Trisecant lemma for nonequidimensional varieties

Let X be an irreducible projective variety over an algebraically closed field of characteristic zero. For ≥ 3, if every (r−2)-plane , where the x _i are generic points, also meets X in a point x _r different from x ₁,..., x _r−1, then X is contained in a linear subspace L such that codim _L X ≥ r − 2. In this paper, our purpose is to present another derivation of this result for r = 3 and then to introduce a generalization to nonequidimensional varieties. For the sake of clarity, we shall reformulate our problem as follows. Let Z be an equidimensional variety (maybe singular and/or reducible) of dimension n, other than a linear space, embedded into ℙ^r, where r ≥ n + 1. The variety of trisecant lines of Z, say V _1,3(Z), has dimension strictly less than 2n, unless Z is included in an (n + 1)-dimensional linear space and has degree at least 3, in which case dim V _1,3(Z) = 2n. This also implies that if dim V _1,3(Z) = 2n, then Z can be embedded in ℙ ^{n + 1}. Then we inquire the more general case, where Z is not required to be equidimensional. In that case, let Z be a possibly singular variety of dimension n, which may be neither irreducible nor equidimensional, embedded into ℙ^r, where r ≥ n + 1, and let Y be a proper subvariety of dimension k ≥ 1. Consider now S being a component of maximal dimension of the closure of . We show that S has dimension strictly less than n + k, unless the union of lines in S has dimension n + 1, in which case dim S = n + k. In the latter case, if the dimension of the space is strictly greater than n + 1, then the union of lines in S cannot cover the whole space. This is the main result of our paper. We also introduce some examples showing that our bound is strict. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 2, pp. 71–87, 2006.     

Metal Catalyzed Polymerization: From Stereoregular Poly(α-olefins) to Tailor-Made Biodegradable/Biorenewable Polymers and Copolymers

Metal catalyzed polymerizations are among the most important chemical reactions, accounting for the production of about 400 million tons per year of polymeric materials, 50 % of which are polyolefins. The CIRCC research units at the University of Salerno, founded by the late Professor Adolfo Zambelli, a coworker of Giulio Natta and a pioneer in the studies of stereospecific polymerization catalysts, has a consolidated expertise in this field. Although often considered a “mature” area of research, olefin polymerization catalysis continues to drive great interest of both industrial and academic scientists. On the other hand, strong political and economic pressure toward the development of “green” and possibly biodegradable alternatives to olefin-based polymers stimulated our group to direct increasing research efforts in the area of sustainable polymers. In this perspective, we focus on the most recent work from the CIRCC research units involved in homogeneous catalysis for polymerization of a variety of monomers, with the aim to address how the concepts and the expertise developed for olefin polymerization can be applied to the development of different metal-catalyzed polymerizations and copolymerizations. Of course, although the results are discussed in the frame of the most important literature contributions, a comprehensive review of such a wide and diversified topic is out of the scope of the paper. References to reviews covering the different types of metal catalyzed polymerizations are provided in each chapter.     

Synthesis and characterization of a novel nano-Fe<Subscript>3</Subscript>O<Subscript>4</Subscript>-copoly[(styrene/acrylic acid)/grafted ethylene oxide and its application as a magnetic and recyclable phase-transfer catalyst in the preparation of β-azido alcohols and β-nitro alcohols

A facile method was developed for the synthesis of β-azido alcohols and β-nitro alcohols in the presence of a novel nano-Fe₃O₄-copoly[(styrene/acrylic acid)/grafted ethylene oxide (nano-Fe₃O₄-PS-Co-[PAA-g-PEG]) as a phase-transfer catalyst in water. The catalyst was characterized with IR, SEM, and TGA. This procedure offers several advantages, including excellent regioselectivity, high yields, short reaction times, a recyclable catalyst, easy separation of the catalyst through an external magnet, and easy workup.     

