Foci of Algebraic Curves

2015 ◽  
Vol 3 (3) ◽  
pp. 4-17 ◽  
Author(s):  
Гирш ◽  
A. Girsh
Keyword(s):  
Algebraic Curves ◽  
Focal Point ◽  
Conic Section ◽  
Real Point ◽  
Algebraic Equations ◽  
The Real ◽  
Isotropic Line ◽  
Real Curve ◽  
Line Contacts ◽  
Geometric Picture

Curves have always been part geometry. Initially, there were lines and circle, then it was added to a conic section and later, with the advent of analytic geometry, they added more complex curves. Particularly in a number of lines are algebraic curves that are described by algebraic equations. Curves found application mostly in mechanics. Today algebraic curves used in engineering and in mathematics, in number theory, knot theory, computer science, criminology, etc. With the bringing to account of complex numbers became possible to consider curves in the complex plane. It has expanded the horizons of geometry and enriched their knowledge on curves, particularly on algebraic curves. Our goal is to give a geometric picture of the foci of algebraic curves clearly show the position of the foci in the plane, show how the number of foci associated with a class curve. The solution of this problem we see in the application we have developed ways to visualize imaginary images to the study of foci and focal centers of algebraic curves. This article explains the concept of the foci of algebraic curves shows the basic principle of the curve-theory and offers a method for the identification of the foci. The geometric picture of the foci is shown in a diagram, which is putted together from two tables. One table shows the real curve with her foci, the other table shows an imaginary cut of the curve, on which the isotropic line contacts the cut and under them intersects in a real point. The point is a focal point of the real curve. This project shows 16 diagrams for conic, cubes and quadrics.

On Graeffe's Method for Complex Roots of Algebraic Equations

1924 ◽  
Vol 22 (2) ◽  
pp. 83-87 ◽  
Author(s):  
S. Brodetsky ◽  
G. Smeal
Keyword(s):  
Nineteenth Century ◽  
Real Axis ◽  
Practical Method ◽  
Algebraic Equations ◽  
Argand Diagram ◽  
Considerable Difficulty ◽  
The Real ◽  
Real Roots ◽  
Bipolar Coordinates ◽  
Complex Roots

The only really useful practical method for solving numerical algebraic equations of higher orders, possessing complex roots, is that devised by C. H. Graeffe early in the nineteenth century. When an equation with real coefficients has only one or two pairs of complex roots, the Graeffe process leads to the evaluation of these roots without great labour. If, however, the equation has a number of pairs of complex roots there is considerable difficulty in completing the solution: the moduli of the roots are found easily, but the evaluation of the arguments often leads to long and wearisome calculations. The best method that has yet been suggested for overcoming this difficulty is that by C. Runge (Praxis der Gleichungen, Sammlung Schubert). It consists in making a change in the origin of the Argand diagram by shifting it to some other point on the real axis of the original Argand plane. The new moduli and the old moduli of the complex roots can then be used as bipolar coordinates for deducing the complex roots completely: this also checks the real roots.

scholarly journals Helyettesítő áldozat

2016 ◽  
Vol 55 (1-2) ◽  
Author(s):  
Gerda Széplaky
Keyword(s):  
Focal Point ◽  
The Real ◽  
Abstract Structure ◽  
Real Self ◽  
Second Period ◽  
The Way

The issue of subjectivity became particularly relevant in the second half of Szilárd Borbély’s oeuvre. While his first period in the 1990s is dominated by the poetical power hidden in silence and the unspeakable, the works after 2000 have the characteristics of a closeness between the lyrical self and the real self, the former previously defined as ironical and reserved. These are the results of a fatal tragedy, the deadly attack on his parents, which has become the focal point of Borbély’s individual mythology. The thematisation of subjectivity, however, did not end in the formation of an autoreferential horizon. Instead, the poet created a net of meanings where the events of his own life are blended together with the Christian narrative of salvation, different myths, literary and philosphical parables. In my paper I investigate the way the personal and abstract structure of the lyrical self is represented in the subsitute sacrifice as a form of identity and in the theological and metaphysical topos of eternity, both of which being the defining motifs of Borbély’s second period.

