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Journal articles on the topic 'Algebraic Modeling'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 January 2023

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1

Letychevskyi, O. О. "Algebraic modeling and its application." Visnik Nacional'noi' academii' nauk Ukrai'ni, no. 03 (March 25, 2021): 59–66. http://dx.doi.org/10.15407/visn2021.03.059.

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The article is devoted to the scientific development of the Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine on the application of algebraic and insertional modeling technologies created on the basis of behavioral algebra. Technologies of formalization, algebraic verification, and testing of software and hardware specifications within the model-driven development method are considered. The use of algebraic modeling in biological research, development of systems based on blockchain platforms, analysis of legal and economic models is covered. One of the main areas of application of these technologies is the field of cybersecurity, which uses the method of algebraic matching and formalization of patterns of vulnerabilities and cyberattacks.

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Panaras, Argyris G. "Algebraic Turbulence Modeling for Swept." AIAA Journal 35, no. 3 (March 1997): 456–63. http://dx.doi.org/10.2514/2.151.

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Andrianov, S. N., N. S. Edamenko, and A. A. Dyatlov. "Algebraic modeling and parallel computing." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 558, no. 1 (March 2006): 150–53. http://dx.doi.org/10.1016/j.nima.2005.11.036.

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4

Jusevičius, Vaidas, and Remigijus Paulavičius. "Web-Based Tool for Algebraic Modeling and Mathematical Optimization." Mathematics 9, no. 21 (October 29, 2021): 2751. http://dx.doi.org/10.3390/math9212751.

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In this article, we present a new open-source tool for algebraic modeling and mathematical optimization. We begin by distilling the main gaps within the existing algebraic modeling languages and tools (varying performance, limited cross-compatibility, complex syntax, and different solver, feature, and problem type support). Later, we propose a state-of-the-art web-based tool (WebAML and Optimization System) for algebraic modeling languages and mathematical optimization. The tool does not require specific algebraic language knowledge, allows solving problems using different solvers, and utilizes the best characteristics of existing algebraic modeling languages. We also provide clear extension points and ideas on how we could further improve such a tool.

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Patrikalakis, N. M., and P. V. Prakash. "Surface Intersections for Geometric Modeling." Journal of Mechanical Design 112, no. 1 (March 1, 1990): 100–107. http://dx.doi.org/10.1115/1.2912565.

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Evaluation of planar algebraic curves arises in the context of intersections of algebraic surfaces with piecewise continuous rational polynomial parametric surface patches useful in geometric modeling. We address a method of evaluating these curves of intersection that combines the advantageous features of analytic representation of the governing equation of the algebraic curve in the Bernstein basis within a rectangular domain, adaptive subdivision and polyhedral faceting techniques, and the computation of turning and singular points, to provide the basis for a reliable and efficient solution procedure. Using turning and singular points, the intersection problem can be partitioned into subdomains that can be processed independently and which involve intersection segments that can be traced with faceting methods. This partitioning and the tracing of individual segments is carried out using an adaptive subdivision algorithm for Bezier/B-spline surfaces followed by Newton correction of the approximation. The method has been successfully tested in tracing complex algebraic curves and in solving actual intersection problems with diverse features.

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Wang, Bo, Yi Li, Wei Yan Xing, and Dong Liu. "Algebraic Modeling for Dynamic Gates in Dynamic Fault Trees." Applied Mechanics and Materials 232 (November 2012): 573–77. http://dx.doi.org/10.4028/www.scientific.net/amm.232.573.

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This paper proposed a novel algebraic framework for modeling dynamic gates in dynamic fault trees (DFTs). The algebraic modeling of DFTs tries to avoid the ambiguities and inconsistencies of the natural languages-based original definitions. Aim to solve this issue, preliminarily a formal framework is defined, including the definitions, properties, rules and theorems. Then, under the framework, algebraic approaches and automatic conversion algorithms for any form of dynamic gates are developed. Finally, an instance verifies the validity of the approaches. Algebraic modeling helps to build the more rigorous mathematical theoretical systems of DFTs. Meanwhile, automatic conversion algorithms are conducive to effective computer-aided modeling for DFTs.

