Kyparisis proved in 1985 that a strict version of the MangasarianFromovitz constraint qualification (MFCQ) is equivalent to the uniqueness of Lagrange multipliers. However, the definition of this strict version of MFCQ requires the existence of a Lagrange multiplier and is not a constraint qualification (CQ) itself. In this note we show that LICQ is the weakest CQ which ensures (existence and) ...

We study calculus of variations problems, where the Lagrange function depends on the Caputo-Katugampola fractional derivative. This type of fractional operator is a generalization of the Caputo and the Caputo–Hadamard fractional derivatives, with dependence on a real parameter ρ. We present sufficient and necessary conditions of first and second order to determine the extremizers of a functiona...

q-analogs of the Catalan numbers c', = (I/(n + I))($) are studied from the viewpoint of Lagrange inversion. The first, due to Carhtz, corresponds to the Andrews-Gessel-Garsia q-Lagrange inversion theory, satisfies a nice recurrence relation and counts inversions of Catalan words. The second, tracing back to Mac Mahon, arise from Krattenthaler's and Gessel and Stanton's q-Lagrange inversion form...

there are many occasions where the base of a robotic manipulator is attached to a moving platform, such as on a moving ship, terrain or space shuttle. in this paper a dynamic model of a robotic manipulator mounted on a moving base is derived using both newton-euler and lagrange-euler methods. the presented models are simulated for a mitsubishi pa10-6ce robotic manipulator characteristics mounte...

We introduce a novel technique for constructing higher-order variational integrators for Hamiltonian systems of ODEs. In particular, we are concerned with generating globally smooth approximations to solutions of a Hamiltonian system. Our construction of the discrete Lagrangian adopts Hermite interpolation polynomials and the Euler–Maclaurin quadrature formula, and involves applying collocation...

Most researches on fluid dynamics are mostly dedicated to obtain the solutions of Navier-Stokes equation which governs fluid flow with particular boundary conditions and approximations. We propose an alternative approach to deal with fluid dynamics using the lagrangian. We attempt to develop a gauge invariant lagrangian which reconstructs the Navier-Stokes equation through the Euler-Lagrange eq...

Asking for the optimal protocol of an external control parameter that minimizes the mean work required to drive a nanoscale system from one equilibrium state to another in finite time, Schmiedl and Seifert [T. Schmiedl and U. Seifert, Phys. Rev. Lett. 98, 108301 (2007)] found the Euler-Lagrange equation to be a nonlocal integrodifferential equation of correlation functions. For two linear examp...

We develop the non-di erentiable embedding theory of di erential operators and Lagrangian systems using a new operator on non-di erentiable functions. We then construct the corresponding calculus of variations and we derive the associated non-di erentiable Euler-Lagrange equation, and apply this formalism to the study of PDE's. First, we extend the characteristics method to the non-di erentiabl...