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Journal articles on the topic 'Algebraic analogy'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Junarti, M. Zainudin, and Anita Dewi Utami. "The sequence of algebraic problem-solving paths: Evidence from structure sense of Indonesian student." Journal on Mathematics Education 13, no. 3 (2022): 437–64. http://dx.doi.org/10.22342/jme.v13i3.pp437-464.

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The algebraic structure is one of the axiomatic mathematical materials that consists of definitions and theorems. Learning algebraic structure will facilitate the development of logical reasoning, hence facilitating the study of other aspects of axiomatic mathematics. Even with this, several researchers say a lack of algebraic structure sense is a source of difficulty in acquiring algebraic structures. This study aims to examine a pattern of sequences of problem-solving paths in algebra, which is an illustration of learners' algebraic structure sense so that it can be utilized to enhance the a

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2

Feng, Tony. "Étale Steenrod operations and the Artin–Tate pairing." Compositio Mathematica 156, no. 7 (2020): 1476–515. http://dx.doi.org/10.1112/s0010437x20007216.

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We prove a 1966 conjecture of Tate concerning the Artin–Tate pairing on the Brauer group of a surface over a finite field, which is the analog of the Cassels–Tate pairing. Tate asked if this pairing is always alternating and we find an affirmative answer, which is somewhat surprising in view of the work of Poonen–Stoll on the Cassels–Tate pairing. Our method is based on studying a connection between the Artin–Tate pairing and (generalizations of) Steenrod operations in étale cohomology. Inspired by an analogy to the algebraic topology of manifolds, we develop tools allowing us to calculate the

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Chvalina, Jan, Bedřich Smetana, and Jana Vyroubalová. "Construction of an Infinite Cyclic Group Formed by Artificial Differential Neurons." Mathematics 10, no. 9 (2022): 1571. http://dx.doi.org/10.3390/math10091571.

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Infinite cyclic groups created by various objects belong to the class to the class basic algebraic structures. In this paper, we construct the infinite cyclic group of differential neurons which are modifications of artificial neurons in analogy to linear ordinary differential operators of the n-th order. We also describe some of their basic properties.

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4

Rosen, Julian. "The Completed Finite Period Map and Galois Theory of Supercongruences." International Mathematics Research Notices 2019, no. 23 (2018): 7379–405. http://dx.doi.org/10.1093/imrn/rny004.

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Abstract A period is a complex number arising as the integral of a rational function with algebraic number coefficients over a region cut out by finitely many inequalities between polynomials with rational coefficients. Although periods are typically transcendental numbers, there is a conjectural Galois theory of periods coming from the theory of motives. This paper formalizes an analogy between a class of periods called multiple zeta values and congruences for rational numbers modulo prime powers (called supercongruences). We construct an analog of the motivic period map in the setting of sup

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Sa’adah, Nihayatus, and Siti Faizah. "ANALISIS STRATEGI SISWA KELAS IX SMP DALAM MENYELESAIKAN MASALAH ALJABAR." SIGMA 7, no. 2 (2022): 95. http://dx.doi.org/10.53712/sigma.v7i2.1294.

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One skill that students can develop through the mathematics learning process in the classroom is problem solving skill. Polya said that one of four mathematics problem solving steps was planning. In the planning step, there was a strategy that can be used by students to solve the problem. This qualitative research aimed to analyze the third grade of junior high school student's strategy in solving algebraic problem. The subjects in this research were three students with high mathematics ability and three students with medium mathematics ability. The data were collected by using primer and seco

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6

Matrassulova, Dinara Kutlimuratovna, Yelizaveta Sergeevna Vitulyova, Sergey Vladimirovich Konshin, and Ibragim Esenovich Suleimenov. "Algebraic fields and rings as a digital signal processing tool." Indonesian Journal of Electrical Engineering and Computer Science 29, no. 1 (2022): 206. http://dx.doi.org/10.11591/ijeecs.v29.i1.pp206-216.

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It is shown that algebraic fields and rings can become a very promising tool for digital signal processing. This is mainly due to the fact that any digital signals change in a finite range of amplitudes and, therefore, there are only a finite set of levels that can correspond to the amplitudes of a signal reduced to a discrete form. This allows you to establish a one-to-one correspondence between the set of levels and such algebraic structures as fields, rings, etc. This means that a function that takes values in any of the algebraic structures containing a finite set of elements can serve as

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Matrassulova, Dinara Kutlimuratovna, Yelizaveta Sergeevna Vitulyova, Sergey Vladimirovich Konshin, and Ibragim Esenovich Suleimenov. "Algebraic fields and rings as a digital signal processing tool." Indonesian Journal of Electrical Engineering and Computer Science 29, no. 1 (2023): 206–16. https://doi.org/10.11591/ijeecs.v29.i1.pp206-216.

