‎The Mod $2$ Steenrod algebra is a Hopf algebra that consists of the primary cohomology operations‎, ‎denoted by $Sq^n$‎, ‎between the cohomology groups with $mathbb{Z}_2$ coefficients of any topological space‎. ‎Regarding to its vector space structure over $mathbb{Z}_2$‎, ‎it has many base systems and some of the base systems can also be restricted to its sub algebras‎. ‎On the contrary‎, ‎in ...

A long time ago, since the launch of the first artificial satellite in 1957, controling attitude of satellites has been considered by the designers and engineers of aerospace industry. Considering the importance of this issue various methods of control in response to this need have been presented and analyzed until now. In this paper, we propose and analyze a three-axis optimal control on the s...

Consider a C vector field together with an ergodic invariant probability that has l nonzero Lyapunov exponents. Using orthonormal moving frames along certain transitive orbits we construct a linear system of l differential equations which is a reduced form of Liao’s “standard system”. We show that the Lyapunov exponents of this linear system coincide with all the nonzero exponents of the given ...

the coherent anomaly method and a cluster mean-field approach combined with finite-sizescaling extrapolation were used to determine the critical temperature and the critical exponents of as =1 ising chain with a long-range interaction in the form of 1/ r1+σ . the results of criticaltemperature are in good agreement with the recent results of the finite-range scaling method and aremore accurate ...