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Journal articles on the topic 'Rule commutation'

Author: Grafiati

Published: 14 December 2024

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1

Evans, D. Gwion, John E. Gough, and Matthew R. James. "Non-abelian Weyl commutation relations and the series product of quantum stochastic evolutions." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1979 (2012): 5437–51. http://dx.doi.org/10.1098/rsta.2011.0525.

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We show that the series product, which serves as an algebraic rule for connecting state-based input–output systems, is intimately related to the Heisenberg group and the canonical commutation relations. The series product for quantum stochastic models then corresponds to a non-abelian generalization of the Weyl commutation relation. We show that the series product gives the general rule for combining the generators of quantum stochastic evolutions using a Lie–Trotter product formula.

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2

Bulathsinghala, D. L., and K. A. I. L. Wijewardena Gamalath. "Implementation of a Quantized Line Element in Klein-Gordon and Dirac Fields." International Letters of Chemistry, Physics and Astronomy 48 (March 2015): 68–86. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.48.68.

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In this paper an ansatz that the anti-commutation rules hold only as integrated average over time intervals and not at every instant giving rise to a time-discrete form of Klein-Gordon equation is examined. This coarse-grained validation of the anti-commutation rules enables us to show that the relativistic energy-momentum relation holds only over discrete time intervals, fitting well with the time-energy uncertainty relation. When this time-discrete scheme is applied to four vector notations in relativity, the line-element can be quantized and thereby how the physical attributes associated with time, space and matter can be quantized is sketched. This potentially enables us to discuss the Zeno’s arrow paradox within the classical limit. As the solutions of the Dirac equation can be used to construct solutions to the Klein-Gordon equation, this temporal quantization rule is applied to the Dirac equation and the solutions associated with the Dirac equation under such conditions are interpreted. Finally, the general relativistic effects are introduced to a line-element associated with a particle in relativistic motion and a time quantized line-element associated with gravity is obtained.

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3

Bulathsinghala, D. L., and K. A. I. L. Wijewardena Gamalath. "Implementation of a Quantized Line Element in Klein-Gordon and Dirac Fields." International Letters of Chemistry, Physics and Astronomy 48 (March 25, 2015): 68–86. http://dx.doi.org/10.56431/p-36k0sm.

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In this paper an ansatz that the anti-commutation rules hold only as integrated average over time intervals and not at every instant giving rise to a time-discrete form of Klein-Gordon equation is examined. This coarse-grained validation of the anti-commutation rules enables us to show that the relativistic energy-momentum relation holds only over discrete time intervals, fitting well with the time-energy uncertainty relation. When this time-discrete scheme is applied to four vector notations in relativity, the line-element can be quantized and thereby how the physical attributes associated with time, space and matter can be quantized is sketched. This potentially enables us to discuss the Zeno’s arrow paradox within the classical limit. As the solutions of the Dirac equation can be used to construct solutions to the Klein-Gordon equation, this temporal quantization rule is applied to the Dirac equation and the solutions associated with the Dirac equation under such conditions are interpreted. Finally, the general relativistic effects are introduced to a line-element associated with a particle in relativistic motion and a time quantized line-element associated with gravity is obtained.

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4

Narendran, Paliath, and Friedrich Otto. "Preperfectness is undecidable for thue systems containing only length-reducing rules and a single commutation rule." Information Processing Letters 29, no. 3 (1988): 125–30. http://dx.doi.org/10.1016/0020-0190(88)90049-x.

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5

Chin, Hee-Kwon. "The Study of the Commutation Principles (of General rule) in T’ang Code." Journal of Social Thoughts and Culture 21, no. 4 (2018): 143–71. http://dx.doi.org/10.17207/jstc.2018.12.21.4.5.

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6

Savasta, Salvatore, Omar Di Stefano, and Franco Nori. "Thomas–Reiche–Kuhn (TRK) sum rule for interacting photons." Nanophotonics 10, no. 1 (2020): 465–76. http://dx.doi.org/10.1515/nanoph-2020-0433.

