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Journal articles on the topic 'Algebra - Intermediate'

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Published: 4 June 2021
Last updated: 27 January 2023

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1

Habbishaw, Gordon, Andrew Demetropoulos, and Kenneth C. Wolff. "Intermediate Algebra." Mathematical Gazette 69, no. 450 (December 1985): 306. http://dx.doi.org/10.2307/3617591.

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2

Chen, Haibo, Jianzhi Han, Yucai Su, and Ying Xu. "Loop Schrödinger–Virasoro Lie conformal algebra." International Journal of Mathematics 27, no. 06 (June 2016): 1650057. http://dx.doi.org/10.1142/s0129167x16500579.

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In this paper, we introduce two kinds of Lie conformal algebras, associated with the loop Schrödinger–Virasoro Lie algebra and the extended loop Schrödinger–Virasoro Lie algebra, respectively. The conformal derivations, the second cohomology groups of these two conformal algebras are completely determined. And nontrivial free conformal modules of rank one and [Formula: see text]-graded free intermediate series modules over these two conformal algebras are also classified in the present paper.
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3

Bakshi, Keshab Chandra. "Intermediate planar algebra revisited." International Journal of Mathematics 29, no. 12 (November 2018): 1850077. http://dx.doi.org/10.1142/s0129167x18500775.

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In this paper, we explicitly work out the subfactor planar algebra [Formula: see text] for an intermediate subfactor [Formula: see text] of an irreducible subfactor [Formula: see text] of finite index. We do this in terms of the subfactor planar algebra [Formula: see text] by showing that if [Formula: see text] is any planar tangle, the associated operator [Formula: see text] can be read off from [Formula: see text] by a formula involving the so-called biprojection corresponding to the intermediate subfactor [Formula: see text] and a scalar [Formula: see text] carefully chosen so as to ensure that the formula defining [Formula: see text] is multiplicative with respect to composition of tangles. Also, the planar algebra of [Formula: see text] can be obtained by applying these results to [Formula: see text]. We also apply our result to the example of a semi-direct product subgroup-subfactor.
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4

Brown, Jonathan, Ruy Exel, Adam Fuller, David Pitts, and Sarah Reznikoff. "Intermediate C*-algebras of Cartan embeddings." Proceedings of the American Mathematical Society, Series B 8, no. 3 (January 14, 2021): 27–41. http://dx.doi.org/10.1090/bproc/66.

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Let A A be a C ∗ ^* -algebra and let D D be a Cartan subalgebra of A A . We study the following question: if B B is a C ∗ ^* -algebra such that D ⊆ B ⊆ A D \subseteq B \subseteq A , is D D a Cartan subalgebra of B B ? We give a positive answer in two cases: the case when there is a faithful conditional expectation from A A onto B B , and the case when A A is nuclear and D D is a C ∗ ^* -diagonal of A A . In both cases there is a one-to-one correspondence between the intermediate C ∗ ^* -algebras B B , and a class of open subgroupoids of the groupoid G G , where Σ → G \Sigma \rightarrow G is the twist associated with the embedding D ⊆ A D \subseteq A .
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5

LEE, C. W. H., and S. G. RAJEEV. "A REVIEW OF SYMMETRY ALGEBRAS OF QUANTUM MATRIX MODELS IN THE LARGE N LIMIT." International Journal of Modern Physics A 14, no. 28 (November 10, 1999): 4395–455. http://dx.doi.org/10.1142/s0217751x99002074.

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This is a review article in which we will introduce, in a unifying fashion and with more intermediate steps in some difficult calculations, two infinite-dimensional Lie algebras of quantum matrix models, one for the open string sector and the other for the closed string sector. Physical observables of quantum matrix models in the large N limit can be expressed as elements of these Lie algebras. We will see that both algebras arise as quotient algebras of a larger Lie algebra. We will also discuss some properties of these Lie algebras not published elsewhere yet, and briefly review their relationship with well-known algebras like the Cuntz algebra, the Witt algebra and the Virasoro algebra. We will also review how the Yang–Mills theory, various low energy effective models of string theory, quantum gravity, string-bit models, and the quantum spin chain models can be formulated as quantum matrix models. Studying these algebras thus help us understand the common symmetry of these physical systems.
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6

Brothier, Arnaud, and Chenxu Wen. "The cup subalgebra has the absorbing amenability property." International Journal of Mathematics 27, no. 02 (February 2016): 1650013. http://dx.doi.org/10.1142/s0129167x16500130.