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Kallrath, Josef. "Polylithic modeling and solution approaches using algebraic modeling systems." Optimization Letters 5, no. 3 (April 8, 2011): 453–66. http://dx.doi.org/10.1007/s11590-011-0320-4.

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Santri, Diah Dwi, Yusuf Hartono, and Somakim Somakim. "Mathematical modeling for learning algebraic operation." Journal of Education and Learning (EduLearn) 13, no. 2 (May 1, 2019): 201. http://dx.doi.org/10.11591/edulearn.v13i2.8996.

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Ennassiri, Brahim, Marouane Moukhliss, Said Abouhanifa, Elmostapha Elkhouzai, Azizi Elmostafa, and Benkenza Najia. "Analysis of the Institutional Relationship of the Modeling Activity in a Moroccan High School Textbook." Academic Journal of Interdisciplinary Studies 12, no. 1 (January 5, 2023): 248. http://dx.doi.org/10.36941/ajis-2023-0020.

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To identify the institutional relationship to modeling as an element of algebraic thinking, this article aims at analyzing the algebraic potential residing in the modeling activities that appear in the school textbook "Al-Moufid"; referring to the Anthropological Theory of Didactics (TAD) developed by Chevalard(1999) and to the Epistemological Reference Model of Algebraic Thinking (MERPA) proposed by Najar et al.( 2021). This official textbook is for 1st-year secondary Moroccan students (Age 12 to 13), as a level in which the arithmetic-algebra transition is manifested. In this institution, the pedagogical guidelines treat modeling as a skill to be developed in students without making an explicit definition or a link with the development of algebraic thinking. This analysis shows the considerable presence of modeling activities but with insufficient algebraic potential. On the other hand, several proposed modeling activities do not allow students to go completely through the modeling process as described by Chevallard (Chevallard, 1989). Received: 17 October 2022 / Accepted: 29 December 2022 / Published: 5 January 2023

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Yusrina, Siti Laiyinun, and Masriyah Masriyah. "Profil Berpikir Aljabar Siswa SMP dalam Memecahkan Masalah Matematika Kontekstual Ditinjau dari Kemampuan Matematika." MATHEdunesa 8, no. 3 (August 12, 2019): 477–84. http://dx.doi.org/10.26740/mathedunesa.v8n3.p477-484.

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Algebra is one of the important concepts in mathematics and began to be taught in class VII of junior high school. One way to find out students' thinking and reasoning abilities algebraically is to algebraic thinking. Algebraic thinking is a mental activity consisting of generalization, abstraction, dynamic thinking, modeling, analytic thinking, and organization. The means that can be used to explore students' algebraic thinking is problem solving. The problem used in this research is contextual mathematical problems. Algebraic thinking in each student in solving contextual mathematical problems varies based on the level of mathematical abilities. The purpose of this research is to describe the algebraic thinking’s profile of junior high school students in solving contextual mathematical problems based on mathematical abilities. This research uses a qualitative approach with methods of collecting data through tests and interviews. The subjects of this research were one student with high mathematical abilities, one student with medium mathematical abilities, and one student with low mathematical abilities. The results of this research indicate algebraic thinking of student with high mathematical abilities, consists of generalization, abstraction, dynamic thinking, modeling, analytic thinking, and organization. Algebraic thinking of student with medium mathematical abilities, consists of generalization, abstraction, dynamic thinking, modeling, analytic thinking, and organization. Algebraic thinking of student with low mathematical abilities, consists of generalization, dynamic thinking, and organization.Keywords: algebraic thinking, problem solving, contextual mathematical problems, mathematical abilities

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11

Reddy Anapana, Vikram, Venkata Kowshik Sivva, Pranav Sai, Venkatesh Gongolu, and Lanka Mithin Chakravarthy. "Electromagnetic Problems Modeling Using Algebraic Topological Method." American Journal of Electromagnetics and Applications 9, no. 2 (2021): 13. http://dx.doi.org/10.11648/j.ajea.20210902.11.

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Хаю, Х., М. А. Орлова, and Л. И. Абросимов. "ALGEBRAIC METHODOLOGY FOR MODELING LOOP-FREE ROUTING." ВЕСТНИК ВОРОНЕЖСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА, no. 1 (March 14, 2022): 47–61. http://dx.doi.org/10.36622/vstu.2022.18.1.006.

