A fast procedure to immobilize polyethylene glycols in glass capillary columns

Polyethylene glycols can be immobilized in glass capillary columns by a new procedure involving covering the glass walls with a layer of graphitized carbon black and by flowing a mixture of the stationary phase and dicumyl peroxide. After curing and conditioning the column is ready for use. Excellent performance is reported for Carbowax 20 M and high molecular weight glycols. For other glycols the immobilized layer is less stable and can be washed out.     

Pseudo-orthogonality for graph 1-Laplacian eigenvectors and applications to higher Cheeger constants and data clustering

The data clustering problem consists in dividing a data set into prescribed groups of homogeneous data. This is an NP-hard problem that can be relaxed in the spectral graph theory, where the optimal cuts of a graph are related to the eigenvalues of graph 1-Laplacian. In this paper, we first give new notations to describe the paths, among critical eigenvectors of the graph 1-Laplacian, realizing sets with prescribed genus. We introduce the pseudo-orthogonality to characterize m₃(G), a special eigenvalue for the graph 1-Laplacian. Furthermore, we use it to give an upper bound for the third graph Cheeger constant h₃(G), that is, h₃(G) 6 m₃(G). This is a first step for proving that the k-th Cheeger constant is the minimum of the 1-Laplacian Raylegh quotient among vectors that are pseudo-orthogonal to the vectors realizing the previous k - 1 Cheeger constants. Eventually, we apply these results to give a method and a numerical algorithm to compute m₃(G), based on a generalized inverse power method.     

Transition state localization by a density functional method. Applications to isomerization and symmetry-forbidden reactions

Summary A new transition state algorithm incorporated into the density functional code deMon, has been used to study thetrans cis-hydroxymethylene andtrans-hydroxymethylene formaldehyde isomerization processes and to localize the transition state for the decomposition of 1,3-diazacyclobutane to methyleneimine. Calculations have been performed using both local (LSD) and nonlocal spin density (NLSD) gradient-corrected approximations. Two different basis sets of small and large size have been used for the study in order to analyze the effect of the basis set dimension other than that of the nonlocal corrections on the activation energy barrier value. The results seem to confirm that density functional methods can be considered practical and reliable tools for the localization of transition states.     

Superexponential stability of KAM tori

We study the dynamics in the neighborhood of an invariant torus of a nearly integrable system. We provide an upper bound to the diffusion speed, which turns out to be of superexponentially small size exp[-exp(1/)], being the distance from the invariant torus. We also discuss the connection of this result with the existence of many invariant tori close to the considered one.     

Catalysis of cationic surfactants in organic solvent: Hydrolysis of 2-nitro-4-carboxyphenyl acetate

The hydrolysis reaction of 2-nitro-4-carboxyphenyl acetate was studied in dichloromethane in the presence of an added electrolyte (NaOH) and cationic surfactants systems with varying quantities of added water at 25°C. The kinetic and conductivity data were correlated.     

The Dunford-Pettis Property for some Function Algebras in Several Complex Variables

The Dunford-Pettis property is shown to hold for the uniformalgebra A() and its dual for some standard domains , includingstrongly pseudoconvex bounded domains in Cⁿ, pseudoconvex boundeddomains of finite type in C², and bounded domains in C. Previouslythe result was known for the unit ball and unit polydisc inCⁿ. Techniques used involve Bourgain algebras, Hankel operators,properties of the Bergman kernel, quasi-metrics on the boundary,and -theory.     

An exact algorithm for the maximum stable set problem

We describe a new branch-and-bound algorithm for the exact solution of the maximum cardinality stable set problem. The bounding phase is based on a variation of the standard greedy algorithm for finding a colouring of a graph. Two different node-fixing heuristics are also described. Computational tests on random and structured graphs and very large graphs corresponding to real-life problems show that the algorithm is competitive with the fastest algorithms known so far.This work has been supported by Agenzia Spaziale Italiana.     

Central polynomials and matrix invariants

LetK be a field, charK=0 andM _n (K) the algebra ofn×n matrices overK. If λ=(λ₁,…,λ _m ) andμ=(μ ₁,…,μ _m ) are partitions ofn ² let wherex ₁,…,x _n ²,y ₁,…,y _n ² are noncommuting indeterminates andS _n ² is the symmetric group of degreen ². The polynomialsF ^{λ, μ} , when evaluated inM _n (K), take central values and we study the problem of classifying those partitions λ,μ for whichF ^{λ, μ} is a central polynomial (not a polynomial identity) forM _n (K). We give a formula that allows us to evaluateF ^{λ, μ} inM(K) in general and we prove that if λ andμ are not both derived in a suitable way from the partition δ=(1, 3,…, 2n−3, 2n−1), thenF ^{λ, μ} is a polynomial identity forM _n (K). As an application, we exhibit a new class of central polynomials forM _n (K). In memory of Shimshon Amitsur Research supported by a grant from MURST of Italy.