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Journal articles on the topic 'Algebraic transition'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

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

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2

Rahman, M. M. "Predicting transition with algebraic intermittency function." Physics of Fluids 34, no. 3 (2022): 034113. http://dx.doi.org/10.1063/5.0077513.

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An algebraic intermittency function is developed for “laminar-to-turbulent” transition flow within the framework of Bradshaw stress–intensity factor (ratio of principal shear-stress over turbulent kinetic energy in the boundary layer), which is parameterized with a “flow-structure-adaptive” variable (eddy-to-laminar viscosity ratio). Naturally, the intermittency inherits the “flow-structure-adaptive” character and captures various transition phenomena like bypass, separation-induced, and natural transitions when incorporated in an undamped eddy-viscosity transport equation. An additional visco

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Rahman, M. M., Baojun Li, K. Hasan, and Sheng Chen. "An algebraic transition model for fluid flows." Journal of Physics: Conference Series 2512, no. 1 (2023): 012004. http://dx.doi.org/10.1088/1742-6596/2512/1/012004.

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Abstract An algebraic (zero-equation) transition model is developed to capture multiple transition mechanisms. The newly devised algebraic transition model is parameterized using “flow-structure-adaptive” variables and coupled with the truncated Spalart-Allmaras (SA) turbulence model. The intermittency factor γ relies on “local flow information” and is directly linked to the “vorticity-based production” term of the SA model. Splitting γ into lower and higher regimes of the “free-stream turbulence intensity” enhances the model coefficient calibration and predictions of various phenomena (“natur

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4

Beyne, Tim, and Michiel Verbauwhede. "Integral Cryptanalysis Using Algebraic Transition Matrices." IACR Transactions on Symmetric Cryptology 2023, no. 4 (2023): 244–69. http://dx.doi.org/10.46586/tosc.v2023.i4.244-269.

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In this work we introduce algebraic transition matrices as the basis for a new approach to integral cryptanalysis that unifies monomial trails (Hu et al., Asiacrypt 2020) and parity sets (Boura and Canteaut, Crypto 2016). Algebraic transition matrices allow for the computation of the algebraic normal form of a primitive based on the algebraic normal forms of its components by means of wellunderstood operations from linear algebra. The theory of algebraic transition matrices leads to better insight into the relation between integral properties of F and F−1. In addition, we show that the link be

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Niestegge, Gerd. "Quantum Probability’s Algebraic Origin." Entropy 22, no. 11 (2020): 1196. http://dx.doi.org/10.3390/e22111196.

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Max Born’s statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. Although the latter always result from an assumed probability measure, the first include transition probabilities with a purely algebraic origin. Moreover, the general definition of transition probability introduced here comprises not only the well-known quantum mechanical transition probabilities between pure states or wave functions, but further physically meaningful and experimentally verifiab

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Bolognesi, Tommaso. "Integrated Information in Process-Algebraic Compositions." Entropy 21, no. 8 (2019): 805. http://dx.doi.org/10.3390/e21080805.

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Integrated Information Theory (IIT) is most typically applied to Boolean Nets, a state transition model in which system parts cooperate by sharing state variables. By contrast, in Process Algebra, whose semantics can also be formulated in terms of (labeled) state transitions, system parts—“processes”—cooperate by sharing transitions with matching labels, according to interaction patterns expressed by suitable composition operators. Despite this substantial difference, questioning how much additional information is provided by the integration of the interacting partners above and beyond the sum

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Cakmakcioglu, Samet Caka, Onur Bas, and Unver Kaynak. "A correlation-based algebraic transition model." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 21 (2017): 3915–29. http://dx.doi.org/10.1177/0954406217743537.

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A correlation-based algebraic transition model that relies on local flow information is proposed. The model is qualified as an algebraic model, or a zero-equation model since it includes an intermittency function in place of an intermittency equation that is found in one- or two-equation models. The basic idea behind the model is that, instead of deriving new equations for intermittency transport, existing transport terms of the Spalart–Allmaras (S-A) turbulence model can be used. To this end, the production term of the S-A model is multiplied with the proposed intermittency function γBC; ther

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8

Mischaikow, Konstantin. "Transition systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 112, no. 1-2 (1989): 155–75. http://dx.doi.org/10.1017/s0308210500028225.