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Consider an inclusion of diffuse von Neumann algebras [Formula: see text]. We say that [Formula: see text] has the absorbing amenability property (AAP) if for any diffuse subalgebra [Formula: see text] and any amenable intermediate algebra [Formula: see text] we have that [Formula: see text] is contained in [Formula: see text] We prove that the cup subalgebra associated to any subfactor planar algebra has the AAP.
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7

AMRUTAM, TATTWAMASI, and MEHRDAD KALANTAR. "On simplicity of intermediate -algebras." Ergodic Theory and Dynamical Systems 40, no. 12 (June 6, 2019): 3181–87. http://dx.doi.org/10.1017/etds.2019.34.

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We prove simplicity of all intermediate $C^{\ast }$-algebras $C_{r}^{\ast }(\unicode[STIX]{x1D6E4})\subseteq {\mathcal{B}}\subseteq \unicode[STIX]{x1D6E4}\ltimes _{r}C(X)$ in the case of minimal actions of $C^{\ast }$-simple groups $\unicode[STIX]{x1D6E4}$ on compact spaces $X$. For this, we use the notion of stationary states, recently introduced by Hartman and Kalantar [Stationary $C^{\ast }$-dynamical systems. Preprint, 2017, arXiv:1712.10133]. We show that the Powers’ averaging property holds for the reduced crossed product $\unicode[STIX]{x1D6E4}\ltimes _{r}{\mathcal{A}}$ for any action $\unicode[STIX]{x1D6E4}\curvearrowright {\mathcal{A}}$ of a $C^{\ast }$-simple group $\unicode[STIX]{x1D6E4}$ on a unital $C^{\ast }$-algebra ${\mathcal{A}}$, and use it to prove a one-to-one correspondence between stationary states on ${\mathcal{A}}$ and those on $\unicode[STIX]{x1D6E4}\ltimes _{r}{\mathcal{A}}$.
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8

Stephens, Larry J., and John Konvalina. "Factors Influencing Success in Intermediate Algebra." Computers in the Schools 17, no. 1-2 (May 31, 2001): 77–84. http://dx.doi.org/10.1300/j025v17n01_07.

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9

Brown, Jonathan H., Lisa Orloff Clark, and Astrid an Huef. "Dense subalgebras of purely infinite simple groupoid C*-algebras." Proceedings of the Edinburgh Mathematical Society 63, no. 3 (March 30, 2020): 609–29. http://dx.doi.org/10.1017/s0013091520000036.

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AbstractA simple Steinberg algebra associated to an ample Hausdorff groupoid G is algebraically purely infinite if and only if the characteristic functions of compact open subsets of the unit space are infinite idempotents. If a simple Steinberg algebra is algebraically purely infinite, then the reduced groupoid $C^*$-algebra $C^*_r(G)$ is simple and purely infinite. But the Steinberg algebra seems too small for the converse to hold. For this purpose we introduce an intermediate *-algebra B(G) constructed using corners $1_U C^*_r(G) 1_U$ for all compact open subsets U of the unit space of the groupoid. We then show that if G is minimal and effective, then B(G) is algebraically properly infinite if and only if $C^*_r(G)$ is purely infinite simple. We apply our results to the algebras of higher-rank graphs.
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10

SZLACHÁNYI, K. "CHIRAL DECOMPOSITION AS A SOURCE OF QUANTUM SYMMETRY IN THE ISING MODEL." Reviews in Mathematical Physics 06, no. 04 (August 1994): 649–71. http://dx.doi.org/10.1142/s0129055x94000225.

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The superselection sectors of three closely related models are studied and compared. I. The full Ising model with observable algebra [Formula: see text], the universal algebra of local even CAR algebras on the circle. [Formula: see text] has four sectors with Z(2) × Z(2) symmetry. II. The chiral Ising model with observable algebra [Formula: see text] (c = L or R), which is the universal algebra of local even Majorana algebras, has three sectors with quantum symmetry Gc ≅ M1⊕M1⊕M2. The Mack-Schomerus endomorphism creating the non-Abelian sector of [Formula: see text], respectively of [Formula: see text] is shown to coincide with the restriction [Formula: see text], respectively [Formula: see text] of a Z (2) charge creating automorphism ρ of [Formula: see text]. III. As an intermediate step the superselection sectors of the algebra [Formula: see text] — which can be interpreted as the observable algebra of the conformal Ising model — are found to have ordinary group symmetry described by the dihedral group D4. The relation between the sectors of [Formula: see text] and [Formula: see text] is explained in terms of a strange 'symmetry breaking': symmetry enhancement in the Neveu-Schwarz sector and symmetry breaking in the Ramond. Covariant charged fields are constructed in all three cases and the truncation in Gc is shown to arise from the failure of the Cuntz algebra relations for the chiral charged fields.
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11

Cameron, Jan M., and Roger R. Smith. "Intermediate subalgebras and bimodules for general crossed products of von Neumann algebras." International Journal of Mathematics 27, no. 11 (October 2016): 1650091. http://dx.doi.org/10.1142/s0129167x16500919.

