2×2 Matrix summation method for multiple reflections and transmissions in a biaxial slab between two anisotropic media

1999 ◽  
Vol 163 (1-3) ◽  
pp. 9-14 ◽  
Author(s):  
I. Abdulhalim
Keyword(s):  
Anisotropic Media ◽  
Summation Method ◽  
Multiple Reflections ◽  
Matrix Summation

scholarly journals Using matrix summation method for three dimensional dose calculation in brachytherapy

2012 ◽  
Vol 17 (2) ◽  
pp. 110-114
Author(s):  
Mahmoud Zibandeh-Gorji ◽  
Ali Asghar Mowlavi ◽  
Saeed Mohammadi
Keyword(s):  
Three Dimensional ◽  
Dose Calculation ◽  
Summation Method ◽  
Matrix Summation

Hausdorff dimension of the set of almost convergent sequences

2022 ◽  
pp. 1-7
Author(s):  
Alexandr Usachev
Keyword(s):  
Hausdorff Dimension ◽  
Summation Method ◽  
Binary Representation ◽  
Hausdorff Dimensions ◽  
Summation Methods ◽  
Wide Range ◽  
Matrix Summation ◽  
Convergent Sequences

Abstract The paper deals with the sets of numbers from [0,1] such that their binary representation is almost convergent. The aim of the study is to compute the Hausdorff dimensions of such sets. Previously, the results of this type were proved for a single summation method (e.g. Cesàro, Abel, Toeplitz). This study extends the results to a wide range of matrix summation methods.

Reckoning electromagnetic principles with polarimetric measurements of anisotropic optically active crystals

2012 ◽  
Vol 45 (2) ◽  
pp. 279-291 ◽  
Author(s):  
Oriol Arteaga ◽  
John Freudenthal ◽  
Bart Kahr
Keyword(s):  
Optical Activity ◽  
Light Propagation ◽  
Anisotropic Media ◽  
Mueller Matrix ◽  
Electromagnetic Theory ◽  
Optically Active ◽  
Multiple Reflections

A method is introduced to correlate electromagnetic theory and polarimetric experiments for anisotropic optically active crystals at oblique angles of incidence. It is based on the 4 × 4 algebraic descriptions of light propagation in layered anisotropic media, which can be simplified to 2 × 2 matrices when multiple reflections are disregarded. Spectroscopic Mueller matrix measurements in transmission and at oblique angles of incidence have been made on two uniaxial crystals: α-quartz and silver thiogallate. Their optical activity tensors have been spectroscopically determined using the method presented here.

Partial Summation Method for XANES Calculation

1997 ◽  
Vol 7 (C2) ◽  
pp. C2-99-C2-102
Author(s):  
T. Fujikawa ◽  
R. Yanagisawa ◽  
N. Yiwata
Keyword(s):  
Summation Method ◽  
Partial Summation

The Impact of Light Polarisation on Light Field of Scenes with Multiple Reflections

2020 ◽  
pp. 108-115 ◽  
Author(s):  
Vladimir P. Budak ◽  
Anton V. Grimaylo
Keyword(s):  
Mathematical Model ◽  
Light Field ◽  
Global Illumination ◽  
Multiple Reflections ◽  
Software Environment ◽  
The Monte Carlo Method ◽  
Mueller Matrices ◽  
Volume Integration ◽  
The Impact

The article describes the role of polarisation in calculation of multiple reflections. A mathematical model of multiple reflections based on the Stokes vector for beam description and Mueller matrices for description of surface properties is presented. On the basis of this model, the global illumination equation is generalised for the polarisation case and is resolved into volume integration. This allows us to obtain an expression for the Monte Carlo method local estimates and to use them for evaluation of light distribution in the scene with consideration of polarisation. The obtained mathematical model was implemented in the software environment using the example of a scene with its surfaces having both diffuse and regular components of reflection. The results presented in the article show that the calculation difference may reach 30 % when polarisation is taken into consideration as compared to standard modelling.

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