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SynopsisThe concept of a transition system is extended to a parametrised family of differential equationswhere x ∊ ℝn and λ ∊ Λ = [0, l]m, an m-cube. Furthermore, algebraic formulae for comparing connection matrices at the various parameter values are obtained. Finally, several applications of these techniques are indicated.

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9

BALKAN, İhsan. "Investigation of Seventh Grade Students’ Transition Skills among Representations." Journal of Computer and Education Research 11, no. 22 (2023): 552–71. http://dx.doi.org/10.18009/jcer.1312608.

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This descriptive case study was aimed at revealing the level of students’ transition skills among representations (verbal, numeric, algebraic, graphic) at the completion of 7th grade. The participants included 133 students attending 7th grade at a state school located in Ankara in Turkey. Students’ skills in transitioning between representations were tested using the “Test of Skills in Transitioning between Representations (TSTBR)”, which included 12 open-ended questions and analyzed student answers through a graded rubric developed by the researcher. Descriptive statistics such as frequency a

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10

Nering, Konrad, and Krzysztof Nering. "Validation of Modified Algebraic Model during Transitional Flow in HVAC Duct." Energies 14, no. 13 (2021): 3975. http://dx.doi.org/10.3390/en14133975.

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Airflow occurring in a ventilation duct is characterized by low velocity and hence low Reynolds number. In these conditions, either a laminar, transitional or turbulent flow will occur. Different flow conditions result in different values of the friction coefficient. To achieve the transitional flow in numerical simulation, a modified algebraic model for bypass transition (modified k−ω) was used. Numerical simulation was validated using Particle Tracking Velocimetry (PTV) in the circular channel. The modified algebraic model consists of only two partial differential equations, which leads to m

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11

Wahyuni, Reni, Tatang Herman, and Siti Fatimah. "Letters in Algebra as The Transition from Arithmetic Thinking to Algebraic Thinking." Mosharafa: Jurnal Pendidikan Matematika 12, no. 3 (2023): 441–52. http://dx.doi.org/10.31980/mosharafa.v12i3.818.

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Huruf-huruf aljabar biasanya hanya dikenal sebagai variabel oleh siswa, padahal huruf-huruf aljabar ini memiliki ragam makna pada suatu permasalahan matematis. Pada penelitian ini bertujuan untuk menyelidiki interpretasi siswa terhadap makna dari huruf-huruf aljabar dalam menyelesaikan masalah matematis dengan perspektif siswa dalam masa transisi berpikir aritmetik ke berpikir aljabar. Penelitian yang digunakan pada penelitian kualitatif dengan jenis penelitian pada penelitian fenomenologi. Partisipan penelitian ini merupakan 18 siswa SMP yang diambil dari tiga sekolah yang terdapat di Riau. T

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Wahyuni, Reni, Tatang Herman, and Siti Fatimah. "Letters in Algebra as the Transition from Arithmetic Thinking to Algebraic Thinking." Mosharafa: Jurnal Pendidikan Matematika 12, no. 3 (2023): 441–52. http://dx.doi.org/10.31980/mosharafa.v12i3.2369.

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Huruf-huruf aljabar biasanya hanya dikenal sebagai variabel oleh siswa, padahal huruf-huruf aljabar ini memiliki ragam makna pada suatu permasalahan matematis. Pada penelitian ini bertujuan untuk menyelidiki interpretasi siswa terhadap makna dari huruf-huruf aljabar dalam menyelesaikan masalah matematis dengan perspektif siswa dalam masa transisi berpikir aritmetik ke berpikir aljabar. Penelitian yang digunakan pada penelitian kualitatif dengan jenis penelitian pada penelitian fenomenologi. Partisipan penelitian ini merupakan 18 siswa SMP yang diambil dari tiga sekolah yang terdapat di Riau. T

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13

Arnold, André, and Anne Dicky. "An algebraic characterization of transition system equivalences." Information and Computation 82, no. 2 (1989): 198–229. http://dx.doi.org/10.1016/0890-5401(89)90054-0.

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14

Mavoungou, J. P., and C. Nkuimi-Jugnia. "On a characterization of the lattice of subsystems of a transition system." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–4. http://dx.doi.org/10.1155/ijmms/2006/82318.

