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Journal articles on the topic 'Comparison Algebra'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

Fang, Xiaochun, Nung-Sing Sze, and Xiao-Ming Xu. "The Cuntz Comparison in the StandardC*-Algebra." Abstract and Applied Analysis 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/623520.

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The Cuntz comparison, introduced by Cuntz in early 1978, associates eachC*-algebra with an abelian semigroup which is an invariant for the classification of the nuclearC*-algebras and called the Cuntz semigroup. In this paper, we study the Cuntz comparison in the standardC*-algebra. We characterize the Cuntz comparison in terms of the dimension of the operator range. Also, we consider the structure of the semilinear map which preserves the Cuntz comparison.

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2

Gerima Tefera, Dejen. "Hilbert Implication Algebra and Some Properties." Journal of Applied Mathematics 2021 (July 20, 2021): 1–5. http://dx.doi.org/10.1155/2021/3635185.

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The concepts of Hilbert implication algebra and generalized Hilbert implication algebra are introduced. The comparison theorem of Hilbert implication algebra and generalized Hilbert implication algebra is proved. In addition, the idea of groupoid and commutative Hilbert implication algebras is investigated. Ideals and filters in Hilbert implication algebras are also discussed. In general, different theorems which show different properties are proved.

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3

Star, Jon R., Courtney Pollack, Kelley Durkin, et al. "Learning from comparison in algebra." Contemporary Educational Psychology 40 (January 2015): 41–54. http://dx.doi.org/10.1016/j.cedpsych.2014.05.005.

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4

Dziobiak, Wieslaw. "The subvariety lattice of the variety of distributive double p-algebras." Bulletin of the Australian Mathematical Society 31, no. 3 (1985): 377–87. http://dx.doi.org/10.1017/s0004972700009345.

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Let L denote the subvariety lattice of the variety of distributive double p-algebras, that is, the lattice whose universe consists of all varieties of distributive double p-algebras and whose ordering is the inclusion relation. We prove in this paper that each proper filter in L is uncountable. Moreover, we prove that except for the trivial variety (the zero in L) and the variety of Boolean algebras (the unique atom in L) every other element of L, generated by a finite algebra, has infinitely many covers in L, among which at least one is not generated by any finite algebra. The former result s

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5

Toën, Bertrand, and Gabriele Vezzosi. "Algèbres simplicialesS1-équivariantes, théorie de de Rham et théorèmes HKR multiplicatifs." Compositio Mathematica 147, no. 6 (2011): 1979–2000. http://dx.doi.org/10.1112/s0010437x11005501.

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AbstractThis work establishes a comparison between functions on derived loop spaces (Toën and Vezzosi,Chern character, loop spaces and derived algebraic geometry, inAlgebraic topology: the Abel symposium 2007, Abel Symposia, vol. 4, eds N. Baas, E. M. Friedlander, B. Jahren and P. A. Østvær (Springer, 2009), ISBN:978-3-642-01199-3) and de Rham theory. IfAis a smooth commutativek-algebra andkhas characteristic 0, we show that two objects,S1⊗Aand ϵ(A), determine one another, functorially inA. The objectS1⊗Ais theS1-equivariant simplicialk-algebra obtained by tensoringAby the simplicial groupS1:=

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6

Elsner, L., and P. van den Driessche. "Max-algebra and pairwise comparison matrices." Linear Algebra and its Applications 385 (July 2004): 47–62. http://dx.doi.org/10.1016/s0024-3795(03)00476-2.

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7

Bosa, Joan, and Henning Petzka. "Comparison Properties of the Cuntz Semigroup and Applications to C* -algebras." Canadian Journal of Mathematics 70, no. 1 (2018): 26–52. http://dx.doi.org/10.4153/cjm-2016-049-8.

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AbstractWe study comparison properties in the category Cu aiming to lift results to the C* -algebraic setting. We introduce a new comparison property and relate it to both the corona factorization property (CFP) and ω-comparison. We show differences of all properties by providing examples that suggest that the corona factorization for C* -algebras might allow for both finite and infinite projections. In addition, we show that Rørdam's simple, nuclear C* -algebra with a finite and an inifnite projection does not have the CFP.

