On the number of directions determined by a pair of functions over a prime field

A three-dimensional analogue of the classical direction problem is proposed and an asymptotically sharp bound for the number of directions determined by a non-planar set in AG(3,p), p prime, is proved. Using the terminology of permutation polynomials the main result states that if there are more than pairs with the property that f(x)+ag(x)+bx is a permutation polynomial, then there exist elements c,d,e∈Fp with the property that f(x)=cg(x)+dx+e.     

Cation substitution effects in the system Sr2-xBaxBi3 (0 < or = x < or = 1.3): structural distortions induced by chemical pressure

Crystals of the composition Sr(2-x)Ba(x)Bi(3) (0 < or = x < or = 1.3) have been synthesized from the elements and were characterized by single-crystal and powder X-ray diffraction methods. The compounds crystallize for x = 0, 0.45, 0.86, 1.08, 1.28 in the structure type of the parent compound Sr 2Bi 3 with space group Pnna (No. 52) and Z = 4. Substitution of Sr by Ba leads to a site preference for Ba. The anionic Bi substructures in the pseudoternary system simultaneously distort under remarkable elongation of one distinct Bi-Bi contact. Magnetic measurements for samples with x = 0, 0.45 and 1.08 reveal superconducting transitions at low temperatures. Linear muffin-tin orbital band structure calculations of Sr(2)Bi(3) show strong cation-anion interactions that greatly stabilize the structure. Besides showing characteristics of a typical metal, the band structure plot unveils the co-instantaneous occurrence of flat and steep bands around the Fermi level indicative for superconductivity.     

Ion trap mass spectrometry on a comet nucleus: the Ptolemy instrument and the Rosetta space mission

In May 2014, the Rosetta spacecraft is scheduled to rendezvous with the comet Churyumov-Gerasimenko ('67P'). One of the instruments on board the 'Lander' which will descend on to the surface of the comet is a miniaturised GC/MS system that incorporates an ion trap mass spectrometer, specially developed for isotope ratio analysis. This article describes the development and optimisation of the ion trap for this unique application, and presents a summary of the range of pre-programmed experiments that will contribute to the characterisation of the solid and volatile cometary materials.     

Non-Birational Twisted Derived Equivalences in Abelian GLSMs

In this paper we discuss some examples of abelian gauged linear sigma models realizing twisted derived equivalences between non-birational spaces, and realizing geometries in novel fashions. Examples of gauged linear sigma models with non-birational Kähler phases are a relatively new phenomenon. Most of our examples involve gauged linear sigma models for complete intersections of quadric hypersurfaces, though we also discuss some more general cases and their interpretation. We also propose a more general understanding of the relationship between Kähler phases of gauged linear sigma models, namely that they are related by (and realize) Kuznetsov’s ‘homological projective duality.’ Along the way, we shall see how ‘noncommutative spaces’ (in Kontsevich’s sense) are realized physically in gauged linear sigma models, providing examples of new types of conformal field theories. Throughout, the physical realization of stacks plays a key role in interpreting physical structures appearing in GLSMs, and we find that stacks are implicitly much more common in GLSMs than previously realized.     

A von Neumann alternating method for finding common solutions to variational inequalities

By modifying von Neumann’s alternating projections algorithm, we obtain an alternating method for solving the recently introduced Common Solutions to Variational Inequalities Problem (CSVIP). For simplicity, we mainly confine our attention to the two-set CSVIP, which entails finding common solutions to two unrelated variational inequalities in Hilbert space.     

Effects of emulsifier charge and concentration on pancreatic lipolysis. 1. In the absence of bile salts

An in vitro study is performed with sunflower oil-in-water emulsions to clarify the effects of type of used emulsifier, its concentration, and reaction time on the degree of oil lipolysis, α. Anionic, nonionic, and cationic surfactants are studied as emulsifiers. For all systems, three regions are observed when surfactant concentration is scaled with the critical micelle concentration, C(S)/cmc: (1) At C(S) < cmc, α ≈ 0.5 after 30 min and increases up to 0.9 after 4 h. (2) At C(S) ≈ 3 × cmc, α ≈ 0.15 after 30 min and increases steeply up to 0.9 after 2 h for the cationic and nonionic surfactants, whereas it remains around 0.2 for the anionic surfactants. (3) At C(S) above certain threshold value, α = 0 for all studied surfactants, for reaction time up to 8 h. Additional experiments show that the lipase hydrolyzes molecularly soluble substrate (tributirin) at C(S) > cmc, which is a proof that these surfactants do not denature or block the enzyme active center. Thus, we conclude that the mechanism of enzyme inhibition by these surfactants is the formation of a dense adsorption layer on an oil drop surface, which displaces the lipase from direct contact with the triglycerides.     

