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].     

A Generalization of the Erdos - Szekeres Theorem to Disjoint Convex Sets

Let F denote a family of pairwise disjoint convex sets in the plane. F is said to be in convex position if none of its members is contained in the convex hull of the union of the others. For any fixed k≥ 3 , we estimate P _k (n) , the maximum size of a family F with the property that any k members of F are in convex position, but no n are. In particular, for k=3 , we improve the triply exponential upper bound of T. Bisztriczky and G. Fejes Tóth by showing that P ₃ (n) < 16 ⁿ . <lsiheader> <onlinepub>26 June, 1998 <editor>Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt; <pdfname>19n3p437.pdf <pdfexist>yes <htmlexist>no <htmlfexist>no <texexist>yes <sectionname> </lsiheader> Received March 27, 1997, and in revised form July 10, 1997.     

Variations on the theme of repeated distances

We give an asymptotically sharp estimate for the error term of the maximum number of unit distances determined byn points in ^{d, d}4. We also give asymptotically tight upper bounds on the total number of occurrences of the favourite distances fromn points in ^{d, d}4. Related results are proved for distances determined byn disjoint compact convex sets in ².At the time this paper was written, both authors were visiting the Technion — Israel Institute of Technology.     

A 13-membered crown ether with an azoxy subunit in the macrocycle: Synthesis and X-ray structure

The presented azoxy compound is an example of a new crown ether analogue. It has been synthesized by the reduction of an open chain dinitro compound with stannite under strongly alkaline conditions. A method for the separation of the azo and azoxy compounds formed simultaneously has been proposed. The structures of two crystallographically independent molecules of compound2 have been determined. In spite of the small size of the macroring in compound2, the phenyl residues around the azoxy group have atrans orientation. Supplementary Data relating to this article have been deposited with the British Library as Supplementary Publication No. 82157 (11 pages).     

The IINS, IR and DFT studies of hydrogen bonds in 6-Furfuryl and 6-Benzylaminopurines

FTIR and IINS spectra of 6-Furfurylaminopurine (6-FAP) and 6-Benzylaminopurine (6-BAP) taken at different temperatures have been analysed and compared with the spectra calculated by the ab initio DFT/B3LYP method and the semiempirical PM3 method in the isolated molecule approximation, for the tautomers N3-H, N7-H and N9-H, and dimers with hydrogen bonds. For 6-FAP the best agreement between the calculated and experimental (at 20 K) spectra has been found for the N9-H tautomer, whose structure was established by X-ray diffraction. For 6-BAP the analogous agreement for the N9-H tautomer structure has been poor and much better for the N7-H tautomer. The vibrational spectra calculated for dimers of the molecules studied involved in hydrogen bonds, permitted also an interpretation of the bands whose positions and FWHM in the FTIR spectra changed with temperature.     

Bicyclic [b]-heteroannulated pyridazine derivatives. 4. Cyclization reactions of 4-aryltetrahydropyridazine-3,6-dione 3-hydrazones with some keto esters

Ethoxycarbonylalkylidene derivatives 2 and 6 of the title hydrazones were obtained in the reaction with ethyl pyruvate or ethyl aroylformate and ethyl acetoacetate, respectively, in methanol. Both compounds were mixtures of geometric isomers with high predominance of one of them. Nmr spectroscopy revealed an unexpected magnetic non-equivalence of the CH₂ protons in the ester ethyl group of the major isomer of 6 . On heating (?200°) in an inert medium or on refluxing in ethanolic sodium ethoxide 2 cyclized to the corresponding pyridazino[6,1-c]-triazines 4 , whereas 6 formed pyrazolylpyridazines 7 . The structure of the latter was unambigously established by X-ray analysis. Alkylation of 4a with benzyl bromide in the presence of tetrabutylammonium bromide occurred selectively on the pyridazine N atom.     

Retention of anions on silica-based metalloporphyrin stationary phases.

The silica-based Fe(III)-protoporphyrin and Zn-tetraphenylporphyrin stationary phases were examined for the HPLC separation of anions. The retention of nine common inorganic anions as well as benzoate anion (BA) and its hydroxy analogues (HBA) was examined using tartrate, acetate, and succinate eluents. The retention factors of inorganic anions on the FeProP stationary phase were in the order Cl- < NO3- < ClO4- < I- < SCN- and for organic anions benzoate < p-hydroxybenzoate < m-hydoxybenzoate < o-hydroxybenzoate. The retention factors of organic anions examined for a ZnTPP column were in the order p-HBA < m-HBA < BA < o-HBA.     

Multiple binding modes of the camptothecin family to DNA oligomers

The binding constants of camptothecin, topotecan and its lactone ring-opened carboxylate derivative to DNA octamers were measured by UV and NMR spectroscopy. The self-association of topotecan (TPT) was also measured. The carboxylate form of TPT binds in the same way as the lactone, but more weakly. Titration of TPT into d(GCGATCGC)2 shows a preferred location stacked onto the terminal G1 base. However, the intermolecular NOEs cannot be reconciled with a single conformation of the complex, and suggest a model of a limited number of conformations in fast exchange. MD calculations on four pairs of starting structures with TPT stacked onto the G1-C8 base pair in different orientations were therefore performed. The use of selected experimental "docking" restraints yielded ten MD trajectories covering a wide conformational space. From a combination of calculated free energies, NOEs and chemical shifts, some of the structures produced could be eliminated, and it is concluded that the data are consistent with two major families of conformations in fast exchange. One of these is the conformation found in a crystal of a TPT/DNA/topoisomerase I ternary complex [Proc. Natl. Acad. Sci. USA 2002, 99, 15 387-15 392].     

Study of the winter and summer changes of the air composition in the church of Szalowa, Poland, related to conservation

The St. Michael Archangel’s Church in Szalowa, Poland, was selected for closer investigation with respect to the indoor/outdoor air exchange and its influence on the air quality and work arts preservation. Chemical composition, size and abundance of particulate matter and concentration of gases NO₂, SO₂, O₃ inside and outside the church were determined. To study seasonal variation of the weather condition (temperature, inversion level, wind direction) and the influence of seasonal sources of the air pollution (like heating of the nearby houses), samples were collected in winter and summer time. It was stated that suspended particulate matter inside the wooden church has in general an outdoor source. Several groups of particles were distinguished such as the organic ones, soil dust, nitrates and sulphates. In case of organic and soil dust particles, the concentration inside was higher than outside. From the results, in comparison to literature data, one can conclude that accumulation of particulate suspended matter in the church is more intense than in other types of buildings. Gaseous pollutants were detected but their concentration was negligible.     

The complexity of a class of infinite graphs

IfG _k is the family of countable graphs with nok vertex (or edge) disjoint circuits (1<k<) then there is a countableG _k G _k such that every member ofG _k is an (induced) subgraph of some member ofG _k , but no finiteG _k suffices.