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Validating Mathematical Structures [article]

Kazuhiko Sakaguchi
2020 arXiv   pre-print
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants.  ...  The packed classes methodology is a generic design pattern to define and combine mathematical structures in a dependent type theory with records.  ...  Introduction Mathematical structures are a key ingredient of modern formalized mathematics in proof assistants, e.g., [21, 44, 28, 1] [49, Sect. 4] .  ... 
arXiv:2002.00620v2 fatcat:jk5rbny4vfhk5mdgajzvofccy4

Validating Mathematical Structures [chapter]

Kazuhiko Sakaguchi
2020 Lecture Notes in Computer Science  
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants.  ...  The packed classes methodology is a generic design pattern to define and combine mathematical structures in a dependent type theory with records.  ...  Introduction Mathematical structures are a key ingredient of modern formalized mathematics in proof assistants, e.g., [1, 18, 25, 41] [46, Sect. 4] .  ... 
doi:10.1007/978-3-030-51054-1_8 fatcat:wytjsiyfj5bvvf4mcbcp5v5kya

The Validation of Mathematical Indices of Communication Structure

Jane A. Edwards, Peter R. Monge
1977 Annals of the International Communication Association  
Little research attention has been paid to the systematic validation of mathematical indices of social structure.  ...  The validation strategies in use remain largely implicit anA generally fail to appreciate the multi-dimensionality of structure.  ...  The Validation of Mathematical Indices of Communication Structure The interdependence of theory and observation or measurement practices has often been noted (Woelfel, 1974) .  ... 
doi:10.1080/23808985.1977.11923680 fatcat:ao2hgsj7rvfr7h2dmsr2fma3ha

Structural Equation Model to Validate: Mathematics-Computer Interaction, Computer Confidence, Mathematics Commitment, Mathematics Motivation and Mathematics Confidence

Arturo Garcia-Santillan, Elena Moreno-Garcia, Milka E. Escalera-Chávez, Carlos A. Rojas-Kramer, Felipe Pozos-Texon
2016 International Journal of Research in Education and Science  
The collected data was processed applying multivariate data analysis using structural equation modeling technique.  ...  They developed a theoretical model aiming to explain this phenomenon from the component elements of attitude toward mathematics and computers: Mathematics engagement, mathematics confidence, mathematics  ...  Structural equation modeling technique was utilized in the multivariate analysis, to validate if the model proposed by Galbraith and Haines (2000) fits well the empirical data.  ... 
doi:10.21890/ijres.81576 fatcat:ezxyiqeaqbgnxneesvxalc3ece

The Descriptive Tests of Mathematics Skills:Predictive Validity for an Elementary Mathematics Concepts and Structures Course

John H. Meyer, Peggy G. Woodard, David E. Suddick
1994 Educational and Psychological Measurement  
VALIDITY STUDIES THE DESCRIPTIVE TESTS OF MATHEMATICS SKILLS: PREDICTIVE VALIDITY FOR AN ELEMENTARY MATHEMATICS CONCEPTS AND STRUCTURES COURSE JOHN H. MEYER, PEGGY G. WOODARD, Anp DAVID E.  ...  MEASUREMENT model for elementary education majors who are required to pass an upper- division mathematics concepts and structures course.  ... 
doi:10.1177/0013164494054001015 fatcat:un3rguxdlbdqjcveh72doogncm

MATHEMATICAL MODELLING OF WAVE OVERTOPPING AT COMPLEX STRUCTURES: VALIDATION AND COMPARISON

Cordula Berkenbrink, Ralf Kaiser, Hanz Dieter Niemeyer
2011 Coastal Engineering Proceedings  
A validation study for a mathematical model called OTT-1d from HR-Wallingford modified by the Coastal research Station is presented in this paper.  ...  Furthermore a comparison of the modelling results to actual used calculation methods is done to show the limits of each calculation methods relating to the complexity of the structure.  ...  At the toe of the structure a wave gauge was installed, which is used as the seaward boundary for the mathematical model.  ... 
doi:10.9753/icce.v32.structures.4 fatcat:b6iwkvpskfbtzaopfp2da5uf2u

Sets of Formulas Valid in Finite Structures

Alan L. Selman
1973 Transactions of the American Mathematical Society  
K valid in all structures of cardinality in K.  ...  line ^4 d-{V ) « d(V ) vdfVJ, SETS OF FORMULAS VALID IN FINITE STRUCTURES Abstract A function Ir is defined on the set of all subsets of u) so that for each set K, the value, Ir , is the set of formulas  ...  By the cardinality of a structure 91 we mean the cardinality of its domain. A structure 91 is finite, if its domain is. We write f= <p, if <p is valid in 91. Definition 1 . 1 Let K <£ u>.  ... 
doi:10.2307/1996611 fatcat:rac7aqrqxvgpfegy6peul43xem

