Moderate Deviations for Longest Increasing Subsequences: The Lower Tail

We derive a moderate deviation principle for the lower tail probabilities of the length of a longest increasing subsequence in a random permutation. It refers to the regime between the lower tail large deviation regime and the central limit regime. The present article together with the upper tail moderate deviation principle in Ref. 12 yields a complete picture for the whole moderate deviation regime. Other than in Ref. 12, we can directly apply estimates by Baik, Deift, and Johansson, who obtained a (non-standard) Central Limit Theorem for the same quantity.     

On a generalized $L_2$ projection and some related stability estimates in Sobolev spaces

Summary. In this paper we investigate a stability estimate needed in hybrid finite and boundary element methods, especially in hybrid coupled domain decomposition methods including mortar finite elements. This stability estimate is equivalent to the stability of a generalized projection in certain Sobolev spaces. Using piecewise linear trial spaces and appropriate piecewise constant test spaces, the stability of the generalized projection is proved assuming some mesh conditions locally. Received April 11, 2000 / Revised version received February 15, 2001 / Published online July 25, 2001     

Hyperfine investigations of the magnetic state in ordered Pt3−xFe1+x

Mössbauer effect studies of Pt_3−xFe_1+x fcc ordered alloys in the range 4.2 K <T<300 K, in zero and in external magnetic field, for samples with x = 0.16 to 0.28, are reported. The low-temperature spectra show several satellite lines which are related to different excess-Fe nearest-neighbor configurations. Experiments in external fields give information on the different local spin structure at different concentrations.     

Diastereomer-differentiating hydrolysis of 1,3-diol-acetonides: a simplified procedure for the separation of syn- and anti-1,3-diols

[reaction: see text] A new method to facilitate the separation of diastereomeric syn- and anti-1,3-diols is described. The method relies on the different hydrolysis rates of the corresponding diastereomeric acetonides. Treatment of a dichloromethane solution of syn- and anti-1,3-diol-acetonide with a catalytic amount of diluted aqueous hydrochloric acid leads to the selective cleavage of the anti diastereomer. The resulting anti-1,3-diol can be easily separated from the unchanged syn-1,3-diol-acetonide.     

Novel 99mTc labeled σ receptor ligand as a potential tumor imaging agent

A novel ^99mTc labeled complex, [N-[2-((2-oxo-2-(4-(3-phenylpropyl)piperazin-1-yl)ethyl) (2-mercaptoethyl)amino)acetyl]-2-aminoethanethiolato]Technetium(V) oxide (PPPE-MAMA’-^99mTcO) ([ ^99m Tc]-2) has been designed and prepared based on the integrated approach. The corresponding rhenium complex (PPPE-MAMA’-ReO)(Re-2) has been prepared and characterized. In vitro competition binding assays show moderate affinity of Re-2 towards σ₁ and σ₂ receptors with K _i values of 8.67 ± 0.07 and 5.71 ± 1.88 μmol, respectively. Planar images obtained at 0.5 h, 4 h, 20 h after i.v. injection indicate the accumulation of [ ^99m Tc]-2 in MCF-7 human breast tumor bearing mice at 20 h. Furthermore, the accumulation of [ ^99m Tc]-2 has been inhibited at 20 h after co-injection of [ ^99m Tc]-2 plus haloperidol (1 mg/kg). Biodistribution studies of [ ^99m Tc]-2 display an in vivo tumor uptake of 0.14% ± 0.01% ID/g at 24 h post i.v. injection with a tumor/muscle ratio of 6.02 ± 0.87. The above results suggest that [ ^99m Tc]-2, derived from a previously published lead compound, retains certain tumor uptake and affinity for σ receptors. [ ^99m Tc]-2 may be used as a basis for further structural modifications to develop tumor imaging agents with high affinity for σ receptors.     

On the reaction of 4-substituted trimethyltin aromatics with perchlorylfluoride

To evaluate the suitability of [¹⁸F]perchorylfluoride [¹⁸F]FClO₃ as an electrophilic fluorination agent for the preparation of radiopharmaceuticals, the reactivity non-radioactive FClO₃ towards 4-substituted trimethyltin aromatic compounds was studied. Contrary to the expectation, an electrophilic fluorination of the aromatic nucleus did not occur. The reaction of perchlorylfluoride with aromatic trimethylstannyl compounds resulted in the formation of trimethyltin fluoride and the respective destannylated aromatics in variable yields.