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AbstractThe Thomas–Reiche–Kuhn (TRK) sum rule is a fundamental consequence of the position–momentum commutation relation for an atomic electron, and it provides an important constraint on the transition matrix elements for an atom. Here, we propose a TRK sum rule for electromagnetic fields which is valid even in the presence of very strong light–matter interactions and/or optical nonlinearities. While the standard TRK sum rule involves dipole matrix moments calculated between atomic energy levels (in the absence of interaction with the field), the sum rule here proposed involves expectation values of field operators calculated between general eigenstates of the interacting light–matter system. This sum rule provides constraints and guidance for the analysis of strongly interacting light–matter systems and can be used to test the validity of approximate effective Hamiltonians often used in quantum optics.

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7

Skála, Lubomír, and Vojtěch Kapsa. "Quantum Mechanics Needs No Interpretation." Collection of Czechoslovak Chemical Communications 70, no. 5 (2005): 621–37. http://dx.doi.org/10.1135/cccc20050621.

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Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule, probability density current, commutation and uncertainty relations, momentum operator, rules for including scalar and vector potentials and antiparticles can be derived from the definition of the mean values of powers of space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, Schrödinger equation and Dirac equation are obtained from the requirement of the relativistic invariance of the theory. The limit case of localized probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Many-particle systems are also discussed.

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8

Chin, Hee-Kwon. "The Study of the Commutation Principles (of General rule) in T��ang Code." Journal of Social Thoughts and Culture 21, no. 04 (2018): 143–71. http://dx.doi.org/10.17207/jstc.2018.12.21.4.143.

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9

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” limit with a novel rich operator structure. The existing algebraic structure suggests a possible connection with a lattice neutral plasma of charges, via the fermion-boson correspondence.

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10

Derzhko, O. V., and A. Ph. Moina. "Bose commutation rule approximation in the theory of spin systems and elementary excitation spectrum." physica status solidi (b) 196, no. 1 (1996): 237–41. http://dx.doi.org/10.1002/pssb.2221960123.

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11

JAYARAMAN, J., and R. DE LIMA RODRIGUES. "SUSY BREAKING IN CELKA-HUSSIN'S GENERAL 3D MODEL OSCILLATOR HAMILTONIAN AND THE WIGNER PARAMETER." Modern Physics Letters A 09, no. 12 (1994): 1047–58. http://dx.doi.org/10.1142/s0217732394000873.

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The free parameter of the generalized 3D SUSY model oscillator Hamiltonian of Celka and Hussin is identified here with the Wigner parameter of a related super-realized general 3D Wigner oscillator system satisfying a super-generalized quantum commutation rule. The super-oscillator technique is then advantageously employed to determine fully a previously only partially given spectrum by Celka and Hussin for their Hamiltonian. The dependence of the spectrum on the Wigner parameter and the consequent occurrence of exceptional SUSY breakings in the model are clearly brought out.

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12

KONNO, HITOSHI. "FUSION CONSTRUCTION OF THE VERTEX OPERATORS IN HIGHER LEVEL REPRESENTATION OF THE ELLIPTIC QUANTUM GROUP." International Journal of Modern Physics B 16, no. 14n15 (2002): 1995–2001. http://dx.doi.org/10.1142/s021797920201172x.

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After a short summary on the elliptic quantum group [Formula: see text] and the elliptic algebra [Formula: see text], we present a free field representation of the Drinfeld currents and the vertex operators (VO's) in the level k. We especially demonstrate a construction of the higher spin type I VO's by fusing the spin 1/2 type I VO's and fix a rule of attaching the screening current S(z) associated with the q-deformed ℤk-parafermion theory. As a result we get a free field representation of the higher spin type I VO's which commutation relation by the fused Boltzmann weight coefficients is manifest.

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13

Kauffmann, Steven Kenneth. "Unambiguous Quantization from the Maximum Classical Correspondence that Is Self-consistent: The Slightly Stronger Canonical Commutation Rule Dirac Missed." Foundations of Physics 41, no. 5 (2010): 805–19. http://dx.doi.org/10.1007/s10701-010-9523-2.

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14

Mukhtar, Hamid, Kashif Mahmood Saqib, and Zia-ud-Din Malik. "Chinese Innovative Practices for Transparency in Judicial System." International Research Journal of Education and Innovation 2, no. 3 (2021): 290–96. http://dx.doi.org/10.53575/irjei.v2.03(21)26.290-296.

