An algebraic representation of the affine B�cklund transformation

1992 ◽  
Vol 44 (1) ◽  
Author(s):  
StevenG. Buyske
Keyword(s):  
Algebraic Representation ◽  
Cklund Transformation

scholarly journals Focus and contrastive topic in questions and answers, with particular reference to Turkish

2020 ◽  
Vol 46 (1-2) ◽  
pp. 1-71 ◽  
Author(s):  
Beste Kamali ◽  
Manfred Krifka
Keyword(s):  
Algebraic Representation ◽  
Similar Role ◽  
Discourse Coherence ◽  
Dynamic Interpretation ◽  
Contrastive Topic ◽  
Questions And Answers ◽  
Alternative Questions

AbstractMuch recent research has recognized the importance of focus and contrastive topic in assertions for discourse coherence. However, with few exceptions, it has been neglected that focus and contrastive topic also occur in questions, and have a similar role in establishing coherence. We propose a framework of dynamic interpretation based on the notion of Commitment Spaces that show that a uniform interpretation of focus and contrastive topic is possible. The algebraic representation format is rich enough so that a separate introduction of discourse trees is not necessary. The paper discusses these phenomena for Turkish, a language with an explicit focus marker for polar and alternative questions, which distinguishes focus from contrastive topic.

scholarly journals Investigation of eighth-grade students' understanding of the slope of the linear function

2012 ◽  
Vol 26 (42a) ◽  
pp. 139-162 ◽  
Author(s):  
Osman Birgin
Keyword(s):  
Linear Function ◽  
Analytical Techniques ◽  
Structured Interview ◽  
Linear Functions ◽  
Eighth Grade ◽  
The Black Sea ◽  
Algebraic Representation ◽  
Black Sea Region ◽  
Eighth Grade Students ◽  
Written Questions

This study aimed to investigate eighth-grade students' difficulties and misconceptions and their performance of translation between the different representation modes related to the slope of linear functions. The participants were 115 Turkish eighth-grade students in a city in the eastern part of the Black Sea region of Turkey. Data was collected with an instrument consisting of seven written questions and a semi-structured interview protocol conducted with six students. Students' responses to questions were categorized and scored. Quantitative data was analyzed using the SPSS 17.0 statistical packet program with cross tables and one-way ANOVA. Qualitative data obtained from interviews was analyzed using descriptive analytical techniques. It was found that students' performance in articulating the slope of the linear function using its algebraic representation form was higher than their performance in using transformation between graphical and algebraic representation forms. It was also determined that some of them had difficulties and misunderstood linear function equations, graphs, and slopes and could not comprehend the connection between slope and the x- and y-intercepts.

scholarly journals MultiAspect Graphs: Algebraic Representation and Algorithms

Algorithms ◽  
2016 ◽  
Vol 10 (1) ◽  
pp. 1 ◽  
Author(s):  
Klaus Wehmuth ◽  
Éric Fleury ◽  
Artur Ziviani
Keyword(s):  
Algebraic Representation

scholarly journals LOOPS, SURFACES AND GRASSMANN REPRESENTATION IN TWO- AND THREE-DIMENSIONAL ISING MODELS

1999 ◽  
Vol 14 (29) ◽  
pp. 4549-4574 ◽  
Author(s):  
C. R. GATTRINGER ◽  
S. JAIMUNGAL ◽  
G. W. SEMENOFF
Keyword(s):  
Three Dimensional ◽  
Ising Models ◽  
Algebraic Representation ◽  
Simple Derivation ◽  
Counting Problems ◽  
Intrinsic Geometry ◽  
Geometry Factor ◽  
Loop Expansion ◽  
Loop Surface

We construct an algebraic representation of the geometrical objects (loop and surface variables) dual to the spins in 2 and 3D Ising models. This algebraic calculus is simpler than dealing with the geometrical objects, in particular when analyzing geometry factors and counting problems. For the 2D case we give the corrected loop expansion of the free energy and the radius of convergence for this series. For the 3D case we give a simple derivation of the geometry factor which prevents overcounting of surfaces in the intrinsic geometry representation of the partition function, and find a classification of the surfaces to be summed over. For 2 and 3D we derive a compact formula for 2n-point functions in loop (surface) representation.

Algebraic Representation of Geometric and Size Tolerances

1995 ◽  
Author(s):  
S. H. Mullins ◽  
D. C. Anderson
Keyword(s):  
Tolerance Analysis ◽  
Design Analysis ◽  
Algebraic Representation ◽  
Dimensional Metrology ◽  
Algebraic Form ◽  
Worst Case ◽  
Mechanical Component ◽  
Analysis And Synthesis ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis

Abstract Presented is a method for mathematically modeling mechanical component tolerances. The method translates the semantics of ANSI Y14.5M tolerances into an algebraic form. This algebraic form is suitable for either worst-case or statistical tolerance analysis and seeks to satisfy the requirements of both dimensional metrology and design analysis and synthesis. The method is illustrated by application to datum systems, position tolerances, orientation tolerances, and size tolerances.

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