Pushing Squares Around

We study dynamic self-reconfiguration of modular metamorphic systems. We guarantee the feasibility of motion planning in a rectangular model consisting of square modules that are allowed to slide along or rotate about one another. That is, we show that any two connected configurations of the same number of modules can be transformed into each other by a sequence of moves so that all intermediate configurations are connected. This settles a conjecture formulated in [6].     

Baer orderings with noninvariant valuation ring

We construct division algebras with involution containing a Baer ordering with noninvariant order ring. This gives a negative answer to a question of Holland, whether the order ring is always invariant under inner automorphisms. Furthermore, we give examples of any index. Previously, the only known examples of division algebras containing Baer orderings were of index 2 ⁿ or of indexp forp a prime of the form 4m + 3. Supported in part by the National Science Foundation.     

Click chemistry in materials synthesis. III. Metal‐adhesive polymers from Cu(I)‐catalyzed azide–alkyne cycloaddition

1,2,3‐Triazole‐based polymers generated from the Cu(I)‐catalyzed cycloaddition between multivalent azides and acetylenes are effective adhesive materials for metal surfaces. The adhesive capacities of candidate mixtures of azide and alkyne components were measured by a modified peel test, using a customized adhesive tester. A particularly effective tetravalent alkyne and trivalent azide combination was identified, giving exceptional strength that matches or exceeds the best commercial formulations. The addition of Cu catalyst was found to be important for the synthesis of stronger adhesive polymers when cured at room temperature. Heating also accelerated curing rates, but the maximum adhesive strengths achieved at both room temperature and high temperature were the same, suggesting that crosslinking reaches the same advanced point in all cases. Polytriazoles also form adhesives to aluminum, but copper is bound more effectively, presumably because active Cu(I) ions may be leached from the surface to promote crosslinking and adhesion. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5182–5189, 2007     

The Lifting Model for Reconfiguration

Given a pair of start and target configurations, each consisting of n pairwise disjoint disks in the plane, what is the minimum number of moves that suffice for transforming the start configuration into the target configuration? In one move a disk is lifted from the plane and placed back in the plane at another location, without intersecting any other disk. We discuss efficient algorithms for this task and estimate their number of moves under different assumptions on disk radii. We then extend our results for arbitrary disks to systems of pseudodisks, in particular to sets of homothetic copies of a convex object.     

Semicarbazones and thiosemicarbazones,XII: Crystal structure of salicylaldehyde semicarbazone

Summary The crystal and molecular structure of salicylaldehyde semicarbazone was obtained by single crystal X-ray diffraction. The O atom of the semicarbazone fragment isanti to the N atom of the hydrazinic group. The distribution of bond lengths in the semicarbazone fragment indicates delocalization of the -electrons. The crystal structure is stabilized by intra- and intermolecular hydrogen bonds.

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Semicarbazone und Thiosemicarbazone, 12. Mitt.: Die Kristallstruktur des Salicylaldehyd-Semicarbazons

Zusammenfassung Die Kristallstruktur und die molekulare Struktur des Salicylaldehyd-Semicarbazons wurde über Einkristall-Röntgenstreuung ermittelt. Das O-Atom des Semicarbazonteils stehtanti zum N-Atom der Hydrazin-Gruppierung. Die Bindungslängen in der Semicarbazoneinheit zeigen eine Delokalisierung der -Elektronen an. Die Geometrie der Verbindung wird durch stabilisierende intra- und intermolekulare Wasserstoffbrückenbindungen bestimmt.

     

Transamination Studies on N-(1-Alkenylthio)phthalimides and Related Compounds. Synthesis of 1-Alkenesulfenamides and 1-Alkenesulfonamides(1)

In an attempt to develop a method for the general preparation of 1-alkenesulfenamides, some N,N-bis(trimethylsilyl)-1-alkenesulfenamides (4) were converted to a number of nitrogen functionalized analogs through desilylation and acylation procedures. Mono- and dibenzoylated derivatives 5aand 6a did not undergo transamination reactions with simple amines. Transamination reactions could be achieved once compounds 4 were converted to thiophthalimides 7. The transamination products 8 are unstable to chromatography, but could be oxidized to 1-alkenesulfonamides 9 using MCPBA. Some of the sulfenamides 8 may be stable to distillation. 3-(Alkenylthioimino)phthalides 11, isomers of thiophthalimides 7, also react with amines, but the process of ring opening accompanies transamination. It was found that the transamination reactions of 11 probably involve the intermediacy of isomers 7.     

Cyclobut-2-enones from Alkynes via Dichlorocyclobut-2-enones

The [2 + 2]-cycloaddition of dichloroketene (prepared in situ from CCl₃COCl and Zn(Cu)) with three alkynes 1a–c to form 2,3-dimethyl-( 2a ), 2,3-diethyl-( 2b ) and 3-butyl-4,4-dichlorocyclobut-2-enone ( 2c ) proceeds rapidly in the absence of POCl₃. The primary products 2a–c rearrange in situ to the 2,4-dichlorocyclobut-2-enones 3a–c under the influence of ZnCL₂ produced during the reaction. ZnCl₂ converts both 2a and 3a into a 4:6 equilibrium mixture of the two; this isomerization does not occur with LiCl. The Cl-atoms of both 2a , b and 3a , b and of 2c may reductively be removed with Zn(Cu) in AcOH/pyridine to afford the alkylcyclobutenones 4a-c . Without pyridine, this reduction gives ca. 1:1 mixtures of the double-bond isomers 4 and 5 in low yields. The cyclobutenones 2c and 4c may be deuterated by CD₃COOD in the presence of pyridine. D -Atom is introduced into 2c at C(4) and at C(γ), and into 4c at C(2) and C(4). A mechanism for this deuteration is considered, which does not involve a cyclobutadienolate 7 , but rather a cyclobutenolate of type 8 . The reductions of 2 and 3 to 4 might also pass through the same type of intermediate 8 .     

Synthesis of new mono-functionalised tetrathiafulvalene derivatives by reactions of etrathiafulvalenyllithium with aldehydes and ketones: X-ray crystal structures of TTF-CMe(OH)Fc, TTF-CMe(OMe)Fc and TTF-CH(OMe)TTF (Fc = ferrocenyl)

Reactions of tetrathiafulvalenyllithium (TTF-Li) with a range of aldehydes and ketones have been explored for the first time, to provide an efficient route to mono-functionalised TTF derivatives of general formulae TTF-CH(OH)R (R = alkyl, phenyl, tetrathiafulvalenyl and ferrocenyl) and TTF-CR(OH)R′ (R = alkyl, phenyl, R′ = alkyl, phenyl, tetrathiafulvalenyl, ferrocenyl, and R-R′ = fluorenyl). Subsequent transformations involving the reactive alcohol group of some of these compounds are reported. The structures of the three title compounds have been established by single-crystal X-ray analysis.