The Euler-MacLaurin sum formula has appeared in the titles
of two quite recent papers whose authors were primarily interested
in certain applications. In this paper a somewhat different approach
to the myriad of formulas for summation, integration, differentiation,
etc. , is based on the simple identity which defines the set...
This thesis is concerned with the detailed derivation
of Sheppard's Correction Formula relating the true to the
raw moments by the use of Euler-MacLaurin formula. Special
moment relationships have been derived using different
special functions, whose application is made to derive correction
formula for the semi-invariants. Special investigation
is carried...
Solutions to the variable permeability magnetostatic field
problem are achieved in both rectangular and cylindrical coordinates
for a wide variety of magnet geometries. The resulting
difference equations are solved iteratively and a method is
provided which substantially increases the rate of convergence
for these type of problems. Magnetization curves for...
Quantization is a non-linear operation of converting a continuous
signal into a discrete one, assuming a finite number of levels N. A
study is made of the quantization procedure, starting from the year
1898 to the present time. Conditions for minimum error are derived
with consideration of quantization in magnitude...
The sampling theorem states that any frequency bandlimited signal can be exactly reconstructed from its sampled values. Different forms of this theorem have been reviewed since 1841 up to the present time. Kramer's generalized sampling theorem has been extended to two dimensions, and the form for higher dimensions can be...
