Integration of paths―a faithful representation of paths by non-commutative formal power series
نویسندگان
چکیده
منابع مشابه
Matrix-J-unitary Non-commutative Rational Formal Power Series
Formal power series in N non-commuting indeterminates can be considered as a counterpart of functions of one variable holomorphic at 0, and some of their properties are described in terms of coefficients. However, really fruitful analysis begins when one considers for them evaluations on N-tuples of n× n matrices (with n = 1, 2, . . .) or operators on an infinite-dimensional separable Hilbert s...
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We shall extend the results of [5] and prove that if f = Z o a x ? Z [[X]] is algebraic over Q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over Q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over Q (x) if and only if f , f ,.., f are algebraically independent over Q (x)
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Let $K$ be a field of characteristic$p>0$, $K[[x]]$, the ring of formal power series over $ K$,$K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the fieldof rational functions over $K$. We shall give somecharacterizations of an algebraic function $fin K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $finL[[x]]$ is called differentially algebraic, if it satisfies...
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esl/efl books play a crucial role in shaping language learners worldview of gender roles in society. the present study investigated the status of sexism in two sets of efl textbooks, one developed by non-native iranian authors (ili series) and the other by native authors (top notch series). first, two books from each series was selected randomly. then, a quantitative analysis was carried out wi...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1958
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1958-0106258-0