scholarly journals XI. Analysis of the roots of equations

1837 ◽  
Vol 127 ◽  
pp. 161-178
Keyword(s):  
Roots Of Unity ◽  
Constituent Part ◽  
Roots Of Equations

1. The object of this memoir is to show how the constituent parts of the roots of algebraical equations may be determined, by considering the conditions under which they vanish, and conversely to show the signification of each such constituent part. 2. In equations of degrees higher than the second the same constituent part of the root is found in several places governed by the same radical sign, but affected with the different corresponding roots of unity as multipliers.

scholarly journals Analysis of the roots of equations

1837 ◽  
Vol 3 ◽  
pp. 472-473
Keyword(s):  
Roots Of Unity ◽  
Algebraic Equations ◽  
Constituent Part ◽  
Roots Of Equations

The object of this memoir is to show how the constituent parts of the roots of algebraic equations may be determined by considering the conditions under which they vanish; and, conversely, to show the signification of each such constituent part. The following are the propositions on which the author’s investigations are founded. 1. In equations of degrees higher than the second, the same constituent part of the root is found in several places, governed by the same radical sign, but affected with the different corresponding roots of unity as multipliers.

The Treaty of Northampton (1290): A Scottish Charter of Liberties?

2007 ◽  
Vol 86 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Wendy B. Stevenson
Keyword(s):  
Sense Of Community ◽  
Written Expression ◽  
Traditional Practice ◽  
Detailed Consideration ◽  
Constituent Part ◽  
Community Or ◽  
Per Se ◽  
Edward I

Although little detailed consideration has been given to the Treaty of Northampton of 1290 by Scottish historians, it seems to have been implicitly accepted as the sort of treaty which might have been expected in connection with the marriage of two independent rulers at that time. This is in spite of the fact that throughout the twelfth, thirteenth and fourteenth centuries the traditional practice of the rulers of the Angevin and Plantagenet dominions was to rule each constituent part according to its own law and customs. This article examines the reasons why the Scots were not prepared to rely on tradition but insisted on a written promise from Edward I that Scotland would remain independent of England. It also suggests that the treaty is more than a written expression of traditional practice. It has a number of specific clauses which, it is argued, give the treaty the character of a charter of liberties. These were intended to prevent the imposition on the Scots of particular aspects of Plantagenet rule in England which burdened its subjects much more severely than the rule of Scottish kings had burdened the Scots. The Scots' wish to remain independent after the proposed union of the crowns and their struggle to maintain that independence after the death of the Maid are generally seen as manifestations of a sense of community or regnal solidarity. The terms of the Treaty of 1290 suggest that it was not just from a desire to be a separate political entity per se that the Scots fought during the so-called Wars of Independence but also because the Scots were anxious to avoid the more oppressive aspects of Plantagenet rule even before they had experience of this after Edward I's conquest of 1296.

Hermite-Birkhoff Interpolation in the nth Roots of Unity

1980 ◽  
Vol 259 (2) ◽  
pp. 621 ◽  
Author(s):  
A. S. Cavaretta ◽  
A. Sharma ◽  
R. S. Varga
Keyword(s):  
Roots Of Unity ◽  
Birkhoff Interpolation

THE CENTER OF THE COORDINATE ALGEBRAS OF QUANTUM GROUPS AT pα-th ROOTS OF UNITY

1993 ◽  
Vol 07 (20n21) ◽  
pp. 3547-3550
Author(s):  
BENJAMIN ENRIQUEZ
Keyword(s):  
Quantum Groups ◽  
Roots Of Unity

The coordinate algebras of quantum groups at pα-th roots of unity are finite modules over their centers, at least in a suitable completed sense (cf. [E]). We describe their centers in the completed case, and deduce from this the centers of the non-completed algebras. As in the [dCKP] situation, it is generated by its “Poisson” and “Frobenius” parts.

scholarly journals IDENTITIES OF SYMMETRY FOR GENERALIZED TWISTED BERNOULLI POLYNOMIALS TWISTED BY RAMIFIED ROOTS OF UNITY

2014 ◽  
Vol 60 (1) ◽  
pp. 19-36
Author(s):  
Dae San Kim
Keyword(s):  
Generating Function ◽  
Bernoulli Polynomials ◽  
Roots Of Unity ◽  
Integral Expression ◽  
Power Sums ◽  
Exponential Generating Function

Abstract We derive eight identities of symmetry in three variables related to generalized twisted Bernoulli polynomials and generalized twisted power sums, both of which are twisted by ramified roots of unity. All of these are new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the p-adic integral expression of the generating function for the generalized twisted Bernoulli polynomials and the quotient of p-adic integrals that can be expressed as the exponential generating function for the generalized twisted power sums.

scholarly journals The Deformed Virasoro Algebra at Roots of Unity

1998 ◽  
Vol 196 (2) ◽  
pp. 249-288 ◽  
Author(s):  
Peter Bouwknegt ◽  
Krzysztof Pilch
Keyword(s):  
Virasoro Algebra ◽  
Roots Of Unity ◽  
Deformed Virasoro Algebra

On efficient balanced codes over the mth roots of unity

2006 ◽  
Vol 52 (5) ◽  
pp. 2214-2217 ◽  
Author(s):  
R. Mascella ◽  
L.G. Tallini ◽  
S. Al-Bassam ◽  
B. Bose
Keyword(s):  
Roots Of Unity
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