The motion of a particle about a non-rotating 2nd degree and order-gravity field is investigated. Averaging conditions are applied to the particle motion and a qualitative analysis which reveals the general character of motion in this system is given. It is shown that the orbit plane will either be stationary or precess about the body’s axis of minimum or maximum moment of inertia. It is also s...

Ronald Dworkin and Philip Kitcher recognize that traditional, religious faith—especially in Christian theistic tradition—has virtues that seem to be missing in a secular worldview. To remedy this apparent deficit, they both propose that a secular worldview can provide a satisfying foundation for a flourishing, meaningful life. Moreover, Kitcher argues that secular humanism is far more justified...

We derive dynamical equations for a driven, dissipative quantum system in which the environment-induced relaxation rate is comparable to the Rabi frequency, avoiding assumptions on the frequency dependence of the environmental coupling. When the environmental coupling varies significantly on the scale of the Rabi frequency, secular or rotating wave approximations break down. We avoid these appr...

The homotopy analysis method HAM is employed to propose an approach for solving the nonlinear dynamical system of an electrostatically actuated micro-cantilever in MEMS. There are two relative merits of the presented HAM compared with some usual procedures of the HAM. First, a new auxiliary linear operator is constructed. This operator makes it unnecessary to eliminate any secular terms. Furthe...

Our randomized preprocessing enables pivoting-free and orthogonalization-free solution of homogeneous linear systems of equations. In the case of Toeplitz inputs, we decrease the solution time from quadratic to nearly linear, and our tests show dramatic decrease of the CPU time as well. We prove numerical stability of our randomized algorithms and extend our approach to solving nonsingular line...

We derive upper and lower bounds on the smallest and largest eigenvalues, respectively, of real symmetric Toeplitz matrices. The bounds are rst obtained for positive-deenite matrices and then extended to the general real symmetric case. Our bounds are computed as the roots of rational and polynomial approximations to spectral, or secular, equations. The decomposition of the spectrum into even a...

This article estimates the effects of various parent and child characteristics on the choice of care arrangement of the parent, taking into account the potential endogeneity of some of the child characteristics. Three equations are estimated: a care choice equation, a child location equation, and a child work equation. Results suggest a hierarchy of family decision making; child locations affec...

Spin relaxation in a microscopic model of spin maser is studied theoretically. Seven qualitatively different regimes are found: free induction, collective induction, free relaxation, collective relaxation, weak superradiance, pure superradiance, and triggered superradi-ance. The initiation of relaxation can be originated either by an imposed initial coherence or by local spin fluctuations due t...

We consider methods for regularising the least-squares solution of the linear system Ax = b. In particular, we propose iterative methods for solving large problems in which a trust-region bound ‖x‖ ≤ ∆ is imposed on the size of the solution, and in which the least value of linear combinations of ‖Ax−b‖q2 and a regularisation term ‖x‖ p 2 for various p and q = 1, 2 is sought. In each case, one o...

We consider the initial-value problem for a system of coupled Boussinesq equations on the infinite line for localised or sufficiently rapidly decaying initial data, generating sufficiently rapidly decaying rightand left-propagating waves. We study the dynamics of weakly nonlinear waves, and using asymptotic multiple-scales expansions and averaging with respect to the fast time, we obtain a hier...