Abstract. Algorithms and underlying mathematics are presented for numerical computation with periodic functions via approximations to machine precision by trigonometric polynomials, including the solution of linear and nonlinear periodic ordinary differential equations. Differences from the nonperiodic Chebyshev case are highlighted.
Wireless Body Area Networks (WBANs) are in the spotlight of researchers and engineering industries due to many applications. Remote health monitoring for general as well as military purposes where tiny sensors are attached or implanted inside the skin of the body to sense the required attribute is particularly prominent. To seamlessly accomplish this procedure, there are various challenges, out of which temperature control to reduce thermal effects and optimum power consumption to reduce energy wastage are placed at the highest priority. Regular and consistent operation of a sensor node for a long-time result in a rising of the temperature of respective tissues, where it is attached or implanted. This temperature rise has harmful effects on human tissues, which may lead to the tissue damage. In this paper, a Temperate Aware and Energy Optimized (TAEO) routing protocol is proposed that not only deals with the thermal aspects and hot spot problem, but also extends the stability and lifetime of a network. Analytical simulations are conducted, and the results depict better performance in terms of the network lifetime, throughput, energy preservation, and temperature control with respect to state of the art WBAN protocols.
The error in the trapezoidal rule quadrature formula can be attributed to discretization in the interior and non-periodicity at the boundary. Using a contour integral, we derive a unified bound for the combined error from both sources for analytic integrands. The bound gives the Euler-Maclaurin formula in one limit and the geometric convergence of the trapezoidal rule for periodic analytic functions in another. Similar results are also given for the midpoint rule.
Location is a kind of contextual information that is often realized through localization technologies in strict sense. The technologies such as WSNs provide geographical location as in Cartesian coordinates or in referenced landmarks, rendering a rigid and unilateral interface to multiple applications. A myriad of applications using localization technologies often do not require precise location, instead need to syntactically process location information with newer contexts. The current work in localization does not abridge location and context. In this paper, we have presented the idea of logical groups; a bridge between context and location. The idea is substantiated through LEGATE, a location management tool, whose design and operation is shown to be of relevance and practical significance in commercial applications.
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