Abelian Integrals in Non-symmetric Perturbation of Symmetric Hamiltonian Vector Field

AbstractIt is shown that the vector field x = y, y = -(x3 - x - λ) + ϵ y(α + βx + x2), λ, ϵ small, has 0, 1, 2, or 3 limit cycles. This shows that some of Petov′s estimates concerning nonoscilation of elliptic integrals are not correct. The paper also improves the results of Guckenheimer and Dangelmayer

Number of singular points of an annulus in C2\mathbb{C}^2

Using Bogomolov-Miyaoka-Yau inequality and a Milnor number bound we prove that any algebraic annulus $\mathbb{C}^*$ in $\mathbb{C}^2$ with no self-intersections can have at most three cuspidal singularities.Comment: 15 pages, to appear in Ann. Inst. Fourie

Confocal Raman imaging of live cells

The objective of this thesis is to present the development of Raman microscopy for biochemical imaging of living cells. The main aim was to construct a Raman micro-spectrometer with the ability to perform time-course spectral measurements for the non-invasive study of biochemical processes in individual cells. The work can be divided into two parts: first, the development and characterization of the instrument; and second, completion of two experiments that demonstrate the suitability of Raman technique for studies of live cells. Instrumental development includes the design of optics and software for automated measurement. The experiments involve data collection and development of mathematical methods for analysis of the data. Chapter One provides an overview of techniques used in cell biology, with a special focus on Raman spectroscopy. It also highlights the importance of experiments on living cells, especially at the single cell level. Chapter Two explains the theoretical background of Raman spectroscopy. Furthermore, it presents the Raman spectroscopy techniques suitable for cell and biological studies. Chapter Three details the instrumentation and software development. The main parts of the confocal Raman micro-spectrometer, as designed for studying living cells, are: inverted microscope, 785 nm laser and high quality optics, environmental enclosure for maintaining physiological conditions during measurements of cells, and fluorescence wide-field microscopy facility for validation and confirmation of biochemical findings by Raman studies. Chapter Four focuses on the evaluation of the performance of the Raman setup and explains calibration and analysis methods applied to the data. Chapter Five and Six describe experiments performed on living cells. Chapter Five focuses on studies of the immunological synapse formed between primary dendritic and T cells indicating the polarisation of actin. Chapter Six describes time-course experiment performed on cancerous cells in the early phases of the apoptosis process, which enabled detection of the DNA condensation and accumulation of unsaturated lipids. Chapter Seven summarizes the work and gives concluding remarks

Elucidation of role of graphene in catalytic designs for electroreduction of oxygen

Graphene is, in principle, a promising material for consideration as component (support, active site) of electrocatalytic materials, particularly with respect to reduction of oxygen, an electrode reaction of importance to low-temperature fuel cell technology. Different concepts of utilization, including nanostructuring, doping, admixing, preconditioning, modification or functionalization of various graphene-based systems for catalytic electroreduction of oxygen are elucidated, as well as important strategies to enhance the systems' overall activity and stability are discussed

Evaluation of Reduced-Graphene-Oxide Aligned with WO3-Nanorods as Support for Pt Nanoparticles during Oxygen Electroreduction in Acid Medium

Hybrid supports composed of chemically-reduced graphene-oxide-aligned with tungsten oxide nanowires are considered here as active carriers for dispersed platinum with an ultimate goal of producing improved catalysts for electroreduction of oxygen in acid medium. Here WO3 nanostructures are expected to be attached mainly to the edges of graphene thus making the hybrid structure not only highly porous but also capable of preventing graphene stacking and creating numerous sites for the deposition of Pt nanoparticles. Comparison has been made to the analogous systems utilizing neither reduced graphene oxide nor tungsten oxide component. By over-coating the reduced-graphene-oxide support with WO3 nanorods, the electrocatalytic activity of the system toward the reduction of oxygen in acid medium has been enhanced even at the low Pt loading of 30 microg cm-2. The RRDE data are consistent with decreased formation of hydrogen peroxide in the presence of WO3. Among important issues are such features of the oxide as porosity, large population of hydroxyl groups, high Broensted acidity, as well as fast electron transfers coupled to unimpeded proton displacements. The conclusions are supported with mechanistic and kinetic studies involving double-potential-step chronocoulometry as an alternative diagnostic tool to rotating ring-disk voltammetry.Comment: arXiv admin note: text overlap with arXiv:1805.0315

Confocal Raman imaging of live cells

The objective of this thesis is to present the development of Raman microscopy for biochemical imaging of living cells. The main aim was to construct a Raman micro-spectrometer with the ability to perform time-course spectral measurements for the non-invasive study of biochemical processes in individual cells. The work can be divided into two parts: first, the development and characterization of the instrument; and second, completion of two experiments that demonstrate the suitability of Raman technique for studies of live cells. Instrumental development includes the design of optics and software for automated measurement. The experiments involve data collection and development of mathematical methods for analysis of the data. Chapter One provides an overview of techniques used in cell biology, with a special focus on Raman spectroscopy. It also highlights the importance of experiments on living cells, especially at the single cell level. Chapter Two explains the theoretical background of Raman spectroscopy. Furthermore, it presents the Raman spectroscopy techniques suitable for cell and biological studies. Chapter Three details the instrumentation and software development. The main parts of the confocal Raman micro-spectrometer, as designed for studying living cells, are: inverted microscope, 785 nm laser and high quality optics, environmental enclosure for maintaining physiological conditions during measurements of cells, and fluorescence wide-field microscopy facility for validation and confirmation of biochemical findings by Raman studies. Chapter Four focuses on the evaluation of the performance of the Raman setup and explains calibration and analysis methods applied to the data. Chapter Five and Six describe experiments performed on living cells. Chapter Five focuses on studies of the immunological synapse formed between primary dendritic and T cells indicating the polarisation of actin. Chapter Six describes time-course experiment performed on cancerous cells in the early phases of the apoptosis process, which enabled detection of the DNA condensation and accumulation of unsaturated lipids. Chapter Seven summarizes the work and gives concluding remarks