45,875 research outputs found

    The Lanham Act and the Social Function of Trade-Marks

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    Today\u27s Climate of Opinion Order, the Philosophic Basis of Natural Law

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    Constructing irreducible representations of finitely presented algebras

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    By combining well-known techniques from both noncommutative algebra and computational commutative algebra, we observe that an algorithmic approach can be applied to the study of irreducible representations of finitely presented algebras. In slightly more detail: Assume that nn is a positive integer, that kk is a computable field, that kˉ\bar{k} denotes the algebraic closure of kk, and that Mn(kˉ)M_n(\bar{k}) denotes the algebra of n×nn \times n matrices with entries in kˉ\bar{k}. Let RR be a finitely presented kk-algebra. Calculating over kk, the procedure will (a) decide whether an irreducible representation R→Mn(kˉ)R \to M_n(\bar{k}) exists, and (b) explicitly construct an irreducible representation R→Mn(kˉ)R \to M_n(\bar{k}) if at least one exists. (For (b), it is necessary to assume that k[x]k[x] is equipped with a factoring algorithm.) An elementary example is worked through.Comment: 9 pages. Final version. To appear in J. Symbolic Computatio

    Some Limited-Interest Problems

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    The asymptotic probability distribution of identified black-box transfer function models is studied. The main contribution is that we derive variance expressions for the real and imaginary parts of the identified models that are asymptotic in both the number of measurements and the model order. These expressions are considerably simpler than the corresponding ones that hold for fixed model orders, and yet they frequently approximate the true covariance well already with quite modest model orders. We illustrate the relevance of the asymptotic expressions by using them to compute uncertainty regions for the frequency response of an identified model
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