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Transparency and openness are necessary things in order to develop a fair judicial system that can protect people’s rights and uphold rule of law in the society. Over the past forty years, China has been undertaking massive reforms in judicial sector for turning it into an open, transparent and fair system. Various online mechanisms have been developed with the deployment of information technology into the judicial system, which have effectively turned the Chinese Judicial system into transparent one. Significant improvements have been made by Chinese People’s Courts for making convenience in the cases management system, development of a system of public hearings, disclosure of information related to parole and Commutation, and development of a public information system online containing documents related to cases i.e. hearing notices, orders, judgements and other necessary information. This research paper focuses on the innovative mechanisms developed by the Chinese Government and People’s Courts to showcase those steps as learning experiences for other jurisdiction.

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15

Chashchina, Olga I., Abhijit Sen, and Zurab K. Silagadze. "On deformations of classical mechanics due to Planck-scale physics." International Journal of Modern Physics D 29, no. 10 (2020): 2050070. http://dx.doi.org/10.1142/s0218271820500704.

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Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification may imply a modification of the canonical commutation relations and hence quantum mechanics at the Planck scale. The corresponding modification of classical mechanics is usually considered by replacing modified quantum commutators by Poisson brackets suitably modified in such a way that they retain their main properties (antisymmetry, linearity, Leibniz rule and Jacobi identity). We indicate that there exists an alternative interesting possibility. Koopman–von Neumann’s Hilbert space formulation of classical mechanics allows, as Sudarshan remarked, to consider the classical mechanics as a hidden variable quantum system. Then, the Planck scale modification of this quantum system naturally induces the corresponding modification of dynamics in the classical substrate. Interestingly, it seems this induced modification in fact destroys the classicality: classical position and momentum operators cease to be commuting and hidden variables do appear in their evolution equations.

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16

Vuong, Thanh H. "Théorie des contextes et relations internationales : Départ de la première guerre d’Indochine." Études internationales 17, no. 3 (2005): 571–97. http://dx.doi.org/10.7202/702047ar.

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Bateson's "Eurêka" has been his application of Russell and Whitehead's theory of types to the social sciences. They had postulated a discontinuity between the levels of the members of a class and a class of classes and so on. Hence a class may not be a member of itself. The cat scratches and the word "cat" does not bite. Confusion between levels, or the signifier and the signified, or the map and the territory, or the menu and the meal, is a sign of disorder. Having been introduced to Bateson's ecology, Anthony Wilden has formulated a theory of contexts, already present in "System and Structure". In order to avoid simplicity through the flattening of social and organic levels into inorganic levels of matter-energy, the theory of contexts suggest the organisation of constraints, complexites, or levels of reality into levels of logical types, using the rule of extinction. It goes on to suggest the use of the rule of commutation to eliminate spurious similarities and inappropriate symmetries which lead to oppositions and Imaginary "contradictions". It is suggested to use Korzybski and Hayakawa's rule of communication in order to get over conflicts due to misperception. To illustrate all of this, we propose to dismanthe the processes which have led to the misunderstanding behind the first Indochinese war of 1946-1954. From one misunderstanding to another, the VPA (Vietnam People's Army), in the 1980's, mobilised at the Kmer-Siamese border, at the door of Thailand who since 1939 has claimed to be the land of the Thais and heir to the Champa empire which was established in 192 and, soon after 1471, was dissolved by the "gnawing" of the Vietnamese peasants in their "long march" towards the South. The most revolting of working, conjugal and international disputes is that which emerge from misperceptions where each party is convinced of its own good will and of the foul bad will of the other. A mutual consent regarding the context, that of metacommunication, may lead to a common signification (consensus) of beings, events and objects.

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17

HAQUE, ASRARUL, and T. R. GOVINDARAJAN. "TWISTED BOSONIZATION IN TWO-DIMENSIONAL NONCOMMUTATIVE SPACETIME." Modern Physics Letters A 27, no. 25 (2012): 1250149. http://dx.doi.org/10.1142/s0217732312501490.

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We study the twisted bosonization of massive Thirring model to relate to sine-Gordon model in Moyal spacetime using twisted commutation relations. We obtain the relevant twisted bosonization rules. We show that there exists dual relationship between twisted bosonic and fermionic operators. The strong–weak duality is also observed to be preserved as its commutative counterpart.

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18

KANOVICH, MAX, STEPAN KUZNETSOV, VIVEK NIGAM, and ANDRE SCEDROV. "Subexponentials in non-commutative linear logic." Mathematical Structures in Computer Science 29, no. 8 (2018): 1217–49. http://dx.doi.org/10.1017/s0960129518000117.

