Investigation of lutetium rydberg states by laser multistep resonance ionization spectroscopy

Laser multistep excitation and electric-field ionization spectroscopy have been used to investigate experimentally highly excited states (HES) of lutetium in the vicinity of the first ionization limit. The investigation includes the measurement of energy levels (ionic signal vs last transition frequency) and radiation lifetime (ionic signal vs ionizing electric-field pulse delay) of the states investigated. Even Rydberg states of 4f ¹⁴ 6s ² nd have been observed with two-step laser excitation. The maximum experimental error is 0.3 cm^?1 for the energy and 20% for the radiation lifetime measurements. This is the very first time that results for the lifetimes as well as for a large part of the energy values have been obtained. Our present experimental results compare well with previously calculated values obtained by relativistic perturbation theory using the zero-order model approximation, and with the available experimental values.     

Convergence of the method of chords for solving generalized equations

In this article, we study an iterative procedure of the following form

A hybrid algorithm for the unbounded knapsack problem

This paper presents a new approach for exactly solving the Unbounded Knapsack Problem (UKP) and proposes a new bound that was proved to dominate the previous bounds on a special class of UKP instances. Integrating bounds within the framework of sparse dynamic programming led to the creation of an efficient and robust hybrid algorithm, called EDUK2. This algorithm takes advantage of the majority of the known properties of UKP, particularly the diverse dominance relations and the important periodicity property. Extensive computational results show that, in all but a very few cases, EDUK2 significantly outperforms both MTU2 and EDUK, the currently available UKP solvers, as well the well-known general purpose mathematical programming optimizer CPLEX of ILOG. These experimental results demonstrate that the class of hard UKP instances needs to be redefined, and the authors offer their insights into the creation of such instances.     

Quasimaximality and principal filters isomorphism between

Let I be a quasimaximal subset of a computable basis of the fully efective vector space V . We give a necessary and sufficient condition for the existence of an isomorphism between the principal filter respectivelly. We construct both quasimaximal sets that satisfy and quasimaximal sets that do not satisfy this condition. With the latter we obtain a negative answer to Question 5.4 posed by Downey and Remmel in [3].Based on the authors Ph.D. dissertation.Mathematics Subject Classification (2000): 03D25, 03C57     

Stability of various silicone oil/water emulsion films as a function of surfactant and salt concentration

There have been reports, originally by the Bristol group, and subsequently by others, of the preparation and properties of emulsions of stable, nearly monodisperse droplets of poly(dimethylsiloxane) (PDMS) in water, where no added surfactant is used. It has been assumed that their stability is due to the high density of surface-ionized hydroxyl groups, similar in fact to the closely related St?ber silica particles. In this study we confirm, from droplet lifetime studies, that droplets, prepared from such synthesized PDMS, are significantly more stable to coalescence than similar-sized droplets prepared from three types of commercially available PDMS, containing HO-, MeO-, or Me3-terminated chains, respectively. It is shown, however, that the zeta potentials of the synthesized PDMS and of the various commercial oils are all very similar (as indeed are their Hamaker constants). So some other explanation must be inferred for the enhanced stability to coalescence of the synthesized PDMS droplets compared to the commercial PDMS droplets. It is shown, for droplets formed from n-hexane and the synthesized oil, that stability to coalescence is conferred at PDMS volume fractions (phiPDMS) around 0.2 in the mixture. The synthesized PDMS is known to consist of mixtures of cyclic PDMS and short-chain linear species, with terminal -OH groups. There is some (indirect) evidence that in the interval 0.25 < phiPDMS < 0.35, the linear PDMS chains may be adsorbed close to a monolayer at the mixed oil/water interface, possibly conferring some enhanced Gibbs elasticity to the interface. This underpins the possibility that, in the synthesized oil droplets themselves, there is also preferential adsorption of the linear chains at the PDMS/water interface, and this leads to a value of the Gibbs elasticity, sufficient to significantly reduce coalescence. Unfortunately, the Gibbs elasticity could not be measured in this case. However, such preferential adsorption is unlikely to occur with the commercial PDMS oils, which are not so heterogeneous. Finally, it is shown that droplets of the three commercial PDMS oils could be stabilized against coalescence, if a sufficient, minimum amount of sodium dodecyl sulfate (SDS) is added. Gibbs elasticity values have been estimated in these cases, from plots of interfacial tension against ln(SDS concentration).     

Interactions in lipid stabilised foam films

The interaction between lipid bilayers in water has been intensively studied over the last decades. Osmotic stress was applied to evaluate the forces between two approaching lipid bilayers in aqueous solution. The force–distance relation between lipid mono- or bilayers deposited on mica sheets using a surface force apparatus (SFA) was also measured. Lipid stabilised foam films offer another possibility to study the interactions between lipid monolayers. These films can be prepared comparatively easy with very good reproducibility. Foam films consist usually of two adsorbed surfactant monolayers separated by a layer of the aqueous solution from which the film is created. Their thickness can be conveniently measured using microinterferometric techniques. Studies with foam films deliver valuable information on the interactions between lipid membranes and especially their stability and permeability. Presenting inverse black lipid membrane (BLM) foam films supply information about the properties of the lipid self-organisation in bilayers. The present paper summarises results on microscopic lipid stabilised foam films by measuring their thickness and contact angle. Most of the presented results concern foam films prepared from dispersions of the zwitterionic lipid 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine (DMPC) and some of its mixtures with the anionic lipid — 1,2-dimyristoyl-sn-glycero-3-[phospho-rac-(1-glycerol)] (DMPG).     