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Задачу маршрутизации можно сформулировать следующим образом: учитывая сеть G , необходимо найти наилучший путь между узлами i и j из сети. Однако понятие «лучшее» расплывчато, и оно зависит от того, какие параметры в составной метрике сетевые операторы пытаются оптимизировать. Для разделения проблем была введена алгебра маршрутизации для моделирования того, что пытается решить протокол маршрутизации, сохраняя при этом общий алгоритм маршрутизации. Тем не менее все протоколы маршрутизации должны решать проблему свободы от циклов. Цель этой статьи - представить теорию бесцикловой маршрутизации с произвольной метрикой. Показано, что выбор базовой алгебры может повлиять на производительность самого алгоритма, как в представленном примере для протокола маршрутизации (EIGRP). Кроме того, модификация алгебры маршрутизации может помочь во внедрении новых алгоритмов маршрутизации. Примером может служить протокол DSN (Распределенный порядковый номер), который использует гибридный алгоритм состояния каналов и дистанционно-векторный. В метрику DSN добавлены новые компоненты, которые представляют собой порядковый номер и бит флага для запроса увеличения порядкового номера. Это помогло, как показано в этой статье, решить проблему бесцикловой маршрутизации с незначительными изменениями в исходном дистанционно-векторном алгоритме. В данной работе решены следующие задачи. Условия для бесцикловой маршрутизации и отношения между ними были представлены алгебраически и доказаны. Введена концепция монотонной маршрутизации. Была исследована бесцикловая маршрутизация при наличии и отсутствии монотонности. На основании сформулированных теорем разработана алгебраическая модель и валидация бесциклового алгоритма, используемого в протоколе DSN The routing problem can be formulated as follows: given a network, it is necessary to find the best path between nodes and from the network. However, the concept of “best” is obscure, and it depends on which parameters in the composite metric network operators are trying to optimize. For separation of concerns, routing algebras were introduced to model what the routing protocol is trying to solve while maintaining a generic routing algorithm. However, all routing protocols must address the problem of loop-freedom. The purpose of this article is to present a theory of loop-free routing with an arbitrary metric. It is shown that the choice of the basic algebra can affect the performance of the algorithm itself, as in the presented example for the routing protocol (EIGRP). In addition, the modification of the routing algebra can help in the introduction of new routing algorithms. An example is the DSN protocol (Distributed Sequence Number), which uses a hybrid link-state and distance vector algorithm. New components are added to the DSN metric, which are the sequence number and a flag bit denoting a request to increase the sequence number. This helped, as shown in this article, to solve the problem of loop-free routing with minor changes in the original distance vector algorithm. In this paper, the following tasks have been solved. The conditions for loop-free routing and the relations between them were presented algebraically and proved. The concept of monotonous routing is introduced. Loop-free routing was investigated in the presence and absence of monotony. Based on the formulated theorems, an algebraic model and validation of a loop-free algorithm used in the DSN protocol have been developed

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13

Kallinderis, Yannis. "Algebraic turbulence modeling for adaptive unstructured grids." AIAA Journal 30, no. 3 (March 1992): 631–39. http://dx.doi.org/10.2514/3.10966.

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14

Burigana, Luigi, and Michele Vicovaro. "Algebraic aspects of Bayesian modeling in psychology." Journal of Mathematical Psychology 94 (February 2020): 102296. http://dx.doi.org/10.1016/j.jmp.2019.102296.

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15

Li, Qingde, and Jie Tian. "2D piecewise algebraic splines for implicit modeling." ACM Transactions on Graphics 28, no. 2 (April 2009): 1–19. http://dx.doi.org/10.1145/1516522.1516524.

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16

Plett, G. L. "Algebraic Solution for Modeling SEI Layer Growth." ECS Electrochemistry Letters 2, no. 7 (April 18, 2013): A63—A65. http://dx.doi.org/10.1149/1.004307eel.

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17

Bussieck, Michael R., and Alexander Meeraus. "Algebraic modeling for IP and MIP (GAMS)." Annals of Operations Research 149, no. 1 (December 2, 2006): 49–56. http://dx.doi.org/10.1007/s10479-006-0104-x.

