The Lagrange multiplier for the kinetic energy e is shown to be −γcm on a singular arc, where γ (g/J) is derived from engine and driveline characteristics and cm ≈ 1. Using this value as an approximation for constrained arcs as well, the cost function is J(s, x) ≈ −γcme + C(s) that yields the residual cost φ(x) = −γcme. The factor β corresponds to the constant Lagrange multiplier for time and i...

In this paper, we give a sufficient condition on a linear operator Lp(a, c)g(z) which can guarantee that for α a complex number with Re(α) > 0, Re { (1− α)p c)f(z) Lp(a, c)g(z) + α Lp(a + 1, c)f(z) Lp(a + 1, c)g(z) } > ρ, ρ < 1, in the unit disk E, implies Re { Lp(a, c)f(z) Lp(a, c)g(z) } > ρ ′ > ρ, z ∈ E. Some interesting applications of this result are also given.

On compact manifolds (M, g) without boundary of dimension n ≥ 2, the gradient estimates for unit band spectral projection operators χλ is proved for any second order elliptic differential operators L by maximum principle. A new proof of Hörmander Multiplier Theorem on the eigenfunction expansion of the operator L is given in this setting by using the gradient estimates and the Calderón-Zygmund ...

objective(s): hyperthermia is one of the most common environmental stressors that affect multi-biological systems in the body including the central nervous system as well as the hematopoietic organs. the objective of the present study was to investigate the protective role of ethanolic extract of propolis (eep) on some selective stress markers, hematological, biochemical, and histopathological ...

A simple plausibility argument is given. Let g be a finite-dimensional Lie algebra with generators J a and structure constants f ab c. The brackets are given by [J a , J b ] = f ab c J c. Denote the symmetric Killing metric (proportional to the quadratic Casimir operator) by δ ab = tr J a J b , and let the totally symmetric third Casimir operator be d abc = tr {J a , J b }J c .

A semidiscrete multiplier is an operator between a space of functions or distributions on a locally compact Abelian group G on the one hand, and a space of sequences on a discrete subgroup H of G on the other hand, with the property that it commutes with shifts by H. We describe the basic form of such operators and show a number of representation theorems for classical spaces like Lp, C0, etc. ...