Where LSP refers to stock prices, LOP+ and LGP+ denote the positive

partial sum of oil prices and gold prices respectively.

We propose a protocol that--using a binomial tree topology and Paillier homomorphic encryption--can produce a "quick and dirty"

partial sum even in the event of failures, has adjustable capability of resisting collusion, and can be completed in logarithmic time.

Therefore values of the

partial sum coincide with values of [[sigma].sub.d,N] in points [mathematical expression not reproducible].

Hence the first half adder will be used to add A and B to obtain

partial sum. Formerly the second half adder logic can be used to carry in to the sum produced by the half adder to get the final sum output.

There are [N.sub.s] = [(2N + 1).sup.2] Fourier coefficients in the

partial sum [s.sub.N](f; x, y); that is,

where the

partial sum [mathematical expression not reproducible].

For a function f having a jump-discontinuity, every traditional spectral

partial sum approximation will not converge uniformly on any interval containing the discontinuity.

The

partial sum of Fourier series F (t) of discrete data [f.sub.i] is given by

Similarly to the attacks to 6-round ARIA, the partial encryption and decryption using the

partial sum technique are proceeded as follows.

During the hearing, the second defendant, who was the recipient of the

partial sum, had hesitated to answer a question about the type of fine that was being paid off.

is a

partial sum of an absolutely convergent series restricted to classes p with N(p) sufficiently large.

For example, a smooth periodic function can be approximated by trigonometric polynomials; a square-integrable smooth function can be expanded into a wavelet series and be approximated by

partial sum of the wavelet series; and a smooth function on a cube can be approximated well by polynomials.