The Discounted Limit Theorems

The large deviation theorems, exponential inequalities and a non-uniform estimate of the Berry–Esséen theorem in a discounted version are proved.Dedicated to Professor Vytautas Statulevičius on the occasion of his 75th birthday.     

Statistical Analysis of the Effect of Mineral Admixtures on the Strength of the Interfacial Transition Zone

Microscopic evidence indicates that the thickness of the interfacial transition zone (ITZ) between the aggregate and the cement paste is modified when mineral admixtures partially replace portland cement. Unfortunately, there is limited information on the significance of these microscopic modifications to the mechanical properties of the ITZ. This research reports experimental results on the shear and tensile strength of the ITZ as affected by the addition of the following mineral admixtures: silica fume, fly ash, and natural pozzolan. Statistical analysis was used to identify the significant parameters affecting the tensile and shear strength of the ITZ. Experimental results indicate that not only does the incorporation of silica fume and fly ash increase the strength of the ITZ, these mineral admixtures have a greater influence on the strength increase of the ITZ than in the strength increase of the cement paste.     

Non-local approximation of the Mumford-Shah functional

The Mumford-Shah functional, introduced to study image segmentation problems, is approximated in the sense of -convergence by a sequence of non-local integral functionals. Received June 6, 1996 / Accepted July 11, 1996     

DRIFTS study of surface reactivity to NO2 by zinc nanoparticle aggregates and zinc hollow nanofibers

Zinc nanostructures synthesized with different morphologies from the same evaporation/condensation technique are studied with concern to surface reactivity to NO₂ by Diffuse Reflectance Infrared Fourier Transformed Spectroscopy (DRIFTS). Synthesis of nanopowders is obtained, according to previous work, by gas flow thermal evaporation at 540 °C of bulk Zn grains. Two types of Zn powders are obtained and studied in experiments. The first one is collected on the cold walls of the reactor as a deposit produced by thermophoretic effect. It is constituted by grains (∼10 μm) originated by the stratification of smaller aggregates (∼200 nm) and isolated primary particles (∼50 nm) born in the gas flow. The second type of powder is grown from the condensation of Zn chemical vapors within the expansion orifice of the quartz reactor after relatively long time (∼1 h) deposition process. It is constituted mainly by hollow Zn nanofibers with external and internal diameter about 100 and 60 nm. Preliminary characterization of the two types of powders is made by SEM, TEM, XRD. Thereafter, the two types of samples are studied by DRIFTS at variable temperature (VT). Comparison is made between the home-synthesized nanopowders with respect to commercial Zn standard dust. The Zn hollow nanofibers when exposed to NO₂ are found to exhibit dramatic reactivity, which is not observed at all either in the case of clustered aggregate zinc or of commercial Zn dust powders. Results indicate that, at increasing temperature from RT to 300 °C, the hollow nanofibers surface reacts distinctively with adsorbant gas NO₂, with contemporary formation of a progressively growing narrow absorption band at 2500 cm⁻¹ and contemporary depression of a doublet (∼1600-1628 cm⁻¹) band. In order to justify this striking spectral feature, we propose the occurring of a possible polymerization process at nanofibers surface where most probably as a consequence of pre-treatment and exposure to gas NO₂ a very thin film of ZnO is formed. The possible role of huge specific surface of hollow nanofibers as inferred by preliminary SEM, TEM, XRD studies is discussed.     