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Linear logical frameworks with subexponentials have been used for the specification of, among other systems, proof systems, concurrent programming languages and linear authorisation logics. In these frameworks, subexponentials can be configured to allow or not for the application of the contraction and weakening rules while the exchange rule can always be applied. This means that formulae in such frameworks can only be organised as sets and multisets of formulae not being possible to organise formulae as lists of formulae. This paper investigates the proof theory of linear logic proof systems in the non-commutative variant. These systems can disallow the application of exchange rule on some subexponentials. We investigate conditions for when cut elimination is admissible in the presence of non-commutative subexponentials, investigating the interaction of the exchange rule with the local and non-local contraction rules. We also obtain some new undecidability and decidability results on non-commutative linear logic with subexponentials.

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19

Abrusci, V. Michele. "Phase semantics and sequent calculus for pure noncommutative classical linear propositional logic." Journal of Symbolic Logic 56, no. 4 (1991): 1403–51. http://dx.doi.org/10.2307/2275485.

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The linear logic introduced in [3] by J.-Y. Girard keeps one of the so-called structural rules of the sequent calculus: the exchange rule. In a one-sided sequent calculus this rule can be formulated asThe exchange rule allows one to disregard the order of the assumptions and the order of the conclusions of a proof, and this means, when the proof corresponds to a logically correct program, to disregard the order in which the inputs and the outputs occur in a program.In the linear logic introduced in [3], the exchange rule allows one to prove the commutativity of the multiplicative connectives, conjunction (⊗) and disjunction (⅋). Due to the presence of the exchange rule in linear logic, in the phase semantics for linear logic one starts with a commutative monoid. So, the usual linear logic may be called commutative linear logic.The aim of the investigations underlying this paper was to see, first, what happens when we remove the exchange rule from the sequent calculus for the linear propositional logic at all, and then, how to recover the strength of the exchange rule by means of exponential connectives (in the same way as by means of the exponential connectives ! and ? we recover the strength of the weakening and contraction rules).

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20

CASTELLANI, LEONARDO. "Uq(N) GAUGE THEORIES." Modern Physics Letters A 09, no. 30 (1994): 2835–47. http://dx.doi.org/10.1142/s0217732394002689.

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Improving on an earlier proposal, we construct the gauge theories of the quantum groups U q(N). We find that these theories are also consistent with an ordinary (commuting) space-time. The bicovariance conditions of the quantum differential calculus are essential in our construction. The gauge potentials and the field strengths are q-commuting "fields," and satisfy q-commutation relations with the gauge parameters. The transformation rules of the potentials generalize the ordinary infinitesimal gauge variations. For particular deformations of U (N) ("minimal deformations"), the algebra of quantum gauge variations is shown to close, provided the gauge parameters satisfy appropriate q-commutations. The q-Lagrangian invariant under the U q(N) variations has the Yang–Mills form [Formula: see text], the "quantum metric" gij being a generalization of the Killing metric.

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21

Alpert, Sofiia. "Analysis of “mixing” combination rules and Smet’s combination rule." Ukrainian journal of remote sensing, no. 23 (December 28, 2019): 4–8. http://dx.doi.org/10.36023/ujrs.2019.23.158.

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The process of solution of different practical and ecological problems, using hyperspectral satellite images usually includes a procedure of classification. Classification is one of the most difficult and important procedures. Some image classification methods were considered and analyzed in this work. These methods are based on the theory of evidence. Evidence theory can simulate uncertainty and process imprecise and incomplete information. It were considered such combination rules in this paper: “mixing” combination rule (or averaging), convolutive x-averaging (or c-averaging) and Smet’s combination rule. It was shown, that these methods can process the data from multiple sources or spectral bands, that provide different assessments for the same hypotheses. It was noted, that the purpose of aggregation of information is to simplify data, whether the data is coming from multiple sources or different spectral bands. It was shown, that Smet’s rule is unnormalized version of Dempster rule, that applied in Smet’s Transferable Belief Model. It also processes imprecise and incomplete data. Smet’s combination rule entails a slightly different formulation of Dempster-Shafer theory. Mixing (or averaging) rule was considered in this paper too. It is the averaging operation that is used for probability distributions. This rule uses basic probability assignments from different sources (spectral bands) and weighs assigned according to the reliability of the sources. Convolutive x-averaging (or c-averaging) rule was considered in this paper too. This combination rule is a generalization of the average for scalar numbers. This rule is commutative and not associative. It also was noted, that convolutive x-averaging (c-averaging) rule can include any number of basic probability assignments. It were also considered examples, where these proposed combination rules were used. Mixing, convolutive x-averaging (c-averaging) rule and Smet’s combination rule can be applied for analysis of hyperspectral satellite images, in remote searching for minerals and oil, solving different environmental and thematic problems.

