An Asymptotic Ratio in the Complete Binary Tree

Let T _n be the complete binary tree of height n considered as the Hasse-diagram of a poset with its root 1 _n as the maximum element. For a rooted tree T, define two functions counting the embeddings of T into T _n as follows A(n;T)=|{S T _n  : 1 _n ∈S, S≅T}|, and B(n;T)=|{S T _n :1 _n ∉S, S≅T}|. In this paper we investigate the asymptotic behavior of the ratio A(n;T)/B(n;T), and we show that lim  _n→∞[A(n;T)/B(n;T)]=2^ℓ;−1−1, for any tree T with ℓ leaves. This revised version was published online in June 2006 with corrections to the Cover Date.     

A numerical model of multimode fiber PON frequency response

Frequency response of passive optical network (PON) based on multimode fibers is investigated. The network comprises fibers, connectors and splitters/couplers. It is shown that due to mode filtering at splitters, the frequency response is different for different network nodes in otherwise symmetrical network.     

Electron scattering on C6F6 and SF6 molecules

Total absolute cross sections for electron scattering on hexafluorobenzene, C₆F₆, and sulfur hexafluoride, SF₆, molecules, have been measured as a function of impact energy from 0.6 to 250 eV. The total cross section for C₆F₆ exhibits a very broad peak stretching from 10 to 100 eV with some weak features near 9.5 and 15 eV superimposed on the peak. Apart from the well-known low-energy resonant structures in the SF6 total cross section function, a new weak resonant feature close to 25 eV has been noticed in the present experiment, in accordance with earlier theoretical calculations.     

Porous structure and thermal properties of carbon adsorbents from pitch–polymer compositions

The study results of porous structure and thermal properties of carbon adsorbents (AC) obtained from pitch–polymer compositions were presented. The compositions were carbonized and activated with steam, potassium hydroxide, and magnesium and potassium carbonates. For the obtained AC, the thermal analysis and the determination of adsorption value of iodine and porous structure by adsorption/desorption of nitrogen at 77 K were carried out. The possibility of obtained activated carbons from pitch–polymer compositions was demonstrated. The use of untypical feedstock, as an effect of combination of bituminous substance with polymeric waste and improvement of the methods of production, creates the potential possibility to produce carbon adsorbents of interesting properties and porous structure.     

Fourier analysis of scratches generated on m‐GaN substrates during polishing

Generation of scratches on surface of m‐plane GaN substrates due to polishing was studied by atomic force microscopy (AFM). For epi‐ready substrates AFM images confirm a flat surface with the atomic step roughness while a lot of scratches are visible in AFM images for partially polished GaN substrates. The Fourier analysis of AFM images show that scratches propagate easier along {c‐plane} and {a‐plane} directions on m‐plane GaN surface. This observation is an evidence of anisotropy of mechanical properties of GaN crystals in the micro‐scale. This anisotropy is directly correlated with the symmetry and atomic arrangement of m‐plane GaN.     

Studies of reaction heats and structure of complexes formed between strong N-bases and phenols

The heats of reactions between various phenols and two strong N-bases of guanidine-like character in acetonitrile, are determined. The values can be used as a measure of self-assembly abilities of the phenol molecules in the interactions with strong N-bases, playing a very important role in biological systems. In the case of TBD complexes with corresponding nitrophenols, the protonated N-base is hydrogen-bonded to the nitro group excluding the self-assembly process of the phenols. In the case of other phenols, the self-assembly abilities are dependent on pK_a values of phenols. With increasing acidity of phenols their ability to form the hydrogen-bonded chains decreases. The maximum of length of the chains is observed for 4-methylphenol, which has a similar pK_a value to that in the tyrosine residue in biological systems.     

Synthesis of Some Aminophosphonates Bearing N‐(Fluorophenyl)‐piperazynyl Moiety and Their Activity toward Serotonin Receptors

Syntheses of a series of compounds bearing a 1‐(fluorophenyl)piperazin‐4‐ylmethyl moiety, namely dialkyl 1‐(fluorophenyl)piperazin‐4‐ylmethyl phosphonates 3a–f , diethyl 2‐[1‐(fluorophenyl)piperazin‐4‐yl]‐ethyl phosphonates 4a,b , diethyl 3‐[1‐(4‐fluorophenyl)‐piperazin‐4‐yl]‐propyl phosphonate 5 , and di[1‐(fluorophenyl)piperazin‐4‐yl]methanes 6a,b were performed, and some of them were screened for their affinity for serotonin 5‐HT_1A, 5‐HT₆, and 5‐HT₇ receptors. Moderate interactions with these receptors were demonstrated.     

Kinetics and mechanism of a trans-tetraazamacrocyclic chromium(III) complex oxidation by hexacyanoferrate(III) in strongly alkaline media

Oxidation of the trans-[Cr(cyca)(OH)₂]⁺ complex, where cyca = meso-5,5,7,12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane, by [Fe(CN)₆ ]^3- ion in strongly alkaline media, leading to [Cr^V O(cyca_ox )]³⁺ ion, has been studied using electronic and e.p.r. spectroscopy. The kinetics of the Cr^III → Cr^IV transformation have been studied using a large excess of the reductant and OH^- ion over the oxidant. The reaction is a second order process: first order in [Cr^III] and [Fe^III] at constant [OH^-]. The second order rate constant is higher than linearly dependent on the OH^- concentration. The mechanism of the reaction has been discussed. A relatively inert intermediate chromium(V) species was detected based on characteristic bands in the visible region and the e.p.r. signal at g_iso = 1.987 for the systems where an excess of oxidant was used. The hyperfine structure of the main e.p.r. signal is consistent with the d¹ -electron interactions with four equivalent nitrogen nuclei and [Cr^V = O(cyca_ox)]³⁺ formula, where cyca_ox = oxidized cyca, can be postulated for the intermediate Cr^V complex.     

Epitaxial graphene perfection vs. SiC substrate quality

Polytype instability of SiC epitaxial films was the main focus of attention in the experiment performed since this factor has a decisive influence on graphene growth, which was the second stage of the experiment. Layers deposited in various initial C/Si ratios were analyzed.