An Asymptotic Mean Value Formula

2016 ◽  
pp. 33-37
Author(s):  
Peter Lindqvist
Keyword(s):  
Mean Value ◽  
Mean Value Formula

scholarly journals Almansi Theorem and Mean Value Formula for Quaternionic Slice-regular Functions

2020 ◽  
Vol 30 (4) ◽  
Author(s):  
Alessandro Perotti
Keyword(s):  
Harmonic Functions ◽  
Mean Value ◽  
Zonal Harmonic ◽  
Slice Regular Functions ◽  
Regular Functions ◽  
Quaternionic Polynomials ◽  
Mean Value Formula

Abstract We prove an Almansi Theorem for quaternionic polynomials and extend it to quaternionic slice-regular functions. We associate to every such function f, a pair $$h_1$$ h 1 , $$h_2$$ h 2 of zonal harmonic functions such that $$f=h_1-\bar{x} h_2$$ f = h 1 - x ¯ h 2 . We apply this result to get mean value formulas and Poisson formulas for slice-regular quaternionic functions.

scholarly journals On the Gauss mean-value formula for class number

1998 ◽  
Vol 151 ◽  
pp. 199-208 ◽  
Author(s):  
Fernando Chamizo ◽  
Henryk Iwaniec
Keyword(s):  
Class Number ◽  
Approximate Formula ◽  
Error Term ◽  
Exponential Sums ◽  
Mean Value ◽  
Point Problem ◽  
Class Number Formula ◽  
Modern Notation ◽  
Number Formula ◽  
Mean Value Formula

Abstract.In his masterwork Disquisitiones Arithmeticae, Gauss stated an approximate formula for the average of the class number for negative discriminants. In this paper we improve the known estimates for the error term in Gauss approximate formula. Namely, our result can be written as for every ∊ > 0, where H(−n) is, in modern notation, h(−4n). We also consider the average of h(−n) itself obtaining the same type of result.Proving this formula we transform firstly the problem in a lattice point problem (as probably Gauss did) and we use a functional equation due to Shintani and Dirichlet class number formula to express the error term as a sum of character and exponential sums that can be estimated with techniques introduced in a previous work on the sphere problem.

scholarly journals Density in mandibular trabeculae of beta thalassemia major patients at the age of 11-13 years

2012 ◽  
Vol 24 (3) ◽  
Author(s):  
Nisa Milati Biyantini ◽  
Fahmi Oscandar ◽  
Eriska Riyanti
Keyword(s):  
Sampling Technique ◽  
Thalassemia Major ◽  
Mean Value ◽  
Beta Thalassemia ◽  
Systemic Diseases ◽  
Maximum Score ◽  
Beta Thalassemia Major ◽  
Minimum Score ◽  
Mean Value Formula ◽  
Descriptive Method

Introduction: Density of mandible trabeculae is defined as density of trabeculae at posterior region of mandibulae. Systemic diseases which can affect bone density are osteoporosis and many types of anemia, including which has significant influence that is beta thalassemia major. The objective of this investigation was to obtain the data of density in mandible trabeculae of beta thalassemia major patients at the age of 11-13 years. Methods: The descriptive method was used in this study and the samples were selected using the total sampling technique. 15 periapical photos were obtained using the total sampling echnique. The periapical photos are administered using 3D-Doctor software. Data were analyzed using simple mean value formula. Results: Statistical count resulted in the minimum score of sample which was 98, 039 grayscale, the maximum score of sample which was 231, 34 grayscale, and the range score of sample which was 126.503 grayscale Conclusion: Density of mandible trabeculae of thalassemia beta major patients at the age of 11-13 is 126.503 grayscale.

Sign in / Sign up

Export Citation Format

Share Document