К ВОПРОСУ СИСТЕМАТИЗ АЦИИ β- СПЕКТРОВ

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A contribution to the systematics of -spectra

     

Aggregation on Finite Ordinal Scales by Scale Independent Functions

We define and investigate the scale independent aggregation functions that are meaningful to aggregate finite ordinal numerical scales. Here scale independence means that the functions always have discrete representatives when the ordinal scales are considered as totally ordered finite sets. We also show that those scale independent functions identify with the so-called order invariant functions, which have been described recently. In particular, this identification allows us to justify the continuity property for certain order invariant functions in a natural way. Mathematics Subject Classifications (2000) Primary: 91C05, 91E45; Secondary: 06A99, 39A12.Jean-Luc Marichal: Partially supported by a grant from the David M. Kennedy Center for International Studies, Brigham Young University.Radko Mesiar: Partially supported by grants VEGA 1/0273/03 and APVT-20-023402.     

h-Fuzzy quantum logics

Families of fuzzy subsets equipped by continuous fuzzy connectives which are quantum logics in a traditional sense are studied. As a special case, we obtain a generalized fuzzy quantum logic introduced recently by Pykacz.     

Fuzzy logics and observables

Systems of fuzzy subsets fulfilling quantum logic axioms with respect to fuzzy connectives are studied. An integral representation of a state on a fuzzy logic is shown. Fuzzy observables and their real-valued mean values are introduced in the obvious way. Using the relationship between fuzzy observables and fuzzy real-valued random variables, a fuzzy real-valued mean value of a fuzzy observable is introduced. The relationship between both types of mean values is studied and an example is presented.     

Generalized bipolar product and sum

Aggregation functions on \([0,1]\) with annihilator 0 can be seen as a generalized product on \([0,1]\). We study the generalized product on the bipolar scale \([-1,1]\), stressing the axiomatic point of view ( compare also Greco et al. in IPMU 2014, CCIS 444, Springer International Publishing, New York, 2014). Based on newly introduced bipolar properties, such as the bipolar monotonicity, bipolar unit element, bipolar idempotent element, several kinds of generalized bipolar product are introduced and studied. A special stress is put on bipolar semicopulas, bipolar quasi-copulas and bipolar copulas. Inspired by the truncated sum on \([-1,1]\) we introduce also the class of generalized bipolar sums, which differ from uninorms due to the non-associativity.     

Laser-fabricated dielectric optical components for surface plasmon polaritons

Fabrication of dielectric optical components for surface plasmon polaritons (SPPs) by two-photon polymerization (2PP) is studied. This direct-write femtosecond laser technology provides a low-cost and flexible method for the fabrication and investigation of plasmonic structures and optical components. Using the 2PP technique, we fabricated narrow dielectric ridges with dimensions as small as 150 nm on metal surfaces. SPP excitation with the laser-fabricated structures and guiding along them are demonstrated.     

Compact linearly ordered effect algebras

Compact linearly ordered effect algebras are shown to be Archimedean MV-algebras with unique maximal ideal. Consequently they are isomorphic to the unit interval [0, 1] equipped with restricted addition.     

Electroelution without gel sectioning of proteins from sodium dodecyl sulfate-polyacrylamide gel electrophoresis: fluorescent detection, recovery, isoelectric focusing and matrix assisted laser desorption/ionization-time of flight of the electroeluate

A method of direct electroelution of intact proteins, without gel sectioning and orthogonal to the orientation of electrophoretic migration, was developed in application to Novex gels, using a simple home-made experimental setup. Six model proteins covering the molecular mass range of 14-120 kDa were subjected to sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE), stained with an aqueous solution of the fluorescent dye, SYPRO-red, and electroeluted from the intact gel. The sensitivity of visual detection was 0.1-0.2 microg upon illumination by a green laser and 0.5-1 microg of protein on side-ways UV-illumination. Duration (for each protein) and field strength were optimized to render protein electroelution from the gel near-quantitative (above 80%) and relatively fast (1-12 min at 1 kV). At a given field strength, the optimal duration was found to be inversely proportional to the mobility of proteins in SDS-PAGE. Sequential ultrafiltration was evaluated as a simple approach to concentrate electroeluted proteins and deplete SDS to a level compatible with mass spectrometry of proteins: protein yields in the electroeluate were 25-33% (depending on the protein used) after three steps of ultrafiltration with water. The analysis of the electroeluate by isoelectric focusing in an immobilized pH gradient, to reveal protein heterogeneity under a single SDS-PAGE band (prior, e.g., to mass spectrometric analysis), was demonstrated.