611,397 Hits in 2.6 sec

The Symbolic Model for Algebra: Functions and Mechanisms [chapter]

Albrecht Heeffer
2010 Studies in Computational Intelligence  
In this paper we will discuss the functions and mechanisms of this model and show how the model relates to its arithmetical basis.  ...  The symbolic mode of reasoning in algebra, as it emerged during the sixteenth century, can be considered as a form of model-based reasoning.  ...  The second and third ( The symbolic model for algebra The symbolic model for algebra The symbolic model for algebra  ... 
doi:10.1007/978-3-642-15223-8_29 fatcat:vccm65e5lzhvzkpayrhm37g3lq

Rapid Modeling and Parameter Estimation of Partial Differential Algebraic Equations by a Functional Spreadsheet Paradigm

Chahid Ghaddar
2018 Mathematical and Computational Applications  
We present a systematic spreadsheet method for modeling and optimizing general partial differential algebraic equations (PDAE).  ...  The method exploits a pure spreadsheet PDAE solver function design that encapsulates the Method of Lines and permits seamless integration with an Excel spreadsheet nonlinear programming solver.  ...  In this paper, we exploit the merits of the calculus functions extension to develop a systematic and practical method for modeling and optimizing parameterized partial differential algebraic equations  ... 
doi:10.3390/mca23030039 fatcat:5i53c7ku6nhx3izji5oea2fsrq

Dynamics of a stage structure prey-predator model with ratio-dependent functional response and anti-predator behavior of adult prey

Prabir Panja, ,Department of Applied Science, Haldia Institute of Technology, Haldia-721657, W. B., India, Soovoojeet Jana, Shyamal kumar Mondal, ,Department of Mathematics, Ramsaday College, Amta, Howrah, India, ,Department of Applied Mathematics with Oceanology, and Computer Programming, Vidyasagar University, Midnapore -721102, W. B., India
2019 Numerical Algebra, Control and Optimization  
In this paper, a predator-prey interaction model among juvenile prey, adult prey and predator has been developed where stage structure is considered on prey species.  ...  The functional responses has been considered as ratio dependent. It is assumed that that the adult prey is strong enough such that it has an anti-predator characteristic.  ...  Therefore, to satisfy the above both criteria a functional response should be a function of prey and predator both [2, 5] .  ... 
doi:10.3934/naco.2020033 fatcat:nkqs4krczrcthnviwklaaty36a

A Combinatory Algebra for Sequential Functionals of Finite Type [chapter]

Jaap van Oosten, S. Barry Cooper, John K. Truss
Models and Computability  
It is shown that the type structure of nite-type functionals associated to a combinatory algebra of partial functions from IN t o I N i n t h e s a m e w ay as the type structure of the countable functionals  ...  is associated to the partial combinatory algebra of total functions from IN t o I N, is isomorphic to the type structure generated by o b j e c t N the at domain on the natural numbers in Ehrhard's category  ...  Thirdly it raises the question whether maybe more models of P C Fincluding the fully abstract game models of 9 and 1 can be induced in this way b y c o m binatory algebras.  ... 
doi:10.1017/cbo9780511565670.019 fatcat:dqgsgfzy2bflpapvv3ayu7tm2a

Multiprocessor and distributed system design: The integration of functional specification and performance analysis using Stochastic Process Algebras [chapter]

Norbert Götz, Ulrich Herzog, Michael Rettelbach
Performance Evaluation of Computer and Communication Systems  
We introduce Stochastic Process Algebras as a novel approach for the structured design and analysis of both the functional behaviour and performance characteristics of parallel and distributed systems.  ...  This is achieved by integrating performance modelling and analysis into the powerful and well investigated formal description technique of process algebras.  ...  Constructivity: the Basis for Systematic Modelling and System Design From the very beginning a salient intention of process algebras has been to support a (functional) design methodology which systematically  ... 
doi:10.1007/bfb0013851 dblp:conf/sigmetrics/GotzHR93 fatcat:tzzcr2ap5bdrnbb55jhl5v5awm

The influence of the smoothing component on the quality of algebraic forecasts

Kristina Poskuviene
2017 Vibroengineering PROCEDIA  
Algebraic forecasting results with any internal smoothing model outperformed results of the algebraic forecasting without smoothing.  ...  Computational experiments with real world time series are used to demonstrate the influence of different smoothing techniques in fitness.  ...  experiments with electrical supply time series and compare the functionality of the Algebraic prediction with different smoothing models.  ... 
doi:10.21595/vp.2017.19433 fatcat:vqp4kvdzdrd3rmmto4sff4tjoa

Homomorphism Preserving Algebraic Specifications Require Hidden Sorts

J.A. Bergstra, J. Heering
1995 Information and Computation  
It turns out that, unlike unrestricted initial algebra specication, homomorphism preserving initial algebra speci cation of computable data types requires both hidden sorts and hidden functions. 1991 Mathematics  ...  The latter are reducts of algebras that would be models of the specication if all its functions were visible, whereas the homomorphic images of the data type are independent of the speci cation and need  ...  It may happen that, given a computable data type and an initial algebra speci cation with hidden functions for it, some of the algebras that are homomorphic images of the data type are no longer models  ... 
doi:10.1006/inco.1995.1079 fatcat:3o5ayrukz5g3vicnp4hyvmtshm

