The Euler-Lagrange equations for some class of gravitational actions are calculated by means of Palatini principle. Polynomial structures with Einstein metrics appear among extremals of this variational problem.

The main purpose of this paper is to present a systemic study of some families of multiple q-Euler numbers and polynomials. In particular, by using the q-Volkenborn integration on Zp, we construct p-adic q-Euler numbers and polynomials of higher order. We also define new generating functions of multiple q-Euler numbers and polynomials. Furthermore, we construct Euler q-Zeta function.

Abstract. We study vesicles formed by lipid bilayers that are governed by an elastic bending energy and on which the lipids laterally separate forming two different phases. The energy laden phase interfaces may be modeled as curves on the hyper-surface representing the membrane (sharp interface model). The phase field methodology is another powerful tool to model such phase separation phenomena...

In the present note, we give a simple general proof for the existence of solutions of the following two types of variational problems: PROBLEM A. To minimize fa F(x> u, • • • , Du)dx over a subspace VofW>*(tt). PROBLEM B. TO minimize ƒ« F(x, w, • • • , Du)dx for u in V with / a G(x, u, • • • , D^u)dx^c. The solution of the first problem yields a weak solution of a corresponding elliptic boundar...

This paper deals with twisting motion of a falling cat robot by two torque inputs around her waist. The cat robot consists of two rigid columns and has internally two actuators at the joint to generate torque inputs around the normal coordinates. This system is a nonholonomic system whose angular momentum is conserved. W e obtain the Lagrange’s equation of motion with nonholonomic constraint an...

We establish, as far as we know, the first proof of uniform global asymptotic stability for a mechanical system (Euler-Lagrange) in closed loop with a dynamic controller which makes use only of position measurements. The controller is fairly simple, it is reminiscent of the so-called PadenPanja controller [20] where unavailable generalized velocities are replaced by approximate differentiation ...

We show that there are ordinary differential equations in R with unbounded solutions, for which the difference equations obtained by using the forward Euler method have all solutions bounded.

We shall prove the existence of minimizers of the following functional f(u) = R T 0 L(x, u(x), u ′(x)) dx without convexity assumption. As a consequence of this result and the duality described in [10] we derive the existence of solutions for the Dirichlet problem for a certain differential inclusion being a generalization of the Euler–Lagrange equation of the functional f .

can be found in closed form by means of certain transformations on generating functions and the extraction of coefficients (see the end of section 3) suggested by Ira Gessel, and they comment: “He [Gessel] attributes this elegant technique, the ‘method of coefficients,’ to G. P. Egorychev.” Actually, in his book Integral Representation and Computation of Combinatorial Sums, Egorychev [4] (see [...

In this paper, the analysis is focused on single-time optimal control problems based on simple integral cost functionals from Lagrangians whose order is smaller than the higher order of ODEs constraints. The basic topics of our theory include: variational differential systems, adjoint differential systems, Legendrian duality, single-time maximum principle. The main original results refer to the...