Heteroclinic solutions for a class of the second order Hamiltonian systems

We shall be concerned with the existence of heteroclinic orbits for the second order Hamiltonian system , where q∈Rn and V∈C¹(R×Rn,R), V?0. We will assume that V and a certain subset M⊂Rn satisfy the following conditions. M is a set of isolated points and #M?2. For every sufficiently small ε>0 there exists δ>0 such that for all (t,z)∈R×Rn, if d(z,M)?ε then −V(t,z)?δ. The integrals , z∈M, are equi-bounded and −V(t,z)→∞, as |t|→∞, uniformly on compact subsets of Rn?M. Our result states that each point in M is joined to another point in M by a solution of our system.     

Letters to the Editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to the editor-in-chieX Chandler Davis.     

Multi-player stopping games with redistribution of payoffs and BSDEs with oblique reflection

We examine the connections between a novel class of multi-person stopping games with redistribution of payoffs and multi-dimensional reflected BSDEs in discrete- and continuous-time frameworks. Our goal is to provide an essential extension of classic results for two-player stopping games (Dynkin games) to the multi-player framework. We show the link between certain multi-period m$m$-player stopping games and a new kind of m$m$-dimensional reflected BSDEs. The existence and uniqueness of a solution to continuous-time reflected BSDEs are established. Continuous-time redistribution games are constructed with the help of reflected BSDEs and a characterization of the value of such stopping games is provided.     

On the reflexivity of subspaces of Toeplitz operators on the hardy space on the upper half-plane

The reflexivity and transitivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane are investigated. The dichotomic behavior (transitive or reflexive) of these subspaces is shown. It refers to the similar dichotomic behavior for subspaces of Toeplitz operators on the Hardy space on the unit disc. The isomorphism between the Hardy spaces on the unit disc and the upper half-plane is used. To keep weak* homeomorphism between L ^∞ spaces on the unit circle and the real line we redefine the classical isomorphism between L ¹ spaces.     

Doping‐Induced Absorption Bands in P3HT: Polarons and Bipolarons

In this work, we focus on the formation of different kinds of charge carriers such as polarons and bipolarons upon p‐type doping (oxidation) of the organic semiconductor poly(3‐ hexylthiophene‐2,5‐diyl) (P3HT). We elucidate the cyclic voltammogram during oxidation of this polymer and present spectroscopic changes upon doping in the UV/Vis/near‐IR range as well as in the mid‐IR range. In the low‐oxidation regime, two absorption bands related to sub‐gap transitions appear, one in the UV/Vis range and another one in the mid‐IR range. The UV/Vis absorption gradually decreases upon further doping while the mid‐IR absorption shifts to lower energy. Additionally, electron paramagnetic resonance (EPR) measurements are performed, showing an increase of the EPR signal up to a certain doping level, which significantly decreases upon further doping. Furthermore, the absorption spectra in the UV/Vis range are analyzed in relation to the morphology (crystalline vs. amorphous) by using theoretical models. Finally, the calculated charge carriers from cyclic voltammogram are linked together with optical transitions as well as with the EPR signals upon p‐type doping. We stress that our results indicate the formation of polarons at low doping levels and the existence of bipolarons at high doping levels. The presented spectroscopic data are an experimental evidence of the formation of bipolarons in P3HT.     

Membranes with a plasma deposited titanium isopropoxide layer

Porous polypropylene membranes were coated with plasma polymerized titanium isopropoxide in a 75 kHz plasma reactor. It was noted that the presence of air in the plasma chamber increased the amount of deposited polymer. Selection of the process parameters enabled obtaining membranes with up to 300 εg cm^?2 of polymerized titanium isopropoxide. Deposition of the titanium oxide layer resulted in the reduction of permeate flux but it significantly improved the membrane photocleaning ability. The recovery index reached the level of 95 % for membranes with the highest amount of the titanium oxide deposit.     