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It is shown that algebraic fields and rings can become a very promising tool for digital signal processing. This is mainly due to the fact that any digital signals change in a finite range of amplitudes and, therefore, there are only a finite set of levels that can correspond to the amplitudes of a signal reduced to a discrete form. This allows you to establish a one-to-one correspondence between the set of levels and such algebraic structures as fields, rings, etc. This means that a function that takes values in any of the algebraic structures containing a finite set of elements can serve as

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8

Kotov, A. A., and T. N. Kotova. "Using Pictures as Cultural Means in Finding Similarities between Solutions to Algebraic Tasks." Cultural-Historical Psychology 12, no. 1 (2016): 35–45. http://dx.doi.org/10.17759/chp.2016120104.

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Solving textual algebraic tasks requires finding important mathematical variables in the text and turning them into equations. Many students, following their teacher’s advice or at their own initiative, use pictures as a means of better understanding the mathematical structure of the task. In this study we explored which features of pictures were the most essential to the students in finding the appropriate solution based on their experience. We created a set of pictures that differed in parameters of analogy and completeness of relationships between elements. The subjects were asked to evalua

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9

GAßNER, CHRISTINE. "Computation over algebraic structures and a classification of undecidable problems." Mathematical Structures in Computer Science 27, no. 8 (2016): 1386–413. http://dx.doi.org/10.1017/s0960129516000116.

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We consider a uniform model of computation over algebraic structures resulting from a generalization of the Turing machine and the BSS model of computation. This model allows us to gain more insight into the reasons for unsolvability of algorithmic decision problems from different perspectives. For example, classes of undecidable problems can be introduced in several ways by analogy with the classical arithmetical hierarchy and, for many structures, the different definitions lead to different hierarchies of undecidable problems. Here, we will investigate some classes of a hierarchy that is def

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10

Fujikawa, Kazuo, and C. H. Oh. "Exact algebraic separability criterion for two-qubit systems." Modern Physics Letters A 32, no. 11 (2017): 1750070. http://dx.doi.org/10.1142/s0217732317500705.

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A conceptually simpler proof of the separability criterion for two-qubit systems, which is referred to as “Hefei inequality” in literature, is presented. This inequality gives a necessary and sufficient separability criterion for any mixed two-qubit system unlike the Bell-CHSH inequality that cannot test the mixed-states such as the Werner state when regarded as a separability criterion. The original derivation of this inequality emphasized the uncertainty relation of complementary observables, but we show that the uncertainty relation does not play any role in the actual derivation and the Pe

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11

Huhtanen, Marko. "Differential geometry of matrix inversion." MATHEMATICA SCANDINAVICA 107, no. 2 (2010): 267. http://dx.doi.org/10.7146/math.scand.a-15155.

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Essentially, there exists just the dimension segregating (square) matrix subspaces. In view of algebraic operations, this quantity is not particularly descriptive. For differential geometric information on matrix inversion, the second fundamental form is found for the set of inverses of the invertible elements of a matrix subspace. Several conditions for this form to vanish are given, such as being equivalent to a Jordan subalgebra. Global measures of curvature are introduced in terms of an analogy of the Nash fiber.

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12

Armillotta, Antonio. "A static analogy for 2D tolerance analysis." Assembly Automation 34, no. 2 (2014): 182–91. http://dx.doi.org/10.1108/aa-05-2013-050.

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Purpose – This paper aims to present a method for the tolerance analysis of mechanical assemblies that is suitable to nonlinear problems where explicit functional equations are difficult or even impossible to write down. Such cases are usually modelled by linearised tolerance chains, whose coefficients (or sensitivities) are calculated from assembly data. Design/methodology/approach – The method is based on the free-body diagrams of force analysis, which are shown to be related to the sensitivities of linearised functional equations. Such an analogy allows the conversion of a tolerance chain i

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13

Lopez-Bonilla, José Luis, R. López-Vázquez, and H. Torres-Silva. "Petrov Classification of the Liénard–Wiechert Field." International Frontier Science Letters 2 (October 2014): 16–17. http://dx.doi.org/10.18052/www.scipress.com/ifsl.2.16.

