On isomorphic factorizations of circulant graphs

We investigate the conjecture that every circulant graph X admits a k‐isofactorization for every k dividing |E(X)|. We obtain partial results with an emphasis on small values of k. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 406–414, 2006     

Standardization of BSE rapid test performances and experiences gathered during the implementation of large-scale testing

The accumulation of pathological prion protein is used as a diagnostic marker for transmissible spongiform encephalopathies. According to European Union (EU) regulations cattle older than 30 months of age (Germany, France, Italy, and Spain by national law >24 months) and slaughtered for human consumption must be tested by using rapid tests for bovine spongiform encephalopathy (BSE). Likewise fallen stock and clinically affected animals must be tested. This article gives a short overview of the incidence of BSE in Europe. The diagnostic hierarchy, i.e., the officially approved methodology for the confirmation of suspect rapid test cases, and the organization of the numerous laboratories involved in this large-scale testing for BSE are described. Special emphasis is given to necessary quality control measures currently in place for BSE rapid testing laboratories and to measures intended to assure a consistent performance of the commercially available rapid test kits.Presented at BERM-9—Ninth International Symposium on Biological and Environmental Reference Materials, 15–19 June 2003, Berlin, Germany.     

A generalization of Connor's inequality to t-designs with automorphisms

In this paper the incidence algebra for t-designs with automorphisms and the fundamental theorem discovered in [4] are exploited to obtain a generalization of Connor's inequality.     

Structure and Magnetic Properties of Ce3Ge0.66In4.34 and Ce11Ge4.74In5.26

New indides Ce₃Ge_0.66In_4.34 and Ce₁₁Ge_4.74In_5.26 were synthesized from the elements by arc‐melting and subsequent annealing at 870 K. Single crystals were grown through special annealing procedures in sealed tantalum tubes in a high‐frequency furnace. Both compounds were investigated on the basis of X‐ray powder and single crystal data: I4/mcm, La₃GeIn₄ type, a = 848.8(1), c = 1192.0(2) pm, Z = 4, wR2 = 0.0453, 499 F² values, 17 variables for Ce₃Ge_0.66In_4.34 and I4/mmm, Sm₁₁Ge₄In₆ type (ordered version of the Ho₁₁Ge₁₀ type), a = 1199.3(2), c = 1662.0(3) pm, wR2 = 0.0507, 1217 F² values, 41 variables for Ce₁₁Ge_4.74In_5.26. The Ce₃Ge_0.66In_4.34 structure shows a mixed Ge/In occupancy on the 4c Wyckoff position. This site is octahedrally coordinated by cerium atoms. These octahedra share all edges, leading to a three‐dimensional network. The latter is penetrated by a two‐dimensional indium substructure which consists of flattened tetrahedra at In–In distances of 291 and 300 pm. The Ce₁₁Ge_4.74In_5.26 structure contains three crystallographically independent germanium sites. The latter are coordinated by eight or nine cerium neighbors. These CN8 and CN9 polyhedra are condensed to a complex network which is penetrated by a three‐dimensional indium network with In–In distances of 301–314 pm. The 16m site shows a mixed In/Ge occupancy. Chemical bonding in both compounds is dominated by the p elements. Both ternaries studied exhibit localized magnetism due to the presence of Ce³⁺ ions. The compound Ce₃GeIn₄ remains paramagnetic down to 1.72 K, whereas Ce₁₁Ge₄In₆ orders ferromagnetically at T_C = 7.5 K.     

Fe(III) coordination properties of a new saccharide-based exocyclic trihydroxamate analogue of ferrichrome

The coordination chemistry of a saccharide-based ferrichrome analogue, 1-O-methyl-2,3,4-tris-O-[4-(N-hydroxy-N-methylcarbamoyl)-n-butyrate]-alpha-d-glucopyranoside (H(3)L), is reported, along with its pK(a) values, Fe(III) and Fe(II) chelation constants, and aqueous-solution speciation as determined by spectrophotometric and potentiometric titration techniques. The use of a saccharide platform to synthesize a hexadentate trihydroxamic acid chelator provides some advantages over other approaches to ferrichrome models, including significant water solubility and hydrogen-bonding capability of the backbone that can potentially provide favorable receptor recognition and biological activity. The pK(a) values for the hydroxamate moieties were found to be similar to those of other trihydroxamates. Proton-dependent Fe(III)-H(3)L and Fe(II)-H(3)L equilibrium constants were determined using a model involving the sequential protonation of the iron(III)- and iron(II)-ligand complexes. These results were used to calculate the formation constants, log beta(110) = 31.86 for Fe(III)L and 12.1 for Fe(II)L(-). The calculated pFe value of 27.1 indicates that H(3)L possesses an Fe(III) affinity comparable to or greater than those of ferrichrome and other ferrichrome analogues and is thermodynamically capable of removing Fe(III) from transferrin. E(1/2) for the Fe(III)L/Fe(II)L(-) couple was determined to be -436 mV from quasi-reversible cyclic voltammograms at pH = 9, and the pH-dependent E(1/2) profile was used to determine the Fe(II)L(-) protonation constants.     

Mitt. XV: Struktur und reaktivität von isoanellierten heterocyclischen systemen mit 4nπ- und (4n + 2) π-elektronen. 2-t-butyl-4-methyl-2,4-dihydropyrrolo[3,4-b]indole. reaktionen mit aktivierten CC-dienophilen

Reactions of 2-t-butyl-4-methyl-2,4-dihydropyrrolo[3,4-b]indoles with N-aryl-maleimides have been investigated. The formation of 1:1-cycloadducts is influenced by substituents at 1,3-position. The consecutive transformations of these intermediates can be controlled by nucleophilic solvents or reagents. Ring opening reactions occur at the labile N,O-acetal group of the cycloadducts followed by eliminaton or addition reactions.     

Covalent chemistry and conformational dynamics of topologically chiral amide-based molecular knots

The readily available in gram quantities tris(allyloxy)knot of the amide-type 5 (knotane) can be completely and partially deprotected with nBu(3)SnH in the presence of a palladium catalyst resulting in hydroxyknotanes 7-9. These, in turn, react with diethylchlorophosphate giving rise to knotanes equipped with between one and three phosphoryl groups. Sulfonylation of bis(allyloxy)monohydroxyknotane 8 with p-toluenesulfonyl chloride and, following removal of one or two allyl groups from the intermediate monosulfonate 13, give rise to sulfonyloxy-allyloxy-hydroxy- and sulfonyloxy-dihydroxy-knotanes 15 and 14, respectively. This provides a convenient method for the preparation of knotanes with any substitution pattern. All new knotanes have been isolated in preparative amounts and as highly pure substances with an exception of allyloxy-dihydroxyknotane 9. This compound could only be obtained as a mixture with the corresponding monohydroxy-derivative 8. The structures of all synthesized compounds were established by means of FAB and MALDI TOF mass spectrometry, (1)H and (31)P NMR spectroscopy. The triphosphorylated knotane 10 exhibits high solubility in alcohols, allowing its complete enantiomeric resolution with a commercially available chiral HPLC column. (1)H,(1)H DQF-COSY correlation spectroscopy along with H/D exchange experiments and ab initio calculations provided the first detailed (1)H NMR signal assignments of knotanes in [D(6)]DMSO solution. The combination of variable temperature (1)H and (31)P NMR spectroscopy and molecular modeling has been applied to study the conformational behavior of the new knotanes in different solvents. It has been shown that in DMSO solution at room temperature knotanes exist in a relatively rigid nonsymmetrical conformation similar to that found in the solid state while faster conformational exchange leading to the average D(3) symmetrical structure was detected in a number of other solvents.