Pre-Jordan algebras were introduced recently in analogy with preLie algebras. A pre-Jordan algebra is a vector space A with a bilinear multiplication x · y such that the product x ◦ y = x · y + y · x endows A with the structure of a Jordan algebra, and the left multiplications L·(x) : y 7→ x · y define a representation of this Jordan algebra on A. Equivalently, x ·y satisfies these multilinear ...

In this paper we prove the following result. Let R be a 6−torsion free semiprime ∗−ring and let D : R → R be an additive mapping satisfying the relation D(xyx) = D(x)y∗x∗ + xD(y)x∗ + xyD(x), for all pairs x, y ∈ R. In this case D is a Jordan ∗−derivation. Mathematics Subject Classification: 16W10, 39B05

In this paper we introduce the concepts of generalized higher left centralizer and Jordan Γ-rings M as well proved that every certain Γ-ring is prove triple M.

Association rule mining typically results in large amounts of redundant rules. We introduce efficient methods for deriving tight bounds for confidences of association rules, given their subrules. If the lower and upper bounds of a rule coincide, the confidence is uniquely determined by the subrules and the rule can be pruned as redundant, or derivable, without any loss of information. Experimen...

We present an efficient algorithm for obtaining a canonical system of Jordan chains for an n×n regular analytic matrix function A(λ) that is singular at the origin. For any analytic vector function b(λ), we show that each term in the Laurent expansion of A(λ)−1b(λ) may be obtained from the previous terms by solving an (n+d)× (n+d) linear system, where d is the order of the zero of detA(λ) at λ ...

3. The Implicit Function Theorem and its special case, the Inverse Function Theorem. Relation to the Contraction Mapping Fixed Point Theorem. Computation of several iterates of the approximating sequence to the implicit function. Continuity and differentiability of the implicit function. Application to differentiable variation of the fixed point in the Contraction Mapping Fixed Point Theorem. 4...

The study aimed at analysing temporal and spatial patterns of population distribution in Jordan governorate level. It also to define the influencing geographical factors that affected caused changes over last decades based on census data 1994, 2004, 2015 years. Several approaches statistical methods were used this achieve objectives, including analytical descriptive, evolutionary, analysis alon...