Area-preserving approximations of polygonal paths

Let P be an x-monotone polygonal path in the plane. For a path Q that approximates P let W_A(Q) be the area above P and below Q, and let W_B(Q) be the area above Q and below P. Given P and an integer k, we show how to compute a path Q with at most k edges that minimizes W_A(Q)+W_B(Q). Given P and a cost C, we show how to find a path Q with the smallest possible number of edges such that W_A(Q)+W_B(Q)C. However, given P, an integer k, and a cost C, it is NP-hard to determine if a path Q with at most k edges exists such that max{W_A(Q),W_B(Q)}C. We describe an approximation algorithm for this setting. Finally, it is also NP-hard to decide whether a path Q exists such that |W_A(Q)−W_B(Q)|=0. Nevertheless, in this error measure we provide an algorithm for computing an optimal approximation up to an additive error.     

On the best Sobolev trace constant and extremals in domains with holes

We study the dependence on the subset A⊂Ω of the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. First we find that there exists an optimal subset that makes the trace constant smaller among all the subsets with prescribed and positive Lebesgue measure. In the case that Ω is a ball we prove that there exists an optimal hole that is spherically symmetric. In the case p=2 we prove that every optimal hole is spherically symmetric. Then, we study the behavior of the best constant when the hole is allowed to have zero Lebesgue measure. We show that this constant depends continuously on the subset and we discuss when it is equal to the Sobolev trace constant without the vanishing restriction.     

Immunoaffinity chromatographic isolation of prostate-specific antigen from seminal plasma for capillary electrophoresis analysis of its isoforms

Prostate-specific antigen (PSA) concentration in serum has been the biomarker employed for prostate cancer diagnosis in the last two decades. However, new more specific biomarkers allowing a better differentiation of cancer from non-malignant prostate diseases are necessary. Glycosylation of PSA gives rise to different forms of the protein which can be separated into several isoforms by analytical techniques, such as CE. Because PSA glycosylation is influenced by pathological conditions, the CE pattern of PSA isoforms could be different in prostate cancer than in non-malignant prostate diseases. To study this CE pattern of PSA, prior purification of the protein from the biological fluid is mandatory. In this study an immunoaffinity chromatography method which allows PSA purification without altering the CE pattern is developed. An in-house prepared column produced with commercial anti-PSA antibodies is employed. The use of 1 M propionic acid as elution agent provides higher than 40% recovery of high purity PSA. CE analysis of PSA immunopurified from seminal plasma of a healthy individual shows the same 8 peaks as the commercially available PSA standard. Sample preparation only requires dilution with phosphate buffered saline prior to immunoaffinity purification. High repeatability for the sample preparation step was achieved (RSD% for percentage of corrected peak area in the range 0.6–5.3 for CE analysis of three independently purified seminal plasma aliquots compared to range 0.8–4.9 for a given aliquot analyzed three times by CE). IAC of five microliters seminal plasma provided enough PSA to achieve signal/noise ratio larger than 5 for the smallest CE isoforms.     

Non-invasive NMR stratigraphy of a multi-layered artefact: an ancient detached mural painting

NMR stratigraphy was used to investigate in situ, non-destructively and non-invasively, the stratigraphy of hydrogen-rich layers of an ancient Nubian detached mural painting. Because of the detachment procedure, a complex multi-layered artefact was obtained, where, besides layers of the original mural painting, also the materials used during the procedure all became constitutive parts of the artefact. NMR measurements in situ enabled monitoring of the state of conservation of the artefact and planning of minimum representative sampling to validate results obtained in situ by solid-state NMR analysis of the samples. This analysis enabled chemical characterization of all organic materials. Use of reference compounds and prepared specimens assisted data interpretation.

Effects of Humidity,Temperature and Bismuth Electrodeposition on Electroanalytical Performances of Nafion‐coated Printed Electrodes for Cd2+ and Pb2+ Detection

The synergistic use of Nafion polymeric membrane and in situ electrodeposited bismuth film is a worthwhile strategy to develop electrochemical sensors for the detection of Cd²⁺ and Pb²⁺. However, Nafion thin films morphological and conductivity properties have a strong dependence on the environmental conditions, such as relative humidity and temperature, while the bismuth in situ electroplating can affect the repeatability of measurements. With the aim to overcome these drawbacks, the effects of the storage environmental conditions were investigated to improve the morphological stability and electroanalytical performances of Nafion film‐based sensor for the detection of Cd²⁺ and Pb²⁺. Nafion‐coated graphite‐based screen‐printed electrodes were stored at different humidity and temperature conditions and characterised by using square wave anodic stripping voltammetry, cyclic voltammetry, electrochemical impedance spectroscopy, and scanning electron microscopy. Significant differences were observed at the varying of humidity conditions, with an enhancement of sensor electrochemical performances at lower humidity. Furthermore, different approaches for bismuth in situ electrodeposition on Nafion‐coated screen‐printed electrodes were compared by using overlap or removal approach. This study disclosed considerable differences in the electrochemical performances and morphology of the resulting bismuth‐sensor, obtaining an enhancement of the working stability for the removal approach.     

Unsaturated alkoxy‐substituted poly(p‐phenylene 1,3,4‐oxadiazole)s: Synthesis and chemical–physical characterization

A new series of alkoxy‐substituted poly(p‐phenylene 1,3,4‐oxadiazole)s modified by the insertion of small percentages of various comonomers were synthesized through the precursor polyhydrazides. The comonomers used contained trans double bonds or meta‐alkoxy‐substituted aromatic rings to improve the solubility of the final polymers. The synthesized copolymers were chemically characterized by ¹H NMR and Fourier transform infrared spectroscopy. In some cases, the copolymers really showed improved solubility in organic solvents. The ¹⁵N solid‐state NMR technique was applied to examine the degree of conversion from the precursor polyhydrazides to the final polymers, which determined the effective conjugated length in the target polyoxadiazoles. Thermal stability and structural characteristics of all the polymers as well as a preliminary investigation on the optical properties of polyoxadiazoles are also reported. The copolymers retained high absorbance in the UV region and high transmission in the whole telecommunication range. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3916–3928, 2003     

A simple proof that super-reflexive spaces are -spaces

We demonstrate the title.

     

Incorporation of chemical functionalities in the framework of mesoporous silica

Mesoporous silica, which shows well-defined pore systems, tunable pore diameters (2-30 nm), narrow pore size distributions and high surface areas (>600 m(2) g(-1)), is frequently modified using different methodologies (including in situ and post-synthetic strategies) to introduce various chemical functionalities useful in applications like catalysis, separation, drug delivery, and sensing. This contribution aims to provide a critical overview of the various strategies to incorporate chemical functionalities in mesoporous silica highlighting the advantages of the in situ methods based on the bottom-up construction of mesoporous silica containing various chemical functionalities in its structure.