The effect of nonlinearity on unstable zones of Mathieu equation

Mathieu equation is a well-known ordinary differential equation in which the excitation term appears as the non-constant coefficient. The mathematical modelling of many dynamic systems leads to Mathieu equation. The determination of the locus of unstable zone is important for the control of dynamic systems. In this paper, the stable and unstable regions of Mathieu equation are determined for three cases of linear and nonlinear equations using the homotopy perturbation method. The effect of nonlinearity is examined in the unstable zone. The results show that the transition curves of linear Mathieu equation depend on the frequency of the excitation term. However, for nonlinear equations, the curves depend also on initial conditions. In addition, increasing the amplitude of response leads to an increase in the unstable zone.     

Anionic rearrangements starting with 1-lithio-2-propynyl silyl ethers a route to (β-trimethylsilylvinyl) silyl ketones

The title compounds undergo silyl-Wittig rearrangement at low temperature and lead to allenolates at room temperature.     

Atomic parity violation in a single trapped radium ion

Atomic parity violation (APV) experiments are sensitive probes of the electroweak interaction at low energy. These experiments are competitive with and complementary to high-energy collider experiments. The APV signal is strongly enhanced in heavy atoms and it is measurable by exciting suppressed (M1, E2) transitions. The status of APV experiments and theory are reviewed as well as the prospects of an APV experiment using one single trapped Ra^?+? ion. The predicted enhancement factor of the APV effect in Ra^?+? is about 50 times larger than in Cs atoms. However, certain spectroscopic information on Ra^?+? needed to constrain the required atomic many-body theory, was lacking. Using the AGOR cyclotron and the TRI??P facility at KVI in Groningen, short-lived ^212???214Ra^?+? ions were produced and trapped. First ever excited-state laser spectroscopy was performed on the trapped ions. These measurements provide a benchmark for the atomic theory required to extract the electroweak mixing angle to sub-1% accuracy and are an important step towards an APV experiment in a single trapped Ra^?+? ion.     

<Emphasis Type="Italic">β</Emphasis>-Decay and the electric dipole moment: Searches for time-reversal violation in radioactive nuclei and atoms

One of the greatest successes of the Standard Model of particle physics is the explanation of time-reversal violation (TRV) in heavy mesons. It also implies that TRV is immeasurably small in normal nuclear matter. However, unifying models beyond the Standard Model predict TRV to be within reach of measurement in nuclei and atoms, thus opening an important window to search for new physics. We will discuss two complementary experiments sensitive to TRV: Correlations in the β-decay of ²¹Na and the search for an electric dipole moment (EDM) in radium.