Degrees of logics with Henkin quantifiers in poor vocabularies

We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of the form: what is the degree of the set of L–tautologies in a poor vocabulary (monadic or empty)? We prove that the set of tautologies of the logic with all Henkin quantifiers in empty vocabulary L* is of degree 0. We show that the same holds also for some weaker logics like L(H) and L(E). We show that each logic of the form L^(k)(Q), with the number of variables restricted to k, is decidable. Nevertheless – following the argument of M. Mostowski from [Mos89] – for each reasonable set theory no concrete algorithm can provably decide L^(k)(Q), for some (Q). We improve also some results related to undecidability and expressibility for logics L(H₄) and L(F₂) of Krynicki and M. Mostowski from [KM92].Mathematics Subject Classification (2000): 03C80, 03D35, 03B25Revised version: 28 August 2003     

Vortex fluctuations in underdoped Bi(2)Sr(2)CaCu(2)O(8+delta) crystals

Vortex thermal fluctuations in heavily underdoped Bi(2)Sr(2)CaCu(2)O(8+delta) (T(c)=69.4 K) are studied using Josephson plasma resonance. From the zero-field data, we obtain the c-axis penetration depth lambda(L,c)(0)=230+/-10 micrometer and the anisotropy ratio gamma(T). The low plasma frequency allows us to study phase correlations over the whole vortex solid state and to extract a wandering length r(w) of vortex pancakes. The temperature dependence of r(w) as well as its increase with dc magnetic field is explained by the renormalization of the vortex line tension by the fluctuations, suggesting that this softening is responsible for the dissociation of the vortices at the first order transition.     

A numerical test of analytical methods for reduction of IR and MW spectra of NaCl chi1sigma+ to parameters of radial functions

Two methods for direct inversion of IR and MW spectra of diatomic molecules--a deformational self-consistent procedure (DS-cP) and a computer program RADIATOM based on hypervirial perturbation theory are tested numerically. The test calculations for NaCl chi1sigma+ confirm that the RADIATOM program does not produce sufficiently accurate radial parameters and energy term values for their export to other utilities employed in the spectral analysis of diatomic systems.     

The Gold Partition Conjecture for 6-Thin Posets

We consider the Gold Partition Conjecture (GPC) that implies the 1/3–2/3 Conjecture. We prove the GPC in the case where every element of the poset is incomparable with at most six others. The proof involves the extensive use of computers. This paper contains results obtained using computer resources of the Interdisciplinary Centre for Mathematical and Computational Modelling (ICM), University of Warsaw.     

Reducing Cognitive Effort in Scoring Negotiation Space Using the Fuzzy Clustering Model

Negotiation scoring systems are fundamental tools used in negotiation support to facilitate parties searching for negotiation agreement and analyzing its efficiency and fairness. Such a scoring system is obtained in prenegotiation by implementing selected multiple criteria decision-aiding methods to elicit the negotiator’s preferences precisely and ensure that the support is reliable. However, the methods classically used in the preference elicitation require much cognitive effort from the negotiators, and hence, do not prevent them from using heuristics and making simple errors that result in inaccurate scoring systems. This paper aims to develop an alternative tool that allows scoring the negotiation offers by implementing a sorting approach and the reference set of limiting profiles defined individually by the negotiators in the form of complete packages. These limiting profiles are evaluated holistically and verbally by the negotiator. Then the fuzzy decision model is built that uses the notion of increasing the preference granularity by introducing a series of limiting sub-profiles for corresponding sub-categories of offers. This process is performed automatically by the support algorithm and does not require any additional preferential information from the negotiator. A new method of generating reference fuzzy scores to allow a detailed assignment of any negotiation offer from feasible negotiation space to clusters and sub-clusters is proposed. Finally, the efficient frontier and Nash’s fair division are used to identify the recommended packages for negotiation in the bargaining phase. This new approach allows negotiators to obtain economically efficient, fair, balanced, and reciprocated agreements while minimizing information needs and effort.     

Uncatalyzed peptide bond formation between two double amino acid molecules in the gas phase

The gas phase mechanism for peptide bond formation between two double amino acid (DAA) molecules ((NH₂)₂C(COOH)₂) is investigated in the absence of any catalysts. Two different paths, concerted and stepwise, each leading to both cis and trans DAA‐DAA dipeptide products (four mechanisms total) are examined on the basis of theoretical calculations carried out at the CCSD(T)/aug‐cc‐pVDZ//MP2/aug‐cc‐pVDZ level. The investigation indicates that the concerted mechanism leading to the trans configuration of the peptide bond in the DAA‐DAA dipeptide product is thermodynamically favored by about 5 kcal mol^?1 and requires slightly less energy than the remaining pathways considered. Moreover, the peptide bond formation process between two DAA molecules in the gas phase resembles the analogous reactions between two natural amino acids.     

Analytical Strategy for the Determination of Selenium in Biological Materials by Inductively Coupled Plasma-Mass Spectrometry with a Dynamic Reaction Cell

Selenium was determined in serum, hair, and tobacco by inductively coupled plasma-mass spectrometry using ⁷⁷Se, ⁷⁸Se, and ⁸²Se. The set of standards method (SSM) and the standard addition method (SAM) were applied to calibration with and without the use of internal standards (⁷²Ge and ¹⁰³Rh). In addition, the usefulness of the dynamic reaction cell (DRC) with methane as the reaction gas was characterized. The results obtained in different conditions were evaluated in terms of precision and accuracy. It was demonstrated theoretically and experimentally that an internal standard is a potential source of systematic errors as it can be influenced multiplicatively and additively by its own interferents (independently of selenium). Furthermore, it was shown that—against common opinion—an internal standard can fail in elimination of chemical interference effects influencing selenium and in increasing of precision of selenium determinations. The DRC was shown to be effective in the elimination of additive effects, although the results obtained by both SSM and SAM with DRC were systematically positively erroneous. Finally, selenium was determined accurately in each examined sample when SAM was applied to calibration, and signals were measured either for ⁸²Se without the use of the DRC, or for ⁷⁷Se or ⁷⁸Se with the use of the DRC. In addition, it has also been shown that samples should be diluted prior to analysis to the greatest acceptable extent.     

Silver nanoparticles formed in bio- and chemical syntheses with biosurfactant as the stabilizing agent

In this work, the comparison of the physical properties of silver nanoparticles (AgNPs) obtained via the reduction of silver nitrate (AgNO₃) in biological and chemical (model) syntheses supplemented with the biosurfactant surfactin is described. In the studies, two strains of Bacillus subtilis (denoted T’1 and I’1a) were used. The biological synthesis of AgNPs was performed using supernatants obtained from cultures of bacteria growing on brewery effluents, molasses, and Luria–Bretani (LB) medium. In model experiments, ascorbic acid served as the reductant; surfactin acted as the stabilizing agent. The surfactin concentrations were adjusted to 5 and 30?mg/L, which corresponded to minimum and maximum surfactin concentrations as measured in the supernatants obtained from the B. subtilis cultures. The chemical synthesis was carried out at acidic as well as alkaline pH. Dynamic light scattering (DLS) revealed that in model and biological samples, single AgNPs were accompanied by aggregated structures. Transmission electron microscopy showed that the contribution of the aggregates in bacterial supernatants and in chemical synthesis is negligible under acidic conditions. However, in the alkaline environment, this contribution predominates. In the model experiments, smaller nanoparticles were formed with higher concentrations of surfactant. The presence of surfactin significantly increased the stability of AgNPs in both bio- and chemical syntheses.