The Geometric Product

2008 ◽  
pp. 79-124 ◽  
Keyword(s):  
Geometric Product

scholarly journals Tensor-product versus geometric-product coding

2008 ◽  
Vol 77 (1) ◽  
Author(s):  
Diederik Aerts ◽  
Marek Czachor
Keyword(s):  
Tensor Product ◽  
Geometric Product

ON THE TIME-DEPENDENT BEHAVIOR OF A MARKOVIAN REENTRANT-LINE MODEL

2018 ◽  
Vol 33 (3) ◽  
pp. 367-386
Author(s):  
Brian Fralix
Keyword(s):  
Stationary Distribution ◽  
Time Dependent ◽  
Product Form ◽  
Line Model ◽  
Transition Functions ◽  
Geometric Product ◽  
Dependent Behavior ◽  
Product Technique ◽  
Form Representation ◽  
Similar Product

We use the random-product technique from [5] to study both the steady-state and time-dependent behavior of a Markovian reentrant-line model, which is a generalization of the preemptive reentrant-line model studied in the work of Adan and Weiss [2]. Our results/observations yield additional insight into why the stationary distribution of the reentrant-line model from [2] exhibits an almost-geometric product-form structure: indeed, our generalized reentrant-line model, when stable, admits a stationary distribution with a similar product-form representation as well. Not only that, the Laplace transforms of the transition functions of our reentrant-line model also have a product-form structure if it is further assumed that both Buffers 2 and 3 are empty at time zero.

scholarly journals On affine geometric product objects

1977 ◽  
Vol 34 (2) ◽  
pp. 197-200
Author(s):  
Józef Joachim Telega
Keyword(s):  
Geometric Product

scholarly journals Evaluation and Optimization of Task-oriented Measurement Uncertainty for Coordinate Measuring Machines Based on Geometrical Product Specifications

2018 ◽  
Vol 9 (1) ◽  
pp. 6 ◽  
Author(s):  
Yinbao Cheng ◽  
Zhongyu Wang ◽  
Xiaohuai Chen ◽  
Yaru Li ◽  
Hongyang Li ◽  
...  
Keyword(s):  
Measurement Uncertainty ◽  
Evaluation Model ◽  
Optimization Method ◽  
Practical Significance ◽  
Measuring Instruments ◽  
Coordinate Measuring Machines ◽  
Measurement Instruments ◽  
Practical Applications ◽  
Geometric Product ◽  
Task Oriented

Measuring instruments are intended to be intelligent, precise, multi-functional and developing multidirectionally, scientific, and reasonable; the reliable evaluation of measurement uncertainty of precision instruments is also becoming more and more difficult, and the evaluation of the Coordinate Measuring Machines (CMM) measurement uncertainty is among the typical problems. Based on Geometric Product Specification (GPS), this paper has systematically studied the CMM uncertainty for evaluating the size and geometrical errors oriented toward measurement tasks, and thus has realized the rapid and reliable evaluation of the CMM uncertainty for task-oriented measurement. For overestimation of the CMM uncertainty for task-oriented measurements in the initial evaluation, a systematic optimization solution has been proposed. Finally, the feasibility and validity of the evaluation model and the optimization method have been verified by three different types of measurement examples of diameter, flatness and perpendicularity. It is typical and representative to systematically solve the problem of the CMM uncertainty for evaluating the measurement tasks targeted at dimensions and geometric errors, and the research contents can be effectively applied to solve the uncertainty evaluation problems of other precision instruments, which are of great practical significance not only for promoting the combination of modern uncertainty theory and practical applications but also for improving the application values of precision measurement instruments.

Homomorphic Image Processing Over Geometric Product Spaces and Finite P-Adic Arithmetic

2019 ◽  
Author(s):  
David William Honorio Araujo da Silva ◽  
Hanes Barbosa Marques de Oliveira ◽  
Edward Chow ◽  
Bryan Sosa Barillas ◽  
Carlos Paz de Araujo
Keyword(s):  
Image Processing ◽  
Homomorphic Image ◽  
Product Spaces ◽  
Geometric Product
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