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8

Jaíyéọlá, Tèmítọ́pẹ́, Emmanuel Ilojide, Memudu Olatinwo, and Florentin Smarandache. "On the Classification of Bol-Moufang Type of Some Varieties of Quasi Neutrosophic Triplet Loop (Fenyves BCI-Algebras)." Symmetry 10, no. 10 (2018): 427. http://dx.doi.org/10.3390/sym10100427.

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In this paper, Bol-Moufang types of a particular quasi neutrosophic triplet loop (BCI-algebra), chritened Fenyves BCI-algebras are introduced and studied. 60 Fenyves BCI-algebras are introduced and classified. Amongst these 60 classes of algebras, 46 are found to be associative and 14 are found to be non-associative. The 46 associative algebras are shown to be Boolean groups. Moreover, necessary and sufficient conditions for 13 non-associative algebras to be associative are also obtained: p-semisimplicity is found to be necessary and sufficient for a F 3 , F 5 , F 42 and F 55 algebras to be as

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9

Gavalec, Martin, Zuzana Němcová, and Ján Plavka. "Strong Tolerance and Strong Universality of Interval Eigenvectors in a Max-Łukasiewicz Algebra." Mathematics 8, no. 9 (2020): 1504. http://dx.doi.org/10.3390/math8091504.

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The Łukasiewicz conjunction (sometimes also considered to be a logic of absolute comparison), which is used in multivalued logic and in fuzzy set theory, is one of the most important t-norms. In combination with the binary operation ‘maximum’, the Łukasiewicz t-norm forms the basis for the so-called max-Łuk algebra, with applications to the investigation of systems working in discrete steps (discrete events systems; DES, in short). Similar algebras describing the work of DES’s are based on other pairs of operations, such as max-min algebra, max-plus algebra, or max-T algebra (with a given t-no

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10

Elsner, L., and P. van den Driessche. "Max-algebra and pairwise comparison matrices, II." Linear Algebra and its Applications 432, no. 4 (2010): 927–35. http://dx.doi.org/10.1016/j.laa.2009.10.005.

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11

Juhás, Gabriel. "Petri nets with generalized algebra: a comparison." Electronic Notes in Theoretical Computer Science 27 (1999): 42–56. http://dx.doi.org/10.1016/s1571-0661(05)80294-4.

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12

Lewis, Robert H., and Michael Wester. "Comparison of polynomial-oriented computer algebra systems." ACM SIGSAM Bulletin 33, no. 4 (1999): 5–13. http://dx.doi.org/10.1145/500457.500459.

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13

Lewis, Robert H. "Comparison of polynomial-oriented computer algebra systems." ACM SIGSAM Bulletin 34, no. 1 (2000): 24. http://dx.doi.org/10.1145/373500.373507.

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14

LIU, WENDE, and YONGZHENG ZHANG. "DERIVATIONS OF THE EVEN PARTS FOR MODULAR LIE SUPERALGEBRAS OF CARTAN TYPE W AND S." International Journal of Algebra and Computation 17, no. 04 (2007): 661–714. http://dx.doi.org/10.1142/s0218196707003883.

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Let 𝔽 be the underlying base field of characteristic p < 3 and denote by [Formula: see text] and [Formula: see text] the even parts of the finite-dimensional generalized Witt Lie superalgebra W and the special Lie superalgebra S, respectively. We first give the generator sets of the Lie algebras [Formula: see text] and [Formula: see text]. Using certain properties of the canonical tori of [Formula: see text] and [Formula: see text], we then determine the derivation algebra of [Formula: see text] and the derivation space of [Formula: see text] to [Formula: see text], where [Formula: see text

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15

Kaftal, Victor, Ping Wong Ng, and Shuang Zhang. "Strict Comparison of Positive Elements in Multiplier Algebras." Canadian Journal of Mathematics 69, no. 02 (2017): 373–407. http://dx.doi.org/10.4153/cjm-2016-015-3.

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AbstractMain result: If a C*-algebrais simple,σ-unital, hasfinitely many extremal traces, and has strict comparison of positive elements by traces, then its multiplier algebraalso has strict comparison of positive elements by traces. The same results holds if finitely many extremal traces is replaced byquasicontinuous scale. A key ingredient in the proof is that every positive element in the multiplier algebra of an arbitrary σ-unital C* -algebra can be approximated by a bi-diagonal series. As an application of strict comparison, ifis a simple separable stable C* -algebra with real rank zero,

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16

Osaka, Hiroyuki, and Tamotsu Teruya. "The Jiang–Su Absorption for Inclusions of Unital C*-algebras." Canadian Journal of Mathematics 70, no. 2 (2018): 400–425. http://dx.doi.org/10.4153/cjm-2017-033-7.

