scholarly journals SyNRAC: A Maple-Package for Solving Real Algebraic Constraints

2003 ◽  
pp. 828-837 ◽  
Author(s):  
Hirokazu Anai ◽  
Hitoshi Yanami
Keyword(s):  
Algebraic Constraints ◽  
Maple Package

Formation of Geometric Tolerance Zones for Polyhedral Objects

1997 ◽  
Author(s):  
Utpal Roy ◽  
Bing Li
Keyword(s):  
Variational Model ◽  
Tolerance Zone ◽  
Geometric Tolerance ◽  
Geometric Tolerances ◽  
Polyhedral Objects ◽  
Different Types ◽  
Tolerance Zones ◽  
Algebraic Constraints ◽  
Size Tolerance ◽  
Part Model

Abstract This paper presents a scheme for establishing geometric tolerance zones for polyhedral objects in solid modelers. The proposed scheme is based on a surface-based variational model. Variations are applied to a part model by varying each surface’s model variables. Those model variables are constrained by some algebraic relations derived from the specified geometric tolerances. For size tolerance, two types of tolerance zones are considered in order to reflect two different types of size tolerances. For any other geometric tolerance (form, orientation or positional), the resultant tolerance zone is defined by the combination of size tolerance and that particular geometric tolerance specifications. Appropriate algebraic constraints (on the model variables) are finally used to establish the tolerance zone boundaries in the surface-based variational model.

Operations on Single-Valued Trapezoidal Neutrosophic Numbers using (α,β,γ)-Cuts “Maple Package”

2021 ◽  
pp. 113-122
Author(s):  
Mohamed Bisher Zeina ◽  
◽  
Omar Zeitouny ◽  
Fatina Masri ◽  
Fatima Kadoura ◽  
...  
Keyword(s):  
Decision Making ◽  
Neutrosophic Statistics ◽  
Triangular Neutrosophic Numbers ◽  
Maple Package

In this paper, we present a Maple package called Neutrosophic, which allows users to do operations on trapezoidal and triangular neutrosophic numbers including summation, subtraction, division, and multiplication based on -cuts and plots the results, also the package allows users to rank numbers depending on ambiguity index and value index. This package is very useful in neutrosophic decision-making problems, neutrosophic probabilities, neutrosophic statistics, and in many other fields of neutrosophic researches.

Positive fractional continuous-time linear systems with singular pencils

2012 ◽  
Vol 60 (1) ◽  
pp. 9-12 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
State Variables ◽  
Algebraic Constraints ◽  
Necessary And Sufficient ◽  
Time Linear

Positive fractional continuous-time linear systems with singular pencils A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for the positivity of the fractional descriptor systems are established.

scholarly journals Counting occurrences for a finite set of words: an inclusion-exclusion approach

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Frédérique Bassino ◽  
Julien Clément ◽  
J. Fayolle ◽  
P. Nicodème
Keyword(s):  
Generating Function ◽  
Exclusion Principle ◽  
Complete Proof ◽  
Detailed Proof ◽  
Finite Set ◽  
International Audience ◽  
The One ◽  
Maple Package

International audience In this paper, we give the multivariate generating function counting texts according to their length and to the number of occurrences of words from a finite set. The application of the inclusion-exclusion principle to word counting due to Goulden and Jackson (1979, 1983) is used to derive the result. Unlike some other techniques which suppose that the set of words is reduced (<i>i..e.</i>, where no two words are factor of one another), the finite set can be chosen arbitrarily. Noonan and Zeilberger (1999) already provided a MAPLE package treating the non-reduced case, without giving an expression of the generating function or a detailed proof. We give a complete proof validating the use of the inclusion-exclusion principle and compare the complexity of the method proposed here with the one using automata for solving the problem.

Constraint Manifold Synthesis of Planar Linkages

1996 ◽  
Author(s):  
A. P. Murray ◽  
J. M. McCarthy
Keyword(s):  
Design Theory ◽  
Geometric Constraints ◽  
Design Parameters ◽  
Design Problems ◽  
Constraint Manifold ◽  
Linkage Design ◽  
Versatile Tool ◽  
Algebraic Constraints ◽  
Planar Linkages

Abstract This paper formulates the design theory of planar four-bar linkages using the planar form of dual quaternions known as planar quaternions. The set of positions reachable by the floating link of a dyad is a quadratic algebraic surface called a constraint manifold. Determining the coefficients of the quadratic form defining this manifold is equivalent to setting the design parameters of the linkage. If the task of the linkage is specified as geometric constraints on the location of the floating link, then algebraic constraints are obtained on the quaternion components. We seek the coefficients of the constraint manifold that satisfies these constraints. The result is an algebraic formulation that is symmetric in its characterization of the linkage and task, and provides a versatile tool for the formulation and solution of linkage design problems.

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