排序方式: 共有48条查询结果,搜索用时 15 毫秒
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Bruce Ebanks 《Aequationes Mathematicae》2018,92(3):581-597
We continue the study of additive functions \(f_k:R\rightarrow F \;(1\le k\le n)\) linked by an equation of the form \(\sum _{k=1}^n p_k(x)f_k(q_k(x))=0\), where the \(p_k\) and \(q_k\) are polynomials, R is an integral domain of characteristic 0, and F is the fraction field of R. A method is presented for solving all such equations. We also consider the special case \(\sum _{k=1}^n x^{m_k}f_k(x^{j_k})=0\) in which the \(p_k\) and \(q_k\) are monomials. In this case we show that if there is no duplication, i.e. if \((m_k,j_k)\ne (m_p,j_p)\) for \(k\ne p\), then each \(f_k\) is the sum of a linear function and a derivation of order at most \(n-1\). Furthermore, if this functional equation is not homogeneous then the maximal orders of the derivations are reduced in a specified way. 相似文献
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Bruce R. Ebanks 《Results in Mathematics》1999,35(1-2):23-31
The cocycle functional equation, originating in group theory and playing a role in such areas as cohomology, polyhedral algebra, and information theory, has a long and rich history. Cocycles of higher orders have been introduced in cohomology theory. This paper presents the bounded solutions of cocycle equations of all orders on amenable semigroups. Some related functional equations are treated also. These results generalize some recent results of Pales and Szekelyhidi. 相似文献
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This is one in a series of papers studying measures of information in the so-called mixed theory of information (i.e. considering the events as well as their probabilities) on the open domain (i.e. without empty sets and zero probabilities). In this paper we find all-recursive, 3-semisymmetric inset entropies on the open domain. We do this by solving the fundamental equation of inset information of degree () on the open domain.Dedicated to Professor János Aczél on his 60th birthday. 相似文献
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We show, contrary to some published statements, that spectral synthesis does not generally hold for commutative semigroups that are not groups. On the positive side we prove that it holds if the semigroup is a monoid with no prime ideal. For semigroups with a prime ideal, the picture is not so clear. On the negative side we provide a variety of examples illustrating the failure of spectral synthesis for many semigroups with prime ideals, but we also give examples of semigroups with prime ideals on which spectral synthesis holds.
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Bruce Ebanks 《Results in Mathematics》2015,67(1-2):253-264
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Bruce R. Ebanks 《Linear and Multilinear Algebra》2013,61(3-4):175-184