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Let { P n ( x ) } be a polynomial set.
A polynomial sequence { P n } n ≥ 0 be a polynomial set.
Let ({P_{n}}_{nge0}) be a polynomial set and consider the two polynomials (A_{i}(x)) and (B_{j}(x)) with degrees i and j, respectively, then the solution of the general linearization problem requires one to obtain the linearization coefficients (L_{i,j,k}) such that A_{i}(x) B_{j}(x)=sum _{k=0}^{i+j}L_{i,j,k} P_{k}(x).
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The idea behind applying algebraic geometry to CRNs is that the ODE system derived from a CRN endowed with mass action kinetics is a polynomial set conformed by monomials representing the rates of production and elimination of chemical species.
As introduced previously the MCB is a polynomial set of cycles which can be used to generate the cycle space.
Let F : Set → Set be a polynomial endofunctor.
If g is a polynomial, then we set (g^{n}g^{ k)}-a=K z-z_{0}-a=K z-z_{ere K is a non-zero constant, l is a positive integer.
If g is a polynomial, then we set (g^{n}g^{ k)}-a=K z-z_{0}-a=K z-z_{ere K is a non-zero constant and l is a positive integer.
There is a polynomial time projection from the set (D_{mathrm{doubt}}) to the set of vertices V and from conflicts (f_{ij}) to the set of edges E of a graph (V, E).
Let Q be a set of polynomials in noncommutative indeterminates Zi,j, i∈{1,…,k}, j∈{1,…,ni}.
Let ϕ n ( x ) be a simple set of polynomials and let ϕ n ( x ) belong to the operator J ( x, D ) = ∑ k = 0 ∞ T k ( x ) D k + 1, with T k ( x ) of degree ≤k.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com