Synthesis and luminescence properties of a broad-band red phosphor Ca3Si2O7:Eu2+ for warm white light-emitting diodes

Single-phase broad-band red-emitting Ca₃Si₂O₇:Eu²⁺ phosphors, with photoluminescence features that qualify them as candidates for white light-emitting diodes applications, were successfully synthesized via a modified solid-state reaction method that employed H₃BO₃ as a flux. The phosphors produced have an intense broad red emission band, with a peak at 603 nm, a full width at half maximum of 110 nm, and color coordinates of (0.550, 0.438). Concentration quenching occurred at 0.01 mol Eu²⁺. The discussion of the results shows that Eu²⁺ ions should be accommodated at the Ca-sites of the lattice, dipole–dipole interactions should predominantly govern the energy transfer mechanism among them, and the critical distance between them is ～31 Å.     

Role of surfactants on the approaching velocity of two small emulsion drops

Here we present the exact solution of two approaching spherical droplets problem, at small Reynolds and Peclet numbers, taking into account surface shear and dilatational viscosities, Gibbs elasticity, surface and bulk diffusivities due to the presence of surfactant in both disperse and continuous phases. For large interparticle distances, the drag force coefficient, f, increases only about 50% from fully mobile to tangentially immobile interfaces, while at small distances, f can differ several orders of magnitude. There is significant influence of the degree of surface coverage, θ, on hydrodynamic resistance β for insoluble surfactant monolayers. When the surfactant is soluble only in the continuous phase the bulk diffusion suppresses the Marangoni effect only for very low values of θ, while in reverse situation, the bulk diffusion from the drop phase is more efficient and the hydrodynamic resistance is lower. Surfactants with low value of the critical micelle concentration (CMC) make the interfaces tangentially immobile, while large CMC surfactants cannot suppress interfacial mobility, which lowers the hydrodynamic resistance between drops. For micron-sized droplets the interfacial viscosities practically block the surface mobility and they approach each other as solid spheres with high values of the drag coefficient.     

Interfacial layers from the protein HFBII hydrophobin: dynamic surface tension, dilatational elasticity and relaxation times

The pendant-drop method (with drop-shape analysis) and Langmuir trough are applied to investigate the characteristic relaxation times and elasticity of interfacial layers from the protein HFBII hydrophobin. Such layers undergo a transition from fluid to elastic solid films. The transition is detected as an increase in the error of the fit of the pendant-drop profile by means of the Laplace equation of capillarity. The relaxation of surface tension after interfacial expansion follows an exponential-decay law, which indicates adsorption kinetics under barrier control. The experimental data for the relaxation time suggest that the adsorption rate is determined by the balance of two opposing factors: (i) the barrier to detachment of protein molecules from bulk aggregates and (ii) the attraction of the detached molecules by the adsorption layer due to the hydrophobic surface force. The hydrophobic attraction can explain why a greater surface coverage leads to a faster adsorption. The relaxation of surface tension after interfacial compression follows a different, square-root law. Such behavior can be attributed to surface diffusion of adsorbed protein molecules that are condensing at the periphery of interfacial protein aggregates. The surface dilatational elasticity, E, is determined in experiments on quick expansion or compression of the interfacial protein layers. At lower surface pressures (<11 mN/m) the experiments on expansion, compression and oscillations give close values of E that are increasing with the rise of surface pressure. At higher surface pressures, E exhibits the opposite tendency and the data are scattered. The latter behavior can be explained with a two-dimensional condensation of adsorbed protein molecules at the higher surface pressures. The results could be important for the understanding and control of dynamic processes in foams and emulsions stabilized by hydrophobins, as well as for the modification of solid surfaces by adsorption of such proteins.     

Common Solutions to Variational Inequalities

We study the new variational inequality problem, called the Common Solutions to Variational Inequalities Problem (CSVIP). This problem consists of finding common solutions to a system of unrelated variational inequalities corresponding to set-valued mappings in Hilbert space. We present an iterative procedure for solving this problem and establish its strong convergence. Relations with other problems of solving systems of variational inequalities, both old and new, are discussed as well.