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Algebraic number
About: Algebraic number is a research topic. Over the lifetime, 20611 publications have been published within this topic receiving 315606 citations.
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Book•
21 Oct 1996
TL;DR: The finite element method for the algebraic Eigenvalue problem of distributed-parameter systems was introduced in this article. But it is not suitable for the linear system theory of single-degree-of-freedom (SDF) systems.
Abstract: Concepts and techniques from linear system theory principles of Newtonian and analytical dynamics single-degree-of-freedom systems multi-degree-of-freedom systems qualitative aspects of the algebraic Eigenvalue problem computational techniques for the algebraic Eigenvalue problem distributed-parameter systems approximate methods for distributed-parameter systems the finite element method. Appendices: elements of laplace transformation elements of linear algebra.
1,028 citations
Book•
01 Jan 1990
TL;DR: In this paper, Dedekind Domains and Valuations have been used to define the theory of P-adic fields and to define a local compact Abelian group. But they do not consider the relation between the two types of fields.
Abstract: 1. Dedekind Domains and Valuations.- 2. Algebraic Numbers and Integers.- 3. Units and Ideal Classes.- 4. Extensions.- 5. P-adic Fields.- 6. Applications of the Theory of P-adic Fields.- 7. Analytical Methods.- 8. Abelian Fields.- 9. Factorizations 9.1. 485Elementary Approach.- Appendix I. Locally Compact Abelian Groups.- Appendix II. Function Theory.- Appendix III. Baker's Method.- Problems.- References.- Author Index.- List of Symbols.
984 citations
01 Jan 1987
TL;DR: It is proved that depth k circuits with gates NOT, OR and MODp where p is a prime require Exp(&Ogr;(n1/2k)) gates to calculate MODr functions for any r ≠ pm.
Abstract: We use algebraic methods to get lower bounds for complexity of different functions based on constant depth unbounded fan-in circuits with the given set of basic operations. In particular, we prove that depth k circuits with gates NOT, OR and MODp where p is a prime require Exp(O(n1/2k)) gates to calculate MODr functions for any r ≠ pm. This statement contains as special cases Yao's PARITY result [ Ya 85 ] and Razborov's new MAJORITY result [Ra 86] (MODm gate is an oracle which outputs zero, if the number of ones is divisible by m).
926 citations
TL;DR: In this paper, a decision method for finding a continuous motion connecting two given positions and orientations of the whole collection of bodies is presented. But it is not shown that this problem can be solved in polynomial time.
909 citations