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18

Zhu, Lin, Xiangfu Meng, and Zehui Mi. "Fuzzy Spatiotemporal Data Modeling and Operations in RDF." Information 13, no. 10 (October 18, 2022): 503. http://dx.doi.org/10.3390/info13100503.

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With the emergence of a large number of fuzzy spatiotemporal data on the Web, how to represent and operate fuzzy spatiotemporal data has become an important research issue. Meanwhile, the Resource Description Framework (RDF) is a standard data and knowledge description language of the Semantic Web and has been applied in many application areas, such as geographic information systems and meteorological systems. In this paper, a model for representing fuzzy spatiotemporal data is proposed and a set of algebraic operations for the model are investigated. First, a representation method of fuzzy spatiotemporal RDF data and a fuzzy spatiotemporal RDF graph model are proposed. In addition, a formal fuzzy spatiotemporal RDF algebra is proposed and a set of algebraic operations for manipulating fuzzy spatiotemporal RDF data are developed. The algebraic operations include: set operation, selection operation, projection operation, join operation, and construction operation. Finally, the existing SPARQL query language is extended and an example that shows how to apply the proposed algebraic operations to capture the queries expressed by the extended SPARQL query language is given.

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Zhao, Guodong. "Modeling and Stability Analysis for Markov Jump Networked Evolutionary Games." Mathematical Problems in Engineering 2018 (November 19, 2018): 1–9. http://dx.doi.org/10.1155/2018/5124343.

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This paper investigates the algebraic formulation and stability analysis for a class of Markov jump networked evolutionary games by using the semitensor product method and presents a number of new results. Firstly, a proper algorithm is constructed to convert the given networked evolutionary games into an algebraic expression. Secondly, based on the algebraic expression, the stability of the given game is analyzed and an equivalent criterion is given. Finally, an example works out to support the new results.

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Allouche, Benyamine, Antoine Dequidt, Laurent Vermeiren, and Michel Dambrine. "Modeling and PDC fuzzy control of planar parallel robot." International Journal of Advanced Robotic Systems 14, no. 1 (January 1, 2017): 172988141668711. http://dx.doi.org/10.1177/1729881416687112.

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Many works in the literature have studied the kinematical and dynamical issues of parallel robots. But it is still difficult to extend the vast control strategies to parallel mechanisms due to the complexity of the model-based control. This complexity is mainly caused by the presence of multiple closed kinematic chains, making the system naturally described by a set of differential–algebraic equations. The aim of this work is to control a two-degree-of-freedom parallel manipulator. A mechanical model based on differential–algebraic equations is given. The goal is to use the structural characteristics of the mechanical system to reduce the complexity of the nonlinear model. Therefore, a trajectory tracking control is achieved using the Takagi-Sugeno fuzzy model derived from the differential–algebraic equation forms and its linear matrix inequality constraints formulation. Simulation results show that the proposed approach based on differential–algebraic equations and Takagi-Sugeno fuzzy modeling leads to a better robustness against the structural uncertainties.

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Usiskin, Zalman. "Mathematical Modeling and Pure Mathematics." Mathematics Teaching in the Middle School 20, no. 8 (April 2015): 476–82. http://dx.doi.org/10.5951/mathteacmiddscho.20.8.0476.

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Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics.

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Mavriplis, Dimitri J. "Algebraic turbulence modeling for unstructured and adaptive meshes." AIAA Journal 29, no. 12 (December 1991): 2086–93. http://dx.doi.org/10.2514/3.10845.

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Rai, Gopal N., G. R. Gangadharan, and Vineet Padmanabhan. "Algebraic Modeling and Verification of Web Service Composition." Procedia Computer Science 52 (2015): 675–79. http://dx.doi.org/10.1016/j.procs.2015.05.072.

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Ma, Zongmin, Guanfeng Li, and Li Yan. "Fuzzy data modeling and algebraic operations in RDF." Fuzzy Sets and Systems 351 (November 2018): 41–63. http://dx.doi.org/10.1016/j.fss.2017.11.013.

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Jensen, Kristian, Joao G.R. Cardoso, and Nikolaus Sonnenschein. "Optlang: An algebraic modeling language for mathematical optimization." Journal of Open Source Software 2, no. 9 (January 3, 2017): 139. http://dx.doi.org/10.21105/joss.00139.