Sets of formulas valid in finite structures

Alan L. Selman
1973 Transactions of the American Mathematical Society  
] SETS OF FORMULAS VALID IN FINITE STRUCTURES 501 (3) a is 1, b is 2; (4) V»'i.  ...  Let us define a function Ü on the set of all subsets of w so that for each set K, the value, U", is the set of formulas valid in all structures We write |=_ <f>, if <f> is valid in 21.  ... 
doi:10.1090/s0002-9947-1973-0319730-3 fatcat:ugmb6u3b5jc7nmj7ok5oswe6si

DEVELOPMENT AND VALIDATION OF STRUCTURAL MODELS OF HUMAN POSTURE

R. Barauskas, R. Krušinskiene
2006 Mathematical Modelling and Analysis  
The approach is applicable to structural models with any number of DOF and any structural complexity.  ... 
doi:10.3846/13926292.2006.9637297 fatcat:dumbgklyhrehfmtuvdj6zvodra

Definition, Extraction, and Validation of Pore Structures in Porous Materials [chapter]

Ulrike Homberg, Daniel Baum, Alexander Wiebel, Steffen Prohaska, Hans-Christian Hege
2014 Mathematics and Visualization  
We introduce definitions of the elements of this void space, here called pore space, based on its distance function, and present methods to extract these elements using the extremal structures of the distance  ...  In this chapter, we present a validation of the extracted pore structures.  ...  (c) Link between pore structures and extremal structures of the distance map.  ... 
doi:10.1007/978-3-319-04099-8_15 fatcat:jtys4cdlqvhs7cqlp57zgkbta4

Validating Brouwer's continuity principle for numbers using named exceptions

VINCENT RAHLI, MARK BICKFORD
2017 Mathematical Structures in Computer Science  
Using continuity and the fan theorem, we prove important results of Intuitionistic Mathematics: Brouwer's continuity theorem, bar induction on monotone bars and the negation of the law of excluded middle  ...  There are two principles that distinguish Brouwer's mathematics from other constructive mathematics, namely bar induction and a continuity principle [67; 60; 113; 42; 13; 22; 116; 120; 9; 103; 102; 119  ...  Validity of Rules. A rule of the form (S 1 ∧ · · · ∧ S n ) ⇒ S is valid if assuming that the sequents S 1 , . . . , S n are true then the sequent S is also true. Consistency.  ... 
doi:10.1017/s0960129517000172 fatcat:n7xzyn2zh5cgji26zrj6lrykw4

STRUCTURE, MATHEMATICAL VARIABLE AND VALIDATION ON THE FIELDS AND WEAPONS OF THE COMPETITION MODEL

José Celso Contador
2009 RAI: Revista de Administração e Inovação  
Belonging to the Competitiveness theory and having scientific validity, the model is both qualitative and quantitative, and therefore presents some advantages over Porter's model, as well as over the RBV  ... 
doi:10.5585/rai.v5i3.192 fatcat:4lx7rwgjenhijktyowwwzy6ojm

Attitudes towards mathematics at secondary level: Development and structural validation of the Scale for Assessing Attitudes towards Mathematics in Secondary Education (SATMAS)

Lara Yáñez-Marquina, Lourdes Villardón-Gallego
2016 Electronic Journal of Research in Educational Psychology  
Confirmatory factor analyses were conducted to test the theoretical proposed non-hierarchical structure, consisting of three first-order factors (student's math self-concept, perceived usefulness of mathematics  ...  Therefore, the aim of this paper is to develop and validate an instrument for measuring secondary students' attitudes towards mathematics based on a preliminary detailed theoretical framework.  ...  at secondary level: Development and structural validation of the Scale for Assessing Attitudes towards Mathematics in Secondary Education (SATMAS) Electronic Journal of Research in Educational Psychology  ... 
doi:10.14204/ejrep.40.15163 fatcat:s4iruxvhwncsvlsjyoaz5i5bdy

Attitudes towards mathematics at secondary level: Development and structural validation of the Scale for Assessing Attitudes towards Mathematics in Secondary Education (SATMAS)

Lara Yáñez-Marquina, Lourdes Villardón-Gallego
2017 Electronic Journal of Research in Educational Psychology  
at secondary level: Development and structural validation of the Scale for Assessing Attitudes towards Mathematics in Secondary Education (SATMAS) Electronic Journal of Research in Educational Psychology  ...  Finally, the validity assessments included construct validity, discriminant validity and criterion-related validity.  ... 
doi:10.25115/ejrep.40.15163 fatcat:p5gk3gx54necdg3ww7qergesdm

Longitudinal displacement in viscoelastic arteries: A novel fluid-structure interaction computational model, and experimental validation

Martina Bukač, Sunčica Čanić
2013 Mathematical Biosciences and Engineering  
structure effects.  ...  the structure onto the fluid is counter-balanced by the fluid stress acting onto the structure).  ... 
doi:10.3934/mbe.2013.10.295 pmid:23458302 fatcat:hohqhdz4gfbhljkc5u4fhpfiya
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