Covering numbers of manifolds and critical points of a morse function

For a closed connected triangulatedn-manifoldM, we study some numerical invariants (namedcategory andcovering numbers) ofM which are strictly related to the topological structure ofM. We complete the classical results of 3-manifold topology and then we prove some characterization theorems in higher dimensions. Finally some applications are given about the minimal number of critical points (resp. values) of Morse functions defined on a closed connected smoothn-manifold. Work performed under the auspices of the G.N.S.A.G.A. of the C.N.R. and financially supported by the M.P.I. of Italy within the project “Geometria delle Varietà Differenziabili”.     

Online weighted flow time and deadline scheduling

In this paper we study some aspects of weighted flow time. We first show that the online algorithm Highest Density First is an O(1)-speed O(1)-approximation algorithm for P|r_i,pmtn|∑w_iF_i. We then consider a related Deadline Scheduling Problem that involves minimizing the weight of the jobs unfinished by some unknown deadline D on a uniprocessor. We show that any c-competitive online algorithm for weighted flow time must also be c-competitive for deadline scheduling. We then give an O(1)-competitive algorithm for deadline scheduling.     

Extremal problems involving isotropic sets and functions on spaces of rectangular matrices

Let \(\mathbb{M}_{m,n}\) be the linear space of real matrices of dimension m × n. A variational problem that arises quite often in applications is that of minimizing a real-valued function f on some feasible set \(\Upomega\subseteq \mathbb{M}_{m,n}.\) Matrix optimization problems of such a degree of generality are not always easy to deal with, especially if the decision variable is a high-dimensional rectangular matrix. Sometimes, it is possible to reduce the size and complexity of the matrix optimization problem in the presence of symmetry assumptions (isotropy, orthogonal invariance, etc.). This work establishes a localization result for the solutions to a class of extremal problems involving isotropic sets and functions.     

On solutions of second and fourth order elliptic equations with power-type nonlinearities

We study second and fourth order semilinear elliptic equations with a power-type nonlinearity depending on a power p$p$ and a parameter λ>0$\lambda >0$. For both equations we consider Dirichlet boundary conditions in the unit ball B⊂Rⁿ$B\subset {\mathbb{R}}^n$. Regularity of solutions strictly depends on the power p$p$ and the parameter λ$\lambda$. We are particularly interested in the radial solutions of these two problems and many of our proofs are based on an ordinary differential equation approach.     

Trace level vanadium determination using thermal lens spectrophotometry

Trace level vanadium determination is reported using a dual beam thermal lens spectrometer. The thermal lens was generated using an argon ion beam laser (pump beam) which was focused into a sample cuvette. The thermal lens signal (TLs) was monitored with a He-Ne laser beam and a photodiode detector. Multichannel averager software was developed for processing the transient TLs. The optimal set up, ensuring maximum sensitivity and linear calibration graphs was obtained using experimental design techniques. Under optimized conditions, the detection limits for aqueous and ethanol-water (2+3 v/v) and (4+1 v/v) vanadium complex solutions were, respectively, 0.0071 mg/l, 0.0065 and 0.0039 mg/l.     

Mechanically Interlocked Single‐Wall Carbon Nanotubes

Extensive research has been devoted to the chemical manipulation of carbon nanotubes. The attachment of molecular fragments through covalent‐bond formation produces kinetically stable products, but implies the saturation of some of the C? C double bonds of the nanotubes. Supramolecular modification maintains the structure of the SWNTs but yields labile species. Herein, we present a strategy for the synthesis of mechanically interlocked derivatives of SWNTs (MINTs). In the key rotaxane‐forming step, we employed macrocycle precursors equipped with two π‐extended tetrathiafulvalene SWNT recognition units and terminated with bisalkenes that were closed around the nanotubes through ring‐closing metathesis (RCM). The mechanically interlocked nature of the derivatives was probed by analytical, spectroscopic, and microscopic techniques, as well as by appropriate control experiments. Individual macrocycles were observed by HR STEM to circumscribe the nanotubes.     

Electrochemically controlled formation/dissociation of phosphonate-cavitand/methylpyridinium complexes

The phosphorus-bridged cavitand 1 self-assembles very efficiently in CH2Cl2 with either the monopyridinium guest 2+ or the bispyridinium guest 3(2+). In the first case a 1:1 complex is obtained, whereas in the second case both 1:1 and 2:1 host-guest complexes are observed. The association between 1 and either one of the guests causes the quenching of the cavitand fluorescence; in the case of the adduct between 1 and 3(2+), the fluorescence of the latter is also quenched. Cavitand complexation is found to affect the reduction potential values of the electroactive guests. Voltammetric and spectroelectrochemical measurements show that upon one-electron reduction both guests are released from the cavity of 1. Owing to the chemical reversibility of such redox processes, the supramolecular complexes can be re-assembled upon removal of the extra electron from the guest. Systems of this kind are promising for the construction of switchable nanoscale devices and self-assembling supramolecular materials, the structure and properties of which can be reversibly controlled by electrochemical stimuli.     

