We describe all degenerations of the variety $\mathfrak{Jord}_3$ Jordan algebras dimension three over $\mathbb{C}.$ In particular, we irreducible components in $\mathfrak{Jord}_3.$ For every $n$ define an $n$-dimensional rigid ''marginal'' algebra level one. Also, discuss associative, alternative, left non-commutative Jordan, Leibniz, and anticommutative cases.

In the present paper we study generalized left derivations on Lie ideals of rings with involution. Some of our results extend other ones proven previously just for the action of generalized left derivations on the whole ring. Furthermore, we prove that every generalized Jordan left derivation on a 2-torsion free ∗-prime ring with involution is a generalized left derivation.

In this paper we prove the following result. LetH be a real or complex Hilbert space, let L(H) be the algebra of all bounded linear operators on H and let A(H) ⊆ L(H) be a standard operator algebra. Suppose we have an additive mapping D : A(H) → L(H) satisfying the relation D(An) = D(A)A∗n−1 + AD(An−2)A∗ + An−1D(A) for all A ∈ A(H) and some fixed integer n > 1. In this case there exists a uniqu...

Itemset mining typically results in large amounts of redundant itemsets. Several approaches such as closed itemsets, non-derivable itemsets and generators have been suggested for losslessly reducing the amount of itemsets. We propose a new pruning method based on combining techniques for closed and non-derivable itemsets that allows further reductions of itemsets. This reduction is done without...

The type of a minimalist grammar (MG) as introduced by Stabler [11, 12] provides an attempt of a rigorous algebraic formalization of the new perspectives adopted within the linguistic framework of transformational grammar due to the change from GB–theory to minimalism. Michaelis [6] has shown that MGs constitute a subclass of mildly context–sensitive grammars in the sense that for each MG there...

The main idea of the support vector machine (SVM) classification approach is mapping the data into higher-dimensional linear space where the data can be separated by hyperplane. Based on the Jordan curve theory, a general nonlinear classification method by the use of hypersurface is proposed in this paper. The separating hypersurface is directly used to classify the data according to whether th...

‎Let $R$ be a ring with involution $*$‎. ‎An additive mapping $T:Rto R$ is called a left(respectively right) centralizer if $T(xy)=T(x)y$ (respectively $T(xy)=xT(y)$) for all $x,yin R$‎. ‎The purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.

Introduction Due to structural characteristics of the visual pathways, stimuli that are presented in the right half of the visual field (RVF) are initially projected to the left cerebral hemisphere, while those presented in the left half of the visual field (LVF) are projected to the right cerebral hemisphere. This anatomical feature has frequently been taken to support the notion that the well...

We introduce a new spin-fermion mapping, for arbitrary spin S generating the SU(2) group algebra, that constitutes a natural generalization of the Jordan-Wigner transformation for S = 1/2. The mapping, valid for regular lattices in any spatial dimension d, serves to unravel hidden symmetries. We illustrate the power of the transformation by finding exact solutions to lattice models previously u...