Biembedding Steiner Triple Systems in Surfaces Using the Bose Construction

A uniform framework is presented for biembedding Steiner triple systems obtained from the Bose construction using a cyclic group of odd order, in both orientable and nonorientable surfaces. Within this framework, in the nonorientable case, a formula is given for the number of isomorphism classes and the particular biembedding of Ducrocq and Sterboul (preprint 18pp., 1978) is identified. In the orientable case, it is shown that the biembedding of Grannell et al. (J Combin Des 6 ( 7 ), 325–336) is, up to isomorphism, the unique biembedding of its type. Automorphism groups of the biembeddings are also given.     

The Order of Automorphisms of Quasigroups

We prove quadratic upper bounds on the order of any autotopism of a quasigroup or Latin square, and hence also on the order of any automorphism of a Steiner triple system or 1‐factorization of a complete graph. A corollary is that a permutation σ chosen uniformly at random from the symmetric group will almost surely not be an automorphism of a Steiner triple system of order n, a quasigroup of order n or a 1‐factorization of the complete graph . Nor will σ be one component of an autotopism for any Latin square of order n. For groups of order n it is known that automorphisms must have order less than n, but we show that quasigroups of order n can have automorphisms of order greater than n. The smallest such quasigroup has order 7034. We also show that quasigroups of prime order can possess autotopisms that consist of three permutations with different cycle structures. Our results answer three questions originally posed by D.  Stones.     

A Complete Solution to Spectrum Problem for Five‐Vertex Graphs with Application to Traffic Grooming in Optical Networks

A G‐design of order n is a decomposition of the complete graph on n vertices into edge‐disjoint subgraphs isomorphic to G. Grooming uniform all‐to‐all traffic in optical ring networks with grooming ratio C requires the determination of graph decompositions of the complete graph on n vertices into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The existence spectrum problem of G‐designs for five‐vertex graphs is a long standing problem posed by Bermond, Huang, Rosa and Sotteau in 1980, which is closely related to traffic groomings in optical networks. Although considerable progress has been made over the past 30 years, the existence problems for such G‐designs and their related traffic groomings in optical networks are far from complete. In this paper, we first give a complete solution to this spectrum problem for five‐vertex graphs by eliminating all the undetermined possible exceptions. Then, we determine almost completely the minimum drop cost of 8‐groomings for all orders n by reducing the 37 possible exceptions to 8. Finally, we show the minimum possible drop cost of 9‐groomings for all orders n is realizable with 14 exceptions and 12 possible exceptions.     

Palladium‐Catalyzed Coupling Reaction of Perfluoroarenes with Diarylzinc Compounds

This report describes the first Pd⁰‐catalyzed cross‐coupling of hexafluorobenzene (C₆F₆) with diarylzinc compounds to give a variety of pentafluorophenyl arenes. This reaction could be applied to other perfluoroarenes, such as octafluorotoluene, pentafluoropyridine, and perfluoronaphthalene, to give the corresponding polyfluorinated coupling products. The optimal ligand in this catalytic reaction was PCy₃, and lithium iodide was indispensable as an additive for the coupling reaction. One of the roles of lithium iodide in this catalytic reaction was to promote the oxidative addition of one C?F bond of C₆F₆ to palladium. Stoichiometric reactions revealed that an expected oxidative‐addition product, trans‐[Pd(C₆F₅)I(PCy₃)₂], generated from the reaction of [Pd(PCy₃)₂] with C₆F₆ in the presence of lithium iodide, was not involved in the catalytic cycle. Instead, a transient three‐coordinate, monophosphine‐ligated species, [Pd(C₆F₅)I(PCy₃)], emerged as a potential intermediate in the catalytic cycle. Therefore, we isolated a novel Pd^II complex, [Pd(C₆F₅)I(PCy₃)(py)], in which pyridine (py) acted as a labile ligand to generate the transient species. In fact, in the presence of lithium iodide, this Pd^II complex was found to react smoothly with diphenylzinc to give the desired pentafluorophenyl benzene, whereas the same reaction conducted in the absence of lithium iodide resulted in a decreased yield of pentafluorophenyl benzene, which indicated that the other role of lithium iodide was to enhance the reactivity of the organozinc species during the transmetalation step.     