Estimation scheme for level-dependent uncertainty of analytical result: application for determination of 1-hydroxypyrene in urine

The estimation scheme of uncertainty of determination of 1-hydroxypyrene (1-OHP) in urine was developed analysing the main stages of the analytical procedure: (1) preparation of 1-OHP standards, (2) creation of the calibration curve for the high performance liquid chromatography (HPLC) analysis method with the evaluation of recovery, (3) measuring procedure of aliquot of urine, (4) adjusting the pH of aliquot and hydrolysis with enzyme, (5) solid phase extraction, (6) concentration of the extract, (7) injection of the extract to chromatograph and analysing by the HPLC method, (8) calculation of 1-OHP mass from the calibration curve, (9) calculation of 1-OHP concentration in urine. The evaluation of the uncertainty is based on quantification of individual components. Combined uncertainty was calculated using the law of propagation of uncertainties according to the EURACHEM/CITAC guidelines. Level dependence of the uncertainty arises from the calibration curve. The limits of detection and quantification were found to be equal to 0.03 and 0.1 ng/mL, respectively. The calculated expanded level-dependent uncertainty covers 47–27–25% within the concentration range 0.03–0.1–0.4 ng/mL with the materials and equipment used. These parameters could easily be recalculated according to the proposed scheme if there are some changes in the analysis procedure.     

A novel synthetic method for 2-arylmethyl substituted imidazolines and imidazoles from 2-aryl-1,1-dibromoethenes

Various 2-arylmethylimidazolines were prepared by treating readily available 2-aryl-1,1-dibromoethenes with ethylenediamine under mild conditions and further converted into the corresponding imidazoles smoothly with Swern oxidation.     

Structural basis for recognition of bacterial cell wall teichoic acid by pseudo-symmetric SH3b-like repeats of a viral peptidoglycan hydrolase

Endolysins are bacteriophage-encoded peptidoglycan hydrolases targeting the cell wall of host bacteria via their cell wall-binding domains (CBDs). The molecular basis for selective recognition of surface carbohydrate ligands by CBDs remains elusive. Here, we describe, in atomic detail, the interaction between the Listeria phage endolysin domain CBD500 and its cell wall teichoic acid (WTA) ligands. We show that 3′O-acetylated GlcNAc residues integrated into the WTA polymer chain are the key epitope recognized by a CBD binding cavity located at the interface of tandem copies of beta-barrel, pseudo-symmetric SH3b-like repeats. This cavity consists of multiple aromatic residues making extensive interactions with two GlcNAc acetyl groups via hydrogen bonds and van der Waals contacts, while permitting the docking of the diastereomorphic ligands. Our multidisciplinary approach tackled an extremely challenging protein–glycopolymer complex and delineated a previously unknown recognition mechanism by which a phage endolysin specifically recognizes and targets WTA, suggesting an adaptable model for regulation of endolysin specificity.

Combining genetic, biochemical and computational approaches, we elucidated the molecular mechanisms underlying the recognition of Listeria wall teichoic acid by bacteriophage-encoded SH3b repeats.     

New lower semicontinuity results for polyconvex integrals

Summary We study integral functionals of the formF(u, )= f(u)dx, defined foru C¹(;R ^k), R ⁿ . The functionf is assumed to be polyconvex and to satisfy the inequalityf(A) c₀¦(A)¦ for a suitable constant c₀ > 0, where (A) is then-vector whose components are the determinants of all minors of thek×n matrixA. We prove thatF is lower semicontinuous onC ¹(;R ^k) with respect to the strong topology ofL ¹(;R ^k). Then we consider the relaxed functional , defined as the greatest lower semicontinuous functional onL ¹(;R ^k ) which is less than or equal toF on C¹(;R ^k). For everyu BV(;R ^k) we prove that (u,) f(u)dx+c₀¦D^su¦(), whereDu=u dx+D^su is the Lebesgue decomposition of the Radon measureDu. Moreover, under suitable growth conditions onf, we show that (u,)= f(u)dx for everyu W^1,p(;R ^k), withp min{n,k}. We prove also that the functional (u, ) can not be represented by an inte- gral for an arbitrary functionu BV_loc(R ⁿ;R ^k). In fact, two examples show that, in general, the set function (u, ) is not subadditive whenu BV_loc(R ⁿ;R ^k), even ifu W _loc ^1,p (R ⁿ;R ^k) for everyp < min{n,k}. Finally, we examine in detail the properties of the functionsu BV(;R ^k) such that (u, )= f(u)dx, particularly in the model casef(A)=¦(A)¦.