Characterization of oxidation progress by chemiluminescence: A study of polyethylene with pro-oxidant additives

Non-isothermal chemiluminescence measurements in nitrogen and isothermal measurements in oxygen were used for the evaluation of degradation in pre-oxidized polyethylene either pure or containing Mn-based pro-oxidant additives. The results were compared with infrared spectroscopy data. Chemiluminescence measurements of pure polyethylene and polyethylene with additive made it possible to calculate the set of rate constants, based on the Bolland-Gee oxidation scheme. The oxidation rate constants of polyethylene with additive were significantly higher, while the activation energy of the process appeared lower (65 kJ mol⁻¹), than those of pure polyethylene. The method provides an access to study oxidation processes during the induction period of oxidation when infrared spectroscopy cannot provide sufficient information.     

Utilization of optimized BCR three-step sequential and dilute HCl single extraction procedures for soil-plant metal transfer predictions in contaminated lands

The prediction of soil metal phytoavailability using the chemical extractions is a conventional approach routinely used in soil testing. The adequacy of such soil tests for this purpose is commonly assessed through a comparison of extraction results with metal contents in relevant plants. In this work, the fractions of selected risk metals (Al, As, Cd, Cu, Fe, Mn, Ni, Pb, Zn) that can be taken up by various plants were obtained by optimized BCR (Community Bureau of Reference) three-step sequential extraction procedure (SEP) and by single 0.5 mol L(-1) HCl extraction. These procedures were validated using five soil and sediment reference materials (SRM 2710, SRM 2711, CRM 483, CRM 701, SRM RTH 912) and applied to significantly different acidified soils for the fractionation of studied metals. The new indicative values of Al, Cd, Cu, Fe, Mn, P, Pb and Zn fractional concentrations for these reference materials were obtained by the dilute HCl single extraction. The influence of various soil genesis, content of essential elements (Ca, Mg, K, P) and different anthropogenic sources of acidification on extraction yields of individual risk metal fractions was investigated. The concentrations of studied elements were determined by atomic spectrometry methods (flame, graphite furnace and hydride generation atomic absorption spectrometry and inductively coupled plasma optical emission spectrometry). It can be concluded that the data of extraction yields from first BCR SEP acid extractable step and soil-plant transfer coefficients can be applied to the prediction of qualitative mobility of selected risk metals in different soil systems.     

Separation and determination of terbinafine and its four impurities of similar structure using simple RP-HPLC method

A novel reversed-phase HPLC method for the simultaneous determination of active component terbinafine, its one impurity 1-methylaminomethylnaphtalene and three degradation products, β-terbinafine, Z-terbinafine and 4-methyl-terbinafine occurring in pharmaceutical formulations after long-term stability tests, was developed and validated using propylparaben as an internal standard.The chromatographic separation was performed on a NUCLEOSIL 100-5-CN column, mobile phase for separation of all compounds consisted of a mixture of tetrahydrofurane, acetonitrile and citrate buffer pH 4.50 (10:20:70, v/v/v). The analysis time was less than 32 min at flow-rate of 0.8 ml min⁻¹. UV detection was performed at 226 nm. The method was validated and system suitability parameters were investigated. Method robustness and short-term standard solution stability were verified. Limits of detection for terbinafine degradation products/impurity were from 0.023 to 0.098 μg ml⁻¹, limits of quantitation were from 0.078 to 0.327 μg ml⁻¹. The method was applicable for routine determination of terbinafine and all its found impurities of similar structure with sufficient selectivity, precision and accuracy.     

VUV photon induced fluorescence study of SF5CF3

The interaction of SF(5)CF(3) with vacuum-UV radiation has been investigated by photon induced fluorescence spectroscopy. Total fluorescence yield and dispersed fluorescence spectra of SF(5)CF(3) were recorded in the 200-1000 nm fluorescence window. In all cases, the fluorescence spectra resemble those of CF(3)X (X = H, F, Cl, and Br) molecules. At photon energies below 20 eV, the emission is attributed to the excited CF(3) and CF(2) fragments. The threshold for the CF(3) emission is 10.2 +/- 0.2 eV, giving an upper limit estimate for the SF(5)-CF(3) bond dissociation energy of 3.9 +/- 0.3 eV. The excitation functions of the CF(3) and CF(2) emissions were measured in the photon energy range 13.6-27.0 eV. The resonant structures observed in SF(5)CF(3) are attributed to electronic transitions from valence to Rydberg orbitals, following similar assignments in CF(3)X molecules. The photoabsorption spectrum of SF(5)CF(3) shows features at the same energies, indicating a strong contribution from Rydberg excitations.