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A Tutorial Introduction to Maple
Cryptography Using Chebyshev Polynomials
- G. Fee
- Computer Science, Mathematics
This work considers replacing the monomial xn with the Chebyshev polynomial Tn(x) in the Diffie-Hellman and RSA cryptography algorithms.
Zeros of Partial Sums of the Riemann Zeta Function
It is shown that the zeros of a ζN(s), when reduced into imaginary periods derived from primes less than or equal to N, establish regular patterns and can be embedded as a dense set in the period of a surface in ℝk+1.
The prime factors of Wendt’s binomial circulant determinant
Wendt’s binomial circulant determinant, W„, is the determinant of an m by m circulant matrix of integers, with (i, j)th entry (i, ™.i) whenever 2 divides m but 3 does not. We explain how we found the…
Isogroups of Differential Equations Using Algebraic Computing
ON THE DESIGN AND PERFORMANCE OF THE MAPLE SYSTEM *
Timing comparisons with other symbolic computation systems show that time efficiency is achieved as well as space efficiency in Maple.
Comparison of algorithms for the symbolic computation of the NP spin coefficients and curvature components
The test results confirm the theoretical superiority of the algorithm based on Debever's formalism over the one based directly on Cartan's first structural equations for the computation of the spin coefficients both with respect to execution time and storage requirements.
Asymptotic series of generalized Lambert W function
This work examines series expansions of the generalized version providing computational means for evaluating this function in various regimes and confirming the notion that this generalization is a natural nextension of the standard Lambert W function.
Canonical reduction for dilatonic gravity in 3+1 dimensions
We generalize the 1+1-dimensional gravity formalism of Ohta and Mann to 3+1 dimensions by developing the canonical reduction of a proposed formalism applied to a system coupled with a set of point…
Equivalence of Kramers-Kronig and Fourier Transforms to Convert between Optical Dispersion and Optical Spectra
The complex refractive index relates optical dispersion, which describes the variation of refractive index with wavenumber, to the corresponding absorption spectrum; both phenomena are associated…