We prove by symmetry properties that the Lagrangian of a free pointmass is a quadratic function of the speed in the non-relativistic case, and that the action of the free point-mass between two spacetime points is the proper time passed in the relativistic case. These well known facts are proved in a mathematically rigorous way with a frame independent treatment based on spacetime models introd...

Let A be a hermitian matrix of order n, and b a known vector n H in C . The problem is to determine which vectors make ^(x) = (x-b) A(x-b) H a maximum or minimum on the unit sphere U = fx : x x = 1} . The problem is reduced to the determination of a finite point set, the spectrum of (A,b). The theory reduces to the usual theory of hermitian forms when b = 0. *J Reproduction in Whole or in Part ...

We construct a finitely presented group G with non-quadratic Dehn function f majorizable by a quadratic function on arbitrary long intervals.

Article history: Received 10 November 2011 Revised 19 September 2012 Accepted 24 September 2012 Available online 4 October 2012 Communicated by Stephen D. Cohen

This paper analyzes energy equipartition in linear Hamiltonian systems in a deterministic setting.We consider the group of phase space symmetries of a stable linear Hamiltonian system, and characterize the subgroup of symmetries whose elements preserve the time averages of quadratic functions along the trajectories of the system. As a corollary, we show that if the system has simple eigenvalues...

in this paper, stabilization conditions and controller design for a class of nonlinear systems are proposed. the proposed method is based on the nonlinear feedback, quadratic lyapunov function and heuristic slack matrices definition. these slack matrices in null products are derived using the properties of the system dynamics. based on the lyapunov stability theorem and sum of squares (sos) dec...

This paper presents a simplifiedlagrangian multiplier based algorithm to solve the fixed head hydrothermalscheduling problem. In fixed head hydrothermal scheduling problem, waterdischarge rate is modeled as quadratic function of hydropower generation andfuel cost is modeled as quadratic function of thermal power generation. Thepower output of each hydro unit varies with the rate of water discha...