In 1984, Abaffy, Broyden, and Spediacto (ABS) introduced a class of the so-called ABS algorithms to solve systems of real linear equations. Later, the scaled ABS, the extended ABS, the block ABS, and the integer ABS algorithms were introduced leading to various well-known matrix factorizations. Here, we present a generalization of ABS algorithms containing all matrix factorizations such as triangular, W Z, and ZW . We discuss the octant interlocking factorization and make use of the generalized ABS algorithm as a more general approach for producing the octant interlocking factorization.

The QIF (Quadrant Interlocking Factorization) method of Evans and Hatzopoulos solves linear equation systems using WZ factor-ization. The WZ factorization can be faster than the LU factorization because, it performs the simultaneous evaluation of two columns or two rows. Here, we present a method for computing the real and integer WZ and ZW factorizations by using the null space generators of some special nested submatrices of a matrix A.

Introduction: Interlocking has been widely accepted for treatment of femoral shaft fracture. However, complications still exist. Numerous investigations have been carried out on earlier phase of fracture healing with interlocking nail.Purpose: In this research, a three dimensional model of bone with antegrade interlocking nail in post fracture healing phase during gait cycle is studied. Additionally, published results of others, obtained under different boundary condition, are discussed. Stress distribution pattern in femur with dynamised nail and static nail are investigated.Results: Three dimensional model of the third generation composite femur was considered in which simple stainless steel Gross Kempf femoral nail was inserted in the medullary canal. Simulation was performed with the assistance of Abaqus analysis finite element codes. Two different loading patterns were used in simulations: Simple loading pattern, and Full muscle loading.Discussion: Results were verified through simple analytical beam column model. Good agreement between analytical and numerical results was found. Results proved the importance of exact boundary conditions for interlocked femoral nail testing and simulation. Fifty percent increase in bone stress level after removal of proximal screw was observed.

The history of the new nailing method dates back to Gerhard Kü ntscher, who introduced this concept in Germany in 1940. He believed in two general principles: Stable fixation and fixation of fractures without opening the fracture site. In the beginning, primary nails with various weaknesses were only used in fractures of femur. Over time, effective changes were made in the design and insertion of bone nails. This article aimed to review the evolution of the design of nails and simple but significantly important principles of inserting nails in long bones. In any case, lack of adherence to these simple principles by surgeons leads to lack of desirable fixation.

In this paper, we study the Arens regularity properties of module actions and we extend some proposition from Baker, Dales and Lau into general situations. We establish some relationships between topological centers of module actions and factorization properties of them with some results in group algebras.

In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:X\times Y\to Z$, depended on  a natural number $n$ and a cardinal number $\kappa$; which is called $n$-factorization property of level $\kappa$. Then we study the relation between $n$-factorization property of  level $\kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity and also strong Arens irregularity. These results may help us to prove some previous  problems related to strong Arens irregularity more easier than old. These include some results proved by Neufang in ~\cite{neu1} and ~\cite{neu}.  Some applications to certain bilinear mappings on convolution algebras, on a locally compact group, are also included. Finally, some solutions related to  the Ghahramani-Lau conjecture is raised.

The number of factorizations of a finite abelian group as the product of two subgroups is computed in two different ways and a combinatorial identity involving Gaussian binomial coefficients is presented.