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22

Liu, Zhengjun, Muhammad Ashfaq Ahmad, and Shutian Liu. "Image encryption scheme based on the commutation and anti-commutation rules." Optics Communications 279, no. 2 (2007): 285–90. http://dx.doi.org/10.1016/j.optcom.2007.07.045.

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23

Sajfert, Vjekoslav, Petar Mali, Nikola Bednar, Nicolina Pop, Dušan Popov, and Bratislav Tošić. "Use of Displacement-Momentum Commutation Rules." Quantum Matter 1, no. 2 (2012): 134–35. http://dx.doi.org/10.1166/qm.2012.1011.

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24

Blasiak, Jonah, and Sergey Fomin. "Rules of Three for commutation relations." Journal of Algebra 500 (April 2018): 193–220. http://dx.doi.org/10.1016/j.jalgebra.2016.12.023.

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25

Hubert, Evelyne. "Differential algebra for derivations with nontrivial commutation rules." Journal of Pure and Applied Algebra 200, no. 1-2 (2005): 163–90. http://dx.doi.org/10.1016/j.jpaa.2004.12.034.

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26

Ding, Haigang, and Chen Wang. "Accurate Modeling, Operation Laws and Commutation Timing Matching for Concrete Pumping Systems." Applied Sciences 13, no. 15 (2023): 8821. http://dx.doi.org/10.3390/app13158821.

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The pump system is the heart of the concrete pump truck, and its main function is to deliver high-pressure concrete into the pipeline through the reciprocating motion and cooperation of the main cylinder and the distribution valve driven by the swing cylinder. However, there are currently problems, such as unclear pumping operation rules and mismatched commutation timing, that result in poor pumping efficiency and short life of wear parts such as spectacle plates and cutting rings. To address above problems, based on AMEsim software and system test data, this thesis establishes an accurate simulation model of the pump system with more than 90% precision. Based on this model, the simulation reveals the operating rules of the main cylinder and the swing cylinder during the pumping process; draws the commutation timing diagram of the pumping system; clarifies that the commutation timing has four characteristics: sequential, hysteresis, coupling and cyclic; and proposes an optimization scheme for the commutation timing, i.e., reducing the relief pressure of the main cylinder and shortening the swing time of the distribution valve. The proposed optimization has been proven in the market and significantly improved the life of wearing parts by more than 90%. This study provides technical reference for the structure and parameter optimization of concrete pumping systems.

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27

Hayata, Tomoya. "New QCD sum rules based on canonical commutation relations." Progress in Particle and Nuclear Physics 67, no. 2 (2012): 136–39. http://dx.doi.org/10.1016/j.ppnp.2011.12.007.

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28

Bacchelli, Silvia, Luca Ferrari, Renzo Pinzani, and Renzo Sprugnoli. "Mixed succession rules: The commutative case." Journal of Combinatorial Theory, Series A 117, no. 5 (2010): 568–82. http://dx.doi.org/10.1016/j.jcta.2009.11.005.

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29

Piazza, Mario. "Exchange rules." Journal of Symbolic Logic 66, no. 2 (2001): 509–16. http://dx.doi.org/10.2307/2695028.

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AbstractIn this paper, we show by a proof-theoretical argument that in a logic without structural rules, that is in noncommutative linear logic with exponentials, every formula A for which exchange rules (and weakening and contraction as well) are admissible is provably equivalent to? A. This property shows that the expressive power of “noncommutative exponentials” is much more important than that of “commutative exponentials”.

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30

Muniain, Javier P., and José Wudka. "Anomalous commutator corrections to sum rules." Physical Review D 52, no. 9 (1995): 5194–201. http://dx.doi.org/10.1103/physrevd.52.5194.

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31

Muniain, Javier P., and José Wudka. "Anomalous commutator corrections to sum rules." Physical Review D 53, no. 7 (1996): 4112–13. http://dx.doi.org/10.1103/physrevd.53.4112.2.