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Fragnière, Emmanuel, Jacek Gondzio, Robert Sarkissian, and Jean-Philippe Vial. "A Structure-Exploiting Tool in Algebraic Modeling Languages." Management Science 46, no. 8 (August 2000): 1145–58. http://dx.doi.org/10.1287/mnsc.46.8.1145.12026.

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OURANOS, I., P. STEFANEAS, and P. FRANGOS. "An Algebraic Framework for Modeling of Mobile Systems." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E90-A, no. 9 (September 1, 2007): 1986–99. http://dx.doi.org/10.1093/ietfec/e90-a.9.1986.

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Presti, Stéphane Lo, Didier Bert, and Andrzej Duda. "TAO: Temporal Algebraic Operators for modeling multimedia presentations." Journal of Network and Computer Applications 25, no. 4 (October 2002): 319–42. http://dx.doi.org/10.1006/jnca.2002.0135.

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Konopatskiy, E. V., I. V. Seleznev, O. A. Chernysheva, M. V. Lagunova, and A. A. Bezditnyi. "GEOMETRIC MODELING OF ADAPTIVE ALGEBRAIC CURVES PASSING THROUGH PREDETERMINED POINTS." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 207 (September 2021): 26–34. http://dx.doi.org/10.14489/vkit.2021.09.pp.026-034.

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In this paper, the geometric theory of multidimensional interpolation was further developed in terms of modeling and using adaptive curves passing through predetermined points. A feature of the proposed approach to modeling curved lines is the ability to adapt to any initial data for high-quality interpolation, which excludes unplanned oscillations, due to the uneven distribution of parameter values, the source of which are the initial data. This is the improvement of the previously proposed method for constructing and analytically describing arcs of algebraic curves passing through predetermined points, obtained on the basis of Bezier curves, which are compiled taking into account the expansion coefficients of the Newton binomial. The paper gives an example of using adaptive algebraic curves passing through predetermined points for geometric modeling of the stress-strain state of membrane coatings cylindrical shells using two-dimensional interpolation. The given example an illustrative showed the advantages of the proposed adaptation of algebraic curves passing through predetermined points and obtained on the basis of Bezier curves for geometric modeling of multifactor processes and phenomena. The use of such adaptation allows not only to avoid unplanned oscillations, but also self-intersection of geometric objects when generalized to a multidimensional space. Adaptive algebraic curves can also be effectively used as formative elements for constructing geometric objects of multidimensional space, both as guide lines and as generatrix’s.

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Roig, Pedro Juan, Salvador Alcaraz, Katja Gilly, Cristina Bernad, and Carlos Juiz. "Modeling of a Generic Edge Computing Application Design." Sensors 21, no. 21 (November 1, 2021): 7276. http://dx.doi.org/10.3390/s21217276.

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Edge computing applications leverage advances in edge computing along with the latest trends of convolutional neural networks in order to achieve ultra-low latency, high-speed processing, low-power consumptions scenarios, which are necessary for deploying real-time Internet of Things deployments efficiently. As the importance of such scenarios is growing by the day, we propose to undertake two different kind of models, such as an algebraic models, with a process algebra called ACP and a coding model with a modeling language called Promela. Both approaches have been used to build models considering an edge infrastructure with a cloud backup, which has been further extended with the addition of extra fog nodes, and after having applied the proper verification techniques, they have all been duly verified. Specifically, a generic edge computing design has been specified in an algebraic manner with ACP, being followed by its corresponding algebraic verification, whereas it has also been specified by means of Promela code, which has been verified by means of the model checker Spin.

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Fu, Jun, Jinzhao Wu, and Hongyan Tan. "A Deductive Approach towards Reasoning about Algebraic Transition Systems." Mathematical Problems in Engineering 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/607013.

