The classical generation theorem of conservation laws from known ones for a system of differential equations which uses the action of a canonical Lie–Bäcklund generator is extended to include any Lie–Bäcklund generator. Also, it is shown that the Lie algebra of Lie–Bäcklund symmetries of a conserved vector of a system is a subalgebra of the Lie–Bäcklund symmetries of the system. Moreover, we in...

Abstract Let W (A) denote the field of values (numerical range) of a matrix A. For any polynomial p and matrix A, define the Crouzeix ratio to have numerator max {|p(ζ)| : ζ ∈ W (A)} and denominator ‖p(A)‖2. M. Crouzeix’s 2004 conjecture postulates that the globally minimal value of the Crouzeix ratio is 1/2, over all polynomials p of any degree and matrices A of any order. We derive the subdif...

We discuss a solution algorithm for quasi-static elastoplastic problems with hardening. Such problems can be described by a time dependent variational inequality, where the displacement and the plastic strain fields serve as primal variables. After discretization in time, one variational inequality of the second kind is obtained per time step and can be reformulated as each one minimization pro...

In this work we study necessary and sufficient optimality conditions for variational problems dealing with a new fractional derivative. This derivative combines two known operators: distributed-order derivatives arbitrary kernels. After proving integration by parts formula, obtain the Euler-Lagrange equation natural boundary fundamental problem. Also, integral holonomic constraints a...

We prove duality between the left and right fractional derivatives, independently on the type of fractional operator. Main result asserts that the right derivative of a function is the dual of the left derivative of the dual function or, equivalently, the left derivative of a function is the dual of the right derivative of the dual function. Such duality between left and right fractional operat...

We study the Schwarzian derivative from a variational viewpoint. Firstly we show that defines first integral of Euler--Lagrange equation second order Lagrangian. Secondly, itself is operator for an appropriately chosen class variations.