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AbstractWe introduce the tracial Rokhlin property for a conditional expectation for an inclusion of unital C*-algebras P ⊂ A with index finite, and show that an action α from a finite group G on a simple unital C*- algebra A has the tracial Rokhlin property in the sense of N. C. Phillips if and only if the canonical conditional expectation E: A → AG has the tracial Rokhlin property. Let be a class of infinite dimensional stably finite separable unital C*-algebras that is closed under the following conditions:(1) If A ∊ and B ≅ A, then B ∊ .(2) If A ∊ and n ∊ ℕ, then Mn(A) ∊ .(3) If A ∊ and p ∊

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17

Bratten, Tim. "A comparison theorem for Lie algebra homology groups." Pacific Journal of Mathematics 182, no. 1 (1998): 23–36. http://dx.doi.org/10.2140/pjm.1998.182.23.

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18

Yakes, Christopher, and Jon R. Star. "Using comparison to develop flexibility for teaching algebra." Journal of Mathematics Teacher Education 14, no. 3 (2009): 175–91. http://dx.doi.org/10.1007/s10857-009-9131-2.

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19

Lynch, Kathleen, and Jon R. Star. "Exploring teachers’ implementation of comparison in Algebra I." Journal of Mathematical Behavior 35 (September 2014): 144–63. http://dx.doi.org/10.1016/j.jmathb.2014.07.003.

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20

Isakson, Hans. "The Linear Algebra of the Sales Comparison Approach." Journal of Real Estate Research 24, no. 2 (2002): 117–28. http://dx.doi.org/10.1080/10835547.2002.12091090.

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21

Harrington, Heather A., Kenneth L. Ho, and Nicolette Meshkat. "A Parameter-Free Model Comparison Test Using Differential Algebra." Complexity 2019 (February 17, 2019): 1–15. http://dx.doi.org/10.1155/2019/6041981.

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We present a method for rejecting competing models from noisy time-course data that does not rely on parameter inference. First we characterize ordinary differential equation models in only measurable variables using differential-algebra elimination. This procedure gives input-output equations, which serve as invariants for time series data. We develop a model comparison test using linear algebra and statistics to reject incorrect models from their invariants. This algorithm exploits the dynamic properties that are encoded in the structure of the model equations without recourse to parameter v

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22

Peter Tikuisis, Aaron, and Andrew Toms. "On the Structure of Cuntz Semigroups in (Possibly) Nonunital C*-algebras." Canadian Mathematical Bulletin 58, no. 2 (2015): 402–14. http://dx.doi.org/10.4153/cmb-2014-040-5.

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AbstractWe examine the ranks of operators in semi-finite C*-algebras as measured by their densely defined lower semicontinuous traces. We first prove that a unital simple C*-algebra whose extreme tracial boundary is nonempty and finite contains positive operators of every possible rank, independent of the property of strict comparison. We then turn to nonunital simple algebras and establish criteria that imply that the Cuntz semigroup is recovered functorially from the Murray–von Neumann semigroup and the space of densely defined lower semicontinuous traces. Finally, we prove that these criter

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23

Elliott, George A., and Zhuang Niu. "On the Radius of Comparison of a Commutative C*-algebra." Canadian Mathematical Bulletin 56, no. 4 (2013): 737–44. http://dx.doi.org/10.4153/cmb-2012-012-9.

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Abstract.Let X be a compact metric space. A lower bound for the radius of comparison of the C*-algebra C(X) is given in terms of dimQ X, where dimQ X is the cohomological dimension with rational coefficients. If dimQX = dim X = d, then the radius of comparison of the C*-algebra C(X) is maxf0; (d/1)=2/1g if d is odd, and must be either d=2/1 or d=2/2 if d is even (the possibility d=2 - 1 does occur, but we do not know if the possibility d=2 - 2 can also occur).

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24

Chung, Won Sang. "Parafermion algebra with bilinear relation." Modern Physics Letters A 34, no. 20 (2019): 1950160. http://dx.doi.org/10.1142/s0217732319501608.