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Newman [1] showed analogies between the Liénard–Wiechert field [2-7] and the Robinson-Trautman (RT) solutions [8-10] of the Einstein gravitational equations. Here we present one more analogy: The Maxwell field produced by a point charge in arbitrary motion has the same algebraic type as the RT metrics. This result is possible because the Weert superpotential [3, 6, 7, 11-16] permits to construct an “electromagnetic Weyl tensor” which admits the Petrov classification [8, 17-24] as in general relativity.

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Börner, Christoph J., Ingo Hoffmann, and John H. Stiebel. "On the connection between temperature and volatility in ideal agent systems." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 10 (2023): 103401. http://dx.doi.org/10.1088/1742-5468/ad002c.

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Abstract Models for spin systems known from statistical physics are applied by analogy in econometrics in the form of agent-based models. Researchers suggest that the state variable temperature T corresponds to volatility σ in capital market theory problems. To the best of our knowledge, this has not yet been theoretically derived, for example, for an ideal agent system. In the present paper, we derive the exact algebraic relation between T and σ for an ideal agent system and discuss implications and limitations.

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15

Gu, Lize, and Shihui Zheng. "Conjugacy Systems Based on Nonabelian Factorization Problems and Their Applications in Cryptography." Journal of Applied Mathematics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/630607.

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To resist known quantum algorithm attacks, several nonabelian algebraic structures mounted upon the stage of modern cryptography. Recently, Baba et al. proposed an important analogy from the integer factorization problem to the factorization problem over nonabelian groups. In this paper, we propose several conjugated problems related to the factorization problem over nonabelian groups and then present three constructions of cryptographic primitives based on these newly introduced conjugacy systems: encryption, signature, and signcryption. Sample implementations of our proposal as well as the r

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16

Zhanlav, Tugal, Ochbadrakh Chuluunbaatar, and Gantumur Ankhbayar. "The Continuous Analogy of Newton’s Method for Solving a System of Linear Algebraic Equations." Applied Mathematics 04, no. 01 (2013): 210–16. http://dx.doi.org/10.4236/am.2013.41a032.

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17

Milgrom, Lionel R. "Journeys in the Country of the Blind: Entanglement Theory and the Effects of Blinding on Trials of Homeopathy and Homeopathic Provings." Evidence-Based Complementary and Alternative Medicine 4, no. 1 (2007): 7–16. http://dx.doi.org/10.1093/ecam/nel062.

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The idea of quantum entanglement is borrowed from physics and developed into an algebraic argument to explain how double-blinding randomized controlled trials could lead to failure to provide unequivocal evidence for the efficacy of homeopathy, and inability to distinguish proving and placebo groups in homeopathic pathogenic trials. By analogy with the famous double-slit experiment of quantum physics, and more modern notions of quantum information processing, these failings are understood as blinding causing information loss resulting from a kind of quantum superposition between the remedy and

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18

FEWSTER, CHRISTOPHER J., and DAVID S. HUNT. "QUANTIZATION OF LINEARIZED GRAVITY IN COSMOLOGICAL VACUUM SPACETIMES." Reviews in Mathematical Physics 25, no. 02 (2013): 1330003. http://dx.doi.org/10.1142/s0129055x13300033.

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Linearized Einstein gravity (with possibly non-zero cosmological constant) is quantized in the framework of algebraic quantum field theory by analogy with Dimock's treatment of electromagnetism [Rev. Math. Phys.4 (1992) 223–233]. To achieve this, the classical theory is developed in a full, rigorous and systematic fashion, with particular attention given to the circumstances under which the symplectic product is weakly non-degenerate and to the related question of whether the space of solutions is separated by the classical observables on which the quantum theory is modeled.

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19

Shiah, Y. C., Jin H. Huang, and Y. L. Xue. "The First Damped Frequency with Maximum Sound Pressure of a Miniature Loudspeaker for Cellular Phones." Journal of Mechanics 26, no. 4 (2010): 473–82. http://dx.doi.org/10.1017/s1727719100004676.

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ABSTRACTFor improving the performance of a miniature loudspeaker, engineers have been pursuing a goal of lowering its first damped frequency to have a broad and smooth region of its sound-pressure-level response. This article applies the approach of electro-mechano-acoustical analogy to study the first damped frequency of a miniature loudspeaker used for cellular phones. Using the analogy approach, the authors derive an explicit formulation for the sound-pressure-level of a typical miniature loudspeaker of dynamic type. The veracity of the derived formulation is verified by comparing with the

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20

Zhong, W. X., and F. W. Williams. "Wave Problems for Repetitive Structures and Symplectic Mathematics." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 206, no. 6 (1992): 371–79. http://dx.doi.org/10.1243/pime_proc_1992_206_143_02.

