~ave energy flow conservation is demonstrated for Hermitian differential operators that arise m the Vlasov-Maxwell theory for propagation perpendicular to a magnetic field. The energy fl~w can be related ~o the. bilinear concomitant, for a solution and its complex conjugate, by usmg the Lagrange Identity ofthe operator. This bilinear form obeys a conservation law and is shown to describe the us...

A class of generally nonlinear dynamical systems is considered, for which the Lagrangian is represented as a sum of homogeneous functions of the displacements and their derivatives. It is shown that an energy partition as a single relation follows directly from the Euler-Lagrange equation in its general form. The partition is defined solely by the homogeneity orders. If the potential energy is ...

Abstract In this work, we derive the boundary Schrödinger (functional) equation for wave function of a quantum gravity system on manifold with boundaries together new constraint defined timelike boundary. From detailed analysis condition spatial boundary, find that while lapse and shift functions are independent Lagrange multipliers bulk, these two related; namely, they not independent. Hamilto...

In this paper, smooth Chua’s equation is generalized to a higher order system from a special viewpoint of interconnected systems. Simple conditions for Lagrange stability are established. And a detailed Lagrange stable region analysis is given for the canonical Chua’s oscillator. In addition, a new nonlinearly coupled Chua’s circuit that appeared in the recent literature is also discussed and a...

in this paper a new isolating system is introduced for short to mid-rise buildings. in comparison to conventional systems such as lrb and hrb, the proposed system has the advantage of no need to cutting edge technology and has low manufacturing cost. this system is made up of two orthogonal pairs of pillow-shaped rollers that are located between flat bed and plates. by using this system in two ...