scholarly journals Numerical methods for the deterministic second moment equation of parabolic stochastic PDEs

2020 ◽  
Vol 89 (326) ◽  
pp. 2801-2845
Author(s):  
Kristin Kirchner
Keyword(s):  
Numerical Methods ◽  
Moment Equation ◽  
Stochastic Pdes ◽  
Second Moment

Propagation in waveguides containing random irregularities: the second moment equation

1981 ◽  
Vol 377 (1768) ◽  
pp. 73-98 ◽  
Keyword(s):  
Exact Solution ◽  
Refractive Index ◽  
Wave Propagation ◽  
Moment Equation ◽  
Refractive Index Profile ◽  
Physical Significance ◽  
Moment Equations ◽  
Index Profile ◽  
Second Moment ◽  
Parabolic Profile

The parabolic moment equations can be used to describe wave propagation in a waveguide, with an arbitrary refractive index profile, that contains weakly scattering irregularities. These equations remain valid even in the case of multiple scatter. An exact solution can be given if the guide has a parabolic profile, when the intensity on the axis of the guide exhibits periodic foci which are rapidly blurred as scattering increases. Exact solutions cannot be obtained when the profile is non-parabolic. The paper presents an approximate method of solving the second moment equation for an arbitrary profile. A simplified form of the solution useful in practice is given, and the method is illustrated for a waveguide with a cubic profile. The physical significance of the solution is discussed.

Numerical Methods

2019 ◽  
Author(s):  
Rajesh Kumar Gupta
Keyword(s):  
Numerical Methods

À propos de la folie et de l’amour dans Crime et Châtiment de Dostoïevski

2018 ◽  
pp. 138-144
Author(s):  
Ariane Bazan
Keyword(s):  
Second Moment

Crime et Châtiment raconte l’histoire de Raskolnikov à l’été 1865 à Petersbourg, qui assassine une vieille usurière et sa sœur. Dès avant son geste Raskolnikov se met au travail quant aux questions de la culpabilité, du châtiment et de la rédemption. Le texte présente la folie humaine selon deux modalités, la névrose et la psychose, chacune avec ses deux temporalités, c’est-à-dire un premier moment de conscience d’une séparation d’avec la réalité, et un second moment de séparation effective. Raskolnikov se trouve du côté de la psychose, sur un continuel point de basculement entre les deux temps et les folies de Catherina Ivanovna et, peut-être, d’Arcady Svidrigaïlov, se trouvent du côté de la névrose, avec seul Arcady qui ne bascule pas. La seconde idée est celle de l’enjeu du crime : peut-on se trouver parmi ses frères humains de cet amour inconditionnel qui serait capable d’aimer le criminel le plus abject ? Le paradoxe est que Raskolnikov, qui ne peut supporter la transgression au point de délirer une race pure, met au défi ce monde à aimer le coupable du crime le plus vil. Nous terminerons en proposant que l’amour ne puisse être qu’inconditionnel, même s’il ne peut être illimité.

THE METHODS OF DEVELOPING COMPUTATIONAL THINKING OF STUDENTS WHILE STUDYING THE COURSE "NUMERICAL METHODS" BASED ON BLENDED LEARNING

2019 ◽  
pp. 34-41
Author(s):  
M. M. Klunnikova
Keyword(s):  
Numerical Methods ◽  
Blended Learning ◽  
Computational Thinking ◽  
Individual Characteristics ◽  
Diagnostic Model ◽  
Mathematics Students ◽  
Professional Activities ◽  
Cognitive Component ◽  
Professional Field ◽  
The Individual

The work is devoted to the consideration of improving the quality of teaching students the discipline “Numerical methods” through the development of the cognitive component of computational thinking based on blended learning. The article presents a methodology for the formation of computational thinking of mathematics students, based on the visualization of algorithmic design schemes and the activation of the cognitive independence of students. The characteristic of computational thinking is given, the content and structure of computational thinking are shown. It is argued that a student with such a mind is able to manifest himself in his professional field in the best possible way. The results of the application of the technique are described. To determine the level of development of the cognitive component of computational thinking, a diagnostic model has been developed based on measuring the content, operational and motivational components. It is shown that the proposed method of developing computational thinking of students, taking into account the individual characteristics of students’ thinking, meaningfully based on the theoretical and practical aspects of studying the discipline, increases the effectiveness of learning the course “Numerical methods”. The materials of the article are of practical value for teachers of mathematical disciplines who use information and telecommunication technologies in their professional activities.

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