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Based on the analogy between structural mechanics and optimal control theory, the eigensolutions of a symplectic matrix, the adjoint symplectic ortho-normalization relation and the eigenvector expansion method are introduced into the wave propagation theory for sub-structural chain-type structures, such as space structures, composite material and turbine blades. The positive and reverse algebraic Riccati equations are derived, for which the solution matrices are closely related to the power flow along the sub-structural chain. The power flow orthogonality relation for various eigenvectors is p

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21

Junarti, Junarti, Ahmad Yani T, and Ahmad Kholiqul Amin. "Building Student’s Mathematical Connection Ability in Abstract Algebra: The Combination of Analogy-Contruction-Abstraction Stages." JETL (Journal of Education, Teaching and Learning) 8, no. 1 (2023): 80. http://dx.doi.org/10.26737/jetl.v8i1.3796.

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The objective of the study was to describe the effect of six types of mathematical connections (representation connections, structural connections, procedural connections, implication connections, generalization connections, and hierarchy connections) on abstract algebraic materials through four stages, i.e., abstraction, analogy-abstraction, construction-analogy, and construction. The study employed qualitative descriptive approaches, including tests, questionnaires, and interviews. The subjects of the study were chosen based on the responses to a questionnaire regarding the employed stages.

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22

Hlongwane, Joseph. "Algebraic Solution of the Quantum Harmonic Oscillator." International Journal of Research and Innovation in Applied Science IX, no. IV (2024): 62–75. http://dx.doi.org/10.51584/ijrias.2024.90405.

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The Wave-particle duality and the Schrodinger cat paradox pose important notions on quantum mechanical systems, in which a quantum system can exist in two physically opposite or distinct states. This motivates scientists from the days of Louis de Broglie to confidently look at matter as having a dual nature, which is a physical particle that can also be visualized as a wave entity. This paper seeks to provide an elegant method of solving the time-independent Schrodinger Equation (TISE) for a quantum simple harmonic oscillator (QSHO). A fully algebraic method is presented, the paper explains in

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Jerbi, Houssem, Hadeel Alharbi, Mohamed Omri, et al. "Towards Higher-Order Zeroing Neural Network Dynamics for Solving Time-Varying Algebraic Riccati Equations." Mathematics 10, no. 23 (2022): 4490. http://dx.doi.org/10.3390/math10234490.

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One of the most often used approaches for approximating various matrix equation problems is the hyperpower family of iterative methods with arbitrary convergence order, whereas the zeroing neural network (ZNN) is a type of neural dynamics intended for handling time-varying problems. A family of ZNN models that correlate with the hyperpower iterative methods is defined on the basis of the analogy that was discovered. These models, known as higher-order ZNN models (HOZNN), can be used to find real symmetric solutions of time-varying algebraic Riccati equations. Furthermore, a noise-handling HOZN

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24

Kravets, Victor, Volodymyr Kravets, and Olexiy Burov. "Analytical Modeling of the Dynamic System of the Fourth Order." Transactions on Machine Learning and Artificial Intelligence 9, no. 3 (2021): 14–24. http://dx.doi.org/10.14738/tmlai.93.9947.

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A canonical mathematical model of a fourth-order dynamical system in the form of A.M. Letov. The analytical modeling methods are based on the algebraic concept and the principle of symmetry. The symmetry principle is realized on the set of four indices of the roots of the characteristic equation and the set of four indices of the phase coordinates of the dynamic system. The problem of the quality of dynamic processes in time is reduced to the algebraic problem of distribution of four roots in the complex plane. An analogy is established in the procedure for transforming the characteristi

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Jin, S., B. H. Xie, H. B. Zhang, J. L. Birman, and M. L. Ge. "su(3) algebraic structure of the cuprate superconductor model based on the analogy with atomic nuclei." Philosophical Magazine Letters 86, no. 11 (2006): 743–54. http://dx.doi.org/10.1080/09500830600993303.

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Subanji, Subanji, and Toto Nusantara. "Thinking Process of Pseudo Construction in Mathematics Concepts." International Education Studies 9, no. 2 (2016): 17. http://dx.doi.org/10.5539/ies.v9n2p17.

