Disjoint empty disks supported by a point set

For a planar point-set P, let D(P) be the minimum number of pairwise-disjoint empty disks such that each point in P lies on the boundary of some disk. Further define D(n) as the maximum of D(P) over all n-element point sets. Hosono and Urabe recently conjectured that ${D(n) = \lceil n/2 \rceil}$ . Here we show that ${D(n) \geq n/2 + n/236 - O(\sqrt{n})}$ and thereby disprove this conjecture.     

The boundary layer in the hub area of wind turbine blades at high wind speeds

At low tip speed ratios, the strongest effect at the inboard half-span, when a vortex like flow occurs, is produced. These 3-D rotational effects contribute to a stall delay as well as higher lift and angles of attack at the inboard sections, as compared to 2-D flow conditions. A greater understanding of the mechanisms and properties of the shear layer close to the upper side surface of blade is sought through the development of an analytic theory and then is completed by CFD computations. The results show that the secondary flow has a slip effect on the blade surface and its circumferential velocity is less than that of blade revolution, particularly important for TSR <3.0. While at the high tip speed ratios the flow around the blade is much as the 2-D one, then at the low tip speed ratios, TSR < 3.0 the flow behaves rather like the impinging flow on a rotating disc. Therefore, the 3-D rotational effects dominate the flow at high wind speeds and a special approach of such flows would be to assume. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hole-doped semiconductor nanowire on top of an s-wave superconductor: a new and experimentally accessible system for Majorana fermions

Majorana fermions were envisioned by Majorana in 1935 to describe neutrinos. Recently, it has been shown that they can be realized even in a class of electron-doped semiconductors, on which ordinary s-wave superconductivity is proximity induced, provided the time reversal symmetry is broken by an external Zeeman field above a threshold. Here we show that in a hole-doped semiconductor nanowire the threshold Zeeman field for Majorana fermions can be very small for some magic values of the hole density. In contrast to the electron-doped systems, smaller Zeeman fields and much stronger spin-orbit coupling and effective mass of holes allow the hole-doped systems to support Majorana fermions in a parameter regime which is routinely realized in current experiments.     

Synthesis of methacrylate-functionalized phosphonates and phosphates with long alkyl-chain spacers and their self-aggregation in aqueous solutions

Abstract  Polymerizable amphiphilic organophosphorous compounds were synthesized and their self-aggregation behavior was investigated. The studied molecules contain a hydrophilic phosphorus end group, an alkyl chain spacer with a variable length from 3 to 11 CH₂ groups and a polymerizable methacrylic group at the other chain end. Thus, the molecules represent a class of polymerizable surfactants. Two different reaction methods were used; either unsaturated alcohols or bromine-containing alcohols were applied as starting compounds for the preparation of the organophosphorous surfactants. The self-aggregation and micelle formation of the prepared compounds were investigated in aqueous solution by dynamic light scattering measurements. The critical micelle concentration of the P-containing amphiphiles was in all cases smaller than 0.040 mol/l and strongly dependent on the polarity of the phorphorous head group and the chain length of the spacer. Graphical abstract   The synthesis of organophosphorous amphiphiles as surface active monomers for the modification of metal oxide surfaces is presented. The spacer between the phosphorous head group and the methacrylate group was varied with regard to their length and composition. The self-aggregation behavior of these methacrylate-functionalized phosphates and phosphonates surfactants was investigated.     

DWBA analysis of the reaction 12C(α, n)15O

Angular distributions of neutrons from the reaction ¹²C(α, n)¹⁵O(g.s.) have been measured at lab energies from 18.4 to 23.1 MeV and angles ranging from 0° to 130°, using a time-of-flight technique. The experimental curves generally show a forward peaking and a strong dependence on the incident energy. The data were compared with the angular distributions predicted by the distorted-wave theory of direct Nuclear reactions, and no agreement could be obtained when only a stripping mechanism was taken into account.     

Investigations on electric properties of polymers—III. d.c. and a.c. conductivity of polyphenylacetylene films

d.c. and a.c. Conductivity measurements were made on films of polyphenylacetylene(PPA) having cis-transoidal(c-t) and trans-cisoidal(t-c) isomeric structures. PPA_c-t crystallizes from solution in benzene, while PPA_t-c remains unchanged (amorphous). Films of both polymers have d.c. and a.c. conductivities higher than those of pellets. The d.c. conductivity-temperature curve of the PPA_c-t film consists of four parts (I, II, III and IV) of different slopes. Comparing the activation energies of d.c. conductivity with optical threshold energy (in solid state), the hopping mechanism (over the I, II and IV parts) and band-tunnelling mechanism (over part III) were suggested. The PPA_t-c film shows the hopping mechanism. The a.c. conductivity data were interpreted in terms of either simple quantum hopping or a simple classical hopping mechanism depending on frequency and temperature range.     

In Process Citation

The separation, identification and determination of the fat- and water-soluble vitamins are realized by partition chromatography with a reversed-phase system made by bonding a C(18) group to silica. The water-soluble vitamins are directly separated with the mobile phase 1% acetic acid/acetonitrile (89:11 v/v) and are revealed by an ultraviolet detector, except for pantothenic acid. The separation efficiency and precision of determination of the fat-soluble vitamins depend on the operational conditions. The composition of the excipients and all the constituents of pharmaceuticals (aqueous and oil solutions, injections, dispersions, emulsions) determine the choice of the extraction solvents and the preparation of the solution to be injected; the polarity of the mobile phase (acetonitrile/water 95:5 v/v) can be changed, and the choice depends on the components to be separated. The experimental conditions are specified and some examples are given of application of HPLC to determination of water-soluble vitamins (B1, B2, C, PP, B6) and fat-soluble vitamins (non-saponifiable oils, vitamin A and its esters, cholecalciferol, ergocalciferol, and tocopherol and its acetate) in multivitamin formulations (solutions, suspensions, syrups, fatty excipients etc.).