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MATHEMATICAL MODELING IN FORMAL RESEARCH METHODS

V.V. Zavgorodnii, A.A. Zavgorodnya, K.E. Drobotovich, O.V. Tenigin, M.M. Shmatko
2021 Scientific notes of Taurida National V.I. Vernadsky University. Series: Technical Sciences  
MATHEMATICAL MODELING IN FORMAL RESEARCH METHODS The research of methods of making managerial decisions in the conditions of the conflict based on use of methods of the theory of games is considered in  ...  The mathematical analysis of game situations is carried out in the work and their description in the form of mathematical model is formalized.  ... 
doi:10.32838/2663-5941/2021.6/12 fatcat:qj5hbnu2hbdm7kjubalu7ziovy

Formal methods in artificial intelligence

1990 Discrete Applied Mathematics  
Delahaye, Formal Methods in Artificial Intelligence (Wiley, New York, 1987); Artificial Intelligence (George N. Reeke, Jr., and Gerald M. Edelman). The Songs of Eden (W. Daniel Hillis).  ...  Mathematical Logic in Artificial Intelligence (John McCarthy). Translated by J. Howlett Chapter 1: Artificial Intelligence: An Introduction. Introduction.  ... 
doi:10.1016/0166-218x(90)90027-a fatcat:plqmakv3xjh7ff3ml74txjoxai

Teaching Formal Methods and Discrete Mathematics

Mathieu Jaume, Théo Laurent
2014 Electronic Proceedings in Theoretical Computer Science  
In this paper, we claim that teaching formal methods could be done at the undergraduate level by mixing formal methods and discrete mathematics courses and we illustrate such an approach with a small develop  ...  Despite significant advancements in the conception of (formal) integrated development environments, applying formal methods in software industry is still perceived as a difficult task.  ...  Acknowledgments The authors would like to thank Renaud Rioboo for his help and for enlightening discussions about how to program with FoCaLiZe and about teaching discrete mathematics.  ... 
doi:10.4204/eptcs.149.4 fatcat:skw7camyfjh3fhmpmzjqm2sbay

Formal proofs for theoretical properties of Newton's method

IOANA PAŞCA
2011 Mathematical Structures in Computer Science  
We discuss a formal development for the certification of Newton's method.  ...  An algorithm including rounding is a more accurate model for computations with Newton's method in practice.  ...  Formalized mathematical theories for numerical methods The successful verification of numerical methods depends on having the appropriate mathematical theories formalized in our proof assistant.  ... 
doi:10.1017/s0960129511000077 fatcat:66mxumxmtjf3ljvadak5qabu4q

ACM SIGIR workshop on mathematical/formal methods in information retrieval MF/IR 2005

Sándor Dominich, Iadh Ounis, Jian-Yun Nie
2005 SIGIR Forum  
new knowledge to IR, and that mathematical/formal research in IR can stand as a specialized research area of IR.  ...  /formal techniques, properties and structures in IR; existing and/or new theories and theoretical aspects, interdisciplinary approaches) using formal and mathematical approaches like Sets, Vectors, Similarity  ... 
doi:10.1145/1113343.1113350 fatcat:dugib7a47fbo3b66ozsjbfuhra

Formalization method of the first level variables in the audit systems IT

T.V. Neskorodieva, Vasyl Stus Donetsk National University
2019 Mathematical machines and systems  
Designing DSS IT in accordance with the method of generalized-multiple information display proposed in [11] requires the creation of a method for formalizing primary accounting information for the automated  ...  Therefore, to formulate a method for formalizing the variables of the selected subtasks, we define a set of vectors of the subsystem variables in accordance with the structure of the graph of type 2 G  ... 
doi:10.34121/1028-9763-2019-4-79-86 fatcat:vbmxgi7jfvgvhjlpqh2qsujtfa

Mathematical, logical, and formal methods in information retrieval: An introduction to the special issue

Fabio Crestani, Sandor Dominich, Mounia Lalmas, Cornelis Joost (Keith) van Rijsbergen
2003 Journal of the American Society for Information Science and Technology  
Research on the use of mathematical, logical, and formal methods, has been central to Information Retrieval research for long time.  ...  We conclude highlighting some directions of future research, which are needed in order to better understand the formal characteristics of Information Retrieval.  ...  , United Kingdom 1999 , 2000 , and Munich, Germany 2001) , the First and Second SIGIR Workshop on Mathematical/Formal Methods in Information Retrieval (Athens, Greece, 2000 and New Orleans, USA, 2001)  ... 
doi:10.1002/asi.10208 fatcat:chbsjnf2ufa6jpmjrr67pw2eta

Formal verification of tail distribution bounds in the HOL theorem prover

Osman Hasan, Sofiène Tahar
2009 Mathematical methods in the applied sciences  
Tail distribution bounds play a major role in the estimation of failure probabilities in performance and reliability analysis of systems.  ...  This paper presents the formal verification of Markov's and Chebyshev's inequalities for discrete random variables using a higher-order-logic theorem prover (HOL).  ...  To the best of our knowledge, this is the first time that it has been possible to reason about the tail distribution properties in a mechanized formal methods environment.  ... 
doi:10.1002/mma.1055 fatcat:5p67g3buy5bpld46utlp2escyy