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32

Wildberger, N. J. "Duality and Entropy for Finite Commutative Hypergroups and Fusion Rule Algebras." Journal of the London Mathematical Society 56, no. 2 (1997): 275–91. http://dx.doi.org/10.1112/s0024610797005401.

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33

Kulabukhov, Vladimir S. "A General Principle of Isomorphism: Determining Inverses." Symmetry 11, no. 10 (2019): 1301. http://dx.doi.org/10.3390/sym11101301.

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The problem of determining inverses for maps in commutative diagrams arising in various problems of a new paradigm in algebraic system theory based on a single principle—the general principle of isomorphism is considered. Based on the previously formulated and proven theorem of realization, the rules for determining the inverses for typical cases of specifying commutative diagrams are derived. Simple examples of calculating the matrix maps inverses, which illustrate both the derived rules and the principle of relativity in algebra based on the theorem of realization, are given. The examples also illustrate the emergence of new properties (emergence) in maps in commutative diagrams modeling (realizing) the corresponding systems.

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34

Chajda, I., and J. Krňávek. "MP-CLOSED SUBSETS IN BASIC ALGEBRAS." Asian-European Journal of Mathematics 05, no. 04 (2012): 1250048. http://dx.doi.org/10.1142/s1793557112500489.

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A subset M of a given basic algebra [Formula: see text] is MP-closed if a ∈ M and a → b ∈ M always imply b ∈ M for b ≤ a. We get a characterization of MP-closed subsets for commutative basic algebras in terms of closedness in the derived operation ⊙. If, moreover, the basic algebra is a chain, then a particular simple condition is derived. For basic algebras which are not commutative we derive only a closedness with respect to the deduction rule Modus Tollens.

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35

Mandanici, Gianluca. "On the invariance of the relative rest in doubly special relativity." International Journal of Modern Physics D 24, no. 02 (2015): 1550012. http://dx.doi.org/10.1142/s0218271815500121.

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In the framework of the most-studied doubly special relativity models the use of the naive formula v = dE/dp has been argued to lead to inconsistencies connected to different rules of transformation, under boosts, of particles with the same energy but with different masses. In this paper, we show that, at least in 1 + 1 dimensions, doubly special relativity can be formulated in such a way that the formula v = dE/dp is fully consistent with the invariance of the relative rest, easily fitting to the relativity principle. It is also argued that, always in 1 + 1 dimensions, is not necessary to renounce to the usual (commutative) Minkowski spacetime endowed with energy-independent boost transformations. The compatibility of the approach with superluminal propagation, with linear addition rule for energy, and possible extensions to 3 + 1 dimensions are also discussed.

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36

Wang, Ningkui, Fuyu Liu, and Daijun Wei. "A Modified Combination Rule for D Numbers Theory." Mathematical Problems in Engineering 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/3596517.

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D numbers theory is an appropriate method to deal with the information of uncertainty and incompleteness when making a reasonable decision. Previous D numbers theory provides a rule to combine multiple D numbers. However, the commutative law is not satisfied in the rule of combining multiple D numbers. In this paper, a modified method for multiple D numbers combination is proposed. The proposed method defines a new function for multiple D numbers combination which is mainly determined by the original value of D numbers. Then the proposed combination rule is applied to environmental impact assessment (EIA); our results show that the proposed method is efficient for multiple D numbers combination and it is useful when dealing with uncertainty and incompleteness.

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37

Minkowski, Peter. "Glue-mesons: Their conception needs all of QCD in the infrared: The trace anomaly and modification of canonical structure." Modern Physics Letters A 29, no. 27 (2014): 1430027. http://dx.doi.org/10.1142/s0217732314300274.

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The regularities implied at large distances by complete gauge invariance in QCD are shown to bear nontrivial consequences for the selection among inequivalent representations of canonical (anti-)commutation rules for gauge boson — and quark fields. The trace anomaly forces a modification of the gauge boson Lagrangian and by this of the entire associated canonical structure.

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38

GUGLIELMI, ALESSIO, and LUTZ STRAßBURGER. "A system of interaction and structure V: the exponentials and splitting." Mathematical Structures in Computer Science 21, no. 3 (2011): 563–84. http://dx.doi.org/10.1017/s096012951100003x.

