Fundamental Solutions of Linear Differential Equations in the Sense of Mnemofunctions

In this paper we discuss the definition and construction of the fundamental solution of a linear differential equation with constant coefficients in the algebra of mnemofunctions. This algebra contains the tempered distributions. We also present some examples including a physical illustration of our results for the equation u = .     

Magnetism of cyano-bridged hetero-one-dimensional Ln3+-M3+ complexes (Ln3+ = Sm,Gd, Yb; M3+ = FeLS,Co)

The reaction of Ln(NO(3))(3).aq with K(3)[Fe(CN)(6)] or K(3)[Co(CN)(6)] and 2,2'-bipyridine in water led to five one-dimensional complexes: trans-[M(CN)(4)(mu-CN)(2)Ln(H(2)O)(4) (bpy)](n)().XnH(2)O.1.5nbpy (M = Fe(3+) or Co(3+); Ln = Sm(3+), Gd(3+), or Yb(3+); X = 4 or 5). The structures for [Fe(3)(+)-Sm(3+)] (1), [Fe(3)(+)-Gd(3+)] (2), [Fe(3)(+)-Yb(3+)] (3), [Co(3)(+)-Gd(3+)] (4), and [Co(3)(+)-Yb(3+)] (5) have been solved; they crystallize in the triclinic space P1 and are isomorphous. The [Fe(3+)-Sm(3+)] complex is a ferrimagnet, its magnetic studies suggesting the onset of weak ferromagnetic 3-D ordering at 3.5 K. The [Fe(3+)-Gd(3+)] interaction is weakly antiferromagnetic. The isotropic nature of Gd(3+) allowed us to evaluate the exchange interaction (J = 0.77 cm(-)(1)).     

Examination of the Spatial Distribution of Dyes and Polymers in Thin Films by Two-Photon Microscopy

Summary.  Two-photon absorption induced fluorescence microscopy was used as a tool for the examination of the spatial distribution of a thin dye film. The two-photon absorption induced fluorescence signal is essentially the same as that produced by excitation with a single photon of equivalent energy. When femtosecond pulses are focused into a sample there is an intrinsic spatial selectivity of the two-photon emission signal, since it is dependent upon the square of the light intensity. This has tremendous implications in fluorescence microscopy. Since two-photon absorption is confined in a small region at the focal waist of an objective lens, photodamage and photobleaching of the sample are significantly reduced. In addition, the two-photon signal has inherent z-axis spatial resolution, which facilitates the construction of 3-D images. In the present work an application of this technique to a thin film of a dye is presented. The method can generally be applied to thin films made from photonic polymers. Received June 23, 2000. Accepted (revised) July 31, 2000     

Controlled vinyl‐type polymerization of norbornene with a Nickel(II) diphosphinoamine/methylaluminoxane catalytic system

A novel nickel‐based complex coordinated with an asymmetric diphosphinoamine ligand was synthesized and fully characterized. Single crystals of good quality were also obtained, and the solid‐state structure of the complex was studied via X‐rays diffraction. The catalytic activity of this Ni(II) complex in the vinyl‐type polymerization of norbornene was studied with methylaluminoxane (MAO) as the cocatalyst/activator. The influence of the reaction time, the equivalents of MAO used, and the concentration of the monomer on: (i) the activity of the catalytic system; (ii) the isolated yield of the polymer; and (iii) the molecular weight and molecular weight distribution of the polymer were investigated. The isolated polynorbornene (PNB) yields are significantly higher compared with those reported for other similar nickel‐based systems. The as‐obtained PNBs are characterized by high molecular weights and relatively narrow and monomodal molecular weight distributions (amongst the narrowest reported in the literature). The linear dependence of the molecular weight of the obtained PNB on the concentration of norbornene points toward a controlled polymerization reaction. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5241–5250, 2009     

The assessment of user-perceived web quality: Application of a satisfaction benchmarking approach

The assessment of website quality is considered as a problem of measuring user satisfaction, in order to analyse user perceptions and preferences. The presented pilot user satisfaction survey concerns the major cellular phone service providers in Greece. The analysis is based on a multicriteria preference disaggregation approach for satisfaction benchmarking analysis and consists of the following parts: (1) the user satisfaction analysis, which concerns the identification of customer preferences and includes the estimation of the relative importance and the demanding level of the different user satisfaction dimensions, and (2) the satisfaction benchmarking analysis, which is mainly focused on the performance evaluation of the competitive organisations against the satisfaction criteria, as well as the identification of the competitive advantages of each company. The results presented in this paper demonstrate how business organisations may locate their position against competition, pinpoint their weak points and determine which website characteristics will improve their global performance.     

Ramsey families of subtrees of the dyadic tree

We show that for every rooted, finitely branching, pruned tree of height there exists a family which consists of order isomorphic to subtrees of the dyadic tree with the following properties: (i) the family is a subset of ; (ii) every perfect subtree of contains a member of ; (iii) if is an analytic subset of , then for every perfect subtree of there exists a perfect subtree of such that the set either is contained in or is disjoint from .

     

A new method of glycosylation : anomeric hydroxyl activation by iminium salts

Starting from a free hemiacetalic hydroxyl group, the glycosylation is performed by means of the DMF-COCl₂ Vilsmeier-Haack reagent and silver tosylate. The nature of the reactive species is discussed.     

Applicability of Simplified Models for the Estimation of Ion Exchange Diffusion Coefficients in Zeolites

The applicability of simplified models for the determination of ion exchange diffusion coefficients in zeolites is examined. The simplified models examined are Vermeulen's, Paterson's, and Nernst-Plank's approximations for isotopic and ion exchange processes, used in ion exchange systems analysis. Parameter analysis indicates the limits for fractional attainment of equilibrium U(t), the ratio of exchangeable ions in liquid to solid phase (w), and the ratio of surface diffusion coefficients of exchangeable ions (a), all clearly inter-related, within which the above-mentioned simplified models can be successfully used. Studies of the applicability of the isotopic exchange simplified models to experimental data for batch-type Na(+)-Pb(2+) exchange on clinoptilolite confirm the parameter analysis conducted. Copyright 2001 Academic Press.     

Interrelations between Adsorption Energies and Local Isotherms, Local Monolayer Capacities, and Energy Distribution Functions, as Determined for Heterogeneous Surfaces by Inverse Gas Chromatography

Physicochemical parameters for adsorption of gases at the submonolayer regions of heterogeneous solid surfaces are measured experimentally as a function of time, and then interrelated as local isotherms θ against adsorption energy varepsilon, fractional changes of adsorption sites f(varepsilon)/c*(max) against varepsilon, θ against f(varepsilon)/c*(max), and distribution functions θ f(varepsilon)/c*(max) over adsorption energy values varepsilon, without using at all the well-known integral equation Theta(p, T)=integral(infinity)(0)θ(p, T, varepsilon)f(varepsilon)dvarepsilon and assumptions concerning the pair f(varepsilon) and θ(p, T, varepsilon). The method uses only chromatographic experimental data obtained by the inverse gas chromatography technique known as reversed-flow gas chromatography. It has been applied to the adsorption of cis-2-butene and trans-2-butene onto particles of Penteli marble at temperatures of 302, 314, 323, and 333 K. The results obtained are comparable with those calculated on the basis of the well-known integral equation. Copyright 2001 Academic Press.