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MATHEMATICAL MODELING IN FORMAL RESEARCH METHODS

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*. ...

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Formal methods in artificial intelligence

1990
*
Discrete Applied Mathematics
*

Delahaye,

doi:10.1016/0166-218x(90)90027-a
fatcat:plqmakv3xjh7ff3ml74txjoxai
*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. ...##
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Teaching Formal Methods and Discrete Mathematics

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*. ...

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Formal proofs for theoretical properties of Newton's method

2011
*
Mathematical Structures in Computer Science
*

We discuss a

doi:10.1017/s0960129511000077
fatcat:66mxumxmtjf3ljvadak5qabu4q
*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. ...##
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ACM SIGIR workshop on mathematical/formal methods in information retrieval MF/IR 2005

2005
*
SIGIR Forum
*

new knowledge to IR, and that

doi:10.1145/1113343.1113350
fatcat:dugib7a47fbo3b66ozsjbfuhra
*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 ...##
###
Formalization method of the first level variables in the audit systems IT

2019
*
Mathematical machines and systems
*

Designing DSS IT

doi:10.34121/1028-9763-2019-4-79-86
fatcat:vbmxgi7jfvgvhjlpqh2qsujtfa
*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 ...##
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Mathematical, logical, and formal methods in information retrieval: An introduction to the special issue

2003
*
Journal of the American Society for Information Science and Technology
*

Research on the use of

doi:10.1002/asi.10208
fatcat:chbsjnf2ufa6jpmjrr67pw2eta
*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) ...##
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Formal verification of tail distribution bounds in the HOL theorem prover

2009
*
Mathematical methods in the applied sciences
*

Tail distribution bounds play a major role

doi:10.1002/mma.1055
fatcat:5p67g3buy5bpld46utlp2escyy
*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. ...##
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A review of formal orthogonality in Lanczos-based methods

2002
*
Journal of Computational and Applied Mathematics
*

This theory helps to understand the origin of the algorithms for the implementation of Krylov subspace

doi:10.1016/s0377-0427(01)00412-5
fatcat:6z7y63n7yvcsdia5aqijfpiuky
*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. ...##
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A Method for the Approximation of Functions Defined by Formal Series Expansions in Orthogonal Polynomials

1969
*
Mathematics of Computation
*

The algorithm is similar

doi:10.2307/2004422
fatcat:eedqreeycjcdliqzd4haympsja
*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 + ...##
###
Enhancing the implementation of mathematical formulas for fixed-point and floating-point arithmetics

2009
*
Formal methods in system design
*

This tool should work both

doi:10.1007/s10703-009-0068-y
fatcat:x7nsm3mi7jfg5i3gfbo4k2kbse
*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. ...##
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Developing Corpus-Based Translation Methods between Informal and Formal Mathematics: Project Description
[chapter]

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. ...

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

1969
*
Mathematics of Computation
*

The algorithm is similar

doi:10.1090/s0025-5718-1969-0251412-1
fatcat:5rufe36d5vecncs5oi6q7rrsbi
*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 + ...##
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Generalized Weyl-Wigner-Moyal-Ville Formalism and Topological Groups

2011
*
Mathematical methods in the applied sciences
*

Discussed are some geometric aspects of the phase space

doi:10.1002/mma.1531
fatcat:5jrkbjfpznarjmb6v2dwy6emqy
*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. ...##
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Encapsulating Formal Methods within Domain Specific Languages: A Solution for Verifying Railway Scheme Plans

2014
*
Mathematics in Computer Science
*

This paper introduces a methodology for developing domain specific languages for modelling and verification to aid

doi:10.1007/s11786-014-0174-0
fatcat:oi6htdfup5hu5nyaty6ln4hura
*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. ...
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