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<p class="apa">This article aims at studying pseudo construction of student thinking in mathematical concepts, integer number operation, algebraic forms, area concepts, and triangle concepts. 391 junior high school students from four districts of East Java Province Indonesia were taken as the subjects. Data were collected by means of distributing the main instrument and tracer instrument to the subjects respectively. Both instruments were deployed for the purpose of digging up the construction process. The construction was clustered on the basis of the pseudo contruction cases and follow

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27

Suroto, Ari Wardayani, and Chumaedi Sugihandardji. "TERMINOLOGI DASAR PADA HIMPUNAN SIMETRISASI ALJABAR MIN-PLUS." Jurnal Matematika Sains dan Teknologi 23, no. 2 (2022): 57–67. http://dx.doi.org/10.33830/jmst.v23i2.3033.2023.

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This paper discusses some of the terminology and basic properties of the set of min-plus algebra symmetrization. The results are algebraic structure of the positive or zero part of the set of min-plus algebra symmetrization is a semi-field, and the min-plus algebra can be viewed as the positive or zero part in the context of the set of min-plus algebra symmetrization. Furthermore, the form of the result of the subtraction of the elements in the set of min-plus algebra symmetrization, the multiplicative inverse of element in the non zero-positive and negative part, and some basic properties of

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Сыдыхов, Б., Ж. Т. Кайынбаев та А. С. Исмухамбетова. "ТРАПЕЦИЯҒА БАЙЛАНЫСТЫ КҮРДЕЛІ ЕСЕПТЕР ЖӘНЕ ОЛАРДЫ ШЕШУ ТӘСІЛДЕРІ". Педагогика и Методы Обучения, № 3 (60) 2022 (16 листопада 2022): 45–63. https://doi.org/10.47344/sdu20bulletin.v60i3.819.

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The article is devoted to the discussion of ways to solve complex problems related to the trapezoid, which is one of the most important figures in the content of elementary geometry. To implement this situation, the method of gradual solution of the problem using various theorems, the method of analogy in solving geometric problems, the method of solving the problem based on the construction of additional drawings, the method of solving geometric problems in an algebraic way, etc. are used. Similarly, the article discusses ways to solve complex problems related to the tangential trapezoid.The

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Phillips, Steven. "A reconstruction theory of relational schema induction." PLOS Computational Biology 17, no. 1 (2021): e1008641. http://dx.doi.org/10.1371/journal.pcbi.1008641.

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Learning transfer (i.e. accelerated learning over a series of structurally related learning tasks) differentiates species and age-groups, but the evolutionary and developmental implications of such differences are unclear. To this end, the relational schema induction paradigm employing tasks that share algebraic (group-like) structures was introduced to contrast stimulus-independent (relational) versus stimulus-dependent (associative) learning processes. However, a theory explaining this kind of relational learning transfer has not been forthcoming beyond a general appeal to some form of struc

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Gwak, Kwan-Woong, and Glenn Y. Masada. "Regularization Embedded Nonlinear Control Designs for Input-Constrained and Ill-Conditioned Thermal System." Journal of Dynamic Systems, Measurement, and Control 126, no. 3 (2004): 574–82. http://dx.doi.org/10.1115/1.1789973.

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New regularization embedded nonlinear control designs are proposed for the temperature control of an input-constrained and ill-conditioned thermal process. A classic nonlinear controller applied to such a process is shown to provide good temperature tracking but generates physically unreasonable actuator solutions, i.e. input-constraint-violation. The reason of input-constraint-violating control solutions—ill-conditionedness—is shown by applying singular value decomposition (SVD) on the linear algebraic equivalence of the nonlinear controllers (LAENC). Based on the analogy of LAENC and regular

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NEZHAD, S. REZA HASHEMI, and HAMID REZA VOSOUGHIFAR. "SOLUTION ARRANGEMENT EFFECT ON LINE-BY-LINE METHOD'S ACCURACY IN ANALYSIS OF DAM'S FOUNDATION." International Journal of Computational Methods 08, no. 03 (2011): 583–96. http://dx.doi.org/10.1142/s021987621100268x.

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Line-by-line (LBL) solution method is a numerical and semidirect method, which can be applied for solving algebraic equation set resulted from discretization. In this article, the effect of solution arrangement of the grids (SAG) on accuracy of diffusion equation's solution has been investigated. First of all, diffusion equation had been discrete by finite volume method; in the second place, MATLAB software has been exploited for writing a code for solving algebraic equation set by using LBL solution method with alternative SAG. In the third place, for examining the effect of SAG, water seepag

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Kravets, Viktor, Dmytro Kolosov, Volodymyr Kravets, Olexandr Dolgov, and Serhii Onyshchenko. "Analytical modelling and design of linear controlled dynamic systems." IOP Conference Series: Earth and Environmental Science 1348, no. 1 (2024): 012084. http://dx.doi.org/10.1088/1755-1315/1348/1/012084.

