Shortest Path Auction Algorithm Without Contractions Using Virtual Source Concept

In this paper, the problem of finding a shortest path tree rooted at a given source node on a directed graph (SPT) is considered. A new efficient algorithm based on a primal-dual approach is presented, which improves both the convergence and the complexity of the best known auction-like algorithm. It uses the virtual source (VS) concept based on the following consideration: when a node i is visited for the first time by any algorithm which preserves verified the dual admissibility conditions, then the shortest path (SP) from the source node to i is found. Therefore, the SP from the source to the remaining nodes may be computed by considering i as a virtual source.We propose a very efficient implementation of an auction-like algorithm that uses this concept and enables us to obtain a computational cost of O(n ²), where n is the number of nodes.Numerical experimentsare reported showing that the new method outdoes previously proposed auction-like algorithms and is highly competitive with other state-of-art SP approaches.     

On constant elasticity of substitution – Constant elasticity of transformation Directional Distance Functions

This paper aims to present non-linear CES (Constant Elasticity of Substitution)–CET (Constant Elasticity of Transformation) Directional Distance Functions. These measures inherit the structure of the standard Directional Distance Functions and that of the CES–CET technology. These functions allow non-parametric estimation of efficiency scores through linear programming method. Besides, the CES –CET technology gives the opportunity to explore α-returns to scale assumption for the new distance functions. The duality theory is investigated through pseudo profit, cost and revenue functions. The dual standpoint provides non-linear adjusted prices that can occur into non-linear pricing practices. An application is proposed to give an illustrative example of the primal CES–CET Directional Distance Functions.     

Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme.     

An Existence Result for a Problem with Critical Growth and Lack of Strict Convexity

We prove the existence of a nontrivial solution for a quasilinear elliptic equation involving a nonlinearity having critical growth and a convex principal part, which is not required to be strictly convex. Supported by MURST, Project “Variational Methods and Nonlinear Differential Equations”.     

CO(2) Fixation by Novel Copper(II) and Zinc(II) Macrocyclic Complexes. A Solution and Solid State Study

Solutions containing Zn(II) and Cu(II) complexes with [15]aneN(3)O(2) rapidly adsorb atmospheric CO(2) to give {[ZnL](3)(&mgr;(3)-CO(3))}.(ClO(4))(4) (2) and {[CuL](3)(&mgr;(3)-CO(3))}.(ClO(4))(4) (4) complexes. The crystal structures of both complexes have been solved (for 2, space group R3c, a, b = 22.300(5) ?, c = 17.980(8) ?, V = 7743(4) ?(3), Z = 6, R = 0.0666, R(w)(2) = 0.1719; for 4, space group R3c, a, b = 22.292(7) ?, c = 10.096(8) ?, V = 7788(5) ?(3), Z = 6, R = 0.0598, R(w)(2) = 0.1611), and the spectromagnetic behavior of 4 has been studied. In both compounds a carbonate anion triply bridges three metal cations. Each metal is coordinated by one oxygen of the carbonate, three nitrogens, and an oxygen of the macrocycle; the latter donor weakly interacts with the metals. Although the two compounds are isomorphous, they are not isostructural, because the coordination geometries of Zn(II) in 2 and Cu(II) in 4 are different. The mixed complex {[CuZn(2)L(3)](&mgr;(3)-CO(3))}.(ClO(4))(4) has been synthesized. X-ray analysis (space group R3c, a, b = 22.323(7) ?, c = 17.989(9) ?, V = 7763(5) ?(3), Z = 6, R = 0.0477, R(w)(2) = 0.1371) and EPR measurements are in accord with a &mgr;(3)-carbonate bridging one Cu(II) and two Zn(II) ions in {[CuZn(2)L(3)](&mgr;(3)-CO(3))}(4+). Both the Zn(II) and Cu(II) cations exhibit the same coordination sphere, almost equal to that found in the trinuclear Zn(II) complex 2. The systems Zn(II)/L and Cu(II)/Lhave been studied by means of potentiometric measurements in 0.15 mol dm(-)(1) NaCl and in 0.1 mol dm(-)(3) NaClO(4) aqueous solutions; the species present in solution and their stability constants have been determined. In both systems [ML](2+) species and hydroxo complexes [M(II)LOH](+) (M = Zn, Cu) are present in solution. In the case of Cu(II), a [CuL(OH)(2)] complex is also found. The process of CO(2) fixation is due to the presence of such hydroxo-species, which can act as nucleophiles toward CO(2). In order to test the nucleophilic ability of the Zn(II) complexes, the kinetics of the promoted hydrolysis of p-nitrophenyl acetate has been studied. The [ZnLOH](+) complex promotes such a reaction, where the Zn(II)-bound OH(-) acts as a nucleophile to the carbonyl carbon. The equilibrium constants for the addition of HCO(3)(-) and CO(3)(2)(-) to the [ZnL](2+) complex have been potentiometrically determined. Only [ML(HCO(3))](+) and [ML(CO(3))] species are found in aqueous solution. A mechanism for the formation of {[ML](3)(&mgr;(3)-CO(3))}.(ClO(4))(4) is suggested.     