Evaluation of configurational entropy methods from peptide folding-unfolding simulation

A 4-micros molecular dynamics simulation of the second beta-hairpin of the B1 domain of streptococcal protein G is used to characterize the free energy surface and to evaluate different configurational entropy estimators. From the equilibrium folding-unfolding trajectory, 200 000 conformers are clustered according to their root-mean-square deviation (RMSD). The height of the free energy barrier between pairs of clusters is found to be significantly correlated with their pairwise RMSD. Relative free energies and relative configurational entropies of the clusters are determined by explicit evaluation of the partition functions of the different clusters. These entropies are used to evaluate different entropy estimators for the largest 20 clusters as well as a subensemble comprising exclusively extended conformers. It is found that the quasi-harmonic entropy estimator operating in dihedral angle space performs better than the one using Cartesian coordinates. A recent generalization of the quasi-harmonic approach that computes Shannon entropies of probability distributions obtained by projecting the conformers along the eigenvectors of the covariance matrix performs similarly well. For the best entropy estimators, a linear correlation coefficient between 0.92 and 0.97 is found. Unexpectedly, when correlations between dihedral angles are neglected, the agreement with the reference entropies improved.     

Synthesis of 4‐phenylbutyl‐branched polyethylene from an ethylene‐styrene feed by a half‐titanocene catalyst

Copolymerization of ethylene and styrene with the catalytic system Cp*TiMe₃‐B(C₆F₅)₃ under suitable conditions affords a new polymer having a polyethylenic backbone with 4‐phenyl‐1‐butyl branches as the main product. This unexpected result has been ascribed to the multi‐site nature of the catalytic system, containing a species able to co‐oligomerize ethylene and styrene to 6‐phenyl‐1‐hexene (which was actually identified in the polymerization mixture), and another species able to copolymerize the latter with ethylene.     

Study on the Interaction of the CpG Alternating DNA with CdTe Quantum Dots

A novel sensitive method for detection of DNA methylation was developed with thioglycollic acid (TGA)-capped CdTe quantum dots (QDs) as fluorescence probes. Recognition of methylated DNA sites would be useful strategy due to the important roles of methylation in disease occurrence and developmental processes. DNA methylation occurs most often at cytosine-guanine sites (CpG dinucleotides) of gene promoters. The QDs significantly interacted with hybridized unmethylated and methylated DNA. The interaction of CpG rich methylated and unmethylated DNA hybrid with quantum dots as an optical probe has been investigated by fluorescence spectroscopy and electrophoresis assay. The fluorescence intensity of QDs was highly dependent to unmethylated and methylated DNA. Specific site of CpG islands of Adenomatous polyposis coli (APC), a well-studied tumor suppressor gene, was used as the detection target. Under optimum conditions, upon the addition of unmethylated dsDNA, the fluorescence intensity increased in linear range from 1.0?×?10^??10 to 1.0?×?10^??6M with detection limit of 6.2?×?10^??11 M and on the other hand, the intensity of QDs showed no changes with addition of methylated dsDNA. We also demonstrated that the unmethylated and methylated DNA and QDs complexes showed different mobility in electrophoresis assay. This easy and reliable method could distinguish between methylated and unmethylated DNA sequences.     

Biocompatibility Study of Electrospun Nanocomposite Membranes Based on Chitosan/Polyvinyl Alcohol/Oxidized Carbon Nano-Onions