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Abstract A generalized canonical mathematical model of multidimensional controlled mining transportation complexes and other technical systems in form by A.M. Letov is considered. A principle of symmetry and an algebraic concept are in the basis of the developed analytical methods of design. A principle of symmetry is realized on a set of indexes of roots of a characteristic equation of the system and on a set of indexes of phase coordinates of the mathematical model. The problem of quality of dynamic processes in time is reduced to an algebraic problem of distribution of roots of a correspond

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Ardakov, Konstantin, Andreas Bode, and Simon Wadsley. "-modules on rigid analytic spaces III: weak holonomicity and operations." Compositio Mathematica 157, no. 12 (2021): 2553–84. http://dx.doi.org/10.1112/s0010437x21007521.

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AbstractWe develop a dimension theory for coadmissible $\widehat {\mathcal {D}}$-modules on rigid analytic spaces and study those which are of minimal dimension, in analogy to the theory of holonomic $\mathcal {D}$-modules in the algebraic setting. We discuss a number of pathologies contained in this subcategory (modules of infinite length, infinite-dimensional fibres). We prove stability results for closed immersions and the duality functor, and show that all higher direct images of integrable connections restricted to a Zariski open subspace are coadmissible of minimal dimension. It follows

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Li, Yiyang, and Bin Shu. "Filtrations in Modular Representations of Reductive Lie Algebras." Algebra Colloquium 17, no. 02 (2010): 265–82. http://dx.doi.org/10.1142/s1005386710000283.

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Let G be a connected reductive algebraic group over an algebraically closed field k of prime characteristic p, and 𝔤 = Lie (G). In this paper, we study representations of the reductive Lie algebra 𝔤 with p-character χ of standard Levi form associated with an index subset I of simple roots. With aid of the support variety theory, we prove that a Uχ(𝔤)-module is projective if and only if it is a strong "tilting" module, i.e., admitting both [Formula: see text]- and [Formula: see text]-filtrations. Then by an analogy of the arguments in [2] for G1T-modules, we construct so-called Andersen–Kaneda

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SOW, C. L., and T. T. TRUONG. "QUANTUM GROUP APPROACH TO A SOLUBLE VERTEX MODEL WITH GENERALIZED ICE RULE." International Journal of Modern Physics A 11, no. 10 (1996): 1747–61. http://dx.doi.org/10.1142/s0217751x96000936.

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Using the representation of the quantum group SL q(2) by the Weyl operators of the canonical commutation relations in quantum mechanics, we construct and solve a new vertex model on a square lattice. Random variables on horizontal bonds are Ising variables, and those on the vertical bonds take half positive integer values. The vertex is subjected to a generalized form of the so-called “ice rule,” its property is studied in detail and its free energy calculated with the method of quantum inverse scattering. Remarkably, in analogy with the usual six-vertex model, there exists a “free-fermion” li

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Duplij, Steven. "Graded Medial n-Ary Algebras and Polyadic Tensor Categories." Symmetry 13, no. 6 (2021): 1038. http://dx.doi.org/10.3390/sym13061038.

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Algebraic structures in which the property of commutativity is substituted by the mediality property are introduced. We consider (associative) graded algebras and instead of almost commutativity (generalized commutativity or ε-commutativity), we introduce almost mediality (“commutativity-to-mediality” ansatz). Higher graded twisted products and “deforming” brackets (being the medial analog of Lie brackets) are defined. Toyoda’s theorem which connects (universal) medial algebras with abelian algebras is proven for the almost medial graded algebras introduced here. In a similar way we generalize

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Duplij, Steven. "Polyadic Analogs of Direct Product." Universe 8, no. 4 (2022): 230. http://dx.doi.org/10.3390/universe8040230.

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We propose a generalization of the external direct product concept to polyadic algebraic structures which introduces novel properties in two ways: the arity of the product can differ from that of the constituents, and the elements from different multipliers can be “entangled” such that the product is no longer componentwise. The main property which we want to preserve is associativity, which is gained by using the associativity quiver technique, which was provided previously. For polyadic semigroups and groups we introduce two external products: (1) the iterated direct product, which is compon

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Feeman, Timothy G. "The Bourgain algebra of a nest algebra." Proceedings of the Edinburgh Mathematical Society 40, no. 1 (1997): 151–66. http://dx.doi.org/10.1017/s0013091500023518.