A rapid and reliable size-exclusion chromatographic method for determination of kojic dipalmitate in skin-whitening cosmetic products

A size-exclusion chromatographic method has been developed to determine the relatively novel skin-whitening agent called kojic dipalmitate (KDP) in skin-whitening cosmetic products. Preliminary experiments were carried out in order to select the solvent for standard and sample solution, and also for mobile phase composition. A PLGel Mixed-D (polystyrene/divinylbenzene co-polymer) column and isocratic mobile phase of pure tetrahydrofuran (at 1.5 mL min(-1) flow rate) were used. Detection was carried out by means of an UV/vis spectrometry detector set at 248 nm. A study of interferences reveals that KDP can be determined without interferences coming from cosmetic matrices. Most other cosmetic ingredients usually employed in skin-whitening cosmetic products, such as other whitening agents and common UV filters, do not interfere. The accuracy and precision of the proposed method was tested by the analysis of six laboratory-made and five commercial skin-whitening cosmetic samples. The sensitivity and limit of detection (3 microg mL(-1)) obtained are suitable for the analysis of this type of samples. The chromatographic run takes less than 8 min to complete. All these features make the method easy to apply to quality control in the cosmetic industry.     

Green Synthesis of Gold and Silver Nanoparticles Using Leaf Extract of Capsicum chinense Plant

So far, several studies have focused on the synthesis of metallic nanoparticles making use of extracts from the fruit of the plants from the genus Capsicum. However, as the fruit is the edible, and highly commercial, part of the plant, in this work we focused on the leaves, a part of the plant that is considered agro-industrial waste. The biological synthesis of gold (AuNPs) and silver (AgNPs) nanoparticles using aqueous extracts of root, stem and leaf of Capsicum chinense was evaluated, obtaining the best results with the leaf extract. Gold and silver nanoparticles synthesized using leaf extract (AuNPs-leaf and AgNPs-leaf, respectively) were characterized by UV-visible spectrophotometry (UV-Vis), Fourier Transform Infrared Spectroscopy with Attenuated Total Reflection (FTIR-ATR), X-ray Photoelectron Spectroscopy (XPS), Ultra Hight Resolution Scanning Electron Microscopy coupled to Energy-Dispersive X-ray spectroscopy (UHR-SEM-EDX) and Transmission Electron Microscopy (TEM), and tested for their antioxidant and antimicrobial activities. In addition, different metabolites involved in the synthesis of nanoparticles were analyzed. We found that by the use of extracts derived from the leaf, we could generate stable and easy to synthesize AuNPs and AgNPs. The AuNPs-leaf were synthesized using microwave radiation, while the AgNPs-leaf were synthesized using UV light radiation. The antioxidant activity of the extract, determined by ABTS, showed a decrease of 44.7% and 60.7% after the synthesis of the AuNPs-leaf and AgNPs-leaf, respectively. After the AgNPs-leaf synthesis, the concentration of polyphenols, reducing sugars and amino acids decreased by 15.4%, 38.7% and 46.8% in the leaf extract, respectively, while after the AuNPs-leaf synthesis only reducing sugars decreased by 67.7%. These results suggest that these groups of molecules are implicated in the reduction/stabilization of the nanoparticles. Although the contribution of these compounds in the synthesis of the AuNPs-leaf and the AgNPs-leaf was different. Finally, the AgNPs-leaf inhibited the growth of S. aureus, E. coli, S. marcescens and E. faecalis. All of them are bacterial strains of clinical importance due to their fast antibiotic resistance development.     

Isotope dilution-thermal ionisation mass spectrometric analysis for tin in a fly ash material

Isotope dilution-thermal ionisation mass spectrometry (ID-TIMS) analysis has been applied to the determination of tin in a fly ash sample supplied by the EC Joint Research Centre (Ispra, Italy). The proposed procedure includes the silica gel/phosphoric acid technique for tin thermal ionisation activation and a strict heating protocol for isotope ratio measurements. Instrumental mass discrimination factor has been previously determined measuring a natural tin standard solution. Spike solution has been prepared from ¹¹²Sn-enriched metal and quantified by reverse isotope dilution analysis. Two sample aliquots were spiked and tin was extracted with 4.5 M HCl during 25 min ultrasound exposure time. Due to the complex matrix of this fly ash material, a two-step purification stage using ion-exchange chromatography was required prior TIMS analysis. Obtained results for the two sample-spike blends (10.11 ± 0.55 and 10.50 ± 0.64 μmol g⁻¹) are comparable, both value and uncertainty. Also a good reproducibility is observed between measurements. The proposed ID-TIMS procedure, as a primary method and due to the lack of fly ash reference materials certified for tin content, can be used to validate more routine methodologies applied to tin determination in this kind of samples.