Real polynomial representations of multi-valued logic

1964 ◽  
Author(s):  
Howard Tilford Hendrickson
Keyword(s):  
Real Polynomial ◽  
Polynomial Representations

scholarly journals On the lexicographic degree of two-bridge knots

2016 ◽  
Vol 25 (07) ◽  
pp. 1650044 ◽  
Author(s):  
Erwan Brugallé ◽  
Pierre-Vincent Koseleff ◽  
Daniel Pecker
Keyword(s):  
Lower Bound ◽  
Knot Theory ◽  
Theoretical Method ◽  
Plane Curves ◽  
Real Plane ◽  
Real Polynomial ◽  
Torus Knots ◽  
Polynomial Curves ◽  
Polynomial Representations ◽  
Sharp Lower Bound

We study the degree of polynomial representations of knots. We obtain the lexicographic degree for two-bridge torus knots and generalized twist knots. The proof uses the braid theoretical method developed by Orevkov to study real plane curves, combined with previous results from [Chebyshev diagrams for two-bridge knots, Geom. Dedicata 150 (2010) 405–425; E. Brugallé, P.-V. Koseleff, D. Pecker, Untangling trigonal diagrams, to appear in J. Knot Theory and its Ramifications]. We also give a sharp lower bound for the lexicographic degree of any knot, using real polynomial curves properties.

scholarly journals TOPOLOGICAL NOETHERIANITY FOR ALGEBRAIC REPRESENTATIONS OF INFINITE RANK CLASSICAL GROUPS

2021 ◽  
Author(s):  
R. H. EGGERMONT ◽  
A. SNOWDEN
Keyword(s):  
Classical Groups ◽  
Infinite Rank ◽  
Polynomial Representations ◽  
Algebraic Representations

AbstractDraisma recently proved that polynomial representations of GL∞ are topologically noetherian. We generalize this result to algebraic representations of infinite rank classical groups.

scholarly journals Hyperbolic Polynomials and Convex Analysis

2001 ◽  
Vol 53 (3) ◽  
pp. 470-488 ◽  
Author(s):  
Heinz H. Bauschke ◽  
Osman Güler ◽  
Adrian S. Lewis ◽  
Hristo S. Sendov
Keyword(s):  
Convex Function ◽  
Interior Point ◽  
Convex Analysis ◽  
Symmetric Functions ◽  
Interior Point Methods ◽  
Optimization Problems ◽  
Real Polynomial ◽  
Hyperbolic Polynomials ◽  
Real Roots ◽  
Univariate Polynomial

AbstractA homogeneous real polynomial p is hyperbolic with respect to a given vector d if the univariate polynomial t ⟼ p(x − td) has all real roots for all vectors x. Motivated by partial differential equations, Gårding proved in 1951 that the largest such root is a convex function of x, and showed various ways of constructing new hyperbolic polynomials. We present a powerful new such construction, and use it to generalize Gårding’s result to arbitrary symmetric functions of the roots. Many classical and recent inequalities follow easily. We develop various convex-analytic tools for such symmetric functions, of interest in interior-point methods for optimization problems over related cones.

scholarly journals Partially APN functions with APN-like polynomial representations

2020 ◽  
Vol 88 (6) ◽  
pp. 1159-1177
Author(s):  
Lilya Budaghyan ◽  
Nikolay Kaleyski ◽  
Constanza Riera ◽  
Pantelimon Stănică
Keyword(s):  
Apn Functions ◽  
Polynomial Representations

Polynomial remainders and plane automorphisms

2003 ◽  
Vol 68 (1) ◽  
pp. 73-79
Author(s):  
Takis Sakkalis
Keyword(s):  
Jacobian Conjecture ◽  
Real Polynomial ◽  
Polynomial Automorphisms ◽  
Polynomial Map

This note relates polynomial remainders with polynomial automorphisms of the plane. It also formulates a conjecture, equivalent to the famous Jacobian Conjecture. The latter provides an algorithm for checking when a polynomial map is an automorphism. In addition, a criterion is presented for a real polynomial map to be bijective.

scholarly journals Real Polynomial Maps and Singular Open Books at Infinity

2016 ◽  
Vol 118 (1) ◽  
pp. 57 ◽  
Author(s):  
Raimundo N. Araújo Dos Santos ◽  
Ying Chen ◽  
Mihai Tibăr
Keyword(s):  
Open Book ◽  
Real Polynomial ◽  
Open Books ◽  
Polynomial Maps ◽  
Real Polynomial Maps

We provide significant conditions under which we prove the existence of stable open book structures at infinity, i.e. on spheres $S^{m-1}_R$ of large enough radius $R$. We obtain new classes of real polynomial maps $\mathsf{R}^m \to \mathsf{R}^p$ which induce such structures.

scholarly journals Generator of PRN's on the norm group

2021 ◽  
Vol 25 (2(36)) ◽  
pp. 26-39
Author(s):  
P. Fugelo ◽  
S. Varbanets
Keyword(s):  
Prime Number ◽  
Quadratic Field ◽  
Exponential Sum ◽  
Random Numbers ◽  
Gaussian Integers ◽  
New Family ◽  
Serial Test ◽  
Polynomial Representations ◽  
Modulo P ◽  
Norm Group

Let $p$ be a prime number, $d\in\mathds{N}$, $\left(\frac{-d}{p}\right)=-1$, $m>2$, and let $E_m$ denotes the set of of residue classes modulo $p^m$ over the ring of Gaussian integers in imaginary quadratic field $\mathds{Q}(\sqrt{-d})$ with norms which are congruented with 1 modulo $p^m$. In present paper we establish the polynomial representations for real and imagimary parts of the powers of generating element $u+iv\sqrt{d}$ of the cyclic group $E_m$. These representations permit to deduce the ``rooted bounds'' for the exponential sum in Turan-Erd\"{o}s-Koksma inequality. The new family of the sequences of pseudo-random numbers that passes the serial test on pseudorandomness was being buit.

scholarly journals Polynomial representations of knots

1992 ◽  
Vol 44 (1) ◽  
pp. 11-17 ◽  
Author(s):  
Anant R. Shastri
Keyword(s):  
Polynomial Representations
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