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derivative
Aliasing error bounds are derived for one- and two-channel sampling series analogous to the Whittaker-Kotel'nikov-Shannon series, and for the multi-band sampling series, and a "derivative" extension of it, due to Dodson, Beaty, et al.
      
Examples are considered, and the frame bounds in the case of sampling of the signal and its first derivative are calculated explicitly.
      
This article also gives a single necessary-and-sufficient condition for a holomorphic function to be the transform of a function f such that any derivative of f multiplied by any polynomial is in Lp (d, ρ).
      
Applying a special derivative reproducing property, we show that when the kernel is real analytic, every function from the RKHS is real analytic.
      
5-Aza analogs were prepared of several tryptamine derivatives and a skatole derivative known to bind at human 5-HT6 receptors and evaluated to determine if they bind in a manner similar to their indolic analogs.
      
Molecules 6f, i, and j inhibited only COX-1, and the disubstituted ethoxy derivative (6g) was inactive as a COX inhibitor (≤ 100?μM).
      
The nitrile derivative 7 was obtained by dehydration of the amide 3 in a mixture of SOCl2 and Dimethylformamide (DMF).
      
Cyclocondensation reaction of 7 with anhydrous hydrazine led to the formation of 7-aminopyrazolo[3,4-d]pyridazine 8 derivative.
      
The finding of antibacterial activity study showed that the sulfamide derivative 5 was the best compound of the series, exhibiting antibacterial activity against both Gram-positive and Gram-negative bacteria.
      
A new method to compute the first derivative of 3-D Radon transform is given for cone-beam data taken from any orbit.
      
For real-valued functions defined on Cantor triadic set, a derivative with corresponding formula of Newton-Leibniz's type is given.
      
In this paper the derivative and its exceptional Sct according to the alternatively jump-ing function and self-similar function respectively are discussed.
      
2(2) of "Calculus on Cantor triadic Set (I)-derivative" which is important to the discussion of exceptional Set is given.
      
A class of multiderivative hybrid one-step methods of order at least s+1 is constructed with s+1 parameters, where s is the order of derivative.
      
Furthermore, a class of A-stable 2 parameters hybrid one-step methods of order at least 8 are constructed, which use 4th order derivative.
      
Optimal L2 and H1 estimates for the error and its time derivative are established.
      
It is available for the case that the sign of f(x) changes frequently or the derivative f'(x) does not exist in the neighborhood of the root, while the Newton method is hard to work.
      
By Monte Carlo simulation-based approximations of the objective function and its first (second) derivative, an inexact Lagrange-Newton type method is proposed.
      
Using the duality theory of the linear programming and convex theory, the generalized directional derivative of the general multicommodity minimal cost flow problems is derived.
      
A derivative-free algorithm for unconstrained optimization
      
 

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