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It was first proved by Birkhoff and Frink, and the result now belongs to the folklore, that any algebraic lattice is up to isomorphism the lattice of subuniverses of a universal algebra. A study of subsystems of a transition system yields a new algebraic concept, that of a strongly algebraic lattice. We give here a representation theorem to the manner of Birkhoff and Frink of such lattices.

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15

Ameri, A. A., and A. Arnone. "Transition Modeling Effects on Turbine Rotor Blade Heat Transfer Predictions." Journal of Turbomachinery 118, no. 2 (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

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16

TATE, TATSUYA. "AN ALGEBRAIC STRUCTURE FOR ONE-DIMENSIONAL QUANTUM WALKS AND A NEW PROOF OF THE WEAK LIMIT THEOREM." Infinite Dimensional Analysis, Quantum Probability and Related Topics 16, no. 02 (2013): 1350018. http://dx.doi.org/10.1142/s0219025713500185.

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An algebraic structure for one-dimensional quantum walks is introduced. This structure characterizes, in some sense, one-dimensional quantum walks. A natural computation using this algebraic structure leads us to obtain an effective formula for the characteristic function of the transition probability. Then, the weak limit theorem for the transition probability of quantum walks is deduced by using simple properties of the Chebyshev polynomials.

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17

Apsari, R. A., S. Sariyasa, R. I. P. Putri, G. Gunawan, and S. Prayitno. "Understanding Students’ Transition from Arithmetic to Algebraic Thinking in the Pre-Algebraic Lesson." Journal of Physics: Conference Series 1471 (February 2020): 012056. http://dx.doi.org/10.1088/1742-6596/1471/1/012056.

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18

FERRARI, GIANLUIGI, UGO MONTANARI, and MIRANDA MOWBRAY. "Structured transition systems with parametric observations: observational congruences and minimal realizations." Mathematical Structures in Computer Science 7, no. 3 (1997): 241–82. http://dx.doi.org/10.1017/s0960129597002284.

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A large number of observational semantics for process description languages have been developed, many of which are based on the notion of bisimulation. In this paper, we consider in detail the problem of defining a semantic framework to unify these. The discussion takes place in a purely algebraic setting. We introduce a special class of algebras called Structured Transition Systems. A structured transition system can be viewed as a transition system with an algebraic structure both on states and transitions. In this framework, observations of behaviours are dealt with by means of maps from th

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19

Byvaltsev, P. M., and K. Kawaike. "A Comparative Study of Two Transition Zone Models in Heat Transfer Predictions." Journal of Turbomachinery 127, no. 1 (2005): 230–39. http://dx.doi.org/10.1115/1.1731446.

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A comparative study of two transition zone models was carried out to assess their ability to simulate boundary layer laminar-turbulent transition. Transition modeling is based on the use of an algebraic equation for the intermittency distribution. The crucial difference between the models lies in the nondimensional breakdown rate formulation. A two-dimensional marching code was used to combine these models with the modified Johnson and King turbulence model and the algebraic “nonturbulence” model developed earlier. Flat plate and various turbine blade heat transfer measurements were used in th

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20

Dzhalladova, Irada Agayevna, and Oleg Yevhenovych Kaminsky. "MATHEMATICAL MODELING AND ANALYSIS OF CONTROLLABILITY OF SINGULAR HYBRID SYSTEMS IN APPLIED PROBLEMS." Bulletin of the National Technical University "KhPI". Series: Mathematical modeling in engineering and technologies, no. 1(8) (July 23, 2025): 61–66. https://doi.org/10.20998/2222-0631.2025.01(8).07.

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The article investigates singular hybrid systems (SHS), which combine differential-algebraic structures with hybrid dynamics involving mode switching. A mathematical model is presented, approaches to stability and controllability analysis are substantiated, and numerical simulation is performed. Such systems naturally arise in complex engineering applications – from energy systems to biomedical devices – where the system behavior changes due to faults, mode transitions, or internal structural variations. A mathematical model of SHS is proposed based on matrices, which depend on the discrete mo

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21

Nering, Konrad, and Kazimierz Rup. "Modified algebraic model of laminar-turbulent transition for internal flows." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 4 (2019): 1743–53. http://dx.doi.org/10.1108/hff-10-2018-0597.