An Organotrifluoroborate for Broadly Applicable One‐Step 18F‐Labeling

A new zwitterionic organotrifluoroborate is appended to three radiosynthons that afford undergo facile bioconjugation to several clinically relevant peptides and one enzyme inhibitor. Molecularly complex bioconjugates are ¹⁸F‐labeled in a single aqueous step in rapid time (<15 min) without HPLC purification to afford tracers in good yields (>200 mCi, 20–40 %) at high specific activity (≥3 Ci/μmol) and at >98 % purity. PET imaging shows in vivo stability and tumor uptake.     

Impact of Magnesium(II) on Beryllium Fluorides in Solutions Studied by 19F NMR Spectroscopy

Beryllium fluorides are widely used in protein phosphorylation studies to get stable transition state analogs or near attack conformers, which has attracted much attention. BeF₃^? is one of the optimal phosphoryl (PO₃^?) analogs for its identical geometry and charge, and Mg²⁺ naturally participates in the phosphoryl binding in biological systems. In solutions, BeF₃^? coexists with other beryllium fluorides (BeF₄^2?, BeF₂ and BeF⁺) and magnesium fluorides, and there are equilibriums between these species. In this article, ¹⁹F NMR spectroscopy was applied to the investigation of the impact of magnesium(II) on beryllium fluorides. It has been found that when Mg²⁺ was introduced into the solutions, the chemical shifts, the intensities and the line widths of ¹⁹F signals of various beryllium fluoride complexes were changed. After ionic strength correction, these effects were remarkable only for BeF₄^2? and BeF₃^?, especially BeF₄^2?, when the concentration of the fluoride ion is relatively low. Mechanism of the effects is proposed which involves ion pair formation between Mg²⁺ and beryllium fluorides.     

C–F Bond Cleavage Reactions with Beryllium,Magnesium, Gallium,Hafnium, and Thorium Halides

The work describes unexpected stoichiometric C–F bond cleavage reactions of beryllium, magnesium, gallium, hafnium and thorium halides with α,α,α-trifluorotoluene. The reaction of BeBr₂ / GaBr₃ or MgBr₂ / GaBr₃ mixtures as well as neat GaI₃ with α,α,α-trifluorotoluene in the presence of (OSi₂Me₄)₂ ( I ) yields the carbenium ion containing compounds [Ph-C(O₂Si₂Me₄)][GaX₄] (X = Br: 1 , X = I/F: 2 ). Both compounds were successfully characterized and a defluorination type reaction under incorporation of a siloxy unit was observed. Compound 1 was also characterized by single-crystal X-ray diffraction analysis. The conversion of α,α,α-trifluorotoluene with BeI₂, HfI₄ or ThI₄ turned out to be a halodefluorination-type reaction with formation of α,α,α-triiodotoluene ( 3 ). An adequate NMR spectroscopic and the X-ray crystallographic characterization of 3 were performed for the first time.     

Modification of Hole Transport Layers for Fabricating High Performance Non‐fullerene Polymer Solar Cells