A review of formal orthogonality in Lanczos-based methods

C. Brezinski, M.Redivo Zaglia, H. Sadok
2002 Journal of Computational and Applied Mathematics  
This theory helps to understand the origin of the algorithms for the implementation of Krylov subspace methods and, moreover, the use of formal orthogonal polynomials brings a major simpliÿcation in the  ...  This paper reviews this approach in the case of Lanczos method and its variants, the novelty being the introduction of a preconditioner.  ...  Conclusions In this paper, Lanczos-based methods and the corresponding algorithms for their implementation have been presented using the theory of formal orthogonal polynomials.  ... 
doi:10.1016/s0377-0427(01)00412-5 fatcat:6z7y63n7yvcsdia5aqijfpiuky

A Method for the Approximation of Functions Defined by Formal Series Expansions in Orthogonal Polynomials

Jonas T. Holdeman
1969 Mathematics of Computation  
The algorithm is similar in some respects to the method of Padé approximants. A rational approximation involving Tchebychev polynomials due to H. Maehley and described by E.  ...  ordinary summation method when the series is convergent.  ...  In a similar manner the remainder r(x)/B(x) can formally be expressed as the ratio of the two determinants above except that the sums over the index m in the numerator are over all m such that m > M +  ... 
doi:10.2307/2004422 fatcat:eedqreeycjcdliqzd4haympsja

Enhancing the implementation of mathematical formulas for fixed-point and floating-point arithmetics

Matthieu Martel
2009 Formal methods in system design  
This tool should work both in floatingpoint and fixed-point arithmetics since there are many industrial needs in both contexts.  ...  The error series abstract semantics is used in industrial contexts, to validate safety-critical software. In the future, we aim at implementing a program transformer able to handle large codes.  ...  This method enables one to automatically rewrite a formula into another mathematically equivalent and more precise formula.  ... 
doi:10.1007/s10703-009-0068-y fatcat:x7nsm3mi7jfg5i3gfbo4k2kbse

Developing Corpus-Based Translation Methods between Informal and Formal Mathematics: Project Description [chapter]

Cezary Kaliszyk, Josef Urban, Jiří Vyskočil, Herman Geuvers
2014 Lecture Notes in Computer Science  
methods, (ii) to develop such methods oriented at the formalization task, and in particular (iii) to combine such methods with learning-assisted automated reasoning that will serve as a strong semantic  ...  The goal of this project 4 is to (i) accumulate annotated informal/formal mathematical corpora suitable for training semi-automated translation between informal and formal mathematics by statistical machinetranslation  ...  The last ten years have brought significant progress in formalization of mathematics and in automated reasoning methods for such formalized corpora.  ... 
doi:10.1007/978-3-319-08434-3_34 fatcat:o75tw3gz2rh7pawh355d7anlga

A method for the approximation of functions defined by formal series expansions in orthogonal polynomials

Jonas T. Holdeman
1969 Mathematics of Computation  
The algorithm is similar in some respects to the method of Padé approximants. A rational approximation involving Tchebychev polynomials due to H. Maehley and described by E.  ...  ordinary summation method when the series is convergent.  ...  In a similar manner the remainder r(x)/B(x) can formally be expressed as the ratio of the two determinants above except that the sums over the index m in the numerator are over all m such that m > M +  ... 
doi:10.1090/s0025-5718-1969-0251412-1 fatcat:5rufe36d5vecncs5oi6q7rrsbi

Generalized Weyl-Wigner-Moyal-Ville Formalism and Topological Groups

Jan J. Sławianowski, Vasyl Kovalchuk, Agnieszka Martens, Barbara Gołubowska, Eliza E. Rożko
2011 Mathematical methods in the applied sciences  
Discussed are some geometric aspects of the phase space formalism in quantum mechanics in the sense of Weyl, Wigner, Moyal and Ville.  ...  Indicated are certain physical aspects in quantum dynamics of crystal lattices, including the phenomenon of "Umklapp-Prozessen"  ...  Acknowledgements This paper partially contains results obtained within the framework of the research project 501 018 32/1992 financed from the Scientific Research Support Fund in 2007-2010.  ... 
doi:10.1002/mma.1531 fatcat:5jrkbjfpznarjmb6v2dwy6emqy

Encapsulating Formal Methods within Domain Specific Languages: A Solution for Verifying Railway Scheme Plans

Phillip James, Markus Roggenbach
2014 Mathematics in Computer Science  
This paper introduces a methodology for developing domain specific languages for modelling and verification to aid in the uptake of formal methods within industry.  ...  One particular challenge that remains is the uptake of formal methods into industrial practices.  ...  In this section, we introduce the OnTrack toolset that achieves the goal of encapsulating formal methods for the railway domain.  ... 
doi:10.1007/s11786-014-0174-0 fatcat:oi6htdfup5hu5nyaty6ln4hura
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