The intersection of all maximum stable sets of a tree and its pendant vertices

A stable set in a graph G is a set of mutually non-adjacent vertices, α(G) is the size of a maximum stable set of G, and is the intersection of all its maximum stable sets. It is known that if G is a connected graph of order n≥2 with 2α(G)>n, then , [V.E. Levit, E. Mandrescu, Combinatorial properties of the family of maximum stable sets of a graph, Discrete Applied Mathematics 117 (2002) 149-161; E. Boros, M.C. Golumbic, V.E. Levit, On the number of vertices belonging to all maximum stable sets of a graph, Discrete Applied Mathematics 124 (2002) 17-25]. When we restrict ourselves to the class of trees, we add some structural properties to this statement. Our main finding is the theorem claiming that if T is a tree of order n≥2, with 2α(T)>n, then at least two pendant vertices an even distance apart belong to .     

Preliminary investigation of a medium power argon radiofrequency capacitively coupled plasma as atomization cell in atomic fluorescence spectrometry of cadmium

The single ring electrode radiofrequency capacitively coupled plasma torch (SRTr.f.CCP) operated at 275W, 27.12 MHz and Ar flow rate below 0.7 lmin(-1) was investigated for the first time as atomization cell in atomic fluorescence spectrometry (AFS) using electrodeless discharge lamps (EDL) as primary radiation source and charged coupled devices as detector. The signal to background ratio (SBR) and limit of detection for Cd determination by EDL-SRTr.f.CCP-AFS were compared to those obtained in atomic emission spectrometry using the same plasma torch. The detection limit in fluorescence was 4.3 ngml(-1) Cd compared to 65 ngml(-1) and 40 ngml(-1) reported in r.f.CCP-atomic emission (AES) equipped with single or double ring electrode. The lower detection limit in EDL-SRTr.f.CCP-AFS is due to a much better SBR in fluorescence. The limit of detection was also compared to those in atomic fluorescence with inductively coupled plasma (0.4 ngml(-1)), microwave plasma torch (0.25 ngml(-1)) and air-acetylene flame (8 ngml(-1)). The influence of light-scattering through the plasma and the secondary reflection of the primary radiation on the wall of the quartz tube on the analytical performance are discussed. The non-spectral matrix effects of Ca, Mg and easily ionized elements are much lower in EDL-SRTr.f.CCP-AFS compared to SRTr.f.CCP-AES. The new technique was applied in the determination of Cd in contaminated soils, industrial hazardous waste (0.4-370 mgkg(-1)) and water (113 microgl(-1)) with repeatability of 4-8% and reproducibility in the range of 5-12%, similar to those in ICP-AES. The results were checked by the analysis of a soil and water CRM with a recovery degree of 97+/-9% and 98+/-4%, for a confidence limit of 95%. The present EDL-SRTr.f.CCP-AFS is a promising technique for Cd determination in environmental samples.     

Quantum amplified isomerization in polymers based on triplet chain reactions

Photoinitiated triplet quantum amplified isomerizations (QAI) of substituted Dewar benzene derivatives in polymeric media are reported. The quantum efficiencies and the ultimate extents of reactant-to-product conversions increase significantly with the incorporation of appropriate co-sensitizers; compounds whose triplet energies are similar to or lower than that of the sensitizer and close to that of the reactant. These co-sensitizers serve to promote chain-propagating energy transfer processes and thereby increase the action sphere of photosensitization. Isomerization quantum yields increase, as predicted, with increasing concentrations of the reactants and the co-sensitizers. Chain amplifications as large as approximately 16 and extents of conversion that approach 100% have been achieved. Mechanistic schemes are proposed to account for the dynamics of the inherent energy transfer processes and provide a predictively useful model for the design of a new class of photoresponsive polymers based on changes in the refractive index of the materials.     

On pattern transfer in replica molding

Nano- and micromolding of elastic materials produces smoothed replicas of the mold structures. This limits the technique's resolution. Here we identified surface tension as the cause of smoothing and derived explicit equations for calculating molded feature shapes. The characteristic length scale for smoothing is given by the ratio of the interface tension to Young's modulus of the molded material. This approach offers the possibility to correct for the smoothing caused by surface tension during mold design. Moreover, it can be exploited to measure interface tension.     