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System NEL is the mixed commutative/non-commutative linear logic BV augmented with linear logic's exponentials, or, equivalently, it is MELL augmented with the non-commutative self-dual connective seq. NEL is presented in deep inference, because no Gentzen formalism can express it in such a way that the cut rule is admissible. Other recent work shows that system NEL is Turing-complete, and is able to express process algebra sequential composition directly and model causal quantum evolution faithfully. In this paper, we show cut elimination for NEL, based on a technique that we call splitting. The splitting theorem shows how and to what extent we can recover a sequent-like structure in NEL proofs. When combined with a ‘decomposition’ theorem, proved in the previous paper of this series, splitting yields a cut-elimination procedure for NEL.

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39

García Alvarez, Edgardo T., and Alejandro D. González. "Some general commutation rules and identities for three‐dimensional quantum‐mechanical operators." American Journal of Physics 57, no. 10 (1989): 923–25. http://dx.doi.org/10.1119/1.15848.

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García-Lapresta, José Luis, Bonifacio Llamazares, and Miguel Martínez-Panero. "A Social Choice Analysis of the Borda Rule in a General Linguistic Framework." International Journal of Computational Intelligence Systems 3, no. 4 (2010): 501–13. http://dx.doi.org/10.2991/ijcis.2010.3.4.10.

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AbstractIn this paper the Borda rule is extended by allowing the voters to show their preferences among alternatives through linguistic labels. To this aim, we need to add them up for assigning a qualification to each alternative and then to compare such qualifications. Theoretically, all these assessments and comparisons fall into a totally ordered commutative monoid generated by the initial set of linguistic labels. Practically, we show an example which illustrates the suitability of this linguistic approach. Finally, some interesting properties for this Borda rule are proven in the Social Choice context.

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Romero, Juan M., and J. David Vergara. "The Kepler Problem and Noncommutativity." Modern Physics Letters A 18, no. 24 (2003): 1673–80. http://dx.doi.org/10.1142/s0217732303011472.

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We investigate the Kepler problem using a symplectic structure consistent with the commutation rules of the noncommutative quantum mechanics. We show that a noncommutative parameter of the order of 10-58 m 2 gives observable corrections to the movement of the solar system. In this way, modifications in the physics of smaller scales imply modifications at large scales, something similar to the uv/ir mixing.

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Haller, Kurt. "Consistency questions in the light cone gauge based on equal time commutation rules." Physics Letters B 220, no. 3 (1989): 446–52. http://dx.doi.org/10.1016/0370-2693(89)90901-5.

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Van Enk, S. J., and G. Nienhuis. "Commutation Rules and Eigenvalues of Spin and Orbital Angular Momentum of Radiation Fields." Journal of Modern Optics 41, no. 5 (1994): 963–77. http://dx.doi.org/10.1080/09500349414550911.

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Liao, Y., and K. Sibold. "Time-ordered perturbation theory on non-commutative spacetime: Basic rules." European Physical Journal C 25, no. 3 (2002): 469–77. http://dx.doi.org/10.1007/s10052-002-1017-8.

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Sugi, Masao, Hidetoshi Nagai, Masashi Yamamoto, Yusuke Shiomi, and Jun Ota. "Rescheduling of Train Shunting in Railway Stations." International Journal of Automation Technology 4, no. 6 (2010): 495–501. http://dx.doi.org/10.20965/ijat.2010.p0495.

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This paper is intended to propose rescheduling rules for train shunting in railway stations in the event of delayed arrival of trains or some problems with resources, such as tracks. In particular, we propose an algorithm using the Affected Operation Rescheduling (AOR) approach in combination with appropriatelytimed operational commutation rules to allow for rapid rescheduling operations. In the problem of the magnitude of six resources (i.e. tracks and lines) and four trains, the proposed algorithm has accomplished in about 1 millisecond train-rescheduling operations in the event of a train problemon a certain track, proving the feasibility of the obtained solutions as well as the effectiveness of the proposed algorithm.

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Lennox Trivedi, Samamba. "Commutative and Retributive Justice in the Administration of Disgorgement in Insider Trading Cases—the Case for the Common Law Approach to Damages." Sumerianz Journal of Social Science, no. 74 (October 3, 2024): 84–100. http://dx.doi.org/10.47752/sjss.74.84.100.

