Continuity of Information Transport in Surjective Cellular Automata

We introduce a local version of the Shannon entropy in order to describe information transport in spatially extended dynamical systems, and to explore to what extent information can be viewed as a local quantity. Using an appropriately defined information current, this quantity is shown to obey a local conservation law in the case of one-dimensional reversible cellular automata with arbitrary initial measures. The result is also shown to apply to one-dimensional surjective cellular automata in the case of shift-invariant measures. Bounds on the information flow are also shown.     

Valuing Asian options using the finite element method and duality techniques

The main objective of this paper is to develop an adaptive finite element method for computation of the values, and different sensitivity measures, of the Asian option with both fixed and floating strike. The pricing is based on Black–Scholes PDE-model and a method developed by Ve?e? where the resulting PDEs are of parabolic type in one spatial dimension and can be applied to both continuous and discrete Asian options. We propose using an adaptive finite element method which is based on a posteriori estimates of the error in desired quantities, which we derive using duality techniques. The a posteriori error estimates are tested and verified, and are used to calculate optimal meshes for each type of option. The use of adapted meshes gives superior accuracy and performance with less degrees of freedom than using uniform meshes. The suggested adaptive finite element method is stable, gives fast and accurate results, and can be applied to other types of options as well.     

Dendrimers in thiol‐ene crosslinked networks and the effect of subsequent generations on thermoset properties

A series of well‐defined allyl‐ether functionalized polyester dendrimers has been synthesized via the divergent approach using traditional esterification reactions. Two commercially available trifunctional thiols, trimethylolpropane tri(3‐mercaptopropanoate) (TRIS) and ethoxylated trimethylolpropane tri(3‐mercaptopropanoate) (ETTMP), were incorporated with the dendrimers into the thiol‐ene polymer networks. The thiol‐ene reactions were conducted at room temperature and cured by UV light without the addition of photoinitiatior. Highly crosslinked films were obtained and characterized with respect to mechanical (DMA) and thermal (DSC and TGA) properties. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 589–601, 2009     

Synthesis and thiol–ene photopolymerization of allyl‐ether functionalized dendrimers

Well‐defined, allyl‐ether functional, first‐generation dendrimers have been synthesized. The convergent growth approach was utilized, using the anhydride of the allyl‐ether terminated building block. Three different core moieties were used: trimethylolpropane, trisphenol, and ditrimethylolpropane. The coupling reactions proceeded in good yields and all compounds were characterized by NMR, MALDI‐TOF, and SEC. The allyl‐terminated dendrimers were crosslinked by thiol–ene chemistry, using a multifunctional thiol, TriThiol, to give clear and smooth films. The photopolymerization was conducted in the presence of a photoinitiator, Irgacure 651, and no traces of either allyl‐ether groups or thiols were observed by FT‐Raman after cure. All crosslinked films were characterized with respect to mechanical (DMA) and thermal (DSC) properties. It was found that homogeneous networks were formed and that the core functionality and structure had little effect on the network properties. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1339–1348, 2008     

Crystal Structure,Magnetism, 89Y Solid State NMR,and 121Sb Mössbauer Spectroscopic Investigations of YIrSb

The ternary antimonide YIrSb was synthesized from the binary precursor YIr and elemental antimony by a diffusion controlled solid‐state reaction. Single crystals were obtained by a flux technique with elemental bismuth as an inert solvent. The YIrSb structure (TiNiSi type, space group Pnma) was refined from single‐crystal X‐ray diffractometer data: a = 711.06(9), b = 447.74(5), c = 784.20(8) pm, wR₂ = 0.0455, 535 F² values, 20 variables. ⁸⁹Y solid state MAS NMR and ¹²¹Sb Mössbauer spectra show single resonance lines in agreement with single‐crystal X‐ray data. YIrSb is a Pauli paramagnet.     

Theoretical investigations on the chemical bonding, electronic structure, and optical properties of the metal-organic framework MOF-5

The chemical bonding, electronic structure, and optical properties of metal-organic framework-5 (MOF-5) were systematically investigated using ab initio density functional calculations. The unit cell volume and atomic positions were optimized with the Perdew-Burke-Ernzerhof (PBE) functional leading to a good agreement between the experimental and the theoretical equilibrium structural parameters. The calculated bulk modulus indicates that MOF-5 is a soft material. The estimated band gap from a density of state (DOS) calculation for MOF-5 is about 3.4 eV, indicating a nonmetallic character. As MOFs are considered as potential materials for photocatalysts, active components in hybrid solar cells, and electroluminescence cells, the optical properties of this material were investigated. The detailed analysis of chemical bonding in MOF-5 reveals the nature of the Zn-O, O-C, H-C, and C-C bonds, that is, Zn-O having mainly ionic interaction whereas O-C, H-C, and C-C exhibit mainly covalent interactions. The findings in this paper may contribute to a comprehensive understanding about this kind of material and shed insight into the synthesis and application of novel and stable MOFs.     

Two new layered oxohalides in the system Cu–Yb–Te–O–Cl

Two complex lanthanide(III) transition metal(II) tellurium(IV) oxyhalides, Cu₃Yb₂(TeO₃)₄Cl₄ and Cu₃Yb₃(TeO₃)₄Cl₆ have been synthesized and the crystal structures were determined by single-crystal X-ray diffraction. Both compounds are layered with only weak connections in between the layers. The layers are made up of [YbO₈], [TeO₃] and [CuO_xCl_y] polyhedra. In both compounds the strong Lewis acid cations Yb³⁺ and Te⁴⁺ only form bonds to oxygen while Cu²⁺ form bonds to both oxygen and chlorine. This leads the Cl^? ions to be expelled from the bonding volumes of the crystal structures and protrude from the layers. Magnetic susceptibility measurements were performed on a powder sample of Cu₃Yb₂(TeO₃)₄Cl₄. The Curie–Weiss law found at low temperatures indicates a Curie–Weiss temperature of ca. ?5(1) K. However, indication for long-range magnetic ordering could not be observed down to 1.87 K. The two new phases are to the best of our knowledge the first containing all three of Cu, Yb and Te.