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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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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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Additive maps between standard operator algebras compressing certain spectral functions
Acta Mathematica Sinica, English Series, 2008Li Huang, Hou Jin Chuan
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Rank-one non-increasing additive maps between block triangular matrix algebras
Linear and Multilinear Algebra, 2010Wai Leong Chooi
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