Domination inequality for martingale transforms of a Rademacher sequence

Letf _n = Σ _k=1 ⁿ v _k r _k ,n=1,…, be a martingale transform of a Rademacher sequence (r _n)and let (r _n ^′ ) be an independent copy of (r _n).The main result of this paper states that there exists an absolute constantK such that for allp, 1≤p<∞, the following inequality is true: In order to prove this result, we obtain some inequalities which may be of independent interest. In particular, we show that for every sequence of scalars (a _n)one has where is theK-interpolation norm between ℓ₁ and ℓ₂. We also derive a new exponential inequality for martingale transforms of a Rademacher sequence. This research was supported in part by an NSF grant and an FRPD grant at NCSU.     

Some criteria for the existence of invariant measures and asymptotic stability for random dynamical systems on polish spaces

Tomasz Szarek presented interesting criteria for the existence of invariant measures and asymptotic stability of Markov operators on Polish spaces. Hans Crauel in his book presented the theory of random probabilistic measures on Polish spaces showing that notions of compactness and tightness for such measures are in one-to-one correspondence with such notions for non-random measures on Polish spaces, in addition to the criteria under which the space of random measures is itself a Polish space. This result allowed the transfer of results of Szarek to the case of random dynamical systems in the sense of Arnold. These criteria are interesting because they allow to use the existence of simple deterministic Lyapunov type function together with additional conditions to show the existence of invariant measures and asymptotic stability of random dynamical systems on general Polish spaces.     

Promoted ternary CuO-ZrO2-Al2O3 catalysts for methanol synthesis

Ternary CuO-ZrO₂-Al₂O₃ catalysts promoted by palladium or gold were prepared and tested in CO hydrogenation reaction at 260°C under elevated pressure (4.8 MPa). The promotion effect of palladium or gold addition on the physicochemical and catalytical properties of CuO-ZrO₂-Al₂O₃ catalysts in methanol synthesis (MS) was studied. The catalysts were characterized by BET, XRD, TPR-H₂, TPD-NH₃ methods. The BET results showed that the ternary system CuO-ZrO₂-Al₂O₃ had the largest specific surface area, cumulative pore volume and average pore size in comparison with the promoted catalysts. The yield of methanol can be given through the following sequence: 5%Pd/CuO-ZrO₂-Al₂O₃ > CuO-ZrO₂-Al₂O₃ > 2%Au/CuO-ZrO₂-Al₂O₃. We also found that the presence of gold or palladium on catalyst surface has strong influence on the reaction selectivity. The high selectivity of gold doped ternary catalyst is explained by the gold-oxide interface sites created on the catalyst surface and the acidity of those systems. The higher selectivity to methanol in the case of the palladium catalyst is explained by the spillover effect between Pd and CuO.      

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.     

Synthesis of Functionalized (2-Thienylcarbonyl)thiazoles and 4-(2-Thienyl)pyridines by Reaction of (2-Thienylcarbonyl)thioacetanilides and their Enamine Derivatives

Summary. The condensation of two molecules of 2-(2-thienylcarbonyl)thioacetanilides catalyzed by piperidine yielded thiazole derivatives as confirmed by X-ray crystal structure analysis. The reaction of malononitrile with 3-morpholino-3-(2-thienyl)acrylic acid thioanilides furnished 6-amino-1-aryl-4-(2-thienyl)-1,2-dihydro-2-thioxopyridine-5-carbonitriles. A similar reaction of malononitrile with 3-morpholino-3-(2-thienyl)acrylic acid anilides provided 2-oxopyridine-5-carbonitriles.     

Probing organization and communication at layered interfaces

We have investigated the local organization intrinsic to a variety of interfacial structures, by both electrochemical and spectroscopic means. Our focus has been on the design and construction of biomimetic interfaces, where a lipid bilayer or a hybrid bilayer membrane can be bound to an interface. The goal of this work is ultimately to create an interface on a transducer surface that can support an enzyme in its active form. To this point, we have examined the extent of organization that is achievable in monolayers that will be used to bind bilayer structures to a transducer surface. Our electrochemical data point to the important role of the substrate surface in determining adlayer organization. We have also investigated the fluidity and structural heterogeneity of lipid bilayers using time-resolved and steady state fluorescence spectroscopy. Our data point to the highly interactive nature of lipid bilayer constituents, where perturbations introduced to one region have significant consequences on other regions of the bilayer. Such information is directly relevant to the existence and properties of lipid raft structures in both model and biological bilayers.     

pH gradient high-performance liquid chromatography: theory and applications

pH gradient high-performance liquid chromatography (HPLC) is a method of reversed-phase high-performance liquid chromatography suitable for ionogenic substances. It consists in programmed increase during the chromatographic process of the eluting strength of eluent with respect to the analytes separated. On the analogy of the conventional organic modifier gradient reversed-phase HPLC, in the pH gradient approach the eluting strength of the mobile phase increases due to its changing pH: increasing in case of acids or decreasing in case of bases. At the same time the content of organic modifier remains constant. A theory of the pH gradient HPLC has been elaborated. The resulting mathematical model is easily manageable. Its ability to predict changes in retention and separation of analytes following the changes in chromatographic conditions is demonstrated. The pH gradient method is uniquely suitable to determine pKa values of analytes. An equation is presented allowing to calculate pKa values basing on appropriate retention data. The effects on pKa are discussed of the concentration of methanol in the mobile phase. The RP HPLC-derived pKa data correlate to the reference pKa values (w(w)pKa) but are not identical. That may be explained by the effects on the chromatographically determined pKa of the specific interactions of analytes with stationary phases. The proposed pH gradient RP HPLC procedure offers a fast and convenient means to get comparable acidity parameters for larger series of compounds, like drug candidates, also when the analytes are available only in minute amounts and/or as complex mixtures.