Complex Algebra

2008 ◽  
pp. 11-22
Keyword(s):  
Complex Algebra

A complex algebra for relay circuits

1953 ◽  
Vol 72 (11) ◽  
pp. 992-993 ◽  
Author(s):  
Matthew Raspanti
Keyword(s):  
Complex Algebra

scholarly journals A set of postulates for ordinary complex algebra

1905 ◽  
Vol 6 (2) ◽  
pp. 209-209 ◽  
Author(s):  
Edward V. Huntington
Keyword(s):  
Complex Algebra

2D potential theory using complex algebra: New equations and visualization for the interpretation of potential field data

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. J1-J13 ◽  
Author(s):  
Pauline Le Maire ◽  
Marc Munschy
Keyword(s):  
Magnetic Field ◽  
Complex Plane ◽  
Potential Field ◽  
Single Point ◽  
Magnetic Anomalies ◽  
Analytic Signal ◽  
Power Functions ◽  
Field Equations ◽  
Complex Algebra ◽  
Location Depth

The shape of an anomaly (magnetic or gravity) along a profile provides information on the geometry, horizontal location, depth, and magnetization of the source. For a 2D source, the horizontal location, depth, and geometry of a source are determined through the analysis of the curve of the analytic signal. However, the amplitude of the analytic signal is independent of the dips of the structure, the apparent inclination of magnetization, and the regional magnetic field. To better characterize the parameters of the source, we have developed a new approach for studying 2D potential field equations using complex algebra. Complex equations for different geometries of the sources are obtained for gravity and magnetic anomalies in the spatial and spectral domains. In the spatial domain, these new equations are compact and correspond to logarithmic or power functions with a negative integer exponent. We found that modifying the shape of the source changes the exponent of the power function, which is equivalent to differentiation or integration. We developed anomaly profiles using plots in the complex plane, which is called mapping. The obtained complex curves are loops passing through the origin of the plane. The shape of these loops depends only on the geometry and not on the horizontal location of the source. For source geometries defined by a single point, the loop shape is also independent of the source depth. The orientation of the curves in the complex plane is related to the order of differentiation or integration, the geometry and dips of the structures, and the apparent inclination of magnetization and of the regional magnetic field. The application of these equations and mapping on total field magnetic anomalies across a magmatic dike in Norway shows coherent results, allowing us to determine the geometry and the apparent inclination of magnetization.

Integral Extensions of Commutative Banach Algebras

1973 ◽  
Vol 25 (4) ◽  
pp. 673-686 ◽  
Author(s):  
John A. Lindberg
Keyword(s):  
Identity Element ◽  
Banach Algebras ◽  
Monic Polynomial ◽  
Complex Algebra ◽  
Commutative Banach Algebras ◽  
Made In

In this paper, we continue the study of integral extensions begun in [7]. Whereas in the previous paper, we dealt exclusively with the extension A[x]/(α(x)), α(x) a monic polynomial over A, we now deal with arbitrary integral extensions. Applications of the results presented herein will be made in subsequent papers.To simplify our presentation, we make the following conventions. By an algebra, we will always mean a commutative complex algebra with an identity element, usually denoted by e

scholarly journals Strictly real Banach algebras

1993 ◽  
Vol 47 (3) ◽  
pp. 505-519 ◽  
Author(s):  
John Boris Miller
Keyword(s):  
Banach Algebra ◽  
Uniqueness Theorem ◽  
Banach Algebras ◽  
Complex Algebra ◽  
Conjugation Operator ◽  
Complex Banach Algebra

A complex Banach algebra is a complexification of a real Banach algebra if and only if it carries a conjugation operator. We prove a uniqueness theorem concerning strictly real selfconjugate subalgebras of a given complex algebra. An example is given of a complex Banach algebra carrying two distinct but commuting conjugations, whose selfconjugate subalgebras are both strictly real. The class of strictly real Banach algebras is shown to be a variety, and the manner of their generation by suitable elements is proved. A corollary describes some strictly real subalgebras in Hermitian Banach star algebras, including C* algebras.