A Formal Total Synthesis of (+)-Methyl Trachyloban-18-oate and (+)-Methyl 16-Oxo-17-norkauran-18-oate: Regio- and Diastereoselective Preparation of Methyl (13S)-13-Hydroxyisoatisiren-18-oate from (−)-Abietic Acid

A novel preparation of methyl (13S)-13-hydroxyisoatisiren-18-oate ( 4 ), a key-intermediate in a synthesis of (+)-methyl trachyloban-18-oate ((+)- 1 ), from (?)-abietic acid, is described. Since (?)- 1 has been previously converted into (?)-methyl 16-oxo-17-norkauran-18-oate ((?)- 16 ), our preparation of 4 constitutes also a formal total synthesis, from (?)-abietic acid, of (+)- 16 . Key steps in this approach were the allene photoaddition to podocarp-8(14)-en-13-one ( 5 ) and the conversion of the endo-toluene-4-sulfonate 11 into the exo-benzoate 12b .     

Water-soluble gold nanoparticles protected by fluorinated amphiphilic thiolates

The preparation and the properties of gold nanoparticles (Au NPs) protected by perfluorinated amphiphiles are described. The thiols were devised to form a perfluorinated region close to the gold surface and to have a hydrophilic portion in contact with the bulk solvent to impart solubility in water. The monolayer protected clusters were prepared, in an homogeneous phase using sodium thiolates because of the low nucleophilicity of the alpha-perfluorinated thiols, and fully characterized with (1)H, (19)F NMR spectrometry, IR and UV-vis absorption spectroscopies, transmission electron microscopy (TEM), thermogravimetric analysis (TGA), and X-ray photoelectron spectroscopy (XPS). Au NPs with core diameters ranging from 1.6 to 2.9 nm, depending on the reaction conditions, were obtained. Water-soluble NPs (MPC-F8-PEGs) were obtained with the thiol HS-F8-PEG ending with a short poly(ethylene glycol) unit (PEG-OMe 550), whereas thiols with shorter PEG chains give rise to NPs insoluble in water. MPC-F8-PEGs undergo an exchange reaction with amphiphilic alkyl thiols. ESR investigations, using a hydrophobic radical probe, indicate that the MPC-F8-PEG monolayer shows a greater hydrophobicity compared to the analogous hydrogenated monolayer.     

Marine derived polysaccharides for biomedical applications: chemical modification approaches

Polysaccharide-based biomaterials are an emerging class in several biomedical fields such as tissue regeneration, particularly for cartilage, drug delivery devices and gelentrapment systems for the immobilization of cells. Important properties of the polysaccharides include controllable biological activity, biodegradability, and their ability to form hydrogels. Most of the polysaccharides used derive from natural sources; particularly, alginate and chitin, two polysaccharides which have an extensive history of use in medicine, pharmacy and basic sciences, and can be easily extracted from marine plants (algae kelp) and crab shells, respectively. The recent rediscovery of poly-saccharidebased materials is also attributable to new synthetic routes for their chemical modification, with the aim of promoting new biological activities and/or to modify the final properties of the biomaterials for specific purposes. These synthetic strategies also involve the combination of polysaccharides with other polymers. A review of the more recent research in the field of chemical modification of alginate, chitin and its derivative chitosan is presented. Moreover, we report as case studies the results of our recent work concerning various different approaches and applications of polysaccharide-based biomaterials, such as the realization of novel composites based on calcium sulphate blended with alginate and with a chemically modified chitosan, the synthesis of novel alginate-poly(ethylene glycol) copolymers and the development of a family of materials based on alginate and acrylic polymers of potential interest as drug delivery systems.     

Reactions of indoles with nitrogen dioxide and nitrous acid in an aprotic solvent

The reaction of 2-phenyl- and 1-methyl-2-phenylindole with nitrogen dioxide or with nitrous acid (NaNO2-CH3COOH) in benzene leads mainly to the formation of the isonitroso and 3-nitroso indole derivatives, respectively. When reacted with nitrous acid, 1-methyl-2-phenylindole gives also the corresponding azo-bis-indole in good yields. The reaction of indole with nitrogen dioxide leads to 2-(indol-3-yl)-3H-indol-3-one as the main product together with small amounts of 2-(indol-3-yl)-3H-indol-3-oxime; whereas the major product obtained when the same indole is reacted with nitrous acid is represented by 2-(indol-3-yl)-3H-indol-3-oxime. The reaction of 3-alkyl substituted indoles with nitrogen dioxide is rather complex and results in the formation of different nitro indoles, whereas nitrosation is observed when nitrous acid is used. Crystal structures of 2-(indol-3-yl)-3H-indol-3-one and of 4-nitro-N-acetyltryptamine have been determined by X-ray analysis.