• 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...

Controlling the bias is central to estimating semiparametric models. Many methods have been developed control in conditional expectations while maintaining a desirable variance order. However, these typically do not perform well at moderate sample sizes. Moreover, and perhaps related their performance, nonoptimal windows are selected with undersmoothing needed ensure appropriate In this paper, ...

In this paper we derive some unbiased estimators of the population mean under simple inverse sampling with replacement, using the class of Hansen-Hurwitz and Horvitz-Thompson type estimators and the post-stratification approach. We also compare the efficiency of resulting estimators together with Murthy's estimator. We show that in despite of general belief, the strategy consisting of inverse s...

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...

potential field methods such as gravity and magnetic methods are among the most applied geophysical methods in mineral exploration. a high-resolution technique is developed to image geologic boundaries such as contacts and faults. potential field derivatives are the basis of many interpretation techniques. in boundary detection, the analytic signal quantity is defined by combining the val...