₂, and O₂ concentration of the sample) on the potential stability of the electrodes was analyzed. At controlled temperature, the drift of the planar potassium electrodes with hydrogel and PPy/FeCN solid contact were 0.11±0.02 mV h⁻¹ and 0.03±0.007 mV h⁻¹, respectively. The experimental data proved that there is no aqueous film formation between the PPy/FeCN film and the potassium-selective solvent polymeric membrane.     

Chirality due to deuterium substitution: synthesis and circular dichroism of (+)(R) p -2,7-dideuterio-1,6-methano[10]annulene

Summary The title compound was prepared from (–)(S) _p -2,7-dibromo-1,6-methano[10]annulene by treatment withn-Bu-Li and subsequent quenching with D₂O. The optical rotations at four wavelengths and the circular dichroism spectrum are reported.

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Chiralität durch Deuterium-Substitution: Synthese und Circulardichroismus von (+)(R) _p -2,7-Dideuterio-1,6-methano[10]annulen (Kurze Mitt.)

Zusammenfassung Die Titelverbindung wurde aus (–)(S) _p -2,7-Dibrom-1,6-methano[10]annulen durch Umsetzung mitn-Bu-Li und nachfolgende Reaktion mit D₂O dargestellt. Optische Rotationen bei vier Wellenlängen und das Circulardichroismus-Spektrum wurden bestimmt.