Maximal σ‐polynomials of connected 3‐chromatic graphs

In the set of graphs of order n and chromatic number k the following partial order relation is defined. One says that a graph G is less than a graph H if c_i(G) ≤ c_i(H) holds for every i, k ≤ i ≤ n and at least one inequality is strict, where c_i(G) denotes the number of i‐color partitions of G. In this paper the first ? n/2 ? levels of the diagram of the partially ordered set of connected 3‐chromatic graphs of order n are described. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 210–222, 2003     

Farkas-type results for fractional programming problems

Considering a constrained fractional programming problem, within the present paper we present some necessary and sufficient conditions, which ensure that the optimal objective value of the considered problem is greater than or equal to a given real constant. The desired results are obtained using the Fenchel–Lagrange duality approach applied to an optimization problem with convex or difference of convex (DC) objective functions and finitely many convex constraints. These are obtained from the initial fractional programming problem using an idea due to Dinkelbach. We also show that our general results encompass as special cases some recently obtained Farkas-type results.     

Synthesis and characterization of mid‐ and end‐chain functional telechelics by controlled polymerization methods and coupling processes

Well‐defined polystyrene‐ (PSt) or poly(ε‐caprolactone) (PCL)‐based polymers containing mid‐ or end‐chain 2,5 or 3,5‐ dibromobenzene moieties were prepared by controlled polymerization methods, such as atom transfer radical polymerization (ATRP) or ring opening polymerization (ROP). 1,4‐Dibromo‐2‐(bromomethyl)benzene, 1,3‐dibromo‐5‐(bromomethyl)benzene, and 1,4‐dibromo‐2,5‐di(bromomethyl)benzene were used as initiators in ATRP of styrene (St) in conjunction with CuBr/2,2′‐bipyridine as catalyst. 2,5‐Dibromo‐1,4‐(dihydroxymethyl)benzene initiated the ROP of ε‐caprolactone (CL) in the presence of stannous octoate (Sn(Oct)₂) catalyst. The reaction of these polymers with amino‐ or aldehyde‐functionalized monoboronic acids, in Suzuki‐type couplings, afforded the corresponding telechelics. Further functionalization with oxidable groups such as 2‐pyrrolyl or 1‐naphthyl was attained by condensation reactions of the amino or aldehyde groups with low molecular weight aldehydes or amines, respectively, with the formation of azomethine linkages. Preliminary attempts for the synthesis of fully conjugated poly(Schiff base) with polymeric segments as substituents, by oxidative polymerization of the macromonomers, are presented. All the starting, intermediate, or final polymers were structurally analyzed by spectral methods (¹H NMR, ¹³C NMR, and IR). © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 727–743, 2006     

Subbundles of maximal degree of the normal bundle of algebraic space curves almost complete intersection of special type

Summary LetX⊂P ³ be an irreducible smooth curve which is not a complete intersection. The main result of this paper shows that whenX is an a.c.i. of special type, i.e. its homogeneous ideal is generated by three polynomial of the same degreem, and additionallym>2, the subbundles of maximal degree of the normal bundle ofX inP ³ correspond to the singular points of maximal multiplicity of a plane curve which is the image ofX by a map (the linear system of the surfaces of minimal degree throughX). In particular this normal bundle is stable. The initial case of this family of curves, i.e. form=3, has been studied by E. Ballico-Ph. Ellia with different methods.

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Riassunto SiaX⊂P ³ una curva irriducibile e liscia che non è una completa intersezione. Il risultato principale di questa Nota mostra che quandoX è una almost completa intersezione di tipo speciale, cioè il suo ideale omogeneo è generato minimamente da 3 polinomi dello stesso gradom, e, inoltre,m>2, i sottofibrati di grado massimo del fibrato normale diX inP ³ corrispondono ai punti singolari di molteplicità massima di una curva piana che è l’immagine diX tramite una mappa (il sistema lineare delle superficie di grado minimo passanti perX). In particolare questo fibrato normale è stabile. Il caso iniziale di questa famiglia di curve, i.e. perm=3, è stato studiato da E. Ballico-Ph. Ellia con differenti metodi.

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This research is supported by GNSAGA (Italy).

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The main results of this paper have been the object of a talk at the meeting on ?Curves in Projective Space? held at Rocca di Papa in june 1985.     

Parameterization of peptide 13C carbonyl chemical shielding anisotropy in molecular dynamics simulations.

