In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...

The rotating frame is considered in quantum mechanics on the basis of the position dependent boost relating this frame to the non rotating inertial frame. We derive the Sagnac phase shift and the spin coupling with the rotation in the non relativistic limit by a simple treatment. By taking the low energy limit of the Dirac equation with a spin connection, we obtain the Hamiltonian for the rotat...

In this paper, we propose a novel simultaneous localization and mapping algorithm, R-LIO, which combines rotating multi-line lidar inertial measurement unit. R-LIO can achieve real-time high-precision pose estimation map-building. is mainly composed of four sequential modules, namely nonlinear motion distortion compensation module, frame-to-frame point cloud matching module based on normal dist...

Three weak gravitational effects associated with the gravitomagnetic fields are taken into account in this paper: (i) we discuss the background Lorentz transformation and gauge transformation in a linearized gravity theory, and obtain the expression for the spin of gravitational field by using the canonical procedure and Noether theorem; (ii) we point out that by using the coordinate transforma...

Three weak gravitational effects associated with the gravitomagnetic fields are taken into account in this paper: (i) we discuss the background Lorentz transformation and gauge transformation in a linearized gravity theory, and obtain the expression for the spin of gravitational field by using the canonical procedure and Noether theorem; (ii) we point out that by using the coordinate transforma...

The momentum integral of a baroclinic jet of fluid in a rotating frame determines the relative size of two jets which are produced when the jet is split by a wall. Owing to lateral variation of velocity and depth of the jet, the percentage of fluid which goes to the right or left differs from that of the non-rotating jet, which is generally assumed to have no shew-. For a northern hemisphere je...

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

This paper studies the oscillatory stability of uniformly rotating main-sequence stars of mass 3-8 M⊙ by solving the linearized non-adiabatic, non-radial oscillation equations with a forcing term and searching for resonant response to a complex forcing frequency. By using the traditional approximation the solution of the forced oscillation equations becomes separable, whereby the energy equatio...