Ergodic Theory of Parabolic Horseshoes

In this paper we develop the ergodic theory for a horseshoe map f which is uniformly hyperbolic, except at one parabolic fixed point ω and possibly also on W ^s (ω). We call f a parabolic horseshoe map. In order to analyze dynamical and geometric properties of such horseshoes, by making use of induced maps, we establish, in the context of σ-finite measures, an appropriate version of the variational principle for continuous potentials with mild distortion defined on subshifts of finite type. Staying in this setting, we propose a concept of σ-finite equilibrium states (each classical probability equilibrium state is a σ-finite equilibrium state). We then study the unstable pressure function , the corresponding finite and σ-finite equilibrium states and their associated conditional measures. The main idea is to relate the pressure function to the pressure of an embedded parabolic iterated function system and to apply the developed theory of the symbolic σ-finite thermodynamic formalism. We prove, in particular, an appropriate form of the Bowen-Ruelle-Manning-McCluskey formula, the existence of exactly two σ-finite ergodic conservative equilibrium states for the potential –t ^u log |Df|E ^u | (where t ^u denotes the unstable dimension), one of which is the Dirac δ-measure supported at the parabolic fixed point and the other being non-atomic. We also show that the conditional measures of this non-atomic equilibrium state on unstable manifolds, are equivalent to (finite and positive) packing measures, whereas the Hausdorff measures vanish. As an application of our results we obtain a classification for the existence of a generalized physical measure, as well as a criteria implying the non-existence of an ergodic measure of maximal dimension. The research of the first author was supported in part by the NSF Grant DMS 0400481. The research of the second author was supported in part by the National Science Foundation under Grant No. EPS-0236913 and matching support from the State of Kansas through Kansas Technology Enterprise Corporation.     

Conformations of 2-C:1-N-carbonyl-2-deoxy-d-glycopyranosylamines

Geometry and molecular conformation of theN-toluenesulfonyl1 andN-acetyl-2 derivatives of peracetylated 2-C:1-N-carbonyl-2-deoxy--d-glucopyranosylamine were investigated with the use of X-ray diffraction methods. Compound1 (C₂₀H₂₃NSO₁₀) crystallizes in the monoclinic P2₁ space group, withZ=2 anda=8.238(1),b=7.988(1),c=16.928(2)Å, =99.12(1)°. Compound2 (C₁₅H₁₉NO₉) crystallizes in orthorhombic P2₁2₁2₁ space group withZ=4 anda=8.385(1),b=8.550(1),c=24.000(2) Å. Analysis of differences in bond lengths and angles between compounds1 and2 and other compounds of this class showed that the electronwithdawing effect by the residue located at the nitrogen atom can be manifested by lengthening of the -lactam C-N bonds, with simultaneous shortening of the distance between two carbon atoms at the ring fusion. Semi-empirical calculations suggested that the title compounds displayed two positively charged centers, susceptible for attack of nucleophiles, one at the carbonyl group of -lactam and the second at the anomeric carbon atom. Atomic charges, however, calculated for compounds1 and2 did not explain their different reaction directions during alcoholysis.Part 3. For part 1 and 2, see Refs. 5 and 6.     

EPR spectra of gamma-irradiated DL-alpha-alanine supported on molecular sieves

The aim of the work was to collect information concerning boundary effects which are suspected in alpha-alanine dosimeters consisted of powdered microcrystalline alpha-alanine and binders. In our experiments the conventional binders were replaced by molecular sieves (MS). MS are inorganic porous materials (host structures) with well organized and uniform intra-crystalline pore systems of nano-scale size. The guest molecules can be either physically adsorbed on very large inner MS surface, or chemically bound to the active sites. They can be also encapsulated inside the intracrystalline cavities. The EPR spectra of gamma irradiated DL-alpha-alanine supported on NaY, CeY, SOD, mordenite, ZSM-5 and ALPO(4)-5 were very similar to that one observed for irradiated microcrystalline DL-alpha-alanine. In the case of alanine supported on HY an initial EPR spectrum was different and only after some weeks it made resemble to the well known quintet observed in microcrystalline samples. In sodalites synthesized in the presence of DL-alpha-alanine EPR signal appeared in non-irradiated sample was very low and structureless. The irradiated sample showed a distinct spectrum which was quite different from that one observed for crystalline DL-alpha-alanine.     

Effect of UVC radiation on conformational restructuring of human serum albumin

The study of the influence of UVC-254 nm radiation on spectroscopic and calorimetric properties of human serum albumin in aqueous solutions was conducted. This radiation did not only accelerate aging of albumin solutions but also caused the other qualitative changes. The dose dependent effect on conformational restructuring and thermal stability of albumin for exposure periods from 10 to 60 min was shown. The differences in response to UVC-irradiation between non-defatted and fatty acid-free albumins were found.     

Some relationships among quasidifferential,weak subdifferential and exhausters

In this study, some relationships between quasidifferentiability and weakly subdifferentiability of a function are investigated, and some results on calculating the quasidifferential in terms of weak exhausters are presented. Moreover, under some assumptions weak subdifferentiability of a quasidifferentiable function is proved and the weak subdifferential is obtained by using the quasidifferential. Under some assumptions, it is proved that a positively homogeneous and lower semicontinuous function is quasidifferentiable. It is also shown that directional differentiability and weak subdifferentiability imply quasidifferentiability. Furthermore, a method to evaluate the quasidifferential is given by using reduced weak lower exhausters.     