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Purpose For internal flows with small values of the Reynolds number, there is often at a considerable distance from the pipe inlet cross-section a change of the flow form from laminar to turbulent. To describe this phenomenon of laminar-turbulent transition in the pipe, also parallel-plate channel flow, a modified algebraic intermittency model was used. The original model for bypass transition developed by S. Kubacki and E. Dick was designed for simulating bypass transition in turbomachinery. Design/methodology/approach A modification of mentioned model was proposed. Modified model is suitable

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22

Franzosa, Robert, and Konstantin Mischaikow. "Algebraic transition matrices in the Conley index theory." Transactions of the American Mathematical Society 350, no. 3 (1998): 889–912. http://dx.doi.org/10.1090/s0002-9947-98-01666-3.

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23

Abbouti Temsamani, M., J. M. Champion, and S. Oss. "Infrared transition intensities in acetylene: An algebraic approach." Journal of Chemical Physics 110, no. 6 (1999): 2893–902. http://dx.doi.org/10.1063/1.477932.

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24

Malacaria, Pasquale. "Studying equivalences of transition systems with algebraic tools." Theoretical Computer Science 139, no. 1-2 (1995): 187–205. http://dx.doi.org/10.1016/0304-3975(94)00047-m.

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Jones, Edmund, David Epstein, and Leticia García-Mochón. "A Procedure for Deriving Formulas to Convert Transition Rates to Probabilities for Multistate Markov Models." Medical Decision Making 37, no. 7 (2017): 779–89. http://dx.doi.org/10.1177/0272989x17696997.

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For health-economic analyses that use multistate Markov models, it is often necessary to convert from transition rates to transition probabilities, and for probabilistic sensitivity analysis and other purposes it is useful to have explicit algebraic formulas for these conversions, to avoid having to resort to numerical methods. However, if there are four or more states then the formulas can be extremely complicated. These calculations can be made using packages such as R, but many analysts and other stakeholders still prefer to use spreadsheets for these decision models. We describe a procedur

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Petrellis, Dimitrios, Adam Prášek, Petr Alexa, Dennis Bonatsos, Gabriela Thiamová, and Petr Veselý. "Nuclear shape / phase transitions in the N = 40, 60, 90 regions." EPJ Web of Conferences 304 (2024): 04004. http://dx.doi.org/10.1051/epjconf/202430404004.

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We investigate the isotopes of Se, Zr, Mo and Nd in the regions with N = 40, 60 and 90, where a first-order shape / phase transition, from spherical to deformed, can be observed. The signs of phase transitional behavior become evident by examining structure indicators, such as certain energy ratios and B(E2) transition rates and, in particular, how they evolve with neutron number. Microscopic mean-field calculations using the Skyrme-Hartree-Fock + Bardeen-Cooper-Schrieffer framework also reveal structural changes when considering the evolution of the resulting potential energy curves as functi

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27

Bernardos, Luis, F. Richez, V. Gleize, and G. A. Gerolymos. "Prediction of Separation-Induced Transition on the SD7003 Airfoil Using Algebraic Transition Triggering." AIAA Journal 57, no. 9 (2019): 3812–24. http://dx.doi.org/10.2514/1.j058288.

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28

LI, ZHIQIANG, and DAIZHAN CHENG. "ALGEBRAIC APPROACH TO DYNAMICS OF MULTIVALUED NETWORKS." International Journal of Bifurcation and Chaos 20, no. 03 (2010): 561–82. http://dx.doi.org/10.1142/s0218127410025892.

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Using semi-tensor product of matrices, a matrix expression for multivalued logic is proposed, where a logical variable is expressed as a vector, and a logical function is expressed as a multilinear mapping. Under this framework, the dynamics of a multivalued logical network is converted into a standard discrete-time linear system. Analyzing the network transition matrix, easily computable formulas are obtained to show (a) the number of equilibriums; (b) the numbers of cycles of different lengths; (c) transient period, the minimum time for all points to enter the set of attractors, respectively

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Albeverio, Sergio, and Shao-Ming Fei. "Symmetry, Integrable Chain Models and Stochastic Processes." Reviews in Mathematical Physics 10, no. 06 (1998): 723–50. http://dx.doi.org/10.1142/s0129055x98000239.

