• 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...

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...

in this paper, a novel patch geodesic derivative pattern (pgdp) describing the texture map of a face through its shape data is proposed. geodesic adjusted textures are encoded into derivative patterns for similarity measurement between two 3d images with different pose and expression variations. an extensive experimental investigation is conducted using the publicly available bosphorus and bu-3...

in this paper a new method is proposed for interpretation of 2d magnetic data, using multiples of the analytic signal method, in which the analytic signal of magnetic anomaly is used directly to compute the depth and the structural index of the source instead of using its higher order derivatives. this method only needs the computation of the first order derivatives of the magnetic anomaly, so ...

for every $1leq s< n$, the $s^{th}$ derivative of a polynomial $p(z)$ of degree $n$ is a polynomial $p^{(s)}(z)$ whose degree is $(n-s)$. this paper presents a result which gives generalizations of some inequalities regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle. besides, our result gives interesting refinements of some well-known results.

acylisothiocyanate (1) was allowed to react with benzylidene malononitrile producing oxazine derivative (2). also, compound (1) was reacted with sodium azide followed by refluxing with sodium ethoxide affording thiazinotetrazole derivative (4). the reaction of acetylacetone with compound (1) gave pyridine derivative (5) by intramolecular cycloaddition while it was reacted with n-methyl aniline ...