On Defining Sets of Full Designs with Block Size Three

A defining set of a t-(v, k, λ) design is a subcollection of its blocks which is contained in no other t-design with the given parameters, on the same point set. A minimal defining set is a defining set, none of whose proper subcollections is a defining set. The spectrum of minimal defining sets of a design D is the set {|M| | M is a minimal defining set of D}. We show that if a t-(v, k, λ) design D is contained in a design F, then for every minimal defining set d _D of D there exists a minimal defining set d _F of F such that \({d_D = d_F\cap D}\). The unique simple design with parameters \({{\left(v,k, {v-2\choose k-2}\right)}}\) is said to be the full design on v elements; it comprises all possible k-tuples on a v set. Every simple t-(v, k, λ) design is contained in a full design, so studying minimal defining sets of full designs gives valuable information about the minimal defining sets of all t-(v, k, λ) designs. This paper studies the minimal defining sets of full designs when t = 2 and k = 3. Several families of non-isomorphic minimal defining sets of these designs are found. For given v, a lower bound on the size of the smallest and an upper bound on the size of the largest minimal defining set are given. The existence of a continuous section of the spectrum comprising approximately v values is shown, where just two values were known previously.     

A conjectured property of Hermitian pencils

If (A, B) is any pair of Hermitian matrices, the power of λ dividing det(λI?xA ?yB) will be given by the number of basic singular summands in the pair. Contrary to conjecture, this power can be greater than one even when the pair is unitarily irreducible.     

New routes to 1α-hydroxyvitamin D3

The sulphone (2) and the methyl ester (3, R=H) were used in stereo-selective syntheses of derivatives of 1α-hydroxyprecalciferol₃ and 1α-hydroxytachysterol₃, which were then converted into the title compound.     

A recirculating system for concentrating volatile samples

Summary A recirculating system powered by a diaphragm pump which may be readily dismantled for cleaning, is described. The results of operating this system for dynamic headspace sampling in the closed or open mode to load volatiles onto a Tenax trap over a range of temperatures and loading volumes are shown. The system was designed to facilitate the analysis of volatiles in natural products and tested using an equimolar solution of 7 esters of boiling points ranging from 120°C to 299°C. The results showed that compounds in the boiling point range 120–200°C could be loaded onto the trap at 30°C by passing 1–21 of carrier gas through. In order to trap compounds of boiling points approaching 300°C, a temperature of 50–70°C and a loading volume of 2.5–3 1 was necessary. Using the apparatus, human sweat was analysed to show the degree of concentration possible with a natural sample and the variation in the chromatogram profiles of successive trapping from the same sample. Twelve chromatograms from the sweat of two pairs of identical twins were pattern matched to show the high degree of reproducibility possible using this apparatus to trap biological volatiles.     

Nonlinear diffusion and viral spread through the leaf of a plant

The spread of a virus through the leaf of a plant is both spatially and temporally causal in that the present status depends on the past and the spatial spread is compactly supported and progresses outwards. Such spatial spread is known to occur for certain nonlinear diffusion processes. The first compactly supported solution for nonlinear diffusion equations appears to be that of Pattle published in 1959. In that paper, no explanation is given as to how the solution was derived. Here, we show how the solution can be derived using Lie symmetry analysis. This lays a foundation for exploring the behavior of other choices for nonlinear diffusion and exploring the addition of reaction terms which do not eliminate the compactly supported structure. The implications associated with using the reaction–diffusion equation to model the spatial–temporal spread of a virus through the leaf of a plant are discussed.     

Solid-state Fluorescence from Carbon Dots Widely Tunable from Blue to Deep Red through Surface Ligand Modulation

Carbon dots (CDs) find widespread attention due to their remarkable fluorescent and electronic properties. However, aggregation-caused quenching currently limits the application of CDs in colored displays. The construction of CDs with color-tunable solid-state fluorescence (SSF) is rarely reported, since the preparation of SSF CDs is technically challenging. Herein, through surface ligand modulation, SSF CDs with an emission-color span of almost 300 nm (from blue to deep red) were obtained. In-depth structure-property studies reveal that intra- and inter-molecular hydrogen-bonding inside SSF CDs provokes the emission properties in the aggregated state. Photodynamic characterizations demonstrate emission wavelengths can be switched smoothly by deliberately altering conjugation ability between substituent ligands and CDs core. Three-dimensional printing patterning is used to create a range of emissive objects, demonstrating the commercial potential for use in optical lamps.     

Nachweis und Bestimmung des Wismuts

Ohne Zusammenfassung     

Tantal und Niob

Ohne Zusammenfassung     

Millimetre-wave fibre–wireless transmission systems with reduced effects of fibre chromatic dispersion

This paper describes two techniques for the implementation of millimetre-wave (mm-wave) wireless communication systems incorporating optical fibre distribution networks. Fibre chromatic dispersion can exhibit severe effects on the transportation of mm-wave frequencies over fibre, resulting in greatly reduced post-detection rf powers. Each mm-wave fibre–wireless system demonstrated here incorporates a method for the generation and modulation of an optical mm-wave carrier, which enables the effect of fibre dispersion to be significantly reduced. One set-up is a direct-detection scheme where optical single-sideband (SSB) with carrier modulation is used to overcome fibre dispersion effects. The other system employs a self-heterodyne arrangement in which a dual-frequency optical source generates a low phase-noise mm-wave beat signal. Data transmission is achieved by externally modulating the dual-mode signal and reduced effects of fibre dispersion are observed.     

A Photochemical Route towards Metal Sulfide Nanosheets from Layered Metal Thiolate Complexes

Synthesizing nanomaterials with anisotropic architectures, especially two‐dimensional (2D) nanosheets (NSs), is a key focus of materials science research. Metal sulfide nanosheets (MSNSs) are typically obtained involving exfoliation of bulk metal sulfides with layered structures. The synthesis of NSs of intrinsically non‐layered metal sulfides has received relatively less attention. Metal alkanethiolates with lamellar structures are now shown to serve as effective scaffolds for constructing NSs. A novel photochemical step was employed to transform 2D metal thiolates into MSNSs. By this strategy the 2D nature of metal thiolate precursors was preserved in the final products, resulting in the successful synthesis of NSs of binary PbS, CdS, and Cu₉S₅, as well as ternary wurtzite CuInS₂, Cu₂SnS₃. Results encourage the wider utilization of photochemical strategies in the synthesis of anisotropic MSNSs.