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Using Zambia as a case study, this article examines the efficacy of the Zambian regulatory and institutional framework for public distribution of securities in ensuring commutative justice in the administration of disgorgement by the Securities and Exchange Commission. Using the doctrinal and non-doctrinal approaches to examining the effectiveness of regulatory rules and institutions, the main findings of the study are: When it is applied to non-corporate insider traders, the statutory formula for disgorgement which is provided in the Zambian Securities Act 2016 tends to under-regulate by leaving some of the insider trading gains with the insider trader—a commutative injustice to the public; When it is applied to juristic persons (companies and other styles of bodies corporate), the formula for disgorgement which is provided in the Zambian Securities Act 2016 tends to over-regulate by taking away from the insider trader more than they actually gained from insider trading—a retributive and commutative injustice to the insider trader. The central argument of this article is that regulatory rules and institutions which promote retributive and commutative justice are likely to inspire social willingness to pay the cost of socioeconomic exchanges and regulation, and as such, are efficient. As a possible way of promoting commutative and retributive justice in the administration of disgorgement in insider trading cases, the article makes a case for the application of ‘the common law approach to the award of damages’ in the determination of the amount which is to be disgorged. The article also makes proposals for the repeal of the statutory formula, and its replacement with the standard formula for disgorgement which has been proposed.

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MELJANAC, S., D. MELJANAC, A. SAMSAROV та M. STOJIĆ. "κ-DEFORMED SNYDER SPACETIME". Modern Physics Letters A 25, № 08 (2010): 579–90. http://dx.doi.org/10.1142/s0217732310032652.

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We present Lie-algebraic deformations of Minkowski space with undeformed Poincaré algebra. These deformations interpolate between Snyder and κ-Minkowski space. We find realizations of noncommutative coordinates in terms of commutative coordinates and derivatives. Deformed Leibniz rule, the coproduct structure and star product are found. Special cases, particularly Snyder and κ-Minkowski in Maggiore-type realizations are discussed. Our construction leads to a new class of deformed special relativity theories.

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Woumfo, Francis, Blaise B. Koguep Njionou, Etienne R. Temgoua Alomo, and Celestin Lele. "Ideals and Bosbach States on Residuated Lattices." New Mathematics and Natural Computation 17, no. 02 (2021): 281–302. http://dx.doi.org/10.1142/s1793005721500150.

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In random experiments, the fact that the sets of events has a structure of a Boolean algebra, i.e. it follows the rules of classical logic, is the main hypothesis of classical probability theory. Bosbach states have been introduced on commutative and non-commutative algebras of fuzzy logics as a way of probabilistically evaluating the formulas. In this paper, we focus on the relationship between some properties of ideals and Bosbach states in the framework of commutative residuated lattices. In particular, we introduce the concept of co-kernel of a Bosbach state which is an ideal and we establish the relationship between the notion of co-kernel and the kernel. Moreover, we define and characterize maximal ideals and maximal MV-ideals in residuated lattices.

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Woumfo, Francis, Blaise B. Koguep Njionou, Etienne R. Temgoua Alomo, and Celestin Lele. "Ideals and Bosbach States on Residuated Lattices." New Mathematics and Natural Computation 16, no. 03 (2020): 551–71. http://dx.doi.org/10.1142/s1793005720500337.

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In random experiments, the fact that the sets of events has a structure of a Boolean algebra, i.e. it follows the rules of classical logic, is the main hypothesis of classical probability theory. Bosbach states have been introduced on commutative and non-commutative algebras of fuzzy logics as a way of probabilistically evaluating the formulas. In this paper, we focus on the relationship between some properties of ideals and Bosbach states in the framework of commutative residuated lattices. In particular, we introduce the concept of co-kernel of a Bosbach state which is an ideal and we establish the relationship between the notion of co-kernel and the kernel. Moreover, we define and characterize maximal ideals and maximal MV-ideals in residuated lattices.

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CIABATTONI, AGATA, and ALEXANDER LEITSCH. "Towards an algorithmic construction of cut-elimination procedures." Mathematical Structures in Computer Science 18, no. 1 (2008): 81–105. http://dx.doi.org/10.1017/s0960129507006573.

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We investigate cut elimination in propositional substructural logics. The problem is to decide whether a given calculus admits (reductive) cut elimination. We show that for commutative single-conclusion sequent calculi containing generalised knotted structural rules and arbitrary logical rules the problem can be decided by resolution-based methods. A general cut-elimination proof for these calculi is also provided.

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