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In this paper, we find the parafermion algebra of order [Formula: see text] expressed in terms of bilinear relation (commutator form). We find the correct Hamiltonian of parafermion of order [Formula: see text] by using the parasupersymmetry. Finally, we discuss the comparison of specific heats for several parafermions of order [Formula: see text].

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25

Gomide, Janaína, Raquel Melo-Minardi, Marcos Augusto dos Santos, et al. "Using linear algebra for protein structural comparison and classification." Genetics and Molecular Biology 32, no. 3 (2009): 645–51. http://dx.doi.org/10.1590/s1415-47572009000300032.

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26

Lazzaretto, Andrea. "A critical comparison between thermoeconomic and emergy analyses algebra." Energy 34, no. 12 (2009): 2196–205. http://dx.doi.org/10.1016/j.energy.2008.10.020.

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27

WEIMAR-WOODS, EVELYN. "THE GENERAL STRUCTURE OF G-GRADED CONTRACTIONS OF LIE ALGEBRAS, II: THE CONTRACTED LIE ALGEBRA." Reviews in Mathematical Physics 18, no. 06 (2006): 655–711. http://dx.doi.org/10.1142/s0129055x06002760.

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We continue our study of G-graded contractions γ of Lie algebras where G is an arbitrary finite Abelian group. We compare them with contractions, especially with respect to their usefulness in physics. (Note that the unfortunate terminology "graded contraction" is confusing since they are, by definition, not contractions.)We give a complete characterization of continuous G-graded contractions and note that they are equivalent to a proper subset of contractions. We study how the structure of the contracted Lie algebra Lγdepends on γ, and show that, for discrete graded contractions, applications

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28

Stokes, Tim. "Comparison semigroups and algebras of transformations." Semigroup Forum 81, no. 2 (2010): 325–34. http://dx.doi.org/10.1007/s00233-010-9226-1.

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29

Bonnet, Robert, and Hamza Si-Kaddour. "Comparison of Boolean algebras." Order 4, no. 3 (1987): 273–83. http://dx.doi.org/10.1007/bf00337890.

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30

Gwilliam, Owen, and Kasia Rejzner. "Relating Nets and Factorization Algebras of Observables: Free Field Theories." Communications in Mathematical Physics 373, no. 1 (2020): 107–74. http://dx.doi.org/10.1007/s00220-019-03652-9.

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AbstractIn this paper we relate two mathematical frameworks that make perturbative quantum field theory rigorous: perturbative algebraic quantum field theory (pAQFT) and the factorization algebras framework developed by Costello and Gwilliam. To make the comparison as explicit as possible, we use the free scalar field as our running example, while giving proofs that apply to any field theory whose equations of motion are Green-hyperbolic (which includes, for instance, free fermions). The main claim is that for such free theories, there is a natural transformation intertwining the two construct

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31

Melo, Severino. "A comparison algebra on a cylinder with semi-periodic multiplications." Pacific Journal of Mathematics 146, no. 2 (1990): 281–304. http://dx.doi.org/10.2140/pjm.1990.146.281.

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32

Wainer, Howard, Charles Lewis, Bruce Kaplan, and James Braswell. "Building Algebra Testlets: A Comparison of Hierarchical and Linear Structures." Journal of Educational Measurement 28, no. 4 (1991): 311–23. http://dx.doi.org/10.1111/j.1745-3984.1991.tb00361.x.

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33

RIBEIRO-SILVA, C. I., and N. M. OLIVEIRA-NETO. "GENERALIZED QUANTUM FIELD THEORY BASED ON A NONLINEAR DEFORMED HEISENBERG ALGEBRA." International Journal of Modern Physics A 23, no. 20 (2008): 3113–27. http://dx.doi.org/10.1142/s0217751x08040366.

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We consider a quantum field theory based on a nonlinear Heisenberg algebra which describes phenomenologically a composite particle. Perturbative computation, considering the λϕ4 interaction was done and we also performed some comparison with a quantum field theory based on the q-oscillator algebra.

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34

ABUD, MARIO, LUIGI CAPPIELLO, and JEAN-PIERRE ADER. "EXTENDED BRST ALGEBRA OF THE FREEDMAN-TOWNSEND MODEL." International Journal of Modern Physics A 10, no. 11 (1995): 1577–95. http://dx.doi.org/10.1142/s0217751x95000759.

