‎The aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]‎. ‎In [1]‎, ‎Ungar and Chen showed that the algebra of the group $SL(2,mathbb C)$ naturally leads to the notion of gyrogroups ‎and gyrovector spaces for dealing with the Lorentz group and its ‎underlying hyperbolic geometry‎. ‎They defined the Chen addition and then Chen model of hyperbolic geomet...

Secant Varieties of Segre-Veronese Varieties

Based on the evaluation at t = −1 of the generating polynomial for the hyperoctahedral group by the number of descents, an observation recently made by Hirzebruch, a new q-secant number is derived by working with the Chow-Gessel q-polynomial involving the flag major index. Using the doubloon combinatorial model we show that this new q-secant number is a polynomial with positive integral coeffic...

We introduce an algorithm for calculating, offline or in real time and with no explicit system characterization, the feedforward input required for repetitive motions of a system. The algorithm is based on the secant method of numerical analysis and gives accurate motion at frequencies limited only by the signal-to-noise ratio and the actuator power and range. We illustrate the secant-solver al...

The derivative polynomials introduced by Knuth and Buckholtz in their calculations of the tangent and secant numbers are extended to a multivariable q– environment. The n-th q-derivatives of the classical q-tangent and q-secant are each given two polynomial expressions. The first polynomial expression is indexed by triples of integers, the second by compositions of integers. The functional rela...

the aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. in [1], ungar and chen showed that the algebra of the group sl(2,c) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the lorentz group and its underlying hyperbolic geometry. they defined the chen addition and then chen model of hyperbolic geometry. in this paper,...

1. L’Hôpital’s Rule 1 1.1. The Cauchy Mean Value Theorem 1 1.2. L’Hôpital’s Rule 2 2. Newton’s Method 5 2.1. Introducing Newton’s Method 5 2.2. A Babylonian Algorithm 6 2.3. Questioning Newton’s Method 7 2.4. Introducing Infinite Sequences 7 2.5. Contractions and Fixed Points 8 2.6. Convergence of Newton’s Method 10 2.7. Quadratic Convergence of Newton’s Method 11 2.8. An example of nonconverge...

Conjugate gradient methods have been paid attention to, because they can be directly applied to large-scale unconstrained optimization problems. In order to incorporate second order information of the objective function into conjugate gradient methods, Dai and Liao (2001) proposed a conjugate gradient method based on the secant condition. However, their method does not necessarily generate a de...