Multiplication Groups of Topological Loops

In this brief survey, we discuss the following question: Which Lie groups can occur as the multiplication groups Mult(L) of connected topological loops L? We describe correspondences between the structure of the group Mult(L) and the structure of the loop L.     

Numerical analysis of a frictional contact problem for viscoelastic materials with long-term memory

We consider a mathematical model which describes the bilateral contact between a deformable body and an obstacle. The process is quasistatic, the material is assumed to be viscoelastic with long memory and the friction is modeled with Tresca’s law. The problem has a unique weak solution. Here we study spatially semi-discrete and fully discrete schemes using finite differences and finite elements. We show the convergence of the schemes under the basic solution regularity and we derive order error estimates. Finally, we present an algorithm for the numerical realization and simulations for a two-dimensional test problem.     

Affine Reductive Spaces of Small Dimension and Left A-Loops

In this paper we determine the at least 4-dimensional affine reductive homogeneous manifolds for an at most 9-dimensional simple Lie group or an at most 6-dimensional semi-simple Lie group. Those reductive spaces among them which admit a sharply transitive differentiable section yield local almost differentiable left A-loops. Using this we classify all global almost differentiable left A-loops L having either a 6-dimensional semi-simple Lie group or the group as the group topologically generated by their left translations. Moreover, we determine all at most 5-dimensional left A-loops L with as the group topologically generated by their left translations.     

Examination of typical bacterial strains in septic arthritis by isoperibol calorimeter

The accurate diagnosis of different types of arthritis is a great clinical challenge. It has a special importance to reach the right diagnosis in case of septic joint infections. The clarification of aetiology is crucial to minimize the complications and mortality of these cases. Therefore, novel methods like synovial sample analyses by differential scanning calorimetry (DSC) could have the potential to provide further information in the diagnostic process (Dandé et al. in J Therm Anal Calorim. doi: https://doi.org/10.1007/s10973-017-6179-6, 2017). A retrospective analysis of patients treated with septic joint infections over the last 5 years at the Department of Traumatology and Hand Surgery has been conducted. Human synovial samples were inoculated with six different, frequently occurring human pathogenic bacterial strains. The proliferation of inoculated synovial fluid samples was monitored by SETARAM Micro DSC-II calorimeter in isotherm mode (isoperibol calorimeter). Based on our results, 47.45% of the cases involved small joint (SG) infections and 52.55% of them occurred in large joints (LG). Synovial aspirates collected from infected joints indicated the presence of the following bacteria and incidences: Staphylococcus aureus 43 (22.16%), Staphylococcus epidermidis 3 (1.54%), Methicillin-resistant Staphylococcus aureus, MRSA 4 (2.06%), Streptococcus pyogenes 9 (4.63%), Escherichia coli 1 (0.51%) and Pseudomonas aeruginosa 4 (2.06%). The isoperibolic curves of human synovial samples inoculated with different bacterial strains clearly demonstrated specific/representative results in case of each bacterium. The control of human synovial fluid samples by isotherm calorimetry could be a useful tool in the differential diagnosis of human septic arthritis.     

On generalized neighbourhood systems

It is shown in the paper [1] that every generalized topology can be generated by a generalized neighbourhood system. Following the paper [3], we discuss some questions related to this construction. Research supported by Hungarian Foundation for Scientific Research, grant No. T 49786.     

Development of an extractive-scintillating chromatographic resin for the detection of radioactive isotopes

In this paper, the development of a new-type of resin is presented, which contains selective complexing and scintillating molecules in a chemically bonded form. The resin material is produced via radiation polymerization of a solution of 2-(4-allyloxy-phenyl)-5-phenyl oxazole, 5-(allyloxy-phenyl)-2-[4-(5-phenyl-oxazole-2-il)-phenyl] oxazole, diethylene glycol dimethacrylate (DEGMA), styrene and the allyl derivative of a 18C6 crown ether-dicarbolic acid complexing agent. The product is a macroporous polymer matrix that shows fluorescent properties and ion binding capacity excellent for radioanalytical purposes.     

Mössbauer studies of iron(III)-(indole-3-alkanoic acids) systems in frozen aqueous solutions

Summary This paper describes the M?ssbauer investigations of iron(III) salts in aqueous solutions in the presence of indole-3-alkanoic acid ligands. The measurements showed two parallel reactions between the ligands and ferric ions: a complex formation and a redox process. The oxidation process takes place in the ligands, and a part of Fe³⁺is reduced to Fe²⁺.     

New improved convergence analysis for Newton-like methods with applications

We present a new semilocal convergence analysis for Newton-like methods using restricted convergence domains in a Banach space setting. The main goal of this study is to expand the applicability of these methods in cases not covered in earlier studies. The advantages of our approach include, under the same computational cost as previous studies, a more precise convergence analysis under the same computational cost on the Lipschitz constants involved. Numerical studies including a chemical application are also provided in this study.     

Three-Dimensional Topological Loops with Solvable Multiplication Groups

We prove that each 3-dimensional connected topological loop L having a solvable Lie group of dimension ≤5 as the multiplication group of L is centrally nilpotent of class 2. Moreover, we classify the solvable non-nilpotent Lie groups G which are multiplication groups for 3-dimensional simply connected topological loops L and dim G ≤ 5. These groups are direct products of proper connected Lie groups and have dimension 5. We find also the inner mapping groups of L.