Synthesis and Application of Low Molecular Weight PEI-Based Copolymers for siRNA Delivery with Smart Polymer Blends

Polyethylenimine (PEI) is a commonly used cationic polymer for small-interfering RNA (siRNA) delivery due to its high transfection efficiency at low commercial cost. However, high molecular weight PEI is cytotoxic and thus, its practical application is limited. In this study, different formulations of low molecular weight PEI (LMW-PEI) based copolymers polyethylenimine-g-polycaprolactone (PEI–PCL) (800 Da–40 kDa) and PEI–PCL–PEI (5–5–5 kDa) blended with or without polyethylene glycol-b-polycaprolactone (PEG–PCL) (5 kDa-4 kDa) are investigated to prepare nanoparticles via nanoprecipitation using a solvent displacement method with sizes ≈100 nm. PEG–PCL can stabilize the nanoparticles, improve their biocompatibility, and extend their circulation time in vivo. The nanoparticles composed of PEI–PCL–PEI and PEG–PCL show higher siRNA encapsulation efficiency than PEI–PCL/PEG–PCL based nanoparticles at low N/P ratios, higher cellular uptake, and a gene silencing efficiency of ≈40% as a result of the higher molecular weight PEI blocks. These results suggest that the PEI–PCL–PEI/PEG–PCL nanoparticle system could be a promising vehicle for siRNA delivery at minimal synthetic effort.     

Mass spectrometric approaches for elucidation of antigenantibody recognition structures in molecular immunology

Mass spectrometric approaches have recently gained increasing access to molecular immunology and several methods have been developed that enable detailed chemical structure identification of antigen-antibody interactions. Selective proteolytic digestion and MS-peptide mapping (epitope excision) has been successfully employed for epitope identification of protein antigens. In addition, "affinity proteomics" using partial epitope excision has been developed as an approach with unprecedented selectivity for direct protein identification from biological material. The potential of these methods is illustrated by the elucidation of a beta-amyloid plaque-specific epitope recognized by therapeutic antibodies from transgenic mouse models of Alzheimer's disease. Using an immobilized antigen and antibody-proteolytic digestion and analysis by high resolution Fourier transform ion cyclotron resonance mass spectrometry has lead to a new approach for the identification of antibody paratope structures (paratope-excision; "parex-prot"). In this method, high resolution MS-peptide data at the low ppm level are required for direct identification of paratopes using protein databases. Mass spectrometric epitope mapping and determination of "molecular antibody-recognition signatures" offer high potential, especially for the development of new molecular diagnostics and the evaluation of new vaccine lead structures.     

On Bonding,Structure, and Stability of Ternary Hydrides A2MH2 (A = Li,Na; M = Pd,Pt)

Bonding, structure, and stability of solid A₂MH₂ with A = Li, Na; M = Pd, Pt were investigated with a relativistically corrected density-functional approach, which reliably describes the trends among these four compounds. In order to examine the influence of the ligands (A) and of the crystalline environment, calculations were also made for free A₂MH₂ molecules and MH₂^2– ions. The free MH₂^2– complex is held together by strong bonds between formally closed shell atomic units because of strong M-d,s hybridization. The M–H bonds are further stabilized by the alkali metal ion ligands and by the crystal surrounding. The crystal field expands the H–A distance and enhances the H–A polarity. Relativistic effects contribute to M–H bonding in the solid state. The experimentally determined bond lengths and their trends are in accordance with theory. Due to relativistic and lanthanide effects, the Pt–H bond length becomes nearly as short as the Pd–H one. The small Li ion causes a distortion of the Li₂PtH₂ crystal resulting in an even shorter Pt–H bond length. In the gas-phase, A₂PtH₂ is more stable against dissociation than A₂PdH₂. The stability of the solid compounds is strongly influenced by the cohesive energy of the metal M, and also by the nature of the alkali metal. The evaluated enthalpies of formation favor increasing stability of solid A₂MH₂ against disproportionation into M and AH from Pt to Pd and from Li to Na. This is in agreement with experimental findings. The assignment of the experimental vibrational excitations should be reconsidered.