Mathematical Foundations of VR/AR

2022 ◽  
pp. 401-412
Author(s):  
Ralf Doerner
Keyword(s):  
Mathematical Foundations

Tasks of computer graphics under conditions of fundamentalization of preparation of an informatics teacher

2020 ◽  
pp. 57-63
Author(s):  
Ye. Yi. Bidaibekov ◽  
V. V. Grinshkun ◽  
S. N. Koneva
Keyword(s):  
Computer Graphics ◽  
Basic Principle ◽  
Fundamental Component ◽  
The Future ◽  
Scope Of Application ◽  
Education Training ◽  
Mathematical Foundations

The article deals with computer graphics tasks related to the activities of the future informatics teacher in conditions of fundamentalization of education. Training of future informatics teachers in the context of the fundamentalization of education requires them to know the range of tasks related to computer graphics and the skills to solve them. In order to enhance the fundamental component of computer graphics, methods are proposed that rely on interprandial communications, as well as on in-depth training of computer graphics. In the course of reasoning, the authors come to the conclusion that the content of computer graphics should be enriched with mathematical foundations of computer graphics and as a result update the content of the computer graphics course with machine graphics algorithms. The basic principle of selecting the content of the course offered is the principle of the fundamentalization of education. Since the scope of application of computer graphics is extensive, in our opinion, the system of tasks and tasks on computer graphics is the most interesting. A feature of this system is the orientation towards solving fundamental problems of computer graphics. It was also revealed during the study that it is possible to reduce the tasks of the proposed system to a certain sequence of stages. The application of stages for a certain type of tasks affects the methods of solving them. Thus, the fundamental training of future informatics teachers in computer graphics requires them to know these stages and methods of solving fundamental computer graphics tasks.

Mathematical Foundations of Biomechanics

2010 ◽  
Vol 38 (6) ◽  
pp. 533-577 ◽  
Author(s):  
Peter F. Niederer
Keyword(s):  
Mathematical Foundations

Degenerate Diffusion Operators Arising in Population Biology (AM-185)

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Adjoint Operator ◽  
Integral Kernel ◽  
Mathematical Finance ◽  
Elliptic Operators ◽  
Complete Analysis ◽  
Time Behavior ◽  
Degenerate Elliptic Operators ◽  
Regularity Properties ◽  
Degenerate Elliptic ◽  
Mathematical Foundations

This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the martingale problem and therefore the existence of the associated Markov process. The book uses an “integral kernel method” to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. The book establishes the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. It shows that the semigroups defined by these operators have holomorphic extensions to the right half plane. The book also demonstrates precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.

High-Frequency Financial Econometrics

2014 ◽  
Author(s):  
Yacine Aït-Sahalia ◽  
Jean Jacod
Keyword(s):  
High Frequency ◽  
Practical Importance ◽  
Financial Econometrics ◽  
Trading Strategies ◽  
Financial Data ◽  
Jump Processes ◽  
High Frequency Trading ◽  
Microstructure Noise ◽  
Econometric Methods ◽  
Mathematical Foundations

High-frequency trading is an algorithm-based computerized trading practice that allows firms to trade stocks in milliseconds. Over the last fifteen years, the use of statistical and econometric methods for analyzing high-frequency financial data has grown exponentially. This growth has been driven by the increasing availability of such data, the technological advancements that make high-frequency trading strategies possible, and the need of practitioners to analyze these data. This comprehensive book introduces readers to these emerging methods and tools of analysis. The book covers the mathematical foundations of stochastic processes, describes the primary characteristics of high-frequency financial data, and presents the asymptotic concepts that their analysis relies on. It also deals with estimation of the volatility portion of the model, including methods that are robust to market microstructure noise, and address estimation and testing questions involving the jump part of the model. As the book demonstrates, the practical importance and relevance of jumps in financial data are universally recognized, but only recently have econometric methods become available to rigorously analyze jump processes. The book approaches high-frequency econometrics with a distinct focus on the financial side of matters while maintaining technical rigor, which makes this book invaluable to researchers and practitioners alike.

scholarly journals Time-delay interferometry

2020 ◽  
Vol 24 (1) ◽  
Author(s):  
Massimo Tinto ◽  
Sanjeev V. Dhurandhar
Keyword(s):  
Time Delay ◽  
Laser Interferometer ◽  
Laser Light ◽  
Space Antenna ◽  
Phase Measurements ◽  
Laser Noise ◽  
Future Space ◽  
Laser Interferometer Space Antenna ◽  
Overall Performance ◽  
Mathematical Foundations

AbstractEqual-arm detectors of gravitational radiation allow phase measurements many orders of magnitude below the intrinsic phase stability of the laser injecting light into their arms. This is because the noise in the laser light is common to both arms, experiencing exactly the same delay, and thus cancels when it is differenced at the photo detector. In this situation, much lower level secondary noises then set the overall performance. If, however, the two arms have different lengths (as will necessarily be the case with space-borne interferometers), the laser noise experiences different delays in the two arms and will hence not directly cancel at the photo detector. To solve this problem, a technique involving heterodyne interferometry with unequal arm lengths and independent phase-difference readouts has been proposed. It relies on properly time-shifting and linearly combining independent Doppler measurements, and for this reason it has been called time-delay interferometry (TDI). This article provides an overview of the theory, mathematical foundations, and experimental aspects associated with the implementation of TDI. Although emphasis on the application of TDI to the Laser Interferometer Space Antenna mission appears throughout this article, TDI can be incorporated into the design of any future space-based mission aiming to search for gravitational waves via interferometric measurements. We have purposely left out all theoretical aspects that data analysts will need to account for when analyzing the TDI data combinations.

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