A Nonsymmetric Correlation Inequality for Gaussian Measure

Letμbe a Gaussian measure (say, onRⁿ) and letK,LRⁿbe such thatKis convex,Lis a “layer” (i.e.,L={x: ax, ub} for somea, bRanduRⁿ), and the centers of mass (with respect toμ) ofKandLcoincide. Thenμ(K∩L)μ(K)·μ(L). This is motivated by the well-known “positive correlation conjecture” for symmetric sets and a related inequality of Sidak concerning confidence regions for means of multivariate normal distributions. The proof uses the estimateΦ(x)> 1−((8/π)^1/2/(3x+(x²+8)^1/2))e^−x2/2,x>−1, for the (standard) Gaussian cumulative distribution function, which is sharper than the classical inequality of Komatsu.     

An application of the Lefschetz fixed-point theorem to non-convex differential inclusions on manifolds

A selector theorem for non-convex orientor fields on closed manifolds is given and the Lefschetz fixed point theorem is used to establish an existence result for these ones.

     

The influence of side branches on the structure of crystalline phase in ethylene-1-alkene copolymers

The influence of side branches on the unit cell dimensions in ethylene-1-alkene copolymers was investigated both at room temperature as well as during heating of the samples up to melting. Time resolved X-ray diffraction investigations revealed that in the case of ethylene-1-octene copolymers with low and moderate comonomer content, the transversal expansion of the unit cell occurs due to the limited thickness of lamellae, however the samples with higher comonomer content (above 5 mol %) exhibit distinctly larger expansion resulting from the stresses imparted on the basal surfaces of crystals by the excluded branches. At high temperatures, independently on the thermal expansion, an additional increase of the unit cell volume occurs, caused probably by a penetration of the end-parts of side branches, residing near the crystals surface, into the surface cells. Similar phenomenon is observed for ethylene-1-butene copolymer. On contrary, the ratio of the average unit cell volume in ethylene-1-propene copolymer to the unit cell volume in linear polyethylene at the same temperature, decreases starting from about 50 °C. Such a behavior is a new confirmation of a partial inclusion of methyl branches into the crystalline phase. Most probably, when the temperature increases, the volume of included branch becomes a decreasing fraction of the thermally expanding unit cell volume.     

Structure of the nitrogen-centered radical formed during inactivation of E. coli ribonucleotide reductase by 2'-azido-2'-deoxyuridine-5'-diphosphate: trapping of the 3'-ketonucleotide

Ribonucleotide reductases (RNRs) catalyze the conversion of nucleotides to deoxynucleotides providing the monomeric precursors required for DNA replication and repair. The class I RNRs are composed of two homodimeric subunits: R1 and R2. R1 has the active site where nucleotide reduction occurs, and R2 contains the diiron tyrosyl radical (Y*) cofactor essential for radical initiation on R1. Mechanism-based inhibitors, such as 2'-azido-2'-deoxyuridine-5'-diphosphate (N(3)UDP), have provided much insight into the reduction mechanism. N(3)UDP is a stoichiometric inactivator that, upon interaction with RNR, results in loss of the Y* in R2 and formation of a nitrogen-centered radical (N*) covalently attached to C225 (R-S-N*-X) in the active site of R1. N(2) is lost prior to N* formation, and after its formation, stoichiometric amounts of 2-methylene-3-furanone, pyrophosphate, and uracil are also generated. On the basis of the hyperfine interactions associated with N*, it was proposed that N* is also covalently attached to the nucleotide through either the oxygen of the 3'-OH (R-S-N*-O-R') or the 3'-C (R-S-N*-C-OH). To distinguish between the proposed structures, the inactivation was carried out with 3'-[(17)O]-N(3)UDP and N* was examined by 9 and 140 GHz EPR spectroscopy. Broadening of the N* signal was detected and the spectrum simulated to obtain the [(17)O] hyperfine tensor. DFT calculations were employed to determine which structures are in best agreement with the simulated hyperfine tensor and our previous ESEEM data. The results are most consistent with the R-S-N*-C-OH structure and provide evidence for the trapping of a 3'-ketonucleotide in the reduction process.     

Coulometric titrations in microscale study of ionic equilibria

Summary Coulometric titration, a well established technique in research and in routine analysis, can successfully be applied to the study of ionic equilibria in solution. Processes, where either lyate or lyonium ions serve as titrants, for determination of acids and bases, respectively, were investigated. Among the systems studied are: autoprotolytic equilibria of various amphiprotic solvents, acid-base equilibria in water, organic and mixed solvents and complexation reactions. In all these examples the titration was followed by a potentiometric pH-indicator electrode. In nonaqueous solvents coulometry overcame the limited solubility of electrolytes, the difficulty of standardization on solutions and the necessity of working in isolated systems to avoid contamination of the sample with water vapour or with carbon dioxide.Because volumes below 1 ml and concentrations in the order of 0.001 mol/l can be used, this technique can be successfully applied to the investigation of micromole amounts of compounds, when protolytic properties of substances available in minute quantities should be evaluated. Furthermore this technique was applied to the evaluation of protonation constants of biologically important buffers and the stability constants of their calcium complexes.     