Algebraic Algorithm for the Kinematic Analysis of Slider-Crank/Rocker Mechanisms

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
Giorgio Figliolini ◽  
Marco Conte ◽  
Pierluigi Rea
Keyword(s):  
Kinematic Analysis ◽  
Algebraic Curves ◽  
Algebraic Form ◽  
Complex Algebra ◽  
Geometric Invariants ◽  
Matlab Code ◽  
Algebraic Forms ◽  
Implicit And Explicit ◽  
First Time

This paper deals with the formulation and validation of a comprehensive algebraic algorithm for the kinematic analysis of slider-crank/rocker mechanisms, which is based on the use of geometric loci, as the fixed and moving centrodes, along with their evolutes, the cubic of stationary curvature and the inflection circle. In particular, both centrodes are formulated in implicit and explicit algebraic forms by using the complex algebra. Moreover, the algebraic curves representing the moving centrodes are recognized and proven to be Jeřábek’s curves for the first time. Then, the cubic of stationary curvature along with the inflection circle are expressed in algebraic form by using the instantaneous geometric invariants. Finally, the proposed algorithm has been implemented in a MATLAB code and significant numerical and graphical results are shown, along with the particular cases in which these geometric loci degenerate in lines and circles or give cycloidal positions.

Algebraic Algorithm for the Kinematic Analysis of Slider-Crank/Rocker Mechanisms

2010 ◽  
Author(s):  
Giorgio Figliolini ◽  
Marco Conte ◽  
Pierluigi Rea
Keyword(s):  
Kinematic Analysis ◽  
Algebraic Curves ◽  
Algebraic Form ◽  
Complex Algebra ◽  
Geometric Invariants ◽  
Matlab Code ◽  
Algebraic Forms ◽  
Implicit And Explicit ◽  
First Time

This paper deals with the formulation of an algebraic algorithm for the kinematic analysis of slider-crank/rocker mechanisms, which is based on the use of geometric loci, as the fixed and moving centrodes, the cubic of stationary curvature and the inflection circle. In particular, both centrodes are formulated in implicit and explicit algebraic forms by using the complex algebra. Moreover, the algebraic curves representing the moving centrodes are also recognized and proven to be Jerˇa´bek’s curves for the first time. Then, the cubic of stationary curvature along with the inflection circle are expressed in algebraic form by using the geometric invariants. Finally, the proposed algorithm has been implemented in a Matlab code and interesting numerical and graphical results are shown along with some particular cases in which the geometric loci degenerate in lines and circles.

Language as a complex algebra: Post-structuralism and inflectional morphology in Saussure’s Cours

Semiotica ◽  
2016 ◽  
Vol 2016 (208) ◽  
pp. 133-154
Author(s):  
Raúl Aranovich
Keyword(s):  
Social Science ◽  
Process Models ◽  
Inflectional Morphology ◽  
Word Form ◽  
Acoustic Image ◽  
Complex Algebra ◽  
Linguistic Sign ◽  
Word Forms ◽  
Human Actors ◽  
Static Nature

AbstractIn Item-and-Arrangement models of inflection, morphemes are associations of form and meaning stored in a mental lexicon. Saussure’s notion of the linguistic sign as a unit of an acoustic image (signifier) and a concept (signified) immediately suggests such a model. But close examination of the examples of inflectional morphology throughout the Cours brings Saussure’s ideas more in line with Process morphology, a model in which recurrent elements in word forms are exponents of content features, and realizational rules license a word form inferentially from the word’s content. The Saussurean sign allowed French structuralists to revolutionize the methods of modern social science, eschewing the motives and intentions of human actors to focus on the system of oppositions that make signification possible in each domain. Eventually, post-structuralism rejected the static nature of the linguistic sign, forcing linguistics into relative isolation (since it held on to sign-based models of language). The criticism of structuralist treatments of morphology in Process models of inflection, however, stands as an exception to this tendency. In retrospect, I argue, similar ideas can be found in Saussure’s view of the langue as a complex algebra.

Sign in / Sign up

Export Citation Format

Share Document