Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory...

multiple values per data point. An index with this structure, called a "MultiIndex", allows a single DataFrame to represent multiple dimensions, similar...

high-performance computing. MoFEM is the blend of the Boost (C++ libraries) MultiIndex containers, MOAB (Mesh Oriented Database) and PETSc (Portable, Extensible...

combinations of differential operators xα∂β with |α| + |β| ≤ p (using multiindex notation). The associated graded ring is seen to be isomorphic to the...

summation convention apply to them. Multiindex notation for the latin indices is also introduced as follows. A multiindex I {\textstyle I} of length k {\textstyle...

not be confused with multivariate orthogonal polynomials. Consider a multiindex n → = ( n 1 , … , n r ) ∈ N r {\displaystyle {\vec {n}}=(n_{1},\dots ...

Precisely, this formula express the value of the partial derivative of any multiindex order of a holomorphic function of several variables, in any interior...

U=\prod _{1}^{n}B(a_{j},r_{j})\subset \mathbb {C} ^{n}} , we have: for each multiindex α ∈ N n {\displaystyle \alpha \in \mathbb {N} ^{n}} , | ( ∂ ∂ z α f )...

\alpha =\left(\alpha _{1},\alpha _{2},\ldots ,\alpha _{n}\right)} is a multiindex, | α | = {\displaystyle \textstyle \left\vert \alpha \right\vert =} α...

subsequences can occur in a non-contiguous manner, but gaps are penalized. The multiindex i {\displaystyle \mathbf {i} } gives the positions of the characters matching...