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Using complex database of satellite malfunctions within the period of 1974–1994 and cosmic ray activity indices, calculated by means of high mountain Alma-Ata neutron monitor data it was shown that malfunction frequency increases during seven days after increase of cosmic ray activity indices. It is significant for high altitude satellite with altitude more than 1000 km.

Taiji-1’s in-orbit magnetic property is significant for the improvement of the satellite’s attitude-control performance and the acceleration noise model of gravitational reference sensor. Test data of satellite drifts have been used to construct the model including interaction among the magnetic field; remnant magnetic moment and induced magnetic moment so as to estimate the satellite’s magnetic property. Using the global optimization method, the remnant magnetic moment of Taiji-1 is estimated to be (-1.42 -0.19 -0.06) Am².

Pairs of genus 2 mutant knots can have different Homfly polynomials, for example some 3-string satellites of Conway mutant pairs. We give examples which have different Kauffman 2-variable polynomials, answering a question raised by Dunfield et al. in their study of genus 2 mutants. While pairs of genus 2 mutant knots have the same Jones polynomial, given from the Homfly polynomial by setting v = s², we give examples whose Homfly polynomials differ when v = s³. We also give examples which differ in a Vassiliev invariant of degree 7, in contrast to satellites of Conway mutant knots.

Let $X$ and $Y$ be the complementary regions of a closed hypersurface $M$ in $S^4=X{\cup }_{M}Y$. We use the Massey product structure in $H^{\ast }(M;\mathbb{Z})$ to limit the possibilities for $\chi (X)$ and $\chi (Y)$. We show also that if ${\pi }_1(X)\ne 1$ then it may be modified by a 2-knot satellite construction, while if $\chi (X)\le 1$ and ${\pi }_1(X)$ is abelian then ${\beta }_1(M)\le 4$ or ${\beta }_1(M)=6$. Finally we use TOP surgery to propose a characterization of the simplest embeddings of $F\times S^1$.