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We construct an explicit nilpotent extended BRST/anti-BRST algebra for the Freedman-Townsend model, through a change of basis of the fields and a corresponding deformation of the algebra of the Abelian two-form theory. We also discuss the elimination of some auxiliary fields from the gauge-fixed action and make a comparison with the extended Batalin-Vilkovisky formalism.

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35

Bremke, K., and C. K. Fan. "Comparison ofa-Functions." Journal of Algebra 203, no. 2 (1998): 355–60. http://dx.doi.org/10.1006/jabr.1997.7153.

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36

Hanna, Gerald S., and Joan L. Sonnenschein. "Relative Validity of the Orleans-Hanna Algebra Prognosis Test in the Prediction of Girls' and Boys' Grades in First-Year Algebra." Educational and Psychological Measurement 45, no. 2 (1985): 361–67. http://dx.doi.org/10.1177/001316448504500221.

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The relative predictive validity of girls' and boys' success in algebra is examined. Eighth-grade students took the Orleans-Hanna Algebra Prognosis Test. These prognosis test scores were correlated with grades that 519 girls and 421 boys subsequently earned in first-year algebra. Algebra grades of girls proved to be more predictable than those of boys ( p <.05). Comparison of the present findings with those of an earlier study suggest that no changes during a 14-year period in the differential predictive validity of the sexes is evident. Implications for counselors and teachers are drawn an

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37

Haugen, Kjetil B., and Bret L. Beckner. "A Critical Comparison of Reduced and Conventional EOS Algorithms." SPE Journal 18, no. 02 (2013): 378–88. http://dx.doi.org/10.2118/141399-pa.

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Summary Phase-equilibrium calculations can be a time-consuming part of process simulators and compositional reservoir simulations. Various authors have presented encouraging speed improvements based on reduced methods that can lower the computational cost by reducing the number of independent variables and thus generating a smaller system of equations to solve. This paper presents a careful comparison of conventional and reduced algorithms, showing that they can be expressed as linear transformations of each other. Consequently, the two sets of algorithms exhibit identical convergence behavior

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38

Sherman, Milan F., Candace Walkington, and Elizabeth Howell. "Brief Report: A Comparison of Symbol-Precedence View in Investigative and Conventional Textbooks Used in Algebra Courses." Journal for Research in Mathematics Education 47, no. 2 (2016): 134–46. http://dx.doi.org/10.5951/jresematheduc.47.2.0134.

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Recent reform movements have emphasized students making meaning of algebraic relationships; however, research on student thinking and learning often remains disconnected from the design of widely used curricular materials. Although a previous examination of algebra textbooks (Nathan, Long, & Alibali, 2002) demonstrated a preference for a symbols-first approach, research has demonstrated that Algebra I students' performance on verbally presented problems is better than on symbolic equations, consistent with cognitive theories suggesting the value of concreteness fading. The present study in

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39

Lecomte, P. B. A., P. Mathonet, and E. Tousset. "Comparison of some modules of the Lie algebra of vector fields." Indagationes Mathematicae 7, no. 4 (1996): 461–71. http://dx.doi.org/10.1016/s0019-3577(97)89133-1.

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40

Xin, Yan Ping, Dake Zhang, Joo Young Park, Kinsey Tom, Amanda Whipple, and Luo Si. "A Comparison of Two Mathematics Problem-Solving Strategies: Facilitate Algebra-Readiness." Journal of Educational Research 104, no. 6 (2011): 381–95. http://dx.doi.org/10.1080/00220671.2010.487080.

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41

Achinger, Piotr. "-neighborhoods and comparison theorems." Compositio Mathematica 151, no. 10 (2015): 1945–64. http://dx.doi.org/10.1112/s0010437x15007319.

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A technical ingredient in Faltings’ original approach to$p$-adic comparison theorems involves the construction of$K({\it\pi},1)$-neighborhoods for a smooth scheme$X$over a mixed characteristic discrete valuation ring with a perfect residue field: every point$x\in X$has an open neighborhood$U$whose generic fiber is a$K({\it\pi},1)$scheme (a notion analogous to having a contractible universal cover). We show how to extend this result to the logarithmically smooth case, which might help to simplify some proofs in$p$-adic Hodge theory. The main ingredient of the proof is a variant of a trick of Na

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42

Levine, Marc. "Comparison of cobordism theories." Journal of Algebra 322, no. 9 (2009): 3291–317. http://dx.doi.org/10.1016/j.jalgebra.2009.03.032.