Carbon-mineral adsorbents prepared by pyrolysis of waste materials in the presence of tetrachloromethane

Natural bentonite spent in the process of plant oil bleaching was used as an initial material for preparation of carbon-mineral adsorbents. The spent bleaching earth was treated using four procedures: T (thermal treatment); H (hydrothermal treatment); C (thermal treatment with addition of CCl4 vapor); M (modification of porous structure). Raw bentonite, RB (raw bleaching earth), and carbon materials prepared using plant oil were compared. The physicochemical characteristics of the adsorbents were determined using different methods: nitrogen adsorption/desorption, XRD, TEM, and MS-TPD. Carbon-mineral adsorbents contain from 5.23 to 19.92% C (w/w) and carbon adsorbents include from 84.2 to 91.18% C (w/w). Parallel processes of organic substance carbonization, porous structure modification, sublimation or evaporation of metal chlorides, and removal of hydrogen chloride take place during pyrolysis of waste mineral materials in the CCl4 atmosphere.     

A planar circular detector based on multiple point chemi- or bio-luminescent source within a coaxial cylindrical reactor

An analytical method was proposed for calculating radiative fluxes incident on a planar circular detector from a volume multiple point chemi- or bio-luminescent source inside a coaxial cylindrical reactor. The method was designed for a cylindrical reactor when the surface reflections were neglected and when chemi- or bio-luminescence reaches a detector embedded in the same homogeneous optical medium as the point emitters of the volume multiple point source model. The radiative fluxes from arbitrarily distributed point emitters were expressed by one generalized quadruple-integral formula. Then some double- and single-integral formulas were obtained for calculating radiative fluxes from identically radiating point emitters uniformly distributed within the reactor. Selected results were computed and illustrated graphically. The obtained formulas are suitable for optimizing and/or calibrating the considered source-detectors systems (optical radiometers or luminometers) and determining radiative fluxes generated by chemical, biological, and physical processes leading to chemi-, bio-, radio-, and sono-luminescence for example.     

Thermal expansion of polymers submitted to supercritical CO2 as a function of pressure

Interactions of polymers with compressed supercritical CO₂ has been studied by using pressure‐controlled scanning calorimetry (PCSC). Global cubic thermal expansion coefficients (α_{pol‐g‐int}) for medium density polyethylene (MDPE) and poly(vinylidene fluoride) (PVDF) saturated with supercritical CO₂ have been determined at 352.4 K over the pressure range from 0.1 MPa to 100 MPa. In both cases, the isotherms of global α_{pol‐g‐int} exhibit minima near 20 MPa. At pressures below the minimum, α_{pol‐g‐int} for the PVDF–CO₂ system are higher than for the MDPE–CO₂ system, while at pressures above the minimum the opposite was observed. This proves that incorporation of CO₂ in PVDF is stronger than in MDPE. The appearance of the minimum is attributed to the action of compressed CO₂ molecules, which at higher pressures are forced to enter deep inside the interstitial or other voids in the polymer and cause their mechanical distension, which must be associated with an endothermic effect. The measurements have been performed on polymers used for fabrication of pipelines. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44:185–194, 2006     

Filament temperature stabilizer for a thermal ionization mass spectrometer

A major enhancement in temperature stabilization of a filament has recently been achieved by means of the Halas–Kami ski bridge, in which the reference resistance of one leg is directly proportional to the filament temperature. In this article we describe a novel version of this type of electronic circuit which feeds dc power voltage to the filament via a switching transistor. The switching frequency is regulated by means of a triangular waveform generator incorporated into the system. The duration of the heating peak (square wave) is automatically adjusted properly once at each break between two subsequently appearing heating peaks, which is the interval when the bridge imbalance signal is measured. At the end of each break the bridge imbalance signal is kept on the output of the sample-and-hold amplifier. This signal compared with the generator output voltage provides the square wave for the switching transistor. The application of this circuit for a thermal ionization mass spectrometry is simple and straightforward. The filament temperature is set by two decade low-ohm resistors. Long-term variance of the ion current is approximately 5 times lower than that obtained by use of a commercial voltage stabilizer for the filament supply. It is shown theoretically that stabilization of the filament resistance results in the lowest possible variance of temperature.