Generalizing Computability Theory to Abstract Algebras [chapter]

J. V. Tucker, J. I. Zucker
2015 Turing's Revolution  
We also thank the editors, Giovanni Sommaruga and Thomas Strahm, for the opportunity to participate in this volume, and for their helpfulness during the preparation of this chapter.  ...  We are grateful to Mark Armstrong, Sol Feferman, Diogo Poças and an anonymous referee for very helpful comments on earlier drafts of this chapter.  ...  On generalizing computability theory By a computability theory we mean a theory of functions and sets that are definable using a model of computation.  ... 
doi:10.1007/978-3-319-22156-4_5 fatcat:bj42pmzvjzedjkmtgpvuswn64u

Abstract versus concrete computation on metric partial algebras

J. V. Tucker, J. I. Zucker
2004 ACM Transactions on Computational Logic  
First, we show that with abstract models, one needs algebras with partial operations, and computable functions that are both continuous and many-valued.  ...  This many-valuedness is needed even to compute single-valued functions, and so abstract models must be nondeterministic even to compute deterministic problems.  ...  ACKNOWLEDGMENTS We thank Vasco Brattka and Kristian Stewart for valuable discussions, and three anonymous referees for helpful comments.  ... 
doi:10.1145/1024922.1024924 fatcat:brocaz74bjgm7b3ppal6v2c3l4

Computer Modeling and Programming in Algebra

Arnulfo Perez, Kathy Malone, Siva Meenakshi Renganathan, Kimberly Groshong
2016 Proceedings of the 8th International Conference on Computer Supported Education  
The unit piloted in the study integrates computational thinking and computer modeling into a project-based Algebra unit on linear functions.  ...  This paper introduces a novel approach to providing high school students with access to computer science experiences as part of an Algebra unit on linear functions.  ...  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.  ... 
doi:10.5220/0005907102810286 dblp:conf/csedu/PerezMRG16 fatcat:2gv4yevl4vgx7numjuwnpwvgba

Unifying computers and dynamical systems using the theory of synchronous concurrent algorithms

B.C. Thompson, J.V. Tucker, J.I. Zucker
2009 Applied Mathematics and Computation  
, graphics and process control) to computational models of biological and physical phenomena.  ...  We start the mathematical study of SCA computation, specification and correctness using methods based on computation on many-sorted topological algebras and equational logic.  ...  Acknowledgements We thank the following colleagues for many useful and stimulating discussions on  ... 
doi:10.1016/j.amc.2009.04.058 fatcat:eir2pffsbfhs7ca7pladdm5sv4

Abstract versus Concrete Computation on Metric Partial Algebras [article]

J.V. Tucker and J.I. Zucker (McMaster University, Hamilton, Canada)
2001 arXiv   pre-print
A model of computation is abstract if, when applied to any algebra, the resulting programs for computable functions and sets on that algebra are invariant under isomorphisms, and hence do not depend on  ...  We investigate the relationship between abstract and concrete models of partial metric algebras.  ...  . • Completeness of abstract model: Functions are computable in the abstract model if, and only if, they are computable in the concrete model.  ... 
arXiv:cs/0108007v1 fatcat:hijja3curjbs5f2b46ra73oihe

Abstract computability and algebraic specification

J. V. Tucker, J. I. Zucker
2002 ACM Transactions on Computational Logic  
We investigate the initial algebra semantics of these specifications, and derive situations where algebraic specifications precisely define the computable functions.  ...  approximable by abstract computable functions on any metric algebra.  ...  We consider algebras and functions specified by conditional equational theories.  ... 
doi:10.1145/505372.505375 fatcat:kyocld7xxnatpio3ez5rdlce4e

Universal Object Oriented Languages and Computer Algebra [article]

Alexander Yu. Vlasov
1999 arXiv   pre-print
An extension of the model of an object for manipulation with pure functions and algebraic expressions is considered.  ...  Functional languages like LISP had some advantages and traditions for algebraic and symbolic manipulations. Functional and object oriented programming are not incompatible ones.  ...  In the work [4] already was discussed some kind of extensions to the model of an object. It is some synthesis of functional and object oriented programming.  ... 
arXiv:cs/9901007v1 fatcat:k7x5lfud4bgxndumdmvh2qjt4y

Algebraic geometry foundations for finite element computation

E.L. Wachspress
1980 Mathematical Modelling  
A class of elements for which rational basis functions are numerically expedient is described.  ...  Means for achieving higher order approximation within elements are discussed, including higher order isoparametric elements and generalized isoparametrics.  ...  An intimate relationship between element geometry and algebraic properties of associated basis functions can be exploited with the aid of fundamental results from the theory of algebraic geometry.  ... 
doi:10.1016/0270-0255(80)90055-x fatcat:he4l6dbn35aw3nefg55p5b3gyi
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