Integration Of The Greatest Integer Function

2020 ◽  
Author(s):  
Steve Ligh ◽  
David Fung
Keyword(s):  
Greatest Integer Function

scholarly journals The Greatest Integer Function

2016 ◽  
Vol 6 (2) ◽  
pp. 225-225
Author(s):  
Alanna Rae
Keyword(s):  
Greatest Integer Function

scholarly journals A parabolic differential equation with unbounded piecewise constant delay

1992 ◽  
Vol 15 (2) ◽  
pp. 339-346 ◽  
Author(s):  
Joseph Wiener ◽  
Lokenath Debnath
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Difference Equations ◽  
Infinite Delay ◽  
Parabolic Differential Equation ◽  
Constant Delay ◽  
Partial Differential ◽  
Piecewise Constant ◽  
Greatest Integer Function

A partial differential equation with the argument[λt]is studied, where[•]denotes the greatest integer function. The infinite delayt−[λt]leads to difference equations of unbounded order.

scholarly journals Oscillation criteria for differential equations with piecewise constant argument

2001 ◽  
Vol 32 (4) ◽  
pp. 293-304
Author(s):  
Zhiguo Luo ◽  
Jianhua Shen
Keyword(s):  
Differential Equation ◽  
Continuous Functions ◽  
Variable Coefficients ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Greatest Integer Function ◽  
Special Case ◽  
Oscillation And Nonoscillation Criteria ◽  
Oscillation And Nonoscillation ◽  
Constant Argument

We obtain some new oscillation and nonoscillation criteria for the differential equation with piecewise constant argument $$ x'(t) + a(t)x(t) + b(x) x([t-k]) = 0, $$ where $ a(t) $ and $ b(t) $ are continuous functions on $ [-k, \infty) $, $ b(t) \ge 0 $, $ k $ is a positive integer and $ [ \cdot ] $ denotes the greatest integer function. The method used is based on the treatment of certain difference equation with variable coefficients. Our results extend theorems in [15]. As a special case, our results also improve the conclusions obtained by Aftabizadeh, Wiener and Xu [3].

Some Properties of Beatty Sequences II

1960 ◽  
Vol 3 (1) ◽  
pp. 17-22 ◽  
Author(s):  
Ian G. Connell
Keyword(s):  
Complementary Sequences ◽  
Beatty Sequences ◽  
Greatest Integer Function ◽  
Image Position

In a previous paper [l] we discussed a property of the complementary sequences1where square brackets denote the greatest integer function and α is any positive irrational. We called {un} and {vn} Beatty sequences of argument α.

Counting Triples, Triangles, and Acute Triangles

1999 ◽  
Vol 92 (7) ◽  
pp. 612-619
Author(s):  
Ruth McClintock
Keyword(s):  
Problem Solving ◽  
Difference Equation ◽  
Mathematical Induction ◽  
Modular Arithmetic ◽  
Advanced Students ◽  
Greatest Integer Function ◽  
First Time

Activities involving counting triples, triangles, and acute triangles enrich the curriculum with excursions into modular arithmetic, the greatest-integer function, and summation notation. In addition, more advanced students can apply difference-equation techniques to find closed forms and can use mathematical induction to prove the formulas. Students may be learning about these topics for the first time, or they may be reviewing familiar ideas in different problem-solving contexts. In either situation, personal arsenals of problem-attacking skills are strengthened.

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