Czech project in history of mathematics

The paper describes the Czech project in the history of mathematics which was initiated at the Faculty of Mathematics and Physics of Charles University in Prague at the end of the eighties of the 20th century. Its main aim is to map the development of mathematical research in the Czech lands in the second half of the nineteenth and the first half of the twentieth century. The main result of this project is the production of monographs. These chart out the life and work of some prominent Czech personalities-mathematicians who have had substantial influence on the development of Czech mathematics. The aim of the project, the structure of the monographs and the general method are discussed in the paper.     

A 2 MV Van de Graaff accelerator as a tool for planetary and impact physics research

Investigating the dynamical and physical properties of cosmic dust can reveal a great deal of information about both the dust and its many sources. Over recent years, several spacecraft (e.g., Cassini, Stardust, Galileo, and Ulysses) have successfully characterised interstellar, interplanetary, and circumplanetary dust using a variety of techniques, including in situ analyses and sample return. Charge, mass, and velocity measurements of the dust are performed either directly (induced charge signals) or indirectly (mass and velocity from impact ionisation signals or crater morphology) and constrain the dynamical parameters of the dust grains. Dust compositional information may be obtained via either time-of-flight mass spectrometry of the impact plasma or direct sample return. The accurate and reliable interpretation of collected spacecraft data requires a comprehensive programme of terrestrial instrument calibration. This process involves accelerating suitable solar system analogue dust particles to hypervelocity speeds in the laboratory, an activity performed at the Max Planck Institut fu?r Kernphysik in Heidelberg, Germany. Here, a 2 MV Van de Graaff accelerator electrostatically accelerates charged micron and submicron-sized dust particles to speeds up to 80 km s(-1). Recent advances in dust production and processing have allowed solar system analogue dust particles (silicates and other minerals) to be coated with a thin conductive shell, enabling them to be charged and accelerated. Refinements and upgrades to the beam line instrumentation and electronics now allow for the reliable selection of particles at velocities of 1-80 km s(-1) and with diameters of between 0.05 μm and 5 μm. This ability to select particles for subsequent impact studies based on their charges, masses, or velocities is provided by a particle selection unit (PSU). The PSU contains a field programmable gate array, capable of monitoring in real time the particles' speeds and charges, and is controlled remotely by a custom, platform independent, software package. The new control instrumentation and electronics, together with the wide range of accelerable particle types, allow the controlled investigation of hypervelocity impact phenomena across a hitherto unobtainable range of impact parameters.     

A “four-ferrocene” modified stem-loop structure as a probe for sensitive detection and single-base mismatch discrimination of DNA

We report the use of a four-ferrocene modified oligonucleotide as a probe for DNA detection with a gold electrode microsystem. This oligonucleotide is synthesized by automated solid-phase synthesis with four successive ferrocene moieties at the 5′-end and a C6-thiol modifier group at the 3′-end. The grafting of this 4Fc-DNA probe on a gold electrode microsystem results in the appearance of the ferrocene redox couple in cyclic voltammetry. The probe sequence is a stem-loop structure that folds efficiently on the electrode, thus optimizing electron transfer. Such architecture serves as sensor for DNA detection which is based on hybridization. The resulting disposable voltammetric sensor allowed direct, reagentless DNA detection in a small volume (20 μL). Electrochemical response upon hybridization with complementary short sequence (30-base length) and long sequence (50-base length) strands was observed by differential pulse voltammetry. Current variations were compared. The longer the sequence, the greater the decrease in current. The system's detection limit was estimated at 3.5 pM (0.07 fmol in 20 μL) with the 50-base length target and provided a dynamic detection range between 3.5 pM and 5 nM. Single mismatch detection showed a good level of sensitivity. The system was regenerated twice with no significant loss of Fc signal. Finally, 1 pM sensitivity was reached with a long chain analog of DNA PCR products of Influenza virus.     

Compressive and Tensile Behaviours of PLLA Matrix Composites Reinforced with Randomly Dispersed Flax Fibres

Nowadays, the ecological footprint of a material is becoming tremendously important. The Poly l-Lactide Acid (PLLA) matrix composites reinforced by randomly scattered flax fibres have mechanical properties similar to polyester/glass composites [1], lower environmental impacts and can be compost at the end of their lives. In this study, the mechanical characterization of biocomposites has been pushed further with the determination of the compressive and tensile properties. Furthermore, the mechanical properties of single flax fibres have been measured and implemented in a micro-mechanical estimation of the composite elastic modulus. Tensile and compressive stiffness determined by the mechanical analyses show very good correlations with the mathematical estimation.     

