scholarly journals Simple Approach to Special Polynomials: Laguerre, Hermite, Legendre, Tchebycheff, and Gegenbauer

2019 ◽  
Author(s):  
Vicente Aboites ◽  
Miguel Ramírez
Keyword(s):  
Simple Approach ◽  
Special Polynomials

Influence of X-Ray Induced Fluorescence on Energy Dispersive X-Ray Analysis of Thin Foils

1977 ◽  
Vol 35 ◽  
pp. 328-329
Author(s):  
E. A. Kenik ◽  
J. Bentley
Keyword(s):  
Thin Foil ◽  
Electron Excitation ◽  
Simple Approach ◽  
Foil Thickness ◽  
X Rays ◽  
X Ray ◽  
Hole Spectrum ◽  
Illumination System ◽  
Thin Foils ◽  
Intensity Ratios

Cliff and Lorimer (1) have proposed a simple approach to thin foil x-ray analy sis based on the ratio of x-ray peak intensities. However, there are several experimental pitfalls which must be recognized in obtaining the desired x-ray intensities. Undesirable x-ray induced fluorescence of the specimen can result from various mechanisms and leads to x-ray intensities not characteristic of electron excitation and further results in incorrect intensity ratios.In measuring the x-ray intensity ratio for NiAl as a function of foil thickness, Zaluzec and Fraser (2) found the ratio was not constant for thicknesses where absorption could be neglected. They demonstrated that this effect originated from x-ray induced fluorescence by blocking the beam with lead foil. The primary x-rays arise in the illumination system and result in varying intensity ratios and a finite x-ray spectrum even when the specimen is not intercepting the electron beam, an ‘in-hole’ spectrum. We have developed a second technique for detecting x-ray induced fluorescence based on the magnitude of the ‘in-hole’ spectrum with different filament emission currents and condenser apertures.

Complex Subject : Simple Approach

2004 ◽  
Vol 49 (4) ◽  
pp. 401-403
Author(s):  
Richard B. Makover
Keyword(s):  
Simple Approach ◽  
Complex Subject

A Simple Approach to Evaluating the Stability of Optimal Portfolios

2014 ◽  
Author(s):  
Zhongjin Yang ◽  
Keli Han ◽  
Marat Molyboga ◽  
Georgiy Molyboga
Keyword(s):  
Simple Approach ◽  
Optimal Portfolios ◽  
The Stability

A Simple Approach to the One-Pot Three Component Synthesis of 4Hpyrimido [2,1-b] benzothiazole Derivatives Using Polyethylene Glycol (PEG-400)

2015 ◽  
Vol 12 (3) ◽  
pp. 197-204 ◽  
Author(s):  
Prabhakar Rairala ◽  
Bandi Yadagiri ◽  
Rajashaker Bantu ◽  
Vijayacharan Guguloth ◽  
Lingaiah Nagarapu
Keyword(s):  
Polyethylene Glycol ◽  
Simple Approach ◽  
One Pot ◽  
Benzothiazole Derivatives ◽  
Peg 400 ◽  
The One

Identities related to special polynomials and combinatorial numbers

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4833-4844 ◽  
Author(s):  
Eda Yuluklu ◽  
Yilmaz Simsek ◽  
Takao Komatsu
Keyword(s):  
Generating Functions ◽  
Functional Equations ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Euler Numbers ◽  
Special Polynomials ◽  
Central Factorial Numbers

The aim of this paper is to give some new identities and relations related to the some families of special numbers such as the Bernoulli numbers, the Euler numbers, the Stirling numbers of the first and second kinds, the central factorial numbers and also the numbers y1(n,k,?) and y2(n,k,?) which are given Simsek [31]. Our method is related to the functional equations of the generating functions and the fermionic and bosonic p-adic Volkenborn integral on Zp. Finally, we give remarks and comments on our results.

Simple approach for the rapid estimation of BOD5 in food processing wastewater

2020 ◽  
Vol 27 (16) ◽  
pp. 20554-20564
Author(s):  
Le Thi Bao Ngoc ◽  
Tran Anh Tu ◽  
Luu Thi Thanh Hien ◽  
Duong Nhat Linh ◽  
Nguyen Tri ◽  
...  
Keyword(s):  
Food Processing ◽  
Simple Approach ◽  
Rapid Estimation ◽  
Food Processing Wastewater

scholarly journals The Mean Values of Character Sums and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 318
Author(s):  
Jiafan Zhang ◽  
Yuanyuan Meng
Keyword(s):  
Character Sums ◽  
Gauss Sums ◽  
Mean Values ◽  
Special Polynomials ◽  
Elementary Methods ◽  
The Mean

In this paper, we use the elementary methods and properties of classical Gauss sums to study the calculation problems of some mean values of character sums of special polynomials, and obtained several interesting calculation formulae for them. As an application, we give a criterion for determining that 2 is the cubic residue for any odd prime p.

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