Network externalities in a dynamic monopoly

We reconsider the role of network externalities in a dynamic spatial monopoly where the firm must invest in order to accumulate capacity, while consumers may have either linear or quadratic preferences. We (1) characterise saddle point equilibria, (2) prove that the extent of market coverage is increasing in the network effect and (3) unlike the existing static literature on the same problem, the monopolist may not make introductory price offers. Then, we briefly deal with the socially optimal solution, showing that, in general, a planner would serve more consumers than a profit-seeking monopolist.      

Point-to-Periodic and Periodic-to-Periodic Connections

In this work we consider computing and continuing connecting orbits in parameter dependent dynamical systems. We give details of algorithms for computing connections between equilibria and periodic orbits, and between periodic orbits. The theoretical foundation for these techniques is given by the seminal work of Beyn in 1994, “On well-posed problems for connecting orbits in dynamical systems”, where a numerical technique is also proposed. Our algorithms consist of splitting the computation of the connection from that of the periodic orbit(s). To set up appropriate boundary conditions, we follow the algorithmic approach used by Demmel, Dieci, and Friedman, for the case of connecting orbits between equilibria, and we construct and exploit the smooth block Schur decomposition of the monodromy matrices associated to the periodic orbits. Numerical examples illustrate the performance of the algorithms. This revised version was published online in July 2006 with corrections to the Cover Date.     

Sn/Ge(1 1 1) α-phase: characterization of image resonances by specular electron reflection and selective electron scattering

Image potential resonances on the Sn/Ge(1 1 1) α-phase are investigated by two closely related methods: specular electron reflection and so-called selective electron scattering. Electrons from image resonances are detected on this surface at 120 and 300 K, i.e. below and above the phase transition at about 200 K. The dispersion of the image resonances reveals at these two temperatures equivalent effective electron masses, which are characteristic for this type of electronic surface states. The results of the two methods are consistent according to the similarity of the scattering processes. Changes in the loss peak intensity with the annealing temperature are assigned to the surface quality and are reflected by characteristic photoemission intensities.     

The LEM exponential integrator for advection–diffusion–reaction equations

We implement a second-order exponential integrator for semidiscretized advection–diffusion–reaction equations, obtained by coupling exponential-like Euler and Midpoint integrators, and computing the relevant matrix exponentials by polynomial interpolation at Leja points. Numerical tests on 2D models discretized in space by finite differences or finite elements, show that the Leja–Euler–Midpoint (LEM) exponential integrator can be up to 5 times faster than a classical second-order implicit solver.     

New pi-extended water-soluble squaraines as singlet oxygen generators

[graph: see text] Condensation of squaric acid with a number of differently substituted 2-pyrrolyl derivatives afforded three new classes of squaraines. Their sharp and intense absorption bands in the biological window (700-900 nm), inherent singlet oxygen generation capabilities, together with proper functionalization allowing good water solubility make them suitable candidates as new non-porphyrinic singlet oxygen photosensitizers for photodynamic therapy (PDT).     

Isolation of pure (2S,1'S,2'S)-2-(2'-carboxycyclopropyl)glycine from Blighia sapida (Akee)

The isolation of (2S,1'S,2'S)-2-(2'-carboxycyclopropyl)glycine (CCG I, 2) from Blighia sapida (Akee) was achieved through column chromatography on deactivated silica gel followed by ion-exchange chromatography. A HPLC method has also been devised in order to assess the purity of the isolated product.     

Subcanonical curves and complete intersections in projective 3-space

Summary Un classico teorema di G. Gherardelli afferma che una curvaC P ³ è intersezionè completa se e soltanto se è proiettivamente normale e sottocanonica. Qui si prova che, seC e a- sottocanonica ed inoltre le superficie di grado 1 + (a/2) (a pari) ovvero (a + l)/2 o (a + 3)/2 o (a + 5)/2 (a dispari) tagliano suC serie complete, alloraC è intersezione completa. Si determina inoltre un bound d funzione di a tale che, seC è a-sottocanonica e di grado d d, alloraC è intersezione completa se e soltanto se le superficie di grado a tagliano suC una serie completa. Si discutono poi numerosi esempi di curve sottocanoniche non intersezioni complete.Paper written while P. Valabrega was member of C.N.R. (G.N.A.S.G.A.) and both authors were supported by M.P.I. funds.     

The PLAC1-homology region of the ZP domain is sufficient for protein polymerisation

Background  

Hundreds of extracellular proteins polymerise into filaments and matrices by using zona pellucida (ZP) domains. ZP domain proteins perform highly diverse functions, ranging from structural to receptorial, and mutations in their genes are responsible for a number of severe human diseases. Recently, PLAC1, Oosp1-3, Papillote and CG16798 proteins were identified that share sequence homology with the N-terminal half of the ZP domain (ZP-N), but not with its C-terminal half (ZP-C). The functional significance of this partial conservation is unknown.