Varieties of two-dimensional cylindric algebras.¶Part I: Diagonal-free case

We investigate the lattice of all subvarieties of the variety Df ₂ of two-dimensional diagonal-free cylindric algebras. We prove that a Df ₂-algebra is finitely representable if it is finitely approximable, characterize finite projective Df ₂-algebras, and show that there are no non-trivial injectives and absolute retracts in Df ₂. We prove that every proper subvariety of Df ₂ is locally finite, and hence Df ₂ is hereditarily finitely approximable. We describe all six critical varieties in , which leads to a characterization of finitely generated subvarieties of Df ₂. Finally, we describe all square representable and rectangularly representable subvarieties of Df ₂. Received May 25, 2000; accepted in final form November 2, 2001.     

Efficiency in the trust game: an experimental study of precommitment

We experimentally test a precommitment mechanism for the trust game. Before the investor’s decision, the allocator places an amount into escrow, to be forfeited if he keeps the proceeds of investment for himself. We vary the available escrow amounts—in particular, whether there is a high amount that gives rise to an efficient equilibrium—and whether escrow is voluntary or imposed. We find that when chosen, the high escrow amount does lead to efficient outcomes. We also find substantial investment when the high amount is unavailable or not chosen, though well below that when it is chosen, and declining over time. We find only weak evidence for behavioral theories, such as crowding out and signaling. These results are seen when escrow choices are imposed as well as when they are voluntary.      

Geodesics and almost geodesic cycles in random regular graphs

A geodesic in a graph G is a shortest path between two vertices of G. For a specific function e(n) of n, we define an almost geodesic cycle C in G to be a cycle in which for every two vertices u and v in C, the distance d_G(u, v) is at least d_C(u, v)?e(n). Let ω(n) be any function tending to infinity with n. We consider a random d‐regular graph on n vertices. We show that almost all pairs of vertices belong to an almost geodesic cycle C with e(n) = log_d?1log_d?1n+ ω(n) and |C| = 2log_d?1n+ O(ω(n)). Along the way, we obtain results on near‐geodesic paths. We also give the limiting distribution of the number of geodesics between two random vertices in this random graph. Copyright © 2010 John Wiley & Sons, Ltd. J Graph Theory 66:115‐136, 2011     

p-Adic interpolation of square roots of central L-values of modular forms

We construct a meromorphic function on part of the eigencurve that interpolates a square root of a ratio of quadratic twists of the central modular $L$ -value.     

Pseudo‐Fivefold Diffraction Symmetries in Tetrahedral Packing

We review the way in which atomic tetrahedra composed of metallic elements pack naturally into fused icosahedra. Orthorhombic, hexagonal, and cubic intermetallic crystals based on this packing are all shown to be united in having pseudo‐fivefold rotational diffraction symmetry. A unified geometric model involving the 600‐cell is presented: the model accounts for the observed pseudo‐fivefold symmetries among the different Bravais lattice types. The model accounts for vertex‐, edge‐, polygon‐, and cell‐centered fused‐icosahedral clusters. Vertex‐centered and edge‐centered types correspond to the well‐known pseudo‐fivefold symmetries in I_h and D_5h quasicrystalline approximants. The concept of a tetrahedrally‐packed reciprocal space cluster is introduced, the vectors between sites in this cluster corresponding to the principal diffraction peaks of fused‐icosahedrally‐packed crystals. This reciprocal‐space cluster is a direct result of the pseudosymmetry and, just as the real‐space clusters, can be rationalized by the 600‐cell. The reciprocal space cluster provides insights for the Jones model of metal stability. For tetrahedrally‐packed crystals, Jones zone faces prove to be pseudosymmetric with one another. Lower and upper electron per atom bounds calculated for this pseudosymmetry‐based Jones model are shown to accord with the observed electron counts for a variety of Group 10–12 tetrahedrally‐packed structures, among which are the four known Cu/Cd intermetallic compounds: CdCu₂, Cd₃Cu₄, Cu₅Cd₈, and Cu₃Cd₁₀. The rationale behind the Jones lower and upper bounds is reviewed. The crystal structure of Zn₁₁Au₁₅Cd₂₃, an example of a 1:1 MacKay cubic quasicrystalline approximant based solely on Groups 10–12 elements is presented. This compound crystallizes in Im$\bar 3$ (space group no. 204) with a=13.842(2) Å. The structure was solved with R₁=3.53 %, I>2σ;=5.33 %, all data with 1282/0/38 data/restraints/parameters.     

