Characteristic parameter sets and limits of circulant Hermitian polygon transformations

Characteristic Clause Sets and Proof Transformations

Proof Theory is the branch of mathematical logic that investigates mathematical reasoning and mathematical proofs. This area emanated from Hilbert’s Program calling for consistency proofs of formal theories. In the 1950s the focus of proof theory began shifting towards applications of formal methods to concrete proofs in order to obtain new mathematical results. The method CERES (cut-eliminatio...

On Linear Polygon Transformations

Circulant Preconditioners for Hermitian Toeplitz Systems

We study the solutions of Hermitian positive deenite Toeplitz systems Ax = b by the preconditioned conjugate gradient method for three families of circulant preconditioners C. The convergence rates of these iterative methods depend on the spectrum of C ?1 A. For a Toeplitz matrix A with entries which are Fourier coeecients of a positive function f in the Wiener class, we establish the invertibl...

Speech encryption using circulant transformations

A new analog encryption technique using unitary circulant transformations of the sampled analog signal is proposed. This technique is less vulnerable to attack than other known schemes based on transposition(scramhling) of the signal components in time or frequency domain. The new technique introduces primarily a phase distortion. A new distonion measure capable of quantifying phase distortion ...

Limits of Recursive Triangle and Polygon Tunnels

In this paper we present unsolved problems that involve infinite tunnels of recursive triangles or recursive polygons, either in a decreasing or in an increasing way. The “nedians or order i in a triangle” are generalized to “nedians of ratio r” and “nedians of angle α” or “nedians at angle β”, and afterwards one considers their corresponding “nedian triangles” and “nedian polygons”. This tunne...