Sentient Arithmetic is defined as an extention of Elementary Arithmetic with three more derivation rules and the Incompleteness Theorems are derived within it without using any metalanguage. It is shown that Consistency cannot be chosen as an axiom

Directed paths are obtained by inverting a matrix with elements from a field, showing that it is unnecessary to go through the cumbersome procedure of inverting a matrix with elements from a division ring

Primitive elements of field extension ()/() are counted using (1) principle of inclusion-exclusion, (2) Möbius inversion, and (3) Euler function. Then, an identityis obtained, where > 1, a prime, (·) Euler function, and , …, the all distinct prime divisors of

This paper concerns the harmonic projection methods for computing an approximation to an eigenpair (λ, ) of a large matrix A. Given a subspace that contains an approximation to , a harmonic method returns an approximation to (λ, ). Three convergence results are established as the deviation ε...

The problem of restricted random walks of fixed dimension and finite memory is considered using extension of methods discussed earlier. Inversion of recursion relations, derived in Ref. 1, is derived and recursion relations for restricted random walks of fixed dimension and four and six step...

Thomas-Whitehead projective connections, or TW-connections, are torsionfree linear connections, satisfying certain properties, on a naturally defined principal ℝ-bundle over a manifold. Three equivalence classes of TW-connections will be considered. This leads to a necessary and sufficient...

We present both a mathematical model and a numerical method for simulating induction heating processes. The aim is to determine the temperature field in a workpiece surrounded by an inductor when the inductor total current is known. We assume that all the conductor (the inductor and the...

In this paper we propose a modification of the finite termination algorithm which reduce the dimension of primal-dual linear programming problem. We note that similar approach is possible in any primal-dual algorithm for linear programming

In this paper we introduce two direct methods for solving some classes of linear programming problems. The first method produces the extreme vertex or a neighboring vertex with respect to the extreme point. The second method is based on the game theory. Both of these methods can be used in...

The shift-and-invert Arnoldi method has been popularly used for computing a number of eigenvalues close to a given shift and/or the associated eigenvectors of a large unsymmetric matrix pair, but there is no guarantee for the approximate eigenvectors, Ritz vectors, obtained by this method to...