On sets containing no geometric progression with integer ratio

2021 ◽  
Author(s):  
Jin-Hui Fang
Keyword(s):  
Geometric Progression

scholarly journals A de Casteljau Algorithm for -Bernstein-Stancu Polynomials

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Grzegorz Nowak
Keyword(s):  
Bernstein Polynomials ◽  
Classical Case ◽  
Geometric Progression ◽  
De Casteljau Algorithm ◽  
Stancu Operators

This paper is concerned with a generalization of the -Bernstein polynomials and Stancu operators, where the function is evaluated at intervals which are in geometric progression. It is shown that these polynomials can be generated by a de Casteljau algorithm, which is a generalization of that relating to the classical case and -Bernstein case.

The sum of a geometric progression

Algebra ◽  
2004 ◽  
pp. 83-85
Author(s):  
Israel M. Gelfand ◽  
Alexander Shen
Keyword(s):  
Geometric Progression

scholarly journals Formulation of a Three-Tier Cisternal Grade as a Predictor of In-Hospital Outcome from a Prospective Study of Patients with Traumatic Intracranial Hematoma- A review report.

2018 ◽  
Vol 2 (2) ◽  
pp. 01-01
Author(s):  
Raghunath Avanali
Keyword(s):  
Traumatic Brain Injury ◽  
Brain Injury ◽  
Prospective Study ◽  
Outcome Prediction ◽  
Geometric Progression ◽  
Limited Resources ◽  
Intracranial Hematoma ◽  
Prognostic Prediction ◽  
A Prospective Study ◽  
Traumatic Intracranial Hematoma

Traumatic brain injury (TBI) is an escalating problem with an almost geometric progression. The problem escalated with increasing population and traffic, but with limited resources to handle the issue.1,2 The present study has its objective focused on making a prognosis of the TBI patient.3 The outcome prediction helps in conveying the prognosis to the patient’s family. Needless to say, a prognostic prediction is also helpful in the optimal and timely utilization of available resources.

Functional-discrete Method (FD-method) for Matrix Sturm-Liouville Problems

2005 ◽  
Vol 5 (4) ◽  
pp. 362-386 ◽  
Author(s):  
B. Ĭ. Bandyrskiĭ ◽  
I. P. Gavrilyuk ◽  
I. I. Lazurchak ◽  
V. L. Makarov
Keyword(s):  
Asymptotic Behavior ◽  
Convergence Rate ◽  
Geometric Progression ◽  
Order Number ◽  
Discrete Method ◽  
Numerical Examples ◽  
Matrix Coefficients ◽  
Sturm Liouville ◽  
Theoretical Results

AbstractA new algorithm for Sturm|Liouville problems with matrix coefficients is proposed which possesses the convergence rate of a geometric progression with a denominator depending inversely proportional on the order number of eigenvalues. The asymptotic behavior of the distance between neighboring eigenvalues if the order number tends to infinity is investigated too. Numerical examples confirming the theoretical results are given.

scholarly journals A generalization of the Bernstein polynomials

1999 ◽  
Vol 42 (2) ◽  
pp. 403-413 ◽  
Author(s):  
Haul Oruç ◽  
George M. Phillips ◽  
Philip J. Davis
Keyword(s):  
Bernstein Polynomials ◽  
Classical Case ◽  
Geometric Progression ◽  
Generalized Bernstein Polynomials

This paper is concerned with a generalization of the classical Bernstein polynomials where the function is evaluated at intervals which are in geometric progression. It is shown that, when the function is convex, the generalized Bernstein polynomials Bn are monotonic in n, as in the classical case.

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