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In analogy with a construction from function theory, we herein define right, left, and two-sided Bourgain algebras associated with an operator algebra A. These algebras are defined initially in Banach space terms, using the weak-* topology on A, and our main result is to give a completely algebraic characterization of them in the case where A is a nest algebra. Specifically, if A = alg N is a nest algebra, we show that each of the Bourgain algebras defined has the form A + K ∩ B, where B is the nest algebra corresponding to a certain subnest of N. We also characterize algebraically the second-

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HOWLETT, PHIL. "THE BEST WEIGHTED GRADIENT APPROXIMATION TO AN OBSERVED FUNCTION." Journal of the Australian Mathematical Society 98, no. 1 (2014): 54–68. http://dx.doi.org/10.1017/s1446788713000621.

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AbstractWe find the potential function whose gradient best approximates an observed square integrable function on a bounded open set subject to prescribed weight factors. With an appropriate choice of topology, we show that the gradient operator is a bounded linear operator and that the desired potential function is obtained by solving a second-order, self-adjoint, linear, elliptic partial differential equation. The main result makes a precise analogy with a standard procedure for the best approximate solution of a system of linear algebraic equations. The use of bounded operators means that t

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Jose, Sharath, Anubhab Roy, Rahul Bale, and Rama Govindarajan. "Analytical solutions for algebraic growth of disturbances in a stably stratified shear flow." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2181 (2015): 20150267. http://dx.doi.org/10.1098/rspa.2015.0267.

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We investigate analytically the short-time response of disturbances in a density-varying Couette flow without viscous and diffusive effects. The complete inviscid problem is also solved as an initial value problem with a density perturbation. We show that the kinetic energy of the disturbances grows algebraically at early times, contrary to the well-known algebraic decay at time tending to infinity. This growth can persist for arbitrarily long times in response to sharp enough initial perturbations. The simplest in our three-stage study is a model problem forced by a buoyancy perturbation in t

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Du, Wei, Xiaohua Zhao, Huiming Hou, Jinping Fu, and Jianxin Su. "Analogy of scaling law for heterogeneous interfacial fracture to explain the Gutenberg–Richter formula for earthquakes." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 11 (2022): 113202. http://dx.doi.org/10.1088/1742-5468/ac99d3.

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Abstract We propose a new approach for the statistical law due to the fracture of a heterogeneous interface involving spatial correlation of disorders. The dynamic process of interfacial fracture is governed by three coupled integral equations, which further become a system of linear algebraic equations after discretizing the interface to a set of prismatic elements. By tuning parameters, this model covers the whole cases of interfacial fracture from local-load-sharing to almost equal-load-sharing, extending the classical fiber bundle models to a general form. Numerical simulations present tha

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Petoukhov, Sergey V. "Algebraic Gestalt-archetypes of Probabilities in Genomic DNAs, Cyclic Gray Codes, Quantum Bioinformatics." International Journal of Intelligent Systems and Applications 17, no. 1 (2025): 53–69. https://doi.org/10.5815/ijisa.2025.01.04.

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The article is devoted to the study of the regularities of the statistical organization of nucleotide sequences of single-stranded DNAs in genomes of higher and lower organisms, as well as their connections with cyclic Gray codes and the problem of holistic structures (gestalts) in physiology. The author presents stable statistical structures of an algebraic nature, which are found in many genomic DNAs and are called algebraic gestalt-archetypes of probabilities in genomic DNAs. They are discussed as a possible basis for several genetically inherited physiological and psychophysical properties

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Fring, Andreas, and Samuel Whittington. "Lorentzian Toda field theories." Reviews in Mathematical Physics 33, no. 06 (2021): 2150017. http://dx.doi.org/10.1142/s0129055x21500173.

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We propose several different types of construction principles for new classes of Toda field theories based on root systems defined on Lorentzian lattices. In analogy to conformal and affine Toda theories based on root systems of semi-simple Lie algebras, also their Lorentzian extensions come about in conformal and massive variants. We carry out the Painlevé integrability test for the proposed theories, finding in general only one integer valued resonance corresponding to the energy-momentum tensor. Thus most of the Lorentzian Toda field theories are not integrable, as the remaining resonances,

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Mansour, Toufik, and Mark Shattuck. "Pattern avoidance in inversion sequences." Pure Mathematics and Applications 25, no. 2 (2015): 157–76. http://dx.doi.org/10.1515/puma-2015-0016.

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Abstract A permutation of length n may be represented, equivalently, by a sequence a1a2 • • • an satisfying 0 < ai < i for all z, which is called an inversion sequence. In analogy to the usual case for permutations, the pattern avoidance question is addressed for inversion sequences. In particular, explicit formulas and/or generating functions are derived which count the inversion sequences of a given length that avoid a single pattern of length three. Among the sequences encountered are the Fibonacci numbers, the Schröder numbers, and entry A200753 in OEIS. We make use of both algebraic

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Schuster, Peter, and Daniel Wessel. "The Jacobson radical for an inconsistency predicate." Computability 11, no. 2 (2022): 147–62. http://dx.doi.org/10.3233/com-210365.