In recent decades, the number of patients requiring biocompatible and resistant implants that differ from conventional alternatives dramatically increased. Among the most promising are the nanocomposites of biopolymers and nanomaterials, which pretend to combine the biocompatibility of biopolymers with the resistance of nanomaterials. However, few studies have focused on the in vivo study of the biocompatibility of these materials. The electrospinning process is a technique that produces continuous fibers through the action of an electric field imposed on a polymer solution. However, to date, there are no reports of chitosan (CS) and polyvinyl alcohol (PVA) electrospinning with carbon nano-onions (CNO) for in vivo implantations, which could generate a resistant and biocompatible material. In this work, we describe the synthesis by the electrospinning method of four different nanofibrous membranes of chitosan (CS)/(PVA)/oxidized carbon nano-onions (ox-CNO) and the subdermal implantations after 90 days in Wistar rats. The results of the morphology studies demonstrated that the electrospun nanofibers were continuous with narrow diameters (between 102.1 nm ± 12.9 nm and 147.8 nm ± 29.4 nm). The CS amount added was critical for the diameters used and the successful electrospinning procedure, while the ox-CNO amount did not affect the process. The crystallinity index was increased with the ox-CNO introduction (from 0.85% to 12.5%), demonstrating the reinforcing effect of the nanomaterial. Thermal degradation analysis also exhibited reinforcement effects according to the DSC and TGA analysis, with the higher ox-CNO content. The biocompatibility of the nanofibers was comparable with the porcine collagen, as evidenced by the subdermal implantations in biological models. In summary, all the nanofibers were reabsorbed without a severe immune response, indicating the usefulness of the electrospun nanocomposites in biomedical applications.     

Polymerization of α-olefins promoted by zirconium complexes bearing bis(phenoxy-imine) ligands with ortho-phenoxy halogen substituents

New fluorinated bis(phenoxy-imine)zirconium complexes bearing halogen substituents in the ortho and para positions of the phenolate rings, bis[N-(3,5-dibromosalycilidene)-2,3,4,5,6-pentafluoroaniline]-Zr(IV) dichloride (1) and bis[N-(3,5-dichlorosalycilidene)-2,3,4,5,6-pentafluoroaniline]-Zr(IV) dichloride (2) have been synthesized and used as precatalysts in the polymerization of propylene and 1-hexene. Their catalytic behaviour was compared with that of the analogous fluorinated zirconium complexes bearing alkyl groups in the same positions of the phenolate rings to investigate the effects produced by the introduction of additional electron-withdrawing halogen substituents. Complexes 1 and 2 produce stereoirregular, slightly syndiotactic enriched polypropylenes showing enhanced catalytic activities and an improved primary regioselectivity. Both catalysts promote efficiently the oligomerization of 1-hexene to atactic and regioregular oligomers. Interestingly for both the studied monomers it is possible to control the molecular weights and the structures of end groups of the produced polymeric chains by an appropriate choice of the cocatalyst. Functionalization reactions of the unsaturated polymeric chains selectively produced are also reported.     

Synthesis of collagen-like sequential polypeptides containing O-phospho-L-hydroxyproline and preparation of electrospun composite fibers for possible dental application

A synthetic route is described for collagen-like polypeptides constructed from O-phospho-L-hydroxyproline [Hyp(PO(3)H(2))] residues. Using the synthetic polypeptides and a natural protein, gelatin, fine fibers and their network structures (ESNWs) were prepared via electrospinning. The composite ESNWs can induce the mineralization of calcium phosphate. The phosphoryl groups of the Hyp(PO(3)H(2)) residues affect both the crystalline phase and amount of the calcium phosphate, depending on the chemical structure in the repeating sequence. The composite ESNWs can be developed as a biocompatible replacement of the extracellular matrix of hard tissues, and thus can be applied as dental materials for restoration of dental cavities or as a sealant for pits and fissures.     

Optimum design of dynamic vibration absorbers for a beam, based on H ∞ and H 2 Optimization

The solutions to H _∞ and H ₂ optimization problems of a variant dynamic vibration absorber (DVA) applied to suppress vibration in beam structures are derived analytically. The H _∞ optimum parameters such as tuning frequency and damping ratios are expressed based on fixed-point theory to minimize the resonant vibration amplitude, as well as, the H ₂ optimum parameters to minimize the total vibration energy or the mean square motion of a beam under random force excitation as analytical formulas. The reduction in maximum amplitude responses and mean square motion of a beam using the traditional vibration absorber is compared with the proposed dynamic absorber. Numerical results show the non-traditional DVA under optimum conditions has better vibration suppression performance on beam structures than the traditional design of DVA. Furthermore, comparing H _∞ and H ₂ optimization procedures shows that for a beam under random force excitation, use of H₂ optimum parameters resulting in smaller mean square motion than the other optimization.