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On additive maps of prime rings. II.
Publicationes Mathematicae Debrecen, 1999[For part I see the authors, Bull. Aust. Math. Soc. 51, No. 3, 377-381 (1995; Zbl 0833.16016).] The authors determine the form of maps \(f_1,\dots,f_n\) of \(R\) (a prime ring) satisfying \[ f_1(x)x^{n-1}+xf_2(x)x^{n-2}+\cdots+x^{n-1}f_n(x)=0.\tag{1} \] If \(R\) is a prime ring then \(Z\), \(C\), \(RC\) are the center, the extended centroid and the ...
Brešar, Matej, Hvala, Bojan
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Additive Composition of Supervised Self-Organizing Maps
Neural Processing Letters, 2002The learning of complex relationships can be decomposed into several neural networks. The modular organization is determined by prior knowledge of the problem that permits to split the processing into tasks of small dimensionality. The sub-tasks can be implemented with neural networks, although the learning examples cannot be used anymore to supervise ...
Jean-Luc Buessler +2 more
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On Additive Mappings in a ∗-Ring with an Identity Element
Vietnam Journal of Mathematics, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
ur Rehman, Nadeem, Ansari, Abu Zaid
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Agriculture (Switzerland)Soil organic matter (SOM) is a key soil component. Determining its spatial distribution is necessary for precision agriculture and to understand the ecosystem services that soil provides. However, field SOM studies are severely limited by time and costs.
Liangwei Cheng +5 more
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Additivity of Elementary Maps on Rings
Communications in Algebra, 2004Abstract Let ℛ and ℛ′ be rings. Under some assumptions on ℛ, we study the additivity of maps M: ℛ → ℛ′ and M*: ℛ′ → ℛ that are surjective and satisfy M(x M*(y)z) = M(x)yM(z) and M*(yM(x)u) = M*(y)x M*(u) for x, z ∈ ℛ and y, u ∈ ℛ′. In particular, if ℛ is a prime ring containing a non-trivial idempotent, or a standard operator algebra, or a nest algebra
Pengtong Li, Fangyan Lu
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On Approximately Additive Mappings
1980The stability question for additive mappings under various conditions on their domains and ranges is studied. The main aspects are existence, uniqueness, and continuity of an approximating additive mapping (Sections 4 and 5). Suitable examples demonstrate the limits of the scope of our theorems (Section 6).
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On the Stability of an Additive Mapping
2012In this work, the Hyers–Ulam stability of the functional equation f(x+y+xy)=f(x+y)+f(xy) is proved.
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Additivity of Jordan | ast-Maps on AW ∗ -Algebras
Proceedings of the American Mathematical Society, 1986Let M and N be \(AW^*\)-algebras and let \(\phi\) :M\(\to N\) be a bijective map satisfying \(\phi (xy+yx)=\phi (x)\phi (y)+\phi (y)\phi (x)\) and \(\phi (x^*)=\phi (x)^*\) for all x,y\(\in M\). Problem: Is \(\phi\) additive? Theorem. Suppose that M has no abelian direct summand and that \(\phi\) is uniformly continuous on each abelian \(C ...
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On the additive decomposition for polynomic maps
IEEE Transactions on Automatic Control, 1983Under certain conditions, a linear operator on a Hilbert resolution space can be decomposed into a causal part and an anti causal part. This decomposition plays an important role in the solution of the linear least squares control problem. This theory has been partially generalized to classes of nonlinear problems.
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