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Algebraic transition systems are extended from labeled transition systems by allowing transitions labeled by algebraic equations for modeling more complex systems in detail. We present a deductive approach for specifying and verifying algebraic transition systems. We modify the standard dynamic logic by introducing algebraic equations into modalities. Algebraic transition systems are embedded in modalities of logic formulas which specify properties of algebraic transition systems. The semantics of modalities and formulas is defined with solutions of algebraic equations. A proof system for this logic is constructed to verify properties of algebraic transition systems. The proof system combines with inference rules decision procedures on the theory of polynomial ideals to reduce a proof-search problem to an algebraic computation problem. The proof system proves to be sound but inherently incomplete. Finally, a typical example illustrates that reasoning about algebraic transition systems with our approach is feasible.

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Lichtenberg, Gerwald, Georg Pangalos, Carlos Cateriano Yáñez, Aline Luxa, Niklas Jöres, Leona Schnelle, and Christoph Kaufmann. "Implicit multilinear modeling." at - Automatisierungstechnik 70, no. 1 (January 1, 2022): 13–30. http://dx.doi.org/10.1515/auto-2021-0133.

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Abstract The paper introduces a subclass of nonlinear differential-algebraic models of interest for applications. By restricting the nonlinearities to multilinear polynomials, it is possible to use modern tensor methods. This opens the door to new approximation and complexity reduction methods for large scale systems with relevant nonlinear behavior. The modeling procedures including composition, decomposition, normalization, and multilinearization steps are shown by an example of a local energy system with a nonlinear electrolyzer, a linear buck converter and a PI controller with saturation.

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Zou, Gui Hong, and Hua Qing Liang. "Finite Element Resistivity Forward Modeling Using Algebraic Multigrid Preconditioned Conjugate Gradient Method." Applied Mechanics and Materials 249-250 (December 2012): 792–97. http://dx.doi.org/10.4028/www.scientific.net/amm.249-250.792.

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An algebraic multigrid by smoothed aggregation preconditioned conjugate gradient method is developed to solve the liner system arising from 3-D direct current finite element resistivity forward modeling. The algorithm combines the efficiency of algebraic multigrid method and the stability of conjugate gradient method. Algebraic multigrid by smoothed aggregation keep in high-efficiency while simulation using local quasi-uniform mesh and its convergence effect will reduce while numerical modeling using anisotropic stretched grids. However tensor product non-equidistant mesh, a kind of anisotropic stretched grids, is often used in 3-D direct current resistivity forward modeling. In order to improve this situation, a factor is added to guide correct aggregation. Consequently, a typical example is used to prove that the improvement is the right. Finally, it is natural to conclude that the algorithm suggested in this paper is efficient and robust whether simulation using local quasi-uniform mesh or tensor product non-equidistant mesh

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Baruh, Haim. "Inconsistencies in Modeling Impact with Friction by Algebraic Equations." Dynamics 2, no. 4 (November 28, 2022): 434–48. http://dx.doi.org/10.3390/dynamics2040025.

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This paper is concerned with inconsistent results that can be obtained when modeling rigid body collisions via algebraic equations. Newton’s approach is kinematic and fails in several cases. Poisson’s formulation has been shown lead to energetic inconsistencies, particularly in work done by the impulsive forces. This paper shows that the energetic formulation may lead to unexpected results in the magnitudes of the impulsive forces. These inconsistencies are due to the simplifying assumptions made to model collisions as occurring instantaneously. The inconsistencies increase as friction in the system becomes higher. We propose an optimization procedure for solving the algebraic equations of impact so that inconsistencies are minimized. Using experimental results, we present a discussion about the coefficients of restitution and friction.

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De Villiers, Michael D. "Teaching Modeling and Axiomatization with Boolean Algebra." Mathematics Teacher 80, no. 7 (October 1987): 528–32. http://dx.doi.org/10.5951/mt.80.7.0528.

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Traditionally, Boolean algebra is largely taught in connection with computer programming courses, logic, or set theory. Since Boolean algebra arose from George Boole's application of algebraic principles to the study of logic in 1854, this approach would seem natural.

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Letychevskyi, O. O., S. O. Gorbatuk, and V. A. Gorbatuk. "Algebraic modeling in international and local service logistical systems." PROBLEMS IN PROGRAMMING, no. 4 (December 2020): 088–97. http://dx.doi.org/10.15407/pp2020.04.088.