Polymers for the Cell‐Specific Immobilisation of Megakaryocytic Cell Lines

Primary human megakaryocytes, the precursor cells of platelets, are difficult to collect and cultivate. Polymers that enrich these cells without affecting their regulation or function are of interest for basic research as well as for cord blood transplantation purposes since co‐transplantation of enriched megakaryocyte concentrates increase the success of stem cell therapy. Herein, polymer microarrays were used for the discovery of substrates for MEG‐01 cells, with five polymers identified which selectively bound cells of the megakaryocytic lineage. Flow cytometry and miRNA profiling revealed that immobilisation had only a minor effect on the cellular maturation status, making the identified substrates potential candidates for concentrating megakaryocytes from patients prior to transplantation.

     

Characterization of asymmetric filtered 40 Gb/s RZ-DPSK system-strong filtering considerations

We present the impact of frequency offsetting of strong (e.g. 35 GHz) optical filters on the performance of 42.7 Gb/s 50% RZ-DPSK systems. The performance is evaluated when offsetting the filter by substantial amounts and it is found that with an offset of almost half the bit rate there is a significant improvement in the calculated ‘Q’ (> 1 dB). We deployed balanced, constructive single ended and destructive single ended detection, so that we could investigate the physical origins of the penalty reduction of asymmetric filtering of 42.7 Gb/s 50% RZ-DPSK system.     

Accuracy improvement of laser line scanning for feature measurements on CMM

Because of its high speed and high detail output, laser line scanning is increasingly included in coordinate metrology applications where its performance can satisfy specified tolerances. Increasing its accuracy will open the possibility to use it in other areas where contact methods are still dominant. Multi-sensor systems allow to select discrete probing or scanning methods to measure part elements. Decision is often based on the principle that tight toleranced elements should be measured by contact methods, while other more loose toleranced elements can be laser scanned. This paper aims to introduce a method for improving the output of a CMM mounted laser line scanner for metrology applications. This improvement is achieved by filtering of the scanner's random error and by combination with widely spread and reliable but slow touch trigger probing. The filtered point cloud is used to estimate the form deviation of the inspected element while few tactile obtained points were used to effectively compensate for errors in the point cloud position.     

Anhydrous TEMPO-H: reactions of a good hydrogen atom donor with low-valent carbon centres

In this paper, we report a novel synthesis of anhydrous 1-hydroxy-2,2,6,6-tetramethyl-piperidine (TEMPO-H). An X-ray crystal structure and full characterization of the compound are included. Compared to hydrated TEMPO-H, its anhydrous form exhibits improved stability and a differing chemical reactivity. The reactions of anhydrous TEMPO-H with a variety of low-valent carbon centres are described. For example, anhydrous TEMPO-H was reacted with 1,3-bis(2,4,6-trimethylphenyl)imidazol-2-ylidene (IMes), an unsaturated NHC. Crystals of [CHNC(6)H(2)(CH(3))(3)](2)C···HO(NC(5)H(6)(CH(3))(4)), IMes···TEMPO-H, were isolated and a crystal structure determined. The experimental structure is compared to the results of theoretical calculations on the hydrogen-bonded dimer. Anhydrous TEMPO-H was also reacted with the saturated NHC, 1,3-bis(2,6-diisopropylphenyl)imidazolidin-2-ylidene (SIPr), giving the product [CH(2)Ni-Pr(2)C(6)H(3)](2)CH···O(NC(5)H(6)(CH(3))(4)). In contrast, the reaction of hydrated TEMPO-H with 1,3-bis(2,6-diisopropylphenyl)imidazolidin-2-ylidene gave small amounts of the hydrolysis product, N-(2,6-diisopropylphenyl)-N-[2-(2,6-diisopropylphenylamino)ethyl]formamide. Finally, anhydrous TEMPO-H was reacted with (triphenylphosphoranylidene)ketene to generate Ph(3)PC(H)C(=O)O(NC(5)H(6)(CH(3))(4)). A full characterization of the product, including an X-ray crystal structure, is described.     

Rhodium carbonyl complexes of bulky, anionic nitrogen-based ligands: A comparison of donating ability

Phosphinimine-imine ((C₆H₃i-Pr₂)NC(Me)CH₂PPh₂(NC₆H₃i-Pr₂))Rh(CO)₂ - (1) and β-diketiminate CH(C(Me)(Ni-Pr₂C₆H₃))₂Rh(CO)₂ - (2) rhodium dicarbonyl complexes were prepared as to elucidate any difference among these anionic, nitrogen-based ligands regarding donating ability to the rhodium center. Utilizing infrared spectroscopy and single crystal structural comparisons, differences in electron density donation by the ligands to the rhodium center were not observed. The carbonyl stretching frequencies of the aforementioned rhodium complexes were ν_CO = 2055, 1987 and 2055, 1988 for the phosphinimine-imine (1) and β-diketiminate (2) respectively.