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As a form of the Axiom of Choice about relatively simple structures (posets), Hausdorff’s Maximal Chain Principle appears to be little amenable to computational interpretation. This received view, however, requires revision: maximal chains are more reminiscent of maximal ideals than it seems at first glance. The latter live in richer algebraic structures (rings), and thus are readier to be put under computational scrutiny. Exploiting this, and of course the analogy between maximal chains and maximal ideals, the concept of Jacobson radical carries over from a ring to an arbitrary set with an ab

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Tiefelsdorf, M., and B. Boots. "The Exact Distribution of Moran's I." Environment and Planning A: Economy and Space 27, no. 6 (1995): 985–99. http://dx.doi.org/10.1068/a270985.

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In analogy to the exact distribution of the Durbin—Watson d statistic for serial autocorrelation of regression residuals, the exact small sample distribution of Moran's I statistic (or alternatively Geary's c) can be derived. Use of algebraic results by Koerts and Abrahamse and theoretical results by Imhof, allows the authors to determine by numerical integration the exact distribution function of Moran's I for normally distributed variables. For the case in which the explanatory variables have been neglected, an upper and a lower bound can be given within which the exact distribution of Moran

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SAUSEDO-SOLORIO, JOSE M. "CONSERVATION FEATURES IN BINARY COLLISIONS FOR RULE 110 CELLULAR AUTOMATON." International Journal of Modern Physics C 21, no. 07 (2010): 931–42. http://dx.doi.org/10.1142/s0129183110015579.

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This paper investigates collisions of gliders generated by one-dimensional Rule 110 cellular automaton. A specific value associated with each glider and an algebraic equation that describes the collision between two gliders were found. Because the products of the collision between two gliders may result in no gliders or one, two or more gliders, this equation states that the total sum of the associated values corresponding to colliding gliders equals the sum of the values of the gliders which are products of the collision. Moreover, an analogy is proposed between the glider collisions and the

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Nakayama, A., and H. Koyama. "Numerical Prediction of Turbulent Flow and Heat Transfer Within Ducts of Cross-Shaped Cross Section." Journal of Heat Transfer 108, no. 4 (1986): 841–47. http://dx.doi.org/10.1115/1.3247021.

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Calculations were carried out for fully developed turbulent flows within ducts of cross-shaped cross section using the numerical method based on the pressure correction method developed by Patankar and Spalding. The Reynolds stress driven secondary flows were simulated successfully by Launder and Ying’s algebraic stress model coupled to the k–ε turbulence model. A parametric study was made on the friction and heat transfer characteristics in terms of the parameter α associated with the decrease in the cross-sectional area, namely, α = 0 for a square duct, and α → 1 for infinite parallel plates

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Stalder, Nicolas. "The semisimplicity conjecture for A-motives." Compositio Mathematica 146, no. 3 (2010): 561–98. http://dx.doi.org/10.1112/s0010437x09004448.

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AbstractWe prove the semisimplicity conjecture for A-motives over finitely generated fields K. This conjecture states that the rational Tate modules V𝔭(M) of a semisimple A-motive M are semisimple as representations of the absolute Galois group of K. This theorem is in analogy with known results for abelian varieties and Drinfeld modules, and has been sketched previously by Tamagawa. We deduce two consequences of the theorem for the algebraic monodromy groups G𝔭(M) associated to an A-motive M by Tannakian duality. The first requires no semisimplicity condition on M and states that G𝔭(M) may be

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Ying, Yu, and Mikhail D. Malykh. "On conjugate difference schemes: the midpoint scheme and the trapezoidal scheme." Discrete and Continuous Models and Applied Computational Science 29, no. 1 (2021): 63–72. http://dx.doi.org/10.22363/2658-4670-2021-29-1-63-72.

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The preservation of quadratic integrals on approximate solutions of autonomous systems of ordinary differential equations x=f(x), found by the trapezoidal scheme, is investigated. For this purpose, a relation has been established between the trapezoidal scheme and the midpoint scheme, which preserves all quadratic integrals of motion by virtue of Coopers theorem. This relation allows considering the trapezoidal scheme as dual to the midpoint scheme and to find a dual analogue for Coopers theorem by analogy with the duality principle in projective geometry. It is proved that on the approximate

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