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International and internal service logistics are advancing at a tremendous pace in our modern life, and future forecasts for this area are optimistic. For this reason, we face a task in the control, optimization and safety and security checking of complex logistical systems with many internal agents working in a changing environment. Our paper aims to show how mathematical modeling, especially behavior algebra, can provide an opportunity for predicting the behavior and stability of logistics environments and checking their safety and security properties. The main security properties of complex logistics systems of different capacities and levels are stability of operation, resistance to external threats and detection and elimination of vulnerabilities. During the development of software systems, it is advisable to use a model approach. It involves the creation of models as tools at every stage of software development for the application of verification, testing and validation methods. Algebraic models of logistics systems can be used to analyze the behavior of all agents involved and to prove their ability to fulfill their goals and the ability of the whole system to constantly exist and remain stable. As examples of practical use the application in practice of algebra of behaviors on an example of the operating closed logistic system of a farm is considered.

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Fisher, Diana. "Reorganizing Algebraic Thinking: An Introduction to Dynamic System Modeling." Mathematics Enthusiast 14, no. 1-3 (January 1, 2017): 347–70. http://dx.doi.org/10.54870/1551-3440.1402.

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Hellsten, Antti. "Curvature Corrections for Algebraic Reynolds Stress Modeling: A Discussion." AIAA Journal 40, no. 9 (September 2002): 1909–11. http://dx.doi.org/10.2514/2.1871.

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Молодецька, Катерина Валеріївна. "Modeling extraction process using algebraic properties of differential spectra." Technology audit and production reserves 5, no. 4(13) (October 28, 2013): 15–17. http://dx.doi.org/10.15587/2312-8372.2013.18219.

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Gordon, Brandon W., and Sheng Liu. "A Singular Perturbation Approach for Modeling Differential-Algebraic Systems." Journal of Dynamic Systems, Measurement, and Control 120, no. 4 (December 1, 1998): 541–45. http://dx.doi.org/10.1115/1.2801500.

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Dynamic systems described by an implicit mixed set of Differential and Algebraic Equations (DAEs) are often encountered in control system modeling and analysis due to inherent constraints in the system. A key difficulty in control and simulation of DAE systems is that they are not expressed in an explicit state space representation. This paper describes a general approach based on singular perturbation analysis for adding fast dynamics to a system of DAEs so that they can be expressed in an explicit state space form. Conditions for asymptotic convergence and approximation methods are investigated. The approach is illustrated for a model of a two-phase flow heat exchanger.

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M�ller, P. C. "Aspects of Modeling Dynamical Systems by Differential-Algebraic Equations." Mathematical and Computer Modelling of Dynamical Systems 7, no. 2 (June 1, 2001): 133–43. http://dx.doi.org/10.1076/mcmd.7.2.133.3650.

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Adner, Haya. "Algebraic Versus Programming Approach to Solving Mathematical Modeling Problems." School Science and Mathematics 90, no. 4 (April 1990): 302–16. http://dx.doi.org/10.1111/j.1949-8594.1990.tb15548.x.

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Fourer, Robert, and David M. Gay. "Extending an Algebraic Modeling Language to Support Constraint Programming." INFORMS Journal on Computing 14, no. 4 (November 2002): 322–44. http://dx.doi.org/10.1287/ijoc.14.4.322.2825.

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44

Hellsten, A. "Curvature corrections for algebraic Reynolds stress modeling - A discussion." AIAA Journal 40 (January 2002): 1909–11. http://dx.doi.org/10.2514/3.15276.

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45

Zhang, Yi, Xiaoyang Liu, Jinyuan Zhou, and Paul A. Bottomley. "Ultrafast compartmentalized relaxation time mapping with linear algebraic modeling." Magnetic Resonance in Medicine 79, no. 1 (April 11, 2017): 286–97. http://dx.doi.org/10.1002/mrm.26675.

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Proß, Sabrina, and Bernhard Bachmann. "An Advanced Environment for Hybrid Modeling of Biological Systems Based on Modelica." Journal of Integrative Bioinformatics 8, no. 1 (March 1, 2011): 1–34. http://dx.doi.org/10.1515/jib-2011-152.