Comparison of Cell Sizes for Cost Efficient Deployment of a Sensor Network Aided Cognitive Radio System

To exploit spectrum resources on a secondary basis, a Sensor Network Aided Cognitive Radio Network uses a wireless sensor network that assists a secondary cognitive radio network by providing information about the current primary spectrum occupancy. In this paper we determine the performance for different cell sizes when considering the costs for deployment of base stations in a secondary network that exploits spectrum holes identified by the wireless sensor network. The secondary base station is deployed co-located with a mobile primary network that uses a cellular reuse pattern with seven frequencies. Performance of the secondary system and impact on the primary system are mainly studied in terms of throughput, packet loss and coverage when using spectrum holes in the space, time and frequency domains. Especially, we find that the cell size and configured transmit powers for the secondary system are important for optimal system performance, and that smaller cell sizes and less expensive base stations for the secondary system are beneficial. The impact on primary system performance was found to be low, but that optimal tuning of the sensor network is important.     

Characterisation of CO/NO/SO2 emission and ash-forming elements from the combustion and pyrolysis process

Bioenergy is considered as a sustainable energy which can play a significant role in the future’s energy scenarios to replace fossil fuels, not only in the heat production, but also in the electricity and transportation sectors. Emission formation and release of main ash-forming elements during thermal conversion of biomass fuels at different conditions have been the scope of this study. The experiments were conducted in a quartz glass reactor where the temperature and atmosphere could be controlled. The selected fuels represent a wide range of biomass compositions. They are torrefied softwood, spruce bark, waste wood, miscanthus, and wheat straw. The fuels were first grinded and then pressed with a pellet maker into pellets of the same size and weight. For each fuel, the experiments were carried out under both oxidation and pyrolysis condition, with atmosphere of 3 % O₂ + 97 % N₂ and 100 % N₂, respectively, at four residence times. The selected temperatures under which experiments were performed are 800, 900, and 1,050 °C. The concentration of SO₂, NO, CO, and CO₂ emissions and O₂ were monitored online by three analysers, simultaneously. The residue weight was measured after each process, and the comparison with the ash content of the fresh pellet is made. Additionally, the release of several ash-forming elements (K, Zn, Na, and Mn) from the fuels has been quantified as function of temperature and residence time by inductively coupled plasma mass spectrometry (ICP-MS) and inductively coupled plasma atomic emission spectroscopy (ICP-AES). Time-dependent formation of NO and SO₂ and other emissions is presented and discussed with respect to different temperature and combustion conditions.     

Auslegung von Blasensäulen mithilfe von Compartmentmodellen

In bubble columns, the phenomena of mass and heat transfer as well as the reaction are closely linked to the complex fluid dynamics. Compartment modeling offers the opportunity to integrate these phenomena while enabling an axial and radial distribution with acceptable computing effort. This article includes methods for generating the compartment geometry and fluid dynamic parameters of this modeling approach, facilitating the opportunity to optimize an industrial bubble column.     

Angiogenic potential of boron-containing bioactive glasses: in vitro study

Boron-containing bioactive glasses (BGs) are being extensively researched for the treatment and regeneration of bone defects because of their osteostimulatory and neovascularization potential. In this study, we report the effects of the ionic dissolution products (IDPs) of different boron-doped, borosilicate, and borate BG scaffolds on mouse bone marrow stromal cells in vitro, using an angiogenesis assay. Five different BG scaffolds of the system SiO₂–Na₂O–K₂O–MgO–CaO–P₂O₅–B₂O₃ (with varying amounts of SiO₂ and B₂O₃) were fabricated by the foam replication technique. Bone marrow stromal cells were cultivated in contact with the IDPs of the boron-containing BG scaffolds at different concentrations for 48 h. The expression and secretion of vascular endothelial growth factor (VEGF) from the cultured cells was measured quantitatively using the VEGF ELISA Kit. Cell viability and cell morphology were determined using WST-8 assay and H&E staining, respectively. The cellular response was found to be dependent on boron content and the B release profile from the glasses corresponded to the positive or negative biological activity of the BGs.     

Generalized Lorenz-Mie theory for a sphere with an eccentrically located spherical inclusion

Abstract

The theory of interaction between an arbitrary electromagnetic shaped beam and a sphere with an eccentrically located spherical inclusion is presented. This theory is built as a synthesis between two available theories (i) the generalized Lorenz-Mie theory for a homogeneous sphere (illuminated by an arbitrary shaped beam) and (ii) the theory of interaction between a plane wave and an eccentrically stratified dielectric sphere.