Pseudoeffect Algebras. II. Group Representations

This paper is the continuation of the previous paper by Dvureenskij and Vetterlein (2001), Int. J. Theor. Phys. 40(3). We show that any pseudoeffect algebra fulfilling a certain property of Riesz type is representable by a unit interval of some (not necessarily Abelian) partially ordered group. The relation of pseudoeffect to pseudo-MV algebras is made clear, and the &ell-group representation theorem for the latter structure is re-proved.     

Energy surfaces of rare-earth silicide films on Si(1 1 1)

We report on angle-resolved photoelectron spectroscopy results of thin dysprosium-silicide layers formed on Si(1 1 1), taken with a toroidal analyzer allowing to image the energy surfaces in k_||-space. At monolayer dysprosium coverages, where hexagonal DySi₂ grows with a 1×1 superstructure, electron pockets are observed at the points with highly anisotropic effective masses, and around a hole pocket at the point also an anisotropic dispersion is found. The band filling of these two bands amounts to one, indicating an even number of electrons assigned to the surface unit cell. Similar features are found for multilayer coverages, where hexagonal Dy₃Si₅ layers are formed with a superstructure. Here, the influence of zone folding effects due to the reconstructed layers in the bulk silicide is only weak because of the high surface sensitivity of the experiments.     

Capillary electrophoresis for the characterization of the complex dendrimeric contrast agent Gadomer

A CE method for the characterization of the complex dendrimeric contrast agent Gadomer has been developed and validated. The method was capable of separating the target substance Gadomer 24 from related dendrimers containing amino or carboxyl functions and from impurities of lower molecular weight. The compounds were separated in a fused-silica capillary. The optimized BGE consisted of 15 mM sodium phosphate, pH 6.3, containing 0.5 mM hexadecyltrimethylammonium bromide. The assay was validated with regard to linearity, specificity, accuracy, LOD and LOQ as well as robustness according to the guidelines of the International Conference on Harmonization. The method allows the determination of the purity and stability of the drug substance Gadomer as well as its injectable formulation. On the basis of the present study, a strategy for the quality assurance and quality control of the complex dendrimeric drug candidate Gadomer may be devised. The method may therefore serve as a key component in a set of analytical methodologies designed to assure and control the reproducible quality and safety of this innovative product. To the best of our knowledge, this is the first work reporting a validated method for the characterization, impurity profiling, and stability testing of a dendrimeric agent designed for clinical use.     

Congruences and States on Pseudoeffect Algebras

We study congruences on pseudoeffect algebras, which were recently introduced as a non-commutative generalization of effect algebras. We introduce ideals for these algebras and give a sufficient condition for an ideal to determine a congruence. Furthermore, states on pseudoeffect algebras are considered. It is shown that any interval pseudoeffect algebra maps homomorphically into an effect algebra whose states are in a one-to-one correspondence to the states of the original algebra.     

Partial algebras for Łukasiewicz logics and its extensions

It is a well-known fact that MV-algebras, the algebraic counterpart of Łukasiewicz logic, correspond to a certain type of partial algebras: lattice-ordered effect algebras fulfilling the Riesz decomposition property. The latter are based on a partial, but cancellative addition, and we may construct from them the representing ℓ-groups in a straightforward manner. In this paper, we consider several logics differing from Łukasiewicz logics in that they contain further connectives: the PŁ-, PŁ'-, PŁ'_△-, and ŁΠ-logics. For all their algebraic counterparts, we characterise the corresponding type of partial algebras. We moreover consider the representing f-rings. All in all, we get three-fold correspondences: the total algebras - the partial algebras - the representing rings.     

Formal approaches to rule-based systems in medicine: The case of CADIAG-2

There is no established formal framework for expert systems based on weighted IF–THEN rules. We discuss three mathematical models that have been recently proposed by the authors for CADIAG-2—a well-known system of this kind. The three frameworks are based on fuzzy logics, probability theory and possibilistic logic, respectively. CADIAG-2 is used here as a case study to evaluate these frameworks. We point out their use, advantages and disadvantages. In addition, the described models provide insight into various aspects of CADIAG-2.     

Submicrometer axial resolution optical coherence tomography

Optical coherence tomography (OCT) with unprecedented submicrometer axial resolution achieved by use of a photonic crystal fiber in combination with a compact sub-10-fs Ti:sapphire laser (Femtolasers Produktions) is demonstrated for what the authors believe is the first time. The emission spectrum ranges from 550 to 950 nm (lambda(c)=725 nm , P(out)=27 mW) , resulting in a free-space axial OCT resolution of ~0.75 mum , corresponding to ~0.5 mum in biological tissue. Submicrometer-resolution OCT is demonstrated in vitro on human colorectal adenocarcinoma cells HT-29. This novel light source has great potential for development of spectroscopic OCT because its spectrum covers the absorption bands of several biological chromophores.     

Existence of States on Pseudoeffect Algebras

Pseudoeffect (PE) algebras have been introduced as a noncommutative generalization of effect algebras. We study in this paper PE algebras with the special property of having a nonempty state space. To this end, we consider PE algebras which are po-group intervals and which are, in a certain sense, noncommutative only in the small. Such a PE algebra is shown to possess a nontrivial commutative homomorphic image from which then follows that there exist states. A typical example is given by an interval of the lexicographical product of two po-groups the first of which is abelian.