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Summary Biological systems are often very complex so that an appropriate formalism is needed for modeling their behavior. Hybrid Petri Nets, consisting of time-discrete Petri Net elements as well as continuous ones, have proven to be ideal for this task. Therefore, a new Petri Net library was implemented based on the object-oriented modeling language Modelica which allows the modeling of discrete, stochastic and continuous Petri Net elements by differential, algebraic and discrete equations. An appropriate Modelica-tool performs the hybrid simulation with discrete events and the solution of continuous differential equations. A special sub-library contains so-called wrappers for specific reactions to simplify the modeling process.The Modelica-models can be connected to Simulink-models for parameter optimization, sensitivity analysis and stochastic simulation in Matlab.The present paper illustrates the implementation of the Petri Net component models, their usage within the modeling process and the coupling between the Modelica-tool Dymola and Matlab/Simulink. The application is demonstrated by modeling the metabolism of Chinese Hamster Ovary Cells.

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Ameri, A. A., and A. Arnone. "Transition Modeling Effects on Turbine Rotor Blade Heat Transfer Predictions." Journal of Turbomachinery 118, no. 2 (April 1, 1996): 307–13. http://dx.doi.org/10.1115/1.2836641.

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The effect of transition modeling on the heat transfer predictions from rotating turbine blades was investigated. Three-dimensional computations using a Reynolds-averaged Navier–Stokes code were performed. The code utilized the Baldwin–Lomax algebraic turbulence model, which was supplemented with a simple algebraic model for transition. The heat transfer results obtained on the blade surface and the hub endwall were compared with experimental data for two Reynolds numbers and their corresponding rotational speeds. The prediction of heat transfer on the blade surfaces was found to improve with the inclusion of the transition length model and wake-induced transition effects over the simple abrupt transition model.

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Hulle, Marc M. Van. "Edgeworth-Expanded Gaussian Mixture Density Modeling." Neural Computation 17, no. 8 (August 1, 2005): 1706–14. http://dx.doi.org/10.1162/0899766054026657.

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Instead of increasing the order of the Edgeworth expansion of a single gaussian kernel, we suggest using mixtures of Edgeworth-expanded gaussian kernels of moderate order. We introduce a simple closed-form solution for estimating the kernel parameters based on weighted moment matching. Furthermore, we formulate the extension to the multivariate case, which is not always feasible with algebraic density approximation procedures.

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Dabić-Boričić, Milana, and Marijana Zeljić. "Modelovanje ekvivalencije matematičkih izraza u početnoj nastavi." Inovacije u nastavi 34, no. 2 (2021): 30–43. http://dx.doi.org/10.5937/inovacije2101030d.

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The notion of expression equivalence is one of the terms that has been recognized in the literature as key to understanding algebraic ideas. To understand this term, the context used as a basis for developing meaning is important, as well as the language in which generalizations are expressed. The aim of this paper is twofold: a) to examine whether the context of a textual task and modeling activities influence the understanding of the transformation of expressions into equivalent forms; b) determine whether the understanding of the equivalence of the expression is affected by the level of abstractness of the expression (algebraic or arithmetic). The research is of a quasi-experimental design with two experimental groups and one control group. The sample consists of 148 fourth-graders. The existence of statistically significant differences between the students of the experimental groups and the control group suggests that the modeling process influences the development of the notion of expression equivalence. This research did not show any differences in the results of the students who were taught using algebraic or arithmetic expressions. This implies that the understanding of equivalence developed through the modeling process is not related to the level of abstractness of the mathematical language used, but that, based on understanding the meaning of the term, students can transform arithmetic and algebraic expressions with equal success.

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Bottoni, Paolo, Fabio De Rosa, Kathrin Hoffmann, and Massimo Mecella. "Applying Algebraic Approaches for Modeling Workflows and their Transformations in Mobile Networks." Mobile Information Systems 2, no. 1 (2006): 51–76. http://dx.doi.org/10.1155/2006/704187.

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In emergency scenarios we can obtain a more effective coordination among team members, each of them equipped with hand-held devices, through the use of workflow management software. Team members constitute a Mobile Ad-hoc NETwork (MANET), whose topology both influences and is influenced by the workflow. In this paper we propose an algebraic approach for modeling workflow progress as well as its modifications as required by topology transformations. The approach is based on Algebraic Higher-Order Nets and sees both workflows and topologies as tokens, allowing their concurrent modification.

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