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A general way to construct chain models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. As an example the chain models with An symmetry and the related Temperley–Lieb algebraic structures and representations are discussed. It is shown that corresponding to these An symmetric integrable chain models there are exactly solvable stationary discrete-time (resp. continuous-time) Markov chains with transition matrices (resp. intensity matrices) having spectra which coincide with the ones of the correspondin

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30

Fu, Jun. "Quantitative Specification of Semi-algebraic Transition Systems with Metrics." Journal of Information and Computational Science 12, no. 3 (2015): 993–1000. http://dx.doi.org/10.12733/jics20105417.

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31

Stabnikov, A. S., A. V. Garbaruk, and A. A. Matyushenko. "Comparative Analysis of Algebraic Models of Laminar-Turbulent Transition." Mathematical Models and Computer Simulations 16, no. 3 (2024): 419–30. http://dx.doi.org/10.1134/s2070048224700091.

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32

AMICO, LUIGI. "ALGEBRAIC EQUIVALENCE BETWEEN CERTAIN MODELS FOR SUPERFLUID–INSULATOR TRANSITION." Modern Physics Letters B 14, no. 21 (2000): 759–66. http://dx.doi.org/10.1142/s0217984900000963.

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Algebraic contraction is proposed to realize mappings between Hamiltonian models. This transformation contracts the algebra of the degrees of freedom underlying the Hamiltonian. The rigorous mapping between the anisotropic XXZ Heisenberg model, the quantum phase model and the Bose Hubbard model is established as the contractions of the algebra u(2) underlying the dynamics of the XXZ Heisenberg model.

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Dicky, Anne. "An algebraic and algorithmic method for analysing transition systems." Theoretical Computer Science 46 (1986): 285–303. http://dx.doi.org/10.1016/0304-3975(86)90034-4.

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Patrizi, Stefania, and Enrico Valdinoci. "Long-time behavior for crystal dislocation dynamics." Mathematical Models and Methods in Applied Sciences 27, no. 12 (2017): 2185–228. http://dx.doi.org/10.1142/s0218202517500427.

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We describe the asymptotic states for the solutions of a nonlocal equation of evolutionary type, which have the physical meaning of the atom dislocation function in a periodic crystal. More precisely, we can describe accurately the “smoothing effect” on the dislocation function occurring slightly after a “particle collision” (roughly speaking, two opposite transitions layers average out) and, in this way, we can trap the atom dislocation function between a superposition of transition layers which, as time flows, approaches either a constant function or a single heteroclinic (depending on the a

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Babakov, R. M., A. A. Barkalov, L. A. Titarenko, and M. O. Voitenko. "ALGORITHMIC DIFFERENCES OF COMPLETE AND PARTIAL ALGEBRAIC SYNTHESIS OF A FINITE STATE MACHINE WITH DATAPATH OF TRANSITIONS." Radio Electronics, Computer Science, Control, no. 4 (December 26, 2024): 143–52. https://doi.org/10.15588/1607-3274-2024-4-14.

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Context. The problem of algorithmization the search for formal solutions of the problem of algebraic synthesis of a finite state ma-chine with datapath of transitions is considered. The concept of complete and partial solutions of this problem is proposed. The object of research is the automated synthesis of the finite state machine in the part of the function of transitions without taking into account the function of outputs. The basis of the algebraic implementation of the transition function is the author's approach to the transformation of state codes using a set of arithmetic and logical

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Ibrahim, Zaid. "Language Outlay for the Sokoto Cement Production System Using Deterministic Finite Automata Scheme." European Journal of Theoretical and Applied Sciences 1, no. 6 (2023): 105–14. http://dx.doi.org/10.59324/ejtas.2023.1(6).10.

