Łoś's theorem and the axiom of choice

In set theory without the Axiom of Choice ( $\mathsf{AC}$), we investigate the problem of the placement of ?o?'s Theorem ( $\mathsf{LT}$) in the hierarchy of weak choice principles, and answer several open questions from the book Consequences of the Axiom of Choice by Howard and Rubin, as well as an open question by Brunner. We prove a number of results summarised in § 3.     

Neutron activation analysis for determination of metal ions in biological fluids of patients after CoCrMo arthroplasty

Determination of metals and trace elements in patients with total knee or hip arthroplasty with CoCrMo alloy was performed. Blood, urine and cerebrospinal fluid (CSF) samples were analyzed and compared with samples from healthy people. Levels of Co, Cr as well as Na, Ca, Fe, Zn, Se, Rb, Sb and Br were determined by means of neutron activation analysis. The values of Cr and Co of the blood and urine measurements were elevated in patients with replacement, and according to the statistical analysis, significant differences of the elements Zn, Br, Co and Sb were found in the CSF (p?<?0.05).

     

An experimental and theoretical study of butyl methacrylate in situ radical polymerization kinetics in the presence of graphene oxide nanoadditive

The butyl methacrylate radical polymerization kinetics in the presence of graphene oxide nanoadditive is studied both experimentally and theoretically. The experimental study includes the formation of graphite oxide from the oxidation of graphite and its subsequent transformation to graphene oxide (GO) after ultrasonication and in situ polymerization. Monomer conversion versus time was monitored gravimetrically at various reaction temperatures and initial GO fractions. Formation of GO was verified by X‐ray diffraction spectra and the number and weight average molecular weights of the final polymer were obtained from GPC measurements. A detailed theoretical kinetic model was further developed. The model predictions were found to be in satisfactory agreement with the experimental data. The presence of GO was found to result in reduced initiator efficiency verified theoretically and explained through side reactions of primary radicals. Finally, nanocomposites showed enhanced thermal stability compared to neat PBMA. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 1433–1441     

Weak axioms of choice for metric spaces

In the framework of ZF, i.e., Zermelo-Fraenkel set theory without the axiom of choice AC, we show that if the family of all non-empty, closed subsets of a metric space has a choice function, then so does the family of all non-empty, open subsets of . In addition, we establish that the converse is not provable in ZF.

We also show that the statement ``every subspace of the real line with the standard topology has a choice function for its family of all closed, non-empty subsets" is equivalent to the weak choice form ``every continuum sized family of non-empty subsets of reals has a choice function".

     

On the set‐theoretic strength of the existence of disjoint cofinal sets in posets without maximal elements

In set theory without the Axiom of Choice , we study the deductive strength of the statements (“Every partially ordered set without a maximal element has two disjoint cofinal subsets”), (“Every partially ordered set without a maximal element has a countably infinite disjoint family of cofinal subsets”), (“Every linearly ordered set without a maximum element has two disjoint cofinal subsets”), and (“Every linearly ordered set without a maximum element has a countably infinite disjoint family of cofinal subsets”). Among various results, we prove that none of the above statements is provable without using some form of choice, is equivalent to , + (Dependent Choices) implies , does not imply in (Zermelo‐Fraenkel set theory with the Axiom of Extensionality modified in order to allow the existence of atoms), does not imply in (Zermelo‐Fraenkel set theory minus ) and (hence, ) is strictly weaker than in .     

On Martin's Axiom and Forms of Choice

Martin's Axiom is the statement that for every well‐ordered cardinal , the statement holds, where is “if is a c.c.c. quasi order and is a family of dense sets in P, then there is a ‐generic filter of P”. In , the fragment is provable, but not in general in . In this paper, we investigate the interrelation between and various choice principles. In the choiceless context, it makes sense to drop the requirement that the cardinal κ be well‐ordered, and we can define for any (not necessarily well‐ordered) cardinal the statement to be “if is a c.c.c. quasi order with , and is a family of dense sets in P, then there is a ‐generic filter of P”. We then define to be the statement that for every (not necessarily well‐ordered) cardinal , we have that holds. We then investigate the set‐theoretic strength of the principle .     

Sharp integral inequalities for the dyadic maximal operator and applications

Mathematische Zeitschrift - We prove a sharp integral inequality for the dyadic maximal function of $$\phi \in L^p$$ . This inequality connects certain quantities related to integrals of $$\phi $$...     

Limiting properties of some measures of information

In this paper we investigate the limiting behaviour of the measures of information due to Csiszár, Rényi and Fisher. Conditions for convergence of measures of information and for convergence of Radon-Nikodym derivatives are obtained. Our results extend the results of Kullback (1959,Information Theory and Statistics, Wiley, New York) and Kirmani (1971,Ann. Inst. Statist. Math.,23, 157–162).     

Heuristic optimization methods for motion planning of autonomous agricultural vehicles

In this paper, two heuristic optimization techniques are tested and compared in the application of motion planning for autonomous agricultural vehicles: Simulated Annealing and Genetic Algorithms. Several preliminary experimentations are performed for both algorithms, so that the best neighborhood definitions and algorithm parameters are found. Then, the two tuned algorithms are run extensively, but for no more than 2000 cost function evaluations, as run-time is the critical factor for this application. The comparison of the two algorithms showed that the Simulated Annealing algorithm achieves the better performance and outperforms the Genetic Algorithm. The final optimum found by the Simulated Annealing algorithm is considered to be satisfactory for the specific motion planning application.     

Rheological aspects of dense lignite-water suspensions; time dependence, preshear and solids loading effects

An investigation of the rheological properties of dense lignite-water suspensions is reported here in order to evaluate the parameters that affect the rheology of these suspensions. Different types of particle size distributions were achieved via wet grinding with particle sizes down to 1 μm. Polyelectrolytes and surfactants were used to improve the stability and rheology of suspensions. The achieved solid volume fraction, φ, with acceptable rheological behavior was 0.45, while the ratio of φ/φ _m was close to 0.85; φ _m is the maximum solid volume fraction. Various types of flow tests were performed on lignite-water suspensions with various preshear times and stress levels. Typical shear rates varied in the range between 10^–2 to 10² s^–1. The low shear behavior was found to be quite different from the high shear behavior for the most concentrated suspensions, with a plateau value at low shear rates indicating the appearance of a yield stress. These plateau values, however, depend on shear history, which is responsible for the development of different structures in the sample. The viscosity curves corresponding to the ascending and descending parts of the flow curve were found to be different; these flow curve parts can be described either by well established models or by modified ones. The non-Newtonian time dependent behavior of the lignite-water suspensions is attributed to the high value of the ratio φ/φ _m , the polydispersity of the particle size distribution, and the non-spherical shape of the lignite particles.