This paper provides a brief introduction to automatic diierentiation and relates it to the tangent linear model and adjoint approaches commonly used in meteorology. After a brief review of the forward and reverse mode of automatic diierentiation, the ADIFOR automatic diierentiation tool is introduced, and initial results of a sensitivity-enhanced version of the MM5 PSU/NCAR mesoscale weather mo...

The vulnerability of solar power producers to sunshine fluctuations exposes them the volumetric risk that future electricity generation may deviate from predicted generation. Weather derivatives have recently emerged as a tool for hedging risks these producers. However, state-of-the-art instruments several shortcomings, contributing their limited application in industry. Therefore, novel radiat...

Some of the potentially most destructive effects of severe space weather storms are caused by the geomagnetically induced currents. Geomagnetically induced currents (GICs) can cause failures of electric transformers and result in widespread blackouts. GICs are induced by the time variability of the magnetic field and are closely related to the time derivative of the local magnetic field perturb...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

road accident severity may be influenced by a number of various systematic causal factors. the weather and road accidents have a close relationship with each other and a number of methods have been proposed for measuring the risk of a road accident with rainy, foggy, and snowy weather and high winds. recent studies indicate that road collision rates increase during precipitation. the weather wa...

• Connections in Rn . We have by now defined a number of different notions of differentiation: the differential of maps between manifolds, the exterior derivative of differential forms, and the Lie derivative. To begin to see the need for a new notion of differentiation (which will turn out to be the most fundamental and will apply to general tensor fields) consider first the problem of definin...

We survey recent results on the structure of the range of the derivative of a smooth mapping f between two Banach spaces X and Y . We recall some necessary conditions and some sufficient conditions on a subsetA of (X ,Y) for the existence of a Fréchet differentiable mapping f from X into Y so that f ′(X)= A. Whenever f is only assumed Gâteaux differentiable, new phenomena appear: for instance, ...

approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. in this paper with central difference approximation and newton cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. three...