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43

KITZ, WILLIAM R., and HAROLD W. THORPE. "A Comparison of the Effectiveness of Videodisc and Traditional Algebra Instruction for College-age Students with Learning Disabilities." Remedial and Special Education 16, no. 5 (1995): 295–306. http://dx.doi.org/10.1177/074193259501600506.

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The purpose of this study was to compare the effectiveness of a videodisc program, mastering equations, roots and exponents (system impact, inc., 1989) with a traditional text-based program. this study was conducted as part of a transition program during the summer before these students first entered college. the control group (n = 13) received instruction from a typical intermediate-level college algebra text, whereas the treatment group (n = 13) received instruction from the mastering equations, roots and exponents videodisc program. data analysis indicated that the treatment group receiving

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44

MELIKHOV, SERGEY A., and DUŠAN REPOVŠ. "n-QUASI-ISOTOPY II: COMPARISON." Journal of Knot Theory and Its Ramifications 14, no. 05 (2005): 603–26. http://dx.doi.org/10.1142/s021821650500397x.

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Geometric aspects of the filtration on classical links by k-quasi-isotopy are discussed, including the effect of Whitehead doubling, relations with Smythe's n-splitting and Kobayashi's k-contractibility. One observation is: ω-quasi-isotopy is equivalent to PL isotopy for links in a homotopy 3-sphere (respectively, contractible open 3-manifold) M if and only if M is homeomorphic to S3 (respectively, ℝ3). As a byproduct of the proof of the "if" part, we obtain that every compact subset of an acyclic open set in a compact orientable 3-manifold M is contained in a PL homology 3-ball in M. We show

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45

Kim, Dongkwan. "A comparison of two complexes." Journal of Algebra 514 (November 2018): 76–98. http://dx.doi.org/10.1016/j.jalgebra.2018.07.038.

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46

Kahn, Bruno. "Comparison of Some Field Invariants." Journal of Algebra 232, no. 2 (2000): 485–92. http://dx.doi.org/10.1006/jabr.2000.8380.

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47

Zink, Frnst-Wh Heim. "Comparison ofGLN and Division Algebra Representations-Some Remarks on the Local Case." Mathematische Nachrichten 159, no. 1 (1992): 47–72. http://dx.doi.org/10.1002/mana.19921590105.

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48

Das, A. K., and M. A. Musen. "A Temporal Query System for Protocol-Directed Decision Support." Methods of Information in Medicine 33, no. 04 (1994): 358–70. http://dx.doi.org/10.1055/s-0038-1635036.

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Abstract:Chronus is a query system that supports temporal extensions to the Structured Query Language (SQL) for relational databases. Although the relational data model can store time-stamped data and can permit simple temporal-comparison operations, it does not provide either a closed or a sufficient algebra for manipulating temporal data. In this paper, we outline an algebra that maintains a consistent relational representation of temporal data and that allows the type of temporal queries needed for protocol-directed decision support. We also discuss how Chronus can translate between our tem

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49

Dowbor, Piotr, and Adam Hajduk. "A Comparison of Various Types of Degenerations for Algebras." Algebra Colloquium 14, no. 03 (2007): 361–88. http://dx.doi.org/10.1142/s1005386707000351.

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Three different notions of geometric degeneration for finite dimensional algebras are compared. It is proved that for algebras A0 and A1 of same dimension, if A0 is a CB-degeneration of A1, then A0 is a degeneration of A1 in the classical sense; moreover, if additionally A0 and A1 are basic, then A0 is a CB-degeneration of A1 if and only if A0 is a rigid degeneration of A1. It is also shown that CB-degenerations along affine lines in the different dimension case do not differ so much from those in the equal dimension case.

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50

Bloom, Laura A. "Bijective comparison of optimal planarity algorithms." Linear and Multilinear Algebra 38, no. 3 (1995): 249–66. http://dx.doi.org/10.1080/03081089508818361.

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