Weitzenböck derivations of free metabelian Lie algebras

A nonzero locally nilpotent linear derivation δ   of the polynomial algebra K[_Xd]=K[_x1,…,_xd]$K[X_d]=K[x_1\text{,}\dots \text{,}{x}_d]$ in several variables over a field K   of characteristic 0 is called a Weitzenböck derivation. The classical theorem of Weitzenböck states that the algebra of constants K[_Xd]^δ$K{[X_d]}^{\delta }$ (which coincides with the algebra of invariants of a single unipotent transformation) is finitely generated. Similarly one may consider the algebra of constants of a locally nilpotent linear derivation δ of a finitely generated (not necessarily commutative or associative) algebra which is relatively free in a variety of algebras over K  . Now the algebra of constants is usually not finitely generated. Except for some trivial cases this holds for the algebra of constants (_Ld/_Ld^″)^δ${(L_d/{L_d}^{″})}^{\delta }$ of the free metabelian Lie algebra _Ld/_Ld″$L_d/L_d″$ with d   generators. We show that the vector space of the constants (_Ld/_Ld^″)^δ${(L_d/{L_d}^{″})}^{\delta }$ in the commutator ideal _Ld′/_Ld″$L_d\prime /L_d″$ is a finitely generated K[_Xd]^δ$K{[X_d]}^{\delta }$-module. For small d  , we calculate the Hilbert series of (_Ld/_Ld^″)^δ${(L_d/{L_d}^{″})}^{\delta }$ and find the generators of the K[_Xd]^δ$K{[X_d]}^{\delta }$-module (_Ld/_Ld^″)^δ${(L_d/{L_d}^{″})}^{\delta }$. This gives also an (infinite) set of generators of the algebra (_Ld/_Ld^″)^δ${(L_d/{L_d}^{″})}^{\delta }$.     

Transformation of phase to (x,y,z)-coordinates for the calibration of a fringe projection profilometer

In this work we present a phase to (x,y,z)-coordinates transformation method for the calibration of a fringe projection profilometer. Our technique is divided in two parts: (1) phase to z transformation (for axial calibration) based on the typical polynomial fitting which uses a flat plane placed at several z positions to measure the phase of the projected fringes. (2) Phase to x and y transformation (for transverse calibration) based on the use of a crossed gratings pattern and a Fourier phase measurement method to determine x and y coordinates at several z positions. As will be shown the use of the crossed gratings pattern and the Fourier phase measurement method for transverse calibration is advantageous in several aspects: an unique image can give us x and y information at once. It provides x and y coordinates at each pixel in the image avoiding the use of interpolation methods. We present some experimental results and explain the viability of the proposed technique.     

Control of the water permeability of polyelectrolyte multilayers by deposition of charged paraffin particles

We present a new way to protect polyelectrolyte multilayers from water, consisting in the adsorption and subsequent fusing of charged wax particles atop a multilayer. The formation of the wax layer is demonstrated by different techniques such as ellipsometry, contact angle measurements, and atomic force microscopy. The diffusion of water in protected and unprotected multilayers is studied by in situ neutron reflectometry. Whereas a top layer of wax crystals already allows substantial reduction of the diffusion, the fusion of this top layer leads to the dominating exclusion of water from the multilayers when dipped in water. This method opens up new interesting avenues for polyelectrolyte multilayers in practical applications where permeability of water, ions, or hydrophilic drugs is an issue.     

Phospholipid foam films studied by contact angle measurements and fluorescence microscopy

 Foam films drawn from suspensions of the phospholipid 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine (DMPC) in water/ethanol mixtures were used for the investigation of the relation between the properties of the monolayers and the interaction between the film surfaces. The film thickness and the contact angle between the film and the meniscus were measured as a function of the temperature in a range around the temperature of the main phase transition for the lipid. Additionally, fluorescence microscopy was applied to investigate the distribution of a fluorescent lipidlike dye in the surface of the film and the meniscus. From the contact angle the free energy of film formation was calculated. At the temperature of the chain-melting phase transition the film thickness decreases by 0.7 nm. This can be related to a decrease in the thickness of the hydrocarbon layers of the lipid monolayers at this temperature. The decrease in the film thickness leads to a reduction in the free energy by increasing the van der Waals attraction between the film surfaces. No structures were observed in the monolayers of the film in the fluorescence investigation. However, on formation of the very thin equilibrium film the dye was expelled from the film area, indicating an increase in the packing density of the lipid, if the monolayers are in adhesive contact in the film. Received: 31 January 2000 Accepted: 25 February 2000