Complexes of atmospheric alpha-dicarbonyls with water: FTIR matrix isolation and theoretical study

The complexes of glyoxal (Gly), methylglyoxal (MGly), and diacetyl (DAc) with water have been studied using Fourier transform infrared (FTIR) matrix isolation spectroscopy and MP2 calculations with 6-311++G(2d,2p) basis set. The analysis of the experimental spectra of the Gly(MGly,DAc)/H2O/Ar matrixes indicates formation of one Gly...H2O complex, three MGly...H2O complexes, and two DAc...H2O ones. All the complexes are stabilized by the O-H...O(C) hydrogen bond between the water molecule and carbonyl oxygen as evidenced by the strong perturbation of the O-H, C=O stretching vibrations. The blue shift of the CH stretching vibration in the Gly...H2O complex and in two MGly...H2O ones suggests that these complexes are additionally stabilized by the improper C-H...O(H2) hydrogen bonding. The theoretical calculations confirm the experimental findings. They evidence the stability of three hydrogen-bonded Gly...H2O and DAc...H2O complexes and six MGly...H2O ones stabilized by the O-H...O(C) hydrogen bond. The calculated vibrational frequencies and geometrical parameters indicate that one DAc..H2O complexes, two Gly...H2O, and three MGly...H2O ones are additionally stabilized by the improper hydrogen bonding between the C-H group and water oxygen. The comparison of the theoretical frequencies with the experimental ones allowed us to attribute the calculated structures to the complexes present in the matrixes.     

Matrix isolation spectroscopy and molecular dynamics simulations for 2,7,12,17-tetra-tert-butylporphycene in argon and xenon

Electronic absorption spectra of 2,7,12,17-tetra-tert-butylporphycene (TTPC) have been recorded in low-temperature argon and xenon matrices for various deposition conditions. In the region of the S(0)-S(1) electronic transition, the spectra of TTPC in argon reveal a rich site structure, characterized by a series of more than 30 absorption peaks. Studies of the temperature dependence of the electronic spectra in solid argon demonstrated remarkable spectral changes, resulting in the broadening of all bands with increasing temperature. These temperature-induced spectral changes are, to a large degree, reversible, so lowering of temperature is accompanied by the recovery of the original fine-line spectrum. The absorption spectra in xenon reveal broad bands, on which a rich pattern of lines becomes superimposed at low temperatures. Trapping site distribution and the structure of the microenvironment around the TTPC chromophore, embedded in argon and xenon hosts, have been analyzed using molecular dynamics (MD) simulations. The MD results show that the trapping of TTPC in rare-gas solids is influenced by favorable embedding of the bulky tert-butyl groups inside the matrix cage. The crucial role of the tert-butyl groups for the thermodynamics and kinetics of matrix deposition is demonstrated by comparing the results with those obtained for the parent, unsubstituted porphycene.     

Sodium dithionite initiated addition of CF2Br2 to β-pinene and reactions of the adduct: Synthesis and the reactivity of new 1,1-difluorodienes

Sodium dithionite effectively promotes the addition of dibromodifluoromethane to the exocyclic double bond of β-pinene. The reaction proceeded in a MeCN/H₂O system to give almost quantitatively an adduct, 1-(2-bromo-2,2-difluoroethyl)-4-(2-bromoisopropyl)-cyclohexene, as the sole product. On treatment of the adduct with 2,2,6,6-tetramethylpiperidine elimination of HBr only from the (CH₃)₂CHBr group occurred to give a mixture of regioisomeric dienes, while treatment with 50% KOH under phase transfer catalysis conditions or with K₂CO₃ in DMF resulted in total dehydrobromination to give trienes possessing an exocyclic CHCF₂ group. Surprisingly, the main course of the reactions of the adduct with DBU (1,8-diazabicyclo[5.4.0]undece-7-ene) and also with t-BuOK in THF was elimination of HBr only from the CH₂CF₂Br group to afford 1-(2,2-difluorovinyl)-4-(2-bromoisopropyl)cyclohexene as the main product. Catalytic hydrogenation of the adduct followed by treatment with DBU afforded a conjugated diene, 1-(2,2-difluorovinyl)-4-isopropylcyclohexene. Compounds bearing the CHCF₂ group are new 1,1-difluorodienes which readily reacted with 4-phenyl-3H-1,2,4-triazoline-3,5-dione to give cycloadducts, derivatives of triazolo[1,2-α]cinnoline.     

SAW hydrogen gas sensor based on WO3 and Pd nanostructures

Bi-layer nanostructures of WO₃ (～100 nm and 150 nm) with a very thin film of palladium (Pd～10 nm) on the top, have been studied for hydrogen gas-sensing application at ～700C and medium hydrogen concentrations (1 – 4%) in air. The structures were obtained by vacuum deposition (first the WO₃ and then the Pd film) onto a LiNbO₃ Y- cut Z-propagating substrate and were tested by means of Surface Acoustic Wave method in a three channel delay line configuration. Very repeatable results have been observed for these two nanostructures with changes in frequency on the level of 500 to 1800 Hz for hydrogen concentration from 1 to 4 % in air. The absolute response value depends on the WO₃ film thickness and hydrogen gas concentration and is greater for the nanostructure with a thicker WO₃ film.