An Erdös-Ko-Rado theorem for regular intersecting families of octads

Codewords of weight 8 in the [24, 12] binary Golay code are called octads. A family? of octads is said to be a regular intersecting family if? is a 1-design and |x ∩ y| ≠ 0 for allx, y ∈ ?. We prove that if? is a regular intersecting family of octads then |?| ≤ 69. Equality holds if and only if? is a quasi-symmetric 2-(24, 8, 7) design. We then apply techniques from coding theory to prove nonexistence of this extremal configuration.     

On the edge-colouring problem for unions of complete uniform hypergraphs

For given n∈$\text{N}$ and H?{1,2,…,n} we investigate whether the collection of subsets A?{1,2,…,n} with |A|∈H possesses a parellelism (1-factorization). A complete solution for the case H={1,2,…, h} is given.     

Error-Correcting Codes over an Alphabet of Four Elements

The problem of finding the values of A_q(n,d)—the maximum size of a code of length n and minimum distance d over an alphabet of q elements—is considered. Upper and lower bounds on A₄(n,d) are presented and some values of this function are settled. A table of best known bounds on A₄(n,d) is given for n 12. When q M < 2q, all parameters for which A_q(n,d) = M are determined.     

Direct electrophilic silylation of terminal alkynes

[reaction: see text] A variety of alkynylsilanes were efficiently prepared via direct silylation of terminal alkynes with aminosilanes in the presence of zinc halides. Base- and nucleophile-sensitive functionalities were perfectly tolerated under the above reaction conditions. Initial mechanistic studies support the electrophilic character of this transformation.     

Fracture of thick laminated composites

The fracture of thick laminated graphite/epoxy composites has been the subject of an extensive research program. The program was divided into three major areas of investigation which included laminate thickness, laminate stacking sequence, and part-through surface flaws. The results from this program are reviewed with emphasis placed on their applicability to the design of thick laminated composite structures. Paper was presented at 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas on June 9–14, 1985.     

Current-induced transverse spin-wave instability in a thin nanomagnet

We show that an unpolarized electric current incident perpendicular to the plane of a thin ferromagnet can excite a spin-wave instability transverse to the current direction if source and drain contacts are not symmetric. The instability, which is driven by the current-induced "spin-transfer torque," exists for one current direction only.     

Exponential sensitivity to dephasing of electrical conduction through a quantum dot

According to random-matrix theory, interference effects in the conductance of a ballistic chaotic quantum dot should vanish proportional to (tau(phi)/tau(D))(p) when the dephasing time tau(phi) becomes small compared to the mean dwell time tau(D). Aleiner and Larkin have predicted that the power law crosses over to an exponential suppression proportional to exp((-tau(E)/tau(phi)) when tau(phi) drops below the Ehrenfest time tau(E). We report the first observation of this crossover in a computer simulation of universal conductance fluctuations. Their theory also predicts an exponential suppression proportional to exp((-tau(E)/tau(D)) in the absence of dephasing--which is not observed. We show that the effective random-matrix theory proposed previously for quantum dots without dephasing explains both observations.     

Fluctuating spin g-tensor in small metal grains

In the presence of spin-orbit scattering, the splitting of an energy level varepsilon(&mgr;) in a generic small metal grain due to the Zeeman coupling to a magnetic field B--> depends on the direction of B-->, as a result of mesoscopic fluctuations. The anisotropy is described by the eigenvalues g(2)(j) ( j = 1,2,3) of a tensor G, corresponding to the (squares of) g-factors along three principal axes. We consider the statistical distribution of G and find that the anisotropy is enhanced by eigenvalue repulsion between the g(j).     

Shorter Alkyl Chains Enhance Molecular Diffusion and Electron Transfer Kinetics between Photosensitisers and Catalysts in CO2-Reducing Photocatalytic Liposomes

Covalent functionalisation with alkyl tails is a common method for supporting molecular catalysts and photosensitisers onto lipid bilayers, but the influence of the alkyl chain length on the photocatalytic performances of the resulting liposomes is not well understood. In this work, we first prepared a series of rhenium-based CO₂-reduction catalysts [Re(4,4’-(C_nH_2n+1)₂-bpy)(CO)₃Cl] ( ReC_n ; 4,4’-(C_nH_2n+1)₂-bpy=4,4’-dialkyl-2,2’-bipyridine) and ruthenium-based photosensitisers [Ru(bpy)₂(4,4’-(C_nH_2n+1)₂-bpy)](PF₆)₂ ( RuC_n ) with different alkyl chain lengths (n=0, 9, 12, 15, 17, and 19). We then prepared a series of PEGylated DPPC liposomes containing RuC_n and ReC_n , hereafter noted C_n , to perform photocatalytic CO₂ reduction in the presence of sodium ascorbate. The photocatalytic performance of the C_n liposomes was found to depend on the alkyl tail length, as the turnover number for CO (TON) was inversely correlated to the alkyl chain length, with a more than fivefold higher CO production (TON=14.5) for the C₉ liposomes, compared to C₁₉ (TON=2.8). Based on immobilisation efficiency quantification, diffusion kinetics, and time-resolved spectroscopy, we identified the main reason for this trend: two types of membrane-bound RuC_n species can be found in the membrane, either deeply buried in the bilayer and diffusing slowly, or less buried with much faster diffusion kinetics. Our data suggest that the higher photocatalytic performance of the C₉ system is due to the higher fraction of the more mobile and less buried molecular species, which leads to enhanced electron transfer kinetics between RuC₉ and ReC₉ .