An equidistribution theorem for certain birational maps of ℙk

2021 ◽  
Vol 32 (03) ◽  
pp. 2150017
Author(s):  
Taeyong Ahn
Keyword(s):  
Algebraic Degree ◽  
Birational Maps

We prove an equidistribution theorem of positive closed currents for a certain class of birational maps [Formula: see text] of algebraic degree [Formula: see text] satisfying [Formula: see text], where [Formula: see text] is the inverse of [Formula: see text] and [Formula: see text] are the sets of indeterminacy for [Formula: see text], respectively.

scholarly journals Manin Involutions for Elliptic Pencils and Discrete Integrable Systems

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Matteo Petrera ◽  
Yuri B. Suris ◽  
Kangning Wei ◽  
René Zander
Keyword(s):  
Integrable Systems ◽  
Geometric Description ◽  
Discrete Integrable Systems ◽  
Birational Maps ◽  
Base Points ◽  
Special Geometry ◽  
Low Degree ◽  
Geometric Study

AbstractWe contribute to the algebraic-geometric study of discrete integrable systems generated by planar birational maps: (a) we find geometric description of Manin involutions for elliptic pencils consisting of curves of higher degree, birationally equivalent to cubic pencils (Halphen pencils of index 1), and (b) we characterize special geometry of base points ensuring that certain compositions of Manin involutions are integrable maps of low degree (quadratic Cremona maps). In particular, we identify some integrable Kahan discretizations as compositions of Manin involutions for elliptic pencils of higher degree.

scholarly journals The Algebraic Degree of Phase-Type Distributions

2010 ◽  
Vol 47 (03) ◽  
pp. 611-629
Author(s):  
Mark Fackrell ◽  
Qi-Ming He ◽  
Peter Taylor ◽  
Hanqin Zhang
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Polynomial Algorithm ◽  
Algebraic Degree ◽  
Nonnegative Matrices ◽  
Stieltjes Transform ◽  
Special Cases ◽  
Phase Type ◽  
Phase Type Distributions ◽  
The Matrix

This paper is concerned with properties of the algebraic degree of the Laplace-Stieltjes transform of phase-type (PH) distributions. The main problem of interest is: given a PH generator, how do we find the maximum and the minimum algebraic degrees of all irreducible PH representations with that PH generator? Based on the matrix exponential (ME) order of ME distributions and the spectral polynomial algorithm, a method for computing the algebraic degree of a PH distribution is developed. The maximum algebraic degree is identified explicitly. Using Perron-Frobenius theory of nonnegative matrices, a lower bound and an upper bound on the minimum algebraic degree are found, subject to some conditions. Explicit results are obtained for special cases.

scholarly journals On the monomial birational maps of the projective space

2003 ◽  
Vol 75 (2) ◽  
pp. 129-134 ◽  
Author(s):  
Gérard Gonzalez-Sprinberg ◽  
Ivan Pan
Keyword(s):  
Projective Space ◽  
Group Structure ◽  
Cremona Transformations ◽  
Birational Maps

We describe the group structure of monomial Cremona transformations. It follows that every element of this group is a product of quadratic monomial transformations, and geometric descriptions in terms of fans.

scholarly journals A certain class of quadratures with even Tchebychev weights

2012 ◽  
Vol 20 (1) ◽  
pp. 447-458
Author(s):  
Zlatko Udovičić ◽  
Mirna Udovičić
Keyword(s):  
Weight Function ◽  
Algebraic Degree ◽  
Quadrature Formulas ◽  
Approximate Computation ◽  
Degree Of Exactness

Abstract We are considering the quadrature formulas of “practical type” (with five knots) for approximate computation of integral [xxx] where w(·) denotes (even) Tchebychev weight function. We prove that algebraic degree of exactness of those formulas can not be greater than five. We also determined some admissible nodes and compared proposed formula with some other quadrature formulas.

scholarly journals Monomial Generalized Almost Perfect Nonlinear Functions

2020 ◽  
Vol 31 (03) ◽  
pp. 411-419
Author(s):  
Masamichi Kuroda
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Algebraic Degree ◽  
Apn Functions ◽  
Nonlinear Functions ◽  
Almost Perfect Nonlinear ◽  
Basic Properties ◽  
Almost Perfect Nonlinear Functions

Generalized almost perfect nonlinear (GAPN) functions were defined to satisfy some generalizations of basic properties of almost perfect nonlinear (APN) functions for even characteristic. In particular, on finite fields of even characteristic, GAPN functions coincide with APN functions. In this paper, we study monomial GAPN functions for odd characteristic. We give monomial GAPN functions whose algebraic degree are maximum or minimum on a finite field of odd characteristic. Moreover, we define a generalization of exceptional APN functions and give typical examples.

Constructions of rotation symmetric bent functions with high algebraic degree

2018 ◽  
Vol 251 ◽  
pp. 15-29
Author(s):  
Qinglan Zhao ◽  
Dong Zheng ◽  
Weiguo Zhang
Keyword(s):  
Algebraic Degree ◽  
Bent Functions ◽  
Rotation Symmetric
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