Classical Lagrange Interpolation Based on General Nodal Systems at Perturbed Roots of Unity

The aim of this paper is to study the Lagrange interpolation on the unit circle taking only into account the separation properties of the nodal points. The novelty of this paper is that we do not consider nodal systems connected with orthogonal or paraorthogonal polynomials, which is an interesting approach because in practical applications this connection may not exist. A detailed study of the properties satisfied by the nodal system and the corresponding nodal polynomial is presented. We obtain the relevant results of the convergence related to the process for continuous smooth functions as well as the rate of convergence. Analogous results for interpolation on the bounded interval are deduced and finally some numerical examples are presented.

Distributed Expansion Planning By Using Particle Swarm Optimization Method

This paper exhibits a methodology for distribution expansion planning utilizing multi objective Particle Swarm Optimization (PSO). The Optimization objectives are power losses, Investment & Operating costs, Improve voltage profile. The PSO method has been verified by 30 real time nodal system. While planning the expansion and operation of distribution network, utilities have a complex combination of technical constraints, which must be considered together with the investment decisions on the behavior of the distribution system along the planning horizon.

The nimble node — Million-channel land recording systems have arrived

A new nodal land acquisition system is being developed with successful field tests in both cold- and hot-weather settings and is being compared against several existing industry acquisition systems. This nodal system differs from others in that it has been designed to deliver affordable high-quality seismic data with the lightest, smallest, and lowest-cost seismic channel system in the industry by significant margins. There are three main drivers for this innovation. First, it will significantly improve data quality by reducing the current cost barriers to acquiring high-density seismic surveys (i.e., full sampling in space, azimuth, and offset). Second, it will reduce the environmental footprint of land operations (less line clearance required). Third, it will improve the safety of land operations (fewer people and vehicles required per channel). All three have been achieved by dramatically reducing both the capital expenditure to build a one-million-channel highly portable recording system and the operational expenditure needed to operate such a system in the field.