Mosaics of combinatorial designs for information-theoretic security

Designs, Codes and Cryptography - We study security functions which can serve to establish semantic security for the two central problems of information-theoretic security: the wiretap channel, and...     

Dynamic Interactions in Synthetic Receptors: A Guest Exchange Saturation Transfer Study

The accumulated knowledge regarding molecular architectures is based on established, reliable, and accessible analytical tools that provide robust structural and functional information on assemblies. However, both the dynamicity and low population of noncovalently interacting moieties within studied molecular systems limit the efficiency and accuracy of traditional methods. Herein, the use of a saturation transfer-based NMR approach to study the dynamic binding characteristics of an anion to a series of synthetic receptors derived from bambusuril macrocycles is demonstrated. The exchange rates of BF₄⁻ are mediated by the side chains on the receptor (100 s⁻¹<k_ex<5000 s⁻¹), which play a critical role in receptor-anion binding dynamics. The signal amplification obtained with this approach allows for the identification of different types of intermolecular interactions between the receptor and the anion, something that could not have been detected by techniques hitherto used to study molecular assemblies. These findings, which are supported by a computational molecular dynamic study, demonstrate the uniqueness and added value of this NMR method.     

Congruence criteria for finite subsets of complex projective and complex hyperbolic spaces

We investigate congruence classes and direct congruence classes of m-tuples in the complex projective space ℂP ⁿ . For direct congruence one allows only isometries which are induced by linear (instead of semilinear) mappings. We establish a canonical bijection between the set of direct congruence classes of m-tuples of points in ℂP ⁿ and the set of equivalence classes of positive semidefinite Hermitean m×m-matrices of rank at most n+1 with 1's on the diagonal. As a corollary we get that the direct congruence class of an m-tuple is uniquely determined by the direct congruence classes of all of its triangles, provided that no pair of points of the m-tuple has distance π/2. Examples show that the situation changes drastically if one replaces direct congruence classes by congruence classes or if distances π/2 are allowed. Finally we do the same kind of investigation also for the complex hyperbolic space ℂH ⁿ . Most of the results are completely analogous, however, there are also some interesting differences. Received: 15 January 1996     

Über die Löslichkeit des Berlinerblaus

Ohne ZusammenfassungHerrn Ingenieur E. Hofmann danke ich fÜr seine bewährte UnterstÜtzung.     

The shape invariant of triangles and trigonometry in two-point homogeneous spaces

We define a fourth basic invariant, which, besides the lengths of the three sides of a triangle, determines a triangle in the complex and quaternion projective spaces P ⁿ and P ⁿ (n2) uniquely up to isometry. We give inequalities describing the exact range of the four basic invariants. We express the angular invariants of a triangle with our basic invariants, giving a new completely elementary proof of the laws of trigonometry. As a corollary we derive a large number of congruence theorems. Finally we get, in exactly the same way, the corresponding results for triangles in the complex and quaternion hyperbolic spaces H ⁿ and H ⁿ (n2).     

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Ohne Zusammenfassung     

Analysis of spin states, spin barriers, and trans-effects involved in the coordination and stabilization of dinitrogen by biomimetic iron complexes

Coordination of dinitrogen to Sellmann-type iron (II) complexes in a sulfur-dominated coordination sphere, which emulates the environment of iron centers in the FeMo-cofactor of nitrogenase, is analyzed with respect to spin states, spin barriers, and the effect of trans-ligands. Such detailed investigations became only recently feasible when the reliability of density functional methods, which are the only quantum chemical methods capable of describing large transition metal complexes, could significantly be improved for the calculation of energies for states of different spin. It is found that the actual binding energy of dinitrogen is of sufficient magnitude for a reasonably strong fixation of N₂ by Sellmann-type coordination compounds. However, potential fixation is determined by additional factors which reduce the binding energy. One factor is the change in spin state of the N₂-free metal fragment, which lowers the total energy and quenches the thermodynamic stabilization effect of the binding energy. In addition, the metal fragment rearranges and gains even more stabilization energy for the un-coordinated state. Apart from these thermodynamical effects, the existence of spin barriers, which must be overcome upon binding of dinitrogen, leads to kinetical effects, which cannot be neglected.     

A nonenzymic model for the coenzyme B12-dependent isomerization of methylmalonyl-SCoA to suiccinyl-SCoA

Dimethyl bromomethylmalonate (IV) reacts with vitamin B_12s in aqueous solution yielding a relatively unstable carbon-cobalt bonded adduct V, which shows visible spectra in good accord with expectation. The adduct V was allowed to decompose in water, in the dark, at room temperature and at physiological pH. Three products: succinic acid (VI), methylmalonic acid (VIII) and malonic acid (VII) were formed in 3, 18, and 13% yields respectively. Isolation of the succinic acid rearrangement product provides support for the intermediacy of the carbon-cobalt bond in the coenzyme B₁₂ dependent enzymic carbon-skeleton rearrangement of methylmalonyl-SCoA to succinyl-SCoA.     

Analysis of functional groups on the surface of plasma-treated carbon nanofibers

Plasma chemically modified carbon nanofibers were characterized by X-ray photoelectron spectroscopy with regard to the content of carbon, oxygen, and nitrogen and the contribution of carboxylic groups or ester, carbonyl and hydroxylic groups or ether on the surface. Unfortunately, X-ray photoelectron spectroscopy only provides an average value of the first 10 to 15 molecular layers. For comparison, depth profiles were measured and wet chemical methods were applied to estimate the thickness of the functionalized layer and the distribution of oxygen-containing functional groups within the near-surface layers. The results indicate that the fiber surface is covered by a monomolecular oxygen-containing layer and that plasma treatment allows a complete oxygen functionalization of the uppermost surface layer. The best conditions for plasma treatment found within the set of parameters applied to generate complete functionalization are: plasma gas O(2)/Ar ratio 1:1, gas pressure 1-1.5 hPa, plasma power 80 W, treatment time >or= 5 min. Additionally, three quick and easy methods are presented to estimate the efficiency of plasma treatment with regard to surface functionalization: pyrolysis, contact angle measurements, and light permeability measurements of aqueous carbon nanofiber suspensions.