Whether natural ( allograft, simple demineralized bone matrix) or synthetic ( hydroxyapatite, calcium phosphate), structure is key to an osteoconductive scaffold providing a suitable workplace for bone forming cells. The way a bone grafting technology works depends on many factors including the properties of the graft itself. The novel i-FACTOR Bone Graft “ Attract, Attach, Activate” mechanism of action enhances the body’s natural bone healing process. The high affinity between cells and P-15 supports the physiological mechanism of action in which cells bind to the P-15 and “turn on” to perform their genetically programmed job of making bone. I-FACTOR Bone Graft facilitates and expedites the ingrowth of bone by promoting the migration of mesenchymal stem cells and other progenitor cells from surrounding tissue. These cells have an affinity for and attach to the P-15 found in i-FACTOR Bone Graft in a similar way they would naturally with Type I collagen in bone. This 15-amino acid peptide (P-15) is responsible for the attachment and proliferation of osteogenic cells. I-FACTOR Bone Graft is based on the biological activity of the synthetically derived 15-amino acid peptide found naturally in Type I human collagen. I-FACTOR™ Bone Graft: Mechanism of Action Introducing donor cells ( osteogenesis).Providing instructions to local cells ( osteoinduction).Providing a scaffold for local cells ( osteoconduction).How the bone graft material responds to these cells is referred to as the mechanism of action. This means that the cells seek out attachment points on the Type I collagen, become attached, and activate the cascade of events leading to bone formation. Many of these connective tissue cells are “ attachment activated“. The factors command was updated in Maple 2019.Within tissues are cells that are controlled by and interact with Type I collagen. An improved Multivariate Polynomial Factoring Algorithm, Mathematics of Computation 32, (1978). Factoring multivariate polynomials with many factors and huge coefficients. Using Sparse Interpolation in Hensel Lifting. Mark van Hoeij, Factoring polynomials and the knapsack problem. The following is an example that has a rational function as input. The call factors(a, K) factors the polynomial a over the algebraic number field defined by K. Note, at present this is only implemented for univariate polynomials. If the second argument K is the keyword real or complex, a floating-point factorization is performed over R and C respectively. The call factors(a) factors over the field implied by the coefficients present: thus, if all the coefficients are rational, then the polynomial is factored over the rationals. To explicitly request Wang's algorithm, which was the default in Maple 2018 and earlier versions, use the option method="Wang". The default is the latter, since it is faster on most examples. f n m n where each f k (the factor) is a unit normal irreducible polynomial and each m k (its multiplicity) is a positive integer.įor multivariate polynomials with integer coefficients, the factors command offers two algorithms: Wang's algorithm (see ) and the algorithm by Monagan and Tuncer (, ). The factorization is returned in the form u, f 1, m 1. Unlike the factor function where the input is any expression and the output is a product of sums in the general case, the input to the factors function must be a polynomial or a rational function, and the output is a data structure more suitable for programming purposes. The factors command computes the factorization of a multivariate polynomial over the rationals, an algebraic number field, and with real or complex numeric coefficients. Multivariate polynomial with rational coefficients
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