scholarly journals Masaki Kashiwara and algebraic analysis

2019 ◽  
Author(s):  
Pierre Schapira
Keyword(s):  
Algebraic Analysis

scholarly journals Total Differentiability and Monogenicity for Functions in Algebras of Order 4

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
I. Sabadini ◽  
D. C. Struppa
Keyword(s):  
Analytic Functions ◽  
Associative Algebras ◽  
Basic Tool ◽  
Algebraic Analysis ◽  
Italian School ◽  
Relevant Role

AbstractIn this paper we discuss some notions of analyticity in associative algebras with unit. We also recall some basic tool in algebraic analysis and we use them to study the properties of analytic functions in two algebras of dimension four that played a relevant role in some work of the Italian school, but that have never been fully investigated.

scholarly journals On the Effect of Control-Point Spacing on the Multisolution Phenomenon in the P3P Problem

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
M. Vynnycky ◽  
G. M. M. Reddy
Keyword(s):  
Image Analysis ◽  
Camera Calibration ◽  
Pose Estimation ◽  
Computer Animation ◽  
Solution Structure ◽  
Control Point ◽  
Quartic Equation ◽  
Real Solutions ◽  
Algebraic Analysis ◽  
And Robotics

The perspective 3-point (P3P) problem, also known as pose estimation, has its origins in camera calibration and is of importance in many fields: for example, computer animation, automation, image analysis, and robotics. One possibility is to formulate it mathematically in terms of finding the solution to a quartic equation. However, there is yet no quantitative knowledge as to how control-point spacing affects the solution structure—in particular, the multisolution phenomenon. Here, we consider this problem through an algebraic analysis of the quartic’s coefficients and its discriminant and find that there are significant variations in the likelihood of two or four solutions, depending on how the spacing is chosen. The analysis indicates that although it is never possible to remove the occurrence of the four-solution case completely, it could be possible to choose spacings that would maximize the occurrence of two real solutions. Moreover, control-point spacing is found to impact significantly on the reality conditions for the solution of the quartic equation.

The Differential-Algebraic Analysis of Symplectic and Lax Structures Related with New Riemann-Type Hydrodynamic Systems

2013 ◽  
Vol 71 (3) ◽  
pp. 305-351 ◽  
Author(s):  
Yarema A. Prykarpatsky ◽  
Orest D. Artemovych ◽  
Maxim V. Pavlov ◽  
Anatolij K. Prykarpatski
Keyword(s):  
Algebraic Analysis ◽  
Hydrodynamic Systems
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