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This paper constructs the compact, detailed and extended models, and focuses on the algebraic theoretic strings and language of each transition of the finite automata scheme. It was discovered that from the initial stage to the final stage of cement production processes, each transition or production process can have a particular language. In addition, a language scheme is developed for each of the sub-states (sub-model) that leads to a theoretic study of language scheme and semantics of the model. It can be deduced that when represented as binary codes, the established schemes in the sub-stat

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Zaid, Ibrahim. "Language Outlay for the Sokoto Cement Production System Using Deterministic Finite Automata Scheme." European Journal of Theoretical and Applied Sciences 1, no. 6 (2023): 105–14. https://doi.org/10.59324/ejtas.2023.1(6).10.

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This paper constructs the compact, detailed and extended models, and focuses on the algebraic theoretic strings and language of each transition of the finite automata scheme. It was discovered that from the initial stage to the final stage of cement production processes, each transition or production process can have a particular language. In addition, a language scheme is developed for each of the sub-states (sub-model) that leads to a theoretic study of language scheme and semantics of the model. It can be deduced that when represented as binary codes, the established schemes in the sub-stat

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Jafarizadeh, M. A., A. Jalili Majarshin, and N. Fouladi. "Simultaneous description of low-lying positive and negative parity states in spd, sdf and spdf interacting boson model." International Journal of Modern Physics E 25, no. 11 (2016): 1650089. http://dx.doi.org/10.1142/s0218301316500890.

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In order to investigate negative parity states, it is necessary to consider negative parity-bosons additionally to the usual [Formula: see text]- and [Formula: see text]-bosons. The dipole and octupole degrees of freedom are essential to describe the observed low-lying collective states with negative parity. An extended interacting boson model (IBM) that describes pairing interactions among s, p, d and f-boson based on affine [Formula: see text] Lie algebra in the quantum phase transition (QPT) field, such as spd-IBM, sdf-IBM and spdf-IBM, is composed based on algebraic structure. In this pape

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Kubacki, Slawomir, Daniele Simoni, Davide Lengani, and Erik Dick. "An Extended Version of an Algebraic Intermittency Model for Prediction of Separation-Induced Transition at Elevated Free-Stream Turbulence Level." International Journal of Turbomachinery, Propulsion and Power 5, no. 4 (2020): 28. http://dx.doi.org/10.3390/ijtpp5040028.

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An algebraic intermittency model for boundary layer flow transition from laminar to turbulent state, is extended using an experimental data base on boundary layer flows with various transition types and results by large eddy simulation of transition in a separated boundary layer. The originating algebraic transition model functions well for bypass transition in an attached boundary layer under a moderately high or elevated free-stream turbulence level, and for transition by Kelvin–Helmholtz instability in a separated boundary layer under a low free-stream turbulence level. It also functions we

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Nolte, T. M., W. J. G. M. Peijnenburg, T. J. H. M. van Bergen, and A. J. Hendriks. "Transition-state rate theory sheds light on ‘black-box’ biodegradation algorithms." Green Chemistry 22, no. 11 (2020): 3558–71. http://dx.doi.org/10.1039/d0gc00337a.

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Kuznetsov, А. А., I. P. Kolovanova, D. I. Prokopovych-Tkachenko, and T. Y. Kuznetsova. "Analysis and investigation of algebraic geometric codes properties." Radiotekhnika, no. 195 (December 28, 2018): 70–88. http://dx.doi.org/10.30837/rt.2018.4.195.08.

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Linear block noise-proof codes constructed according to algebraic curves (algebraic geometric codes) are considered, their design properties are evaluated, algorithms of construction and decoding are studied. The energy efficiency of the transmission of discrete messages by M-ary orthogonal signals in the application of algebraic geometric codes is studied; the achievable energy gain from the use of noise-immune coding is estimated. It is shown that in discrete channels without memory it is possible to obtain a significant energy gain, which increases with the transition to long algebraic geom

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Lannin, John K. "Developing Algebraic Reasoning Through Generalization." Mathematics Teaching in the Middle School 8, no. 7 (2003): 342–48. http://dx.doi.org/10.5951/mtms.8.7.0342.

