A differential algebraic (DA) formulation of a normal form theory for repetitive systems is presented. Contrary to previous approaches, no Lie algebraic tools are used. The resulting algorithm is very transparent and not restricted to the treatment of symplectic systems. In the case of symplectic systems, the normal form algorithm provides a nonlinear coordinate transformation in which the moti...

with derivative g b(w) = w n−1 , and use the conjugacy invariant b̂ = b . These normal forms (0.1) and (0.2) are related by the change of variable formula w = nz with b̂ = nĉ , and hence b = nc . (In particular, in the degree two case, b = b̂ is equal to 4c = 4ĉ .) If A is any ring contained in the complex numbers C , it will be convenient to use the non-standard notation A for the integral closur...

For every algebraically closed field k of characteristic different from 2, we prove the following: (1) Generic finite dimensional (not necessarily associative) kalgebras of a fixed dimension, considered up to isomorphism, are parametrized by the values of a tuple of algebraically independent over k rational functions in the structure constants. (2) There exists an “algebraic normal form”, to wh...

An associative ∗-algebra is introduced (containing a TTR-algebra as a subalgebra) that implements the form factor axioms, and hence indirectly the Wightman axioms, in the following sense: Each T -invariant linear functional over the algebra automatically satisfies all the form factor axioms. It is argued that this answers the question (posed in the functional Bethe ansatz) how to select the dyn...

sinc-galerkin method based upon double exponential transformation for solving troesch's problem was given in this study. properties of the sinc-galerkin approach were utilized to reduce the solution of nonlinear two-point boundary value problem to same nonlinear algebraic equations, also, the matrix form of the nonlinear algebraic equations was obtained.the error bound of the method was fo...

in this paper, let $l$ be a completeresiduated lattice, and let {bf set} denote the category of setsand mappings, $lf$-{bf pos} denote the category of $lf$-posets and$lf$-monotone mappings, and $lf$-{bf cslat}$(sqcup)$, $lf$-{bfcslat}$(sqcap)$ denote the category of $lf$-completelattices and $lf$-join-preserving mappings and the category of$lf$-complete lattices and $lf$-meet-preserving mapping...