A linear-algebraic method to compute polynomial PDE conservation laws

2021 ◽  
Author(s):  
Michele Boreale ◽  
Luisa Collodi
Keyword(s):  
Conservation Laws ◽  
Algebraic Method ◽  
Linear Algebraic Method

scholarly journals A linear-algebraic tool for conditional independence inference

2015 ◽  
Vol 6 (2) ◽  
Author(s):  
Kentaro Tanaka ◽  
Milan Studeny ◽  
Akimichi Takemura ◽  
Tomonari Sei
Keyword(s):  
Computational Result ◽  
Conditional Independence ◽  
Algebraic Approach ◽  
Algebraic Method ◽  
Positive Density ◽  
Implication Problem ◽  
Algebraic Tool ◽  
Linear Algebraic Method

In this note, we propose a new linear-algebraic method for the implication problem among conditional independence statements, which is inspired by the factorization characterization of conditional independence. First, we give a criterion in the case of a discrete strictly positive density and relate it to an earlier linear-algebraic approach. Then, we extend the method to the case of a discrete density that need not be strictly positive. Finally, we provide a computational result in the case of six variables. 

scholarly journals Ketercapaian dan Keterkontrolan Sistem Deskriptor Diskrit Linier Positif

2017 ◽  
Vol 3 (2) ◽  
pp. 65-73
Author(s):  
Yulia Retno Sari
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Algebraic Method ◽  
Discrete Systems ◽  
Descriptor System ◽  
Linear Algebraic Method

A positive discrete descriptor system has been widely used in modeling economics, engineering, chemistry and others. In this research, we studied the necessary conditions and sufficient conditions for a positive discrete descriptors system is achieved positive and controlled postively. In addition, it is also studied on sufficient terms and conditions which ensure that discrete systems are null controlled. By using linear algebraic method and Inverse Drazin, this research has proved several theorems for discrete descriptors system achieved positive, controlled positively and controlled null. In addition, examples are given as illustrations to reinforce the validity of the proven theorems.

Generalization of the linear algebraic method to three dimensions

1991 ◽  
Vol 43 (1) ◽  
pp. 172-176
Author(s):  
D. L. Lynch ◽  
B. I. Schneider
Keyword(s):  
Algebraic Method ◽  
Three Dimensions ◽  
Linear Algebraic Method

Determination of Tartaric Acid and the Sum of Malic and Citric Acids in Grape Juices by Potentiometric Titration

1988 ◽  
Vol 71 (5) ◽  
pp. 1028-1032
Author(s):  
Oswaldo E S Godinho ◽  
Nilson E Desouza ◽  
Luiz M Aleixo ◽  
Ari U Ivaska
Keyword(s):  
Citric Acid ◽  
Tartaric Acid ◽  
Potentiometric Titration ◽  
Malic Acid ◽  
Grape Juice ◽  
Algebraic Method ◽  
The Individual ◽  
Grape Juices ◽  
Linear Algebraic Method

Abstract Application of a linear algebraic method to the potentiometric titration of a mixture of tartaric and malic acids makes it possible to determine the individual concentrations of both acids in the same sample. These 2 acids have also been determined in grape juice free of citric acid after their separation from the juice matrix by precipitation as barium salts, followed by selective solubilization. It is also possible to determine tartaric acid and the sum of malic acid and citric acid in grape juice when the latter is present.

Optimal Placement of Fixture Clamps: Maintaining Form Closure and Independent Regions of Form Closure

2002 ◽  
Vol 124 (3) ◽  
pp. 676-685 ◽  
Author(s):  
Rodrigo A. Marin ◽  
Placid M. Ferreira
Keyword(s):  
Screw Theory ◽  
Three Dimensional ◽  
Algebraic Method ◽  
Optimal Placement ◽  
Surface Type ◽  
Form Closure ◽  
Linear Programming Formulation ◽  
Precise Relationship ◽  
External Loads ◽  
Linear Algebraic Method

This paper addresses the problem of computing frictionless optimal clamping schemes with form closure on three-dimensional parts with planar and cylindrical faces. Given a work part with a pre-defined 3-2-1 locator scheme, a set of polygonal convex regions on the clamping faces are defined as the admissible positions of the clamps. The work part-fixture contact is assumed to be of the point-surface type. Using extended screw theory, we present a linear algebraic method that computes the sub-regions of the clamping faces such that clamps located within them are guaranteed to achieve form closure. These are termed dependent regions of form closure, since the clamps must be placed according to a precise relationship. We develop methods to compute these regions on work parts with planar and cylindrical faces. This result is incorporated into a new linear programming formulation to compute frictionless optimal clamping schemes. Clamping schemes with form closure are robust when uncertainty in knowledge of the external loads acting on the work part is present. Next, we extend the method to compute maximal independent regions of form closure. These are sub-regions of the dependent regions of form closure where the clamps can be placed completely independent of each other while maintaining form closure. When the clamps are placed within the independent regions of form closure, the clamping scheme is made robust against errors in their positions.

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