On the Real Foci and Directrices of a Class Cubic and Other Plane Algebraic Curves

1928 ◽  
Vol s2-27 (1) ◽  
pp. 427-434
Author(s):  
Harold Hilton ◽  
Sybil D. Jervis
Keyword(s):  
Algebraic Curves ◽  
The Real

Monte Carlo method for the real and complex fuzzy system of linear algebraic equations

2019 ◽  
Vol 24 (2) ◽  
pp. 1255-1270
Author(s):  
Behrouz Fathi-Vajargah ◽  
Zeinab Hassanzadeh
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Fuzzy System ◽  
Algebraic Equations ◽  
The Real ◽  
Linear Algebraic Equations

scholarly journals Quiet Refusals: Androids as Others in Philip K. Dick’s Do Androids Dream of Electric Sheep?

2018 ◽  
Vol 9 (3) ◽  
pp. 10
Author(s):  
Nima Behroozi Moghadam ◽  
Farideh Porugiv
Keyword(s):  
Science Fiction ◽  
Jacques Lacan ◽  
The Other ◽  
Real Point ◽  
Slavoj Zizek ◽  
The Real ◽  
Objet Petit A ◽  
Slavoj Žižek ◽  
Cultural Theorist ◽  
The Way

This study intends to show how science fiction literature in general and Philip K. Dick’s novel Do Androids Dream of Electric Sheep? in particular can be read as a symptom of the postmodern era we live in. Taking as the main clues the ideas of the cultural theorist Slavoj Žižek, who combines Marxism with the psychoanalysis of Jacques Lacan, as well as his account of “postmodernism,” the study discusses how, contrary to what capitalism dubs a “post-ideological” era, we are more than ever dominated by ideology through its cynical function. It further examines (through such Lacanian concepts as fantasy, desire, objet petit a, and jouissance) the way late capitalistic ideology functions in Dick’s narrative, and discusses how the multiculturalist society prompts new forms of racism through abstract universalization which only accounts for and tolerates the other as long as they appear within the confines of that formal abstraction. Finally, it looks into how ideologies as such can be subverted from the Real point within the symbolic.

Influence Functions in the Numerical Analysis of Bending of Thin Elastic Plates

1984 ◽  
Vol 8 (2) ◽  
pp. 103-114 ◽  
Author(s):  
Mohammed F.N. Mohsen ◽  
Ali A. Al-Gadhib ◽  
Mohammed H. Baluch
Keyword(s):  
Boundary Conditions ◽  
Influence Function ◽  
Infinite Plate ◽  
Thin Plates ◽  
Influence Functions ◽  
Algebraic Equations ◽  
Elastic Plates ◽  
The Real ◽  
Linear Algebraic Equations ◽  
The Moment

A numerical method for the linear analysis of thin plates of arbitrary plan form and subjected to arbitrary loading and boundary conditions is presented in this paper. This method is an extension of the Wu-Altiero method [1] where use has been made of the force influence function for an infinite plate, whereas the work contained in this paper is based on the use of the moment influence function of an infinite plate. The technique basically involves embedding the real plate into a fictitious infinite plate for which the moment influence function is known. N points are prescribed at the plate boundary at which the boundary conditions for the original problem are collocated by means of 2N fictitious moments placed around contours outside the domain of the real plate. A system of 2N linear algebraic equations in the unknown moments is obtained. The solution of the system yields the unknown moments. These may in turn be used to compute deflection, moments or shear at any point in the thin plate. Finally, the method is extended to include influence functions of both concentrated forces and concentrated moments. This is obtained by applying concentrated moments and forces simultaneously on the contours located outside the domain of the plate.

Spaced out

Physics World ◽  
2021 ◽  
Vol 34 (9) ◽  
pp. 23a-24
Author(s):  
Peter Wright
Keyword(s):  
Real Point ◽  
The Real

What was the real point of the flight of Jeff Bezos’s spacecraft?

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