In this paper is presented a parallel algorithm for computing a Lagrange interpolation on a Extended Fibonacci Cube EFC 1(n).The algorithm consists of three phases: initialisation phase, main phase in wich the Lagrange polynomials are computed and final phase in wich the terms of the interpolation formula are added together.

We give new regularity conditions based on epigraphs that assure strong duality between a given primal convex optimization problem and its Lagrange and Fenchel-Lagrange dual problems, respectively, in infinite dimensional spaces. Moreover we completely characterize through equivalent statements the so-called stable strong duality between the initial problem and the mentioned duals.

We consider the problem of semi-cardinal interpolation for polyharmonic splines. For absolutely summable data sequences, we construct a solution to this problem using a Lagrange series representation. The corresponding Lagrange functions are deened using Fourier transforms and the technique of Wiener-Hopf factorizations for semi-space lattices.

Using the reviewed Riemann-Liouville fractional derivative we define the bundle αk E = Osc(M) and highlight geometrical structures with a geometrical character. Also, we introduce the fractional osculator Lagrange space of k order and the main structures on it. The results are applied at the k order fractional prolongation of Lagrange, Finsler and Riemann fractional structures. Mathematics Subj...

The paper deals with a general optimal control problem for age-structured systems. A necessary optimality condition of Pontryagin type is obtained, where the novelty is in that mixed control-state constraints are present. The proof uses an abstract Lagrange multiplier theorem, and the main difficulty is to obtain regularity of the Lagrange multipliers in the particular problem at hand.

A 3D slip-dependent frictional contact problem in elastostatics is discussed. We deliver a variational formulation as a mixed variational problem whose Lagrange multipliers set is solutiondependent. Then, the existence and the boundedness of the solutions is investigated. The proof is based on a recent result for an abstract mixed variational problem with solution-dependent set of Lagrange mult...

Some problems on variations are raised for classical discrete mechanics and field theory and the difference variational approach with variable step-length is proposed motivated by Lee’s approach to discrete mechanics and the difference discrete variational principle for difference discrete mechanics and field theory on regular lattice. Based upon Hamilton’s principle for the vertical variations...

In modern DSL systems, multi-user crosstalk is a major source of performance degradation. Optimal Spectrum Balancing (OSB) is a centralized algorithm that mitigates the effect of crosstalk by allocating optimal transmit spectra to all interfering DSL modems. By the use of Lagrange multipliers the algorithm decouples the spectrum management problem into per-tone optimization problems. The remain...

We summarise research reported in (Efroimsky 2002, 2003; Efroimsky & Goldreich 2003a,b) and develop its application to planetary equations in non-inertial frames. Whenever a standard system of six planetary equations (in the Lagrange, Delaunay, or other form) is employed, the trajectory resides on a 9(N-1)-dimensional submanifold of the 12(N-1)-dimensional space spanned by the orbital elements ...

We summarise research reported in (Efroimsky 2002, 2003; Efroimsky & Goldreich 2003a,b) and develop its application to planetary equations in non-inertial frames. Whenever a standard system of six planetary equations (in the Lagrange, Delaunay, or other form) is employed, the trajectory resides on a 9(N-1)-dimensional submanifold of the 12(N-1)-dimensional space spanned by the orbital elements ...