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In this section we will apply the Young integral and rough path integral of local time defined in sections 2 and 3 to prove a useful extension to Itˆ o’s formula.. Assume the
Finally, the study of the partial symmetry ( 21 ) has been useful not only to obtain a reduction of the initial equations, leading also to new particular solutions, but also to
The 2-BKP hierarchy is rather special among multi-component integrable hierarchies, because it has a scalar Lax formalism as Shiota [ 7 ] and Krichever [ 8 ] presented.. In
Rather it classifies integrable quantum field theoretic models and in addition provides their explicit exact solutions in term of all Wightman functions.. We achieve contact with
We study multivariable Christoffel–Darboux kernels, which may be viewed as reproducing kernels for antisymmetric orthogonal polynomials, and also as correlation func- tions for
Although the string theory has made a significant progress on this problem [ 1 ], the string theory approach is essentially a perturbation theory around the flat spacetime, which
(A problem involving nonlinear PDEs is considered solvable if its solution can be obtained by performing algebraic operations – such as finding the zeros of a given polynomial – and
Gravity theories and differential geometry have been developed on differential manifolds where the functions form an algebra by pointwise multiplication:.. µ { f ⊗ g } = f