Abstract The orthogonality time is examined for different initial states settings interacting locally with types of spin interaction: XX , Ising and anisotropic models. It shown that the number increases, consequently decreases as environment qubits increase. shortest displayed chain model, while largest model. external field increases numbers orthogonality, Dzyaloshinsky–Moriya interaction ort...

A complex fuzzy set is a set whose membership values are vectors in the unit circle in the complex plane. This paper establishes the orthogonality relation of complex fuzzy sets. Two complex fuzzy sets are said to be orthogonal if their membership vectors are perpendicular. We present the basic properties of orthogonality of complex fuzzy sets and various results on orthogonality with respect t...

In this article, using a combination of the necessary and sufficient conditions for the almost regularity of an interpolation scheme, we will determine all plane uniform Birkhoff schemes, when the set of interpolated nodes has n elements and the set of derivatives we are interpolating with is )} 0 , 1 ( ), 0 , 0 {( = A . For the same A we will determine all rectangular Birkhoff uniform interpol...

a chair, he was the very picture of dejection. His small head was hanging, an obstreperous tuft of the coarse, sandy hair standing defiantly upright on the crown of it; his complexion was sallow and pasty, and not in any way enhanced by a sparse scattering of tiny yellow freckles, plainly visible at close view; his generous mouth drooped, like his head, the lips pale, but firmly closed. In his ...

We develop an abstract proof calculus for logics whose sentences are ’Horn sentences’ of the form: (∀X)H =⇒ c and prove an institutional generalization of Birkhoff completeness theorem. This result is then applied to the particular cases of Horn clauses logic, the ’Horn fragment’1 of preorder algebras, order-sorted algebras and partial algebras and their infinitary variants. Mathematics Subject...

We show succinctly that all metric theories with second order field equations obey Birkhoff's theorem: their spherically symmetric solutions are static.

In an earlier work the author has obtained new quadrature formulas (see (1.3)) based on function values and second derivatives on the zeros of nn(i) as defined by (1.2). The proof given earlier was quite long. The object of this paper is to provide a proof of this quadrature formula which is extremely simple and indeed does not even require the use of fundamental polynomials of (0,2) interpolat...