In this general article, we map the one-dimensional transverse field quantum Ising model of ferromagnetism to Kitaev’s p-wave superconductor, which has application in fault-tolerant topological computing. Kitaev chain is an example a new class critical phenomena—the phase transition. Mapping Pauli’s spin operators spinless fermionic creation and annihilation by inverse Jordan-Wigner transformat...

In this paper we prove the following result, which is related to a classical result of Chernoff. Let X be a real or complex Banach space, let A(X) be a standard operator algebra on X and let L(X) be an algebra of all bounded linear operators on X. Suppose we have a linear mapping D : A(X) → L(X) satisfying the relation D(Am+n) = D(Am)An + AmD(An) for all A ∈ A(X) and some fixed integers m ≥ 1, ...

Truth maintenance systems (TMS) provide a method of improving the e ciency of search during problem solving. The problem solver uses the TMS to record the reasons that facts are derivable so that facts need not be rederived during the course of the search. De Kleer's Assumption Based Truth Maintenance system (ATMS) [deKleer 86] overcomes the limitations of many earlier systems, such as not bein...

We present necessary and sufficient conditions for the reducibility of a self-adjoint linear relation in Krein space. Then generalized Nevanlinna function Q represented by A Pontryagin space can be decomposed means reducing subspaces A. The sum two functions $$ {Q}_i\in {N}_{\kappa_i}\left(\mathcal{H}\right) , i = 1, 2, minimally triplets \left({\mathcal{K}}_i,{A}_i,{\Gamma}_i\right) is also st...

let a be a unital r-algebra and m be a unital a-bimodule. it is shown that every jordan derivation of the trivial extension of a by m, under some conditions, is the sum of a derivation and an antiderivation.

People implicitly associate different emotions with different locations in left-right space. Which dimensions of emotion do they spatialize? Across many studies people spatialize emotional valence, mapping positive emotions onto their dominant side of space and negative emotions onto their nondominant side. Yet, other results suggest a contradictory mapping of emotional intensity (a.k.a., emoti...