Relativistic Quantum Mechanical Condition for Expansion of the Universe

In this manuscript, we will discuss about the quantum mechanical system for the movement of non-intractable particle, non-intractable particle which attends every mass state in the universe, the form of a non-intractable particle is n = -m, this manuscript defines the stable cross system for the movement of n-i particles and elementary particles with a perfect black body at centre with proofs of picture of super massive black hole, the linear hamiltonian of the cross quantum mechanical system and with this, it’s co-related matrixes, then by the use of cross system of Non-Intractable Particles defining a new right angel theorem. Then the new black body relation free from plank constant depends on non interactive mechanics and m, which has already mentioned in non-interactive mechanics and it’s relation with galaxies. The unique property of cross system is that it is surrounded by the energy of 10e + e always, and at last the relation between zero point energy and dark energy.

Lower Bounds of Optimal Exponentials of Thickness in Geometry Rigidity Inequality for Shells

The optimal exponentials of thickness in the geometry rigidity inequality of shells represent the geometry rigidity of the shells.The author obtains that the lower bounds of the optimal exponentials are 4/3,3/2,and 1,for hyperbolic shells,parabolic shells,and elliptic shells,respectively,through the construction of the Ans?tze.

Riemannian geometric approach to optimal binocular rotation,pyramid based interpolation and bio-mimetic pan-tilt movement

Over the past several years,we have been studying the problem of optimally rotating a rigid sphere about its center,where the rotation is actuated by a triplet of external torques acting on the body.The control objective is to repeatedly direct a suitable radial vector,called the gaze vector,towards a stationary point target in R^(3).The orientation of the sphere is constrained to lie in a suitable submanifold of SO(3).Historically,the constrained rotational movements were studied by physiologists in the nineteenth century,interested in eye and head movements.In this paper we revisit the gaze control problem,where two visual sensors,are tasked to simultaneously stare at a point target in the visual space.The target position changes discretely and the problem we consider is how to reorient the gaze directions of the sensors,along the optimal pathway of the human eyes,to the new location of the target.This is done by first solving an optimal control problem on the human binocular system.Next,we use these optimal control and show that a pan-tilt system can be controlled to follow the gaze trajectory of the human eye requiring a nonlinear static feedback of the pan and tilt angles and their derivatives.Our problem formulation uses a new Riemannian geometric description of the orientation space.The paper also introduces a new,pyramid based interpolation method,to implement the optimal controller.

Decay Rates of the Hyperbolic Equation in an Exterior Domain with Half-Linear and Nonlinear Boundary Dissipations

This paper considers the energy decay of the wave equation with variable coefficients in an exterior domain.The damping is put on partly the boundary and partly on the interior of the domain.The energy decay results are established by Riemannian geometry method.

On Boundary Stability of Wave Equations with Variable Coefficients

In this paper, we consider the boundary stabilization of the wave equation with variable coefficients by Riemmannian geometry method subject to a different geometric condition which is motivated by the geometric multiplier identities. Several (multiplier) identities (inequalities) which have been built for constant wave equation by Kormornik and Zuazua are generalized to the variable coefficient case by some computational techniques in Riemmannian geometry, so that the precise estimates on the exponential decay rate are derived from those inequalitities. Also, the exponential decay for the solutions of semilinear wave equation with variable coefficients is obtained under natural growth and sign assumptions on the nonlinearity. Our method is rather general and can be adapted to other evolution systems with variable coefficients (e.g. elasticity plates) as well.