in this paper, we introduce the notion of primal strong co-ideals and give some results involving them. it is shown thatsubtractive strong co-ideals are intersection of all primal strong co-ideals that contain them. also we prove that the representation of strong co-ideals as reduced intersections of primal strong co-ideals is unique.

The transfer-matrix of the U(1) lattice gauge theory is investigated in field Fourier space, basis which consists quantized currents on links. Based a version current conservation, elements are shown to be nonzero only between states that differ circulating inside plaquettes. In strong coupling limit, series expansion developed for transfer matrix, diagrammatic representation based occurrence v...

This paper introduces two complexity-theoretic formulations of Bennett’s logical depth: finite-state depth and polynomial-time depth. It is shown that for both formulations, trivial and random infinite sequences are shallow, and a slow growth law holds, implying that deep sequences cannot be created easily from shallow sequences. Furthermore, the E analogue of the halting language is shown to b...

It is common to identify the class of computable functions with the class of functions computable by the Turing machine. The identification is done on the ground of the famous Church-Turing thesis. In fact, the thesis justifies only one implication: computable function are Turing computable. The other implication is quite obviously false if computability means practical computability. I am not ...

subject to c(x) ≥ 0, where f : R → R and c : R → R are twice continuously differentiable functions. Let g(x) denote the gradient of f(x), and J(x) the mxn Jacobian matrix of c(x), with rows the gradients of c(x). A point x∗ is feasible with respect to the constraints c(x) if c(x∗) ≥ 0, and infeasible if c(x∗) < 0. The constraint ci(x) is considered active at x if ci(x) = 0 and inactive if ci(x)...