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Relevant bibliographies by topics / Algebraic system

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Journal articles

Academic literature on the topic 'Algebraic system'

Author: Grafiati

Published: 6 July 2023

Last updated: 12 June 2025

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Journal articles on the topic "Algebraic system"

1

Kravtsov, H. O., S. M. Hrechko, V. V. Nikitchenko, and A. M. Prymushko. "Cognitive Algebraic System." Èlektronnoe modelirovanie 44, no. 3 (2022): 14–30. http://dx.doi.org/10.15407/emodel.44.03.014.

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2

Omarov, A. I. "Orthogonally complete algebraic system." Algebra and Logic 30, no. 2 (1991): 134–39. http://dx.doi.org/10.1007/bf01978833.

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3

Fu, Jun, Jinzhao Wu, and Hongyan Tan. "A Deductive Approach towards Reasoning about Algebraic Transition Systems." Mathematical Problems in Engineering 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/607013.

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Algebraic transition systems are extended from labeled transition systems by allowing transitions labeled by algebraic equations for modeling more complex systems in detail. We present a deductive approach for specifying and verifying algebraic transition systems. We modify the standard dynamic logic by introducing algebraic equations into modalities. Algebraic transition systems are embedded in modalities of logic formulas which specify properties of algebraic transition systems. The semantics of modalities and formulas is defined with solutions of algebraic equations. A proof system for this logic is constructed to verify properties of algebraic transition systems. The proof system combines with inference rules decision procedures on the theory of polynomial ideals to reduce a proof-search problem to an algebraic computation problem. The proof system proves to be sound but inherently incomplete. Finally, a typical example illustrates that reasoning about algebraic transition systems with our approach is feasible.

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4

Holcombe, M. "Algebraic Techniques of System Specification." Irish Mathematical Society Bulletin 0021 (1988): 13–28. http://dx.doi.org/10.33232/bims.0021.13.28.

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Cadzow, J., and O. Solomon. "Algebraic approach to system identification." IEEE Transactions on Acoustics, Speech, and Signal Processing 34, no. 3 (1986): 462–69. http://dx.doi.org/10.1109/tassp.1986.1164849.

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6

Jang, Youngho. "Algebraic Weyl system and application." Annales mathématiques Blaise Pascal 4, no. 2 (1997): 27–40. http://dx.doi.org/10.5802/ambp.95.

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7

HINDMAN, NEIL. "The Topological-Algebraic System(?N, +, ?)." Annals of the New York Academy of Sciences 704, no. 1 Papers on Gen (1993): 155–63. http://dx.doi.org/10.1111/j.1749-6632.1993.tb52519.x.

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8

Letichevskii, A. A., and V. G. Marinchenko. "Objects in algebraic programming system." Cybernetics and Systems Analysis 33, no. 2 (1997): 283–99. http://dx.doi.org/10.1007/bf02665902.

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9

Phusanga, D., and J. Koppitz. "Some varieties of algebraic systems of type ((n),(m))." Asian-European Journal of Mathematics 12, no. 01 (2019): 1950005. http://dx.doi.org/10.1142/s1793557119500050.

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In the present paper, we classify varieties of algebraic systems of the type [Formula: see text], for natural numbers [Formula: see text] and [Formula: see text], which are closed under particular derived algebraic systems. If we replace in an algebraic system the [Formula: see text]-ary operation by an [Formula: see text]-ary term operation and the [Formula: see text]-ary relation by the [Formula: see text]-ary relation generated by an [Formula: see text]-ary formula, we obtain a new algebraic system of the same type, which we call derived algebraic system. We shall restrict the replacement to so-called “linear” terms and atomic “linear” formulas, respectively.

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10

ŚWIRSZCZ, GRZEGORZ. "AN ALGORITHM FOR FINDING INVARIANT ALGEBRAIC CURVES OF A GIVEN DEGREE FOR POLYNOMIAL PLANAR VECTOR FIELDS." International Journal of Bifurcation and Chaos 15, no. 03 (2005): 1033–44. http://dx.doi.org/10.1142/s0218127405012442.

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Given a system of two autonomous ordinary differential equations whose right-hand sides are polynomials, it is very hard to tell if any nonsingular trajectories of the system are contained in algebraic curves. We present an effective method of deciding whether a given system has an invariant algebraic curve of a given degree. The method also allows the construction of examples of polynomial systems with invariant algebraic curves of a given degree. We present the first known example of a degree 6 algebraic saddle-loop for polynomial system of degree 2, which has been found using the described method. We also present some new examples of invariant algebraic curves of degrees 4 and 5 with an interesting geometry.

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