Interfacial engineering is expected to be a feasible strategy to improve the charge transport properties of the hole transport layer (HTL), which is of crucial importance to boost the device performance of organic solar cells (OSCs). In this study, two types of alcohol soluble materials, 2,3,5,6‐tetrafluoro‐7,7,8,8‐tetracyanoquinodimethane (F₄‐TCNQ) and di‐tetrabutylammoniumcis–bis(isothiocyanato)bis (2,2’‐bipyridyl‐4,4’‐dicarboxylato) ruthenium(II) (N719) dye were selected as the dopant for HTL. The doping of F₄‐TCNQ and N719 dye in poly (ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) with and without integrating a graphene quantum‐dots (G‐QDs) layer has been explored in poly[[2,6′‐4‐8‐di(5‐ethylhexylthienyl)benzo[1,2‐b:3,3‐b]dithiophene][3‐fluoro‐2[(2‐ethylhexyl)carbonyl]thieno[3,4‐b]thio‐phenediyl:(2,2′‐((2Z,2′Z)‐(((4,4,9, 9‐tetrakis(4‐hexylphenyl)‐4,9‐dihydro‐s‐indaceno[1,2‐b:5,6‐b′]dithiophene‐2,7‐diyl)bis(4‐((2‐ethylhexyl)oxy)thiophene‐5,2‐diyl))bis(methanylylidene))bis(5,6‐difluoro‐3‐oxo‐2,3‐dihydro‐1H‐indene‐2,1‐diylidene))dimalononitrile (PTB7‐Th:IEICO‐4F) OSCs. The power conversion efficiency of the non‐fullerene OSCs has been increased to 10.12% from 8.84%. The influence of HTL modification on the nano‐morphological structures and photophysical properties is analyzed based on the comparative studies performed on the control and modified devices. The use of chemical doping and bilayer strategy optimizes the energy level alignment, nanomorphology, hole mobility, and work‐function of HTL, leading to considerable reduction of the leakage current and recombination losses. Our work demonstrates that the doping of HTL and the incorporation of G‐QDs layer to constitute a bilayer HTL is an promising strategy to fabricate high performance non‐fullerene polymer solar cells     

Synthesis of [18F]F-γ-T-3, a Redox-Silent γ-Tocotrienol (γ-T-3) Vitamin E Analogue for Image-Based In Vivo Studies of Vitamin E Biodistribution and Dynamics

Vitamin E, a natural antioxidant, is of interest to scientists, health care pundits and faddists; its nutritional and biomedical attributes may be validated, anecdotal or fantasy. Vitamin E is a mixture of tocopherols (TPs) and tocotrienols (T-3s), each class having four substitutional isomers (α-, β-, γ-, δ-). Vitamin E analogues attain only low concentrations in most tissues, necessitating exacting invasive techniques for analytical research. Quantitative positron emission tomography (PET) with an F-18-labeled molecular probe would expedite access to Vitamin E’s biodistributions and pharmacokinetics via non-invasive temporal imaging. (R)-6-(3-[¹⁸F]Fluoropropoxy)-2,7,8-trimethyl-2-(4,8,12-trimethyltrideca-3,7,11-trien-1-yl)-chromane ([¹⁸F]F-γ-T-3) was prepared for this purpose. [¹⁸F]F-γ-T-3 was synthesized from γ-T-3 in two steps: (i) 1,3-di-O-tosylpropane was introduced at C6-O to form TsO-γ-T-3, and (ii) reaction of this tosylate with [¹⁸F]fluoride in DMF/K₂₂₂. Non-radioactive F-γ-T-3 was synthesized by reaction of γ-T-3 with 3-fluoropropyl methanesulfonate. [¹⁸F]F-γ-T-3 biodistribution in a murine tumor model was imaged using a small-animal PET scanner. F-γ-T-3 was prepared in 61% chemical yield. [¹⁸F]F-γ-T-3 was synthesized in acceptable radiochemical yield (RCY 12%) with high radiochemical purity (>99% RCP) in 45 min. Preliminary F-18 PET images in mice showed upper abdominal accumulation with evidence of renal clearance, only low concentrations in the thorax (lung/heart) and head, and rapid clearance from blood. [¹⁸F]F-γ-T-3 shows promise as an F-18 PET tracer for detailed in vivo studies of Vitamin E. The labeling procedure provides acceptable RCY, high RCP and pertinence to all eight Vitamin E analogues.