scholarly journals On Dirichlet convolution method

1998 ◽  
Vol 21 (3) ◽  
pp. 607-611
Author(s):  
Indulata Sukla
Keyword(s):  
Summability Methods ◽  
Dirichlet Convolution ◽  
Convolution Method

In this paper we have proved limitation theorem for(D,h(n))summability methods and have shown that it is best possible.

On ( h(n)) summability methods

1985 ◽  
Vol 97 (2) ◽  
pp. 189-193
Author(s):  
B. Kuttner ◽  
I. L. Sukla
Keyword(s):  
Prime Number ◽  
Sufficient Conditions ◽  
Prime Number Theorem ◽  
Necessary And Sufficient Conditions ◽  
Summability Methods ◽  
Dirichlet Convolution ◽  
Necessary And Sufficient ◽  
Convolution Method

AbstractIn 1967 Segal introduced the Dirichlet convolution (, h(n)), generalizing a method of Ingham developed in studies on the Prime Number Theorem. In this paper we establish necessary and sufficient conditions on the sequence h(n) in order that the convolution method (, h(n)) be conservative. Further conditions are established for the method to be absolutely conservative.

Matrix Transformations Based on Dirichlet Convolution

1997 ◽  
Vol 40 (4) ◽  
pp. 498-508
Author(s):  
Chikkanna Selvaraj ◽  
Suguna Selvaraj
Keyword(s):  
Bounded Variation ◽  
Matrix Transformations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Summability Methods ◽  
The Matrix ◽  
Dirichlet Convolution ◽  
Necessary And Sufficient ◽  
Positive Integers

AbstractThis paper is a study of summability methods that are based on Dirichlet convolution. If f(n) is a function on positive integers and x is a sequence such that then x is said to be Af-summable to L. The necessary and sufficient condition for the matrix Af to preserve bounded variation of sequences is established. Also, the matrix Af is investigated as ℓ − ℓ and G − G mappings. The strength of the Af-matrix is also discussed.

NON-NORMAL STATISTICAL TOLERANCE ANALYSIS USING ANALYTICAL CONVOLUTION METHOD

2008 ◽  
Vol 07 (01) ◽  
pp. 127-130 ◽  
Author(s):  
S. G. LIU ◽  
P. WANG ◽  
Z. G. LI
Keyword(s):  
Normal Distribution ◽  
Closed Loop ◽  
Tolerance Analysis ◽  
Accurate Method ◽  
Probability Density Functions ◽  
Triangular Distribution ◽  
Normal Distributions ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis ◽  
Convolution Method

In statistical tolerance analysis, it is usually assumed that the statistical tolerance is normally distributed. But in practice, there are many non-normal distributions, such as uniform distribution, triangular distribution, etc. The simple way to analyze non-normal distributions is to approximately represent it with normal distribution, but the accuracy is low. Monte-Carlo simulation can analyze non-normal distributions with higher accuracy, but is time consuming. Convolution method is an accurate method to analyze statistical tolerance, but there are few reported works about it because of the difficulty. In this paper, analytical convolution is used to analyze non-normal distribution, and the probability density functions of closed loop component are obtained. Comparing with other methods, convolution method is accurate and faster.

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