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.     

Energy available for the double beta-decay of 76Ge

The Manitoba II high-resolution mass spectrometer has been used to determine the atomic mass difference ${}^{76}\text{Ge}\text{?}{}^{76}\text{Se}\text{= 2040.71 ± 0.52}\text{keV}$. This result, which is superior in precision and accuracy to previous values, should facilitate current searches for the neutrinoless double beta-decay of ⁷⁶Ge.     

Observation of a structural transition from cubic to monoclinic in UMn2

X-ray and neutron experiments have established that UMn₂ distorts from cubic to monoclinic at 211.7 K. No evidence for magnetic ordering has been found. The β angle (90° in cubic phase) becomes 94.9° at 5 K, and large strain effects and an internal rearrangement of the uranium atoms occur. We propose that the transition is caused by the formation of strong 5f bonds.     

Multiplicity distributions and double-scattering effects in π−d interactions at 360 GeV/c

Double-scattering effects are studied in π^?d interactions at 360 GeV/c. The partial cross sections $\text{σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(π}{}^{\mathrm{?}}\text{d}\text{), σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(“π}{}^{\mathrm{?}}\text{p}\text{”)}\text{and}\text{σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(“π}{}^{\mathrm{?}}\text{n}\text{”)}$ are presented. The double-scattering probability per πd collision is found to be $\text{? = 0.15 ± 0.02}$. We have extracted the partial cross section X_N of the double-scattering plus interference contributions, and find that X_N obeys KNO scaling. The data are compared with various theoretical predictions.