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NCTM's (2000) recommendations for algebra in the middle grades strive to assist students' transition to formal algebra by developing meaning for the algebraic symbols that students use. Further, students are expected to have opportunities to develop understanding of patterns and functions, represent and analyze mathematical situations, develop mathematical models, and analyze change. By helping students move from specific numeric situations to develop general rules that model all situations of that type, teachers in fact begin to address the NCTM's recommendations for algebra. Generalizing num

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Filloy, Eugenio, Teresa Rojano, and Armando Solares. "Problems Dealing With Unknown Quantities and Two Different Levels of Representing Unknowns." Journal for Research in Mathematics Education 41, no. 1 (2010): 52–80. http://dx.doi.org/10.5951/jresematheduc.41.1.0052.

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This article centers on studying the progress of algebraic syntax once students have surmounted initial obstacles found in the transition toward symbolic algebra. It specifically analyzes students' progress concerning the operation on the unknown, when the latter is represented by an expression that involves a 2nd unknown. In curricular terms, students face such a situation when they learn the classic methods to solve systems involving 2 linear equations with 2 unknowns. Results from this empirical study show that extending previous algebraic syntax to the 2nd tier of representation of the unk

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RECALDE, LAURA, ENRIQUE TERUEL, and MANUEL SILVA. "ON LINEAR ALGEBRAIC TECHNIQUES FOR LIVENESS ANALYSIS OF P/T SYSTEMS." Journal of Circuits, Systems and Computers 08, no. 01 (1998): 223–65. http://dx.doi.org/10.1142/s0218126698000092.

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Liveness is a basic property that in many discrete event dynamic systems is considered essential for their correct behavior. It expresses that no action (transition in P/T models) will ever become unattainable. A polynomial time necessary condition for the existence of a live and bounded marking of a P/T net is given. This condition is shown to be also sufficient for some subclasses. The applicability of these results is extended by the use of transformation techniques that allow for their exploitation in the analysis of more general nets. Some results for the structural analysis of actual liv

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MESEGUER, JOSÉ, UGO MONTANARI, and VLADIMIRO SASSONE. "On the semantics of place/transition Petri nets." Mathematical Structures in Computer Science 7, no. 4 (1997): 359–97. http://dx.doi.org/10.1017/s0960129597002314.

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Place/transition (PT) Petri nets are one of the most widely used models of concurrency. However, they still lack, in our view, a satisfactory semantics: on the one hand the ‘token game’ is too intensional, even in its more abstract interpretations in terms of nonsequential processes and monoidal categories; on the other hand, Winskel's basic unfolding construction, which provides a coreflection between nets and finitary prime algebraic domains, works only for safe nets. In this paper we extend Winskel's result to PT nets. We start with a rather general category PTNets of PT nets, we introduce

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Muramoto, Kenneth K. "Algebraic Correlation for High-Speed Transition Prediction on Sphere Cones." Journal of Spacecraft and Rockets 40, no. 4 (2003): 598–600. http://dx.doi.org/10.2514/2.3983.

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Stabnikov, A. S., and A. V. Garbaruk. "Analysis of the abilities of algebraic laminar-turbulent transition models." Journal of Physics: Conference Series 1135 (December 2018): 012104. http://dx.doi.org/10.1088/1742-6596/1135/1/012104.

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Pratiwi, W. D., E. Kurniadi, and P. Astuti. "Learning design for transition from arithmetic thinking to algebraic thinking." Journal of Physics: Conference Series 1166 (February 2019): 012031. http://dx.doi.org/10.1088/1742-6596/1166/1/012031.

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Nakamura, Yoshiaki, and Andi Eka Sakya. "Capturing of transition by the RNG based algebraic turbulence model." Computers & Fluids 24, no. 8 (1995): 909–18. http://dx.doi.org/10.1016/0045-7930(95)00021-4.

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ZHANG, YAN, ZHAOHUI ZHU, and JINJIN ZHANG. "On recursive operations over logic LTS." Mathematical Structures in Computer Science 25, no. 6 (2014): 1382–431. http://dx.doi.org/10.1017/s0960129514000073.

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Recently, in order to mix algebraic and logic styles of specification in a uniform framework, the notion of a logic labelled transition system (Logic LTS or LLTS for short) has been introduced and explored. A variety of constructors over LLTS, including usual process-algebraic operators, logic connectives (conjunction and disjunction) and standard temporal modalities (always and unless), have been given. However, no attempt has been made so far to develop the general theory concerning (nested) recursive operations over LLTS and a few fundamental problems are still open. This paper intends to s

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