NMR chemical shielding anisotropy (CSA) relaxation is an important tool in the study of dynamical processes in proteins and nucleic acids in solution. Herein, we investigate how dynamical variations in local geometry affect the chemical shielding anisotropy relaxation of the carbonyl carbon nucleus, using the following protocol: 1) Using density functional theory, the carbonyl (13)C' CSA is computed for 103 conformations of the model peptide group N-methylacetamide (NMA). 2) The variations in computed (13)C' CSA parameters are fitted against quadratic hypersurfaces containing cross terms between the variables. 3) The predictive quality of the CSA hypersurfaces is validated by comparing the predicted and de novo calculated (13)C' CSAs for 20 molecular dynamics snapshots. 4) The CSA fluctuations and their autocorrelation and cross correlation functions due to bond-length and bond-angle distortions are predicted for a chemistry Harvard molecular mechanics (CHARMM) molecular dynamics trajectory of Ca(2+)-saturated calmodulin and GB3 from the hypersurfaces, as well as for a molecular dynamics (MD) simulation of an NMA trimer using a quantum mechanically correct forcefield. We find that the fluctuations can be represented by a 0.93 scaling factor of the CSA tensor for both R(1) and R(2) relaxations for residues in helix, coil, and sheet alike. This result is important, as it establishes that (13)C' relaxation is a valid tool for measurement of interesting dynamical events in proteins.     

Topological indices for molecular fragments and new graph invariants

Whereas the internal fragment topological index (IFTI) is calculated in the normal manner as for any molecule, the external fragment topological index (EFTI) is calculated so as to reflect the interaction between the excised fragment F and the remainder of the molecule (G-F). For selected topological indices (TIs), a survey of EFTI values, formulas and examples is presented. Some requirements as to the fragment indices are formulated and examined. In the discussion of the results, it is shown that for some TIs regularities exist in the dependence of EFTI values upon the branching of fragment F, or upon the marginal versus central position of the fragment F in the graph G. New vortex invariants can be computed as EFTI values for one-atom fragments over all graph vertices; by iteration, it is in principle possible to devise an infinite number of now vertex invariants.     

Unique description of chemical structures based on hierarchically ordered extended connectivities (HOC procedures). V. New topological indices,ordering of graphs,and recognition of graph similarity

The vertex numbering obtained by application of the HOC algorithm can be converted into two sequences of numbers: If each vertex starting with vertex 1 is only counted once, the sums of numberings of adjacent vertices form sequence S_i (i = 1?N), while the sums of S_i values form sequence M_i (i = 1?N). These two sequences can be used for (i) two new topological indices, ?? and ??, the latter being of extremely low degeneracy, and the former correlating with boiling points of alkanes; (ii) a criterion based on sequence S_i for ordering graphs which possess the same number N of vertices; and (iii) a quantitative measure, also based on sequence S_i, for appreciating the similarity or dissimilarity of pairs of graphs. Comparisons with other topological indices, ordering criteria, and similarity measures for graphs show that the newly devised procedures compare favorably with those known previously.     

Development of novel antioxidants: design,synthesis, and reactivity

We are attempting to develop novel synthetic antioxidants aimed at retarding the effects of free-radical induced cell damage. In this paper we discuss the design strategy and report the synthesis of seven novel antioxidants, including six catechols and a benzylic phenol. The bond dissociation enthalpy (BDE) for the most active (weakest) OH bond in each molecule was calculated by theoretical methods, as well as the BDE for the semiquinone radical. Reaction rates with the nitrogen-centered free radical DPPH(*) were measured in ethyl acetate. The log of k(DPPH) for bimolecular reaction correlated well with the primary BDE. The correlation between rate constants and calculated BDEs shows that the BDE is a good predictor of antioxidant activity with DPPH(*), suggesting that our design criteria are useful and that these compounds should undergo further testing in cell cultures and in animal models.     

Synthesis and characterization of PAni–SiO2 and PTh–SiO2 nanocomposites' thin films by plasma polymerization

In the present work, we explore the possibility to deposit polyaniline–silicon dioxide (PAni–SiO₂) and polythiophene–silicon dioxide (PTh–SiO₂) nanocomposites through a plasma polymerization route. The films were generated by spraying of mixtures of nano-sized silica particles dispersed in the liquid monomer into a plasma stream of the DC-plasma discharge reactor. The silica in the resulted polymer matrix changes the conduction mechanisms varying from ohmic to ballistic and traps inducing the space charged limited currents (SCLC). The silica modifies the morphology and composition of the deposited films.     

Formation of Iron Macro-Spheres in Plasma

In this paper the formation mechanism of iron macro-spheres in a plasma medium is dealt with, including the conditions under which such spheres are formed. The geometry of the spheres referred to above depends on the main technological parameters involved in the production of pores. Conditions under which pores occur within macro-spheres are also established. The radii of these pores are sensitive to the velocity distribution within the plasma jet section