A Triazacyclononane‐Based Bifunctional Phosphinate Ligand for the Preparation of Multimeric 68Ga Tracers for Positron Emission Tomography

For application in positron emission tomography (PET), PrP9 , a N,N′,N′′‐trisubstituted triazacyclononane with methyl(2‐carboxyethyl)phosphinic acid pendant arms, was developed as ⁶⁸Ga³⁺ complexing agent. The synthesis is short and inexpensive. Ga^III and Fe^III complexes of PrP9 were characterized by single‐crystal X‐ray diffraction. Stepwise protonation constants and thermodynamic stabilities of metal complexes were determined by potentiometry. The Ga^III complex possesses a high thermodynamic stability (log K_[GaL]=26.24) and a high degree of kinetic inertness. ⁶⁸Ga labeling of PrP9 is possible at ambient temperature and in a wide pH range, also at pH values as low as 1. This means that for the first time, the neat eluate of a TiO₂‐based ⁶⁸Ge/⁶⁸Ga generator (typically consisting of 0.1 M HCl) can be directly used for labeling purposes. The rate of ⁶⁸Ga activity incorporation at pH 3.3 and 20 °C is higher than for the established chelators DOTA and NOTA. Tris‐amides of PrP9 with amino acid esters were synthesized to act as models for multimeric peptide conjugates. These conjugates exhibit radiolabeling properties similar to those of unsubstituted PrP9 .     

A comparison of natural and experimental long-term corrosion of uranium-colored glass

The alteration features of historical U-colored glasses exposed to natural weathering for over 150 years were compared with the experimental alteration of similar glass with ～0.3 wt% of uranium using a long-term (up to 426 days) kinetic laboratory batch leaching test in deionized water. Two types of natural corrosion crusts were identified by a combination of SEM/EDS, HRTEM/SAED, EPMA and XRD: (i) formation of a leached layer (up to ～600 μm thick) depleted in alkalis and enriched in Si with stable concentration of U and Al and (ii) formation of lamellae depleted in alkalis, Si and U and enriched in Al. The presence of newly formed gibbsite (Al(OH)₃) and kaolinite (Al₂Si₂O₅(OH)₄) were confirmed in the second type of corrosion crust by HRTEM. Dissolution of the glass components including uranium was determined during the laboratory leaching test. Several μm thick alkali-depleted alteration zones with stable U content relatively enriched in Si and Al were formed on the glass surface. The PHREEQC-2 modeling also predicted the precipitation of secondary gibbsite and kaolinite in the late stages of the leaching. These phases may form especially when sufficient amounts of Al are available from the environment (e.g., soil). Furthermore, they provide surfaces for sorption and may, in some cases, affect the mobility of U ions released from the glass in dependence on pH and U speciation.     

Mixed ligand palladium(II) complexes of oxalate and malonate with vitamin-B6 molecules: synthesis,crystal structure and kinetics

The synthesis of six mononuclear palladium complexes of general formula [Pd(ox)/(mal)L₂] and [Pd(ox)/(mal)L] (ox = oxalate, mal = malonate, both L and L are vitamin-B₆ molecules (I), L = pyridoxine, pyridoxal and L = pyridoxamine) has been achieved. The structures of these compounds were established by elemental analysis, i.r. and ¹³C-n.m.r. [Pd(oxalate)(pyridoxine)₂] was analyzed by single crystal X-ray diffraction. It exhibits square planar coordination with bond lengths 2.015 (2) Å for Pd—N and 2.010 (2) Å for Pd—O. The interaction of [Pd(ox)₂]^2– and [Pd(mal)₂]^2– with L has been followed kinetically in order to look into the nature of products and the mechanism of formation under the conditions [Pd^II-chelate] [L] and [L].     

On Size Ramsey Numbers of Graphs with Bounded Degree

G on n vertices with maximum degree three and the size Ramsey number where and c are positive constants. Received December 21, 1998     

Strong ramsey properties of simplices

In this paper we will show that every simplexX with circumradiusϱ satisfies the following geometric partition property, which proves a conjecture from [FR90]. For every positive realδ there exists a positive realσ such that everygc-colouring of then-dimensional sphere of radiusϱ+δ withχ≤(1+σ) ⁿ results in a monochromatic copy ofX.     

Right division in groups, dedekind-frobenius group matrices, and ward quasigroups

The variety of quasigroups satisfying the identity (xy)(zy) = xz mirrors the variety of groups, and offers a new look at groups and their multiplication tables. Such quasigroups are constructed from a group using right division instead of multiplication. Their multiplication tables consist of circulant blocks which have additional symmetries and have a concise presentation. These tables are a reincarnation of the group matrices which Frobenius used to give the first account of group representation theory. Our results imply that every group matrix may be written as a block circulant matrix and that this result leads to partial diagonalization of group matrices, which are present in modern applied mathematics. We also discuss right division in loops with the antiautomorphic inverse property.     

Graphs of small dimensions

LetG=(V, E) be a graph withn vertices. The direct product dimension pdim (G) (c.f. [10], [12]) is the minimum numbert such thatG can be embedded into a product oft copies of complete graphsK _n.In [10], Lovász, Neetil and Pultr determined the direct product dimension of matchings and paths and gave sharp bounds for the product dimension of cycles, all logarithmic in the number of vertices.     

Supersaturation For Ramsey-Turán Problems

For an l-graph , the Turán number is the maximum number of edges in an n-vertex l-graph containing no copy of . The limit is known to exist [8]. The Ramsey–Turán density is defined similarly to except that we restrict to only those with independence number o(n). A result of Erdős and Sós [3] states that as long as for every edge E of there is another edge E′of for which |E∩E′|≥2. Therefore a natural question is whether there exists for which . Another variant proposed in [3] requires the stronger condition that every set of vertices of of size at least εn (0<ε<1) has density bounded below by some threshold. By definition, for every . However, even is not known for very many l-graphs when l>2. We prove the existence of a phenomenon similar to supersaturation for Turán problems for hypergraphs. As a consequence, we construct, for each l≥3, infinitely many l-graphs for which . We also prove that the 3-graph with triples 12a, 12b, 12c, 13a, 13b, 13c, 23a, 23b, 23c, abc, satisfies . The existence of a hypergraph satisfying was conjectured by Erdős and Sós [3], proved by Frankl and R?dl [6], and later by Sidorenko [14]. Our short proof is based on different ideas and is simpler than these earlier proofs. * Research supported in part by the National Science Foundation under grants DMS-9970325 and DMS-0400812, and an Alfred P. Sloan Research Fellowship. † Research supported in part by the National Science Foundation under grants DMS-0071261 and DMS-0300529.