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Let [Formula: see text] be a discrete group acting on a von Neumann algebra [Formula: see text] by properly outer ∗-automorphisms. In this paper, we study the containment [Formula: see text] of [Formula: see text] inside the crossed product. We characterize the intermediate von Neumann algebras, extending earlier work of other authors in the factor case. We also determine the [Formula: see text]-bimodules that are closed in the Bures topology and which coincide with the [Formula: see text]-closed ones under a mild hypothesis on [Formula: see text]. We use these results to obtain a general version of Mercer’s theorem concerning the extension of certain isometric [Formula: see text]-continuous maps on [Formula: see text]-bimodules to ∗-automorphisms of the containing von Neumann algebras.
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12

STEPHENS, LARRY J., and JOHN KONVALINA. "The use of computer algebra software in teaching intermediate and college algebra." International Journal of Mathematical Education in Science and Technology 30, no. 4 (July 1999): 483–88. http://dx.doi.org/10.1080/002073999287761.

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13

Zhang, Xiufu, Shaobin Tan, and Haifeng Lian. "Unitary Modules for the Twisted Heisenberg–Virasoro Algebra." Algebra Colloquium 26, no. 03 (August 12, 2019): 529–40. http://dx.doi.org/10.1142/s1005386719000397.

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The conjugate-linear anti-involutions and unitary irreducible modules of the intermediate series over the twisted Heisenberg–Virasoro algebra are classified, respectively. We prove that any unitary irreducible module of the intermediate series over the twisted Heisenberg–Virasoro algebra is of the form [Formula: see text] for [Formula: see text], [Formula: see text] and [Formula: see text].
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14

Stephens, Larry J. "Microsoft Excel as a supplement to intermediate algebra." International Journal of Mathematical Education in Science and Technology 34, no. 4 (January 2003): 575–79. http://dx.doi.org/10.1080/0020739031000148976.

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15

Lavagno, A., and P. Narayana Swamy. "Intermediate statistics as a consequence of deformed algebra." Physica A: Statistical Mechanics and its Applications 389, no. 5 (March 2010): 993–1001. http://dx.doi.org/10.1016/j.physa.2009.11.008.

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16

Vallin, Robert W. "LETTERS TO A FRIEND … WRITING IN INTERMEDIATE ALGEBRA." PRIMUS 4, no. 2 (January 1994): 97–105. http://dx.doi.org/10.1080/10511979408965737.

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17

Abhyankar, S. S., and W. J. Heinzer. "Intermediate Rings." Journal of Algebra 175, no. 3 (August 1995): 926–40. http://dx.doi.org/10.1006/jabr.1995.1219.

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18

Castro Manzano, José Martin. "An Intermediate Term Functor Logic." Argumentos - Revista de Filosofia, no. 22 (November 18, 2019): 17–31. http://dx.doi.org/10.36517/argumentos.22.2.

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In this paper we attempt to do something rather simple: to meet the advances of Sommers and Englebretsen (namely, a plus-minus algebra for syllogistic) together with the developments of Peterson and Thompson (namely, an extension of syllogistic with “most,” “many,” and “few”). The result is an intermediate syllogistic that copes with a wide range of logical patterns but with the virtues of an algebraic approach.
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19

Gao, Ming, Ying Xu, and Xiaoqing Yue. "The Lie Conformal Algebra of a Block Type Lie Algebra." Algebra Colloquium 22, no. 03 (July 14, 2015): 367–82. http://dx.doi.org/10.1142/s1005386715000322.

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Let L be a Lie algebra of Block type over ℂ with basis {Lα,i | α,i ∈ ℤ} and brackets [Lα,i,Lβ,j]=(β(i+1)-α(j+1)) Lα+β,i+j. In this paper, we first construct a formal distribution Lie algebra of L. Then we decide its conformal algebra B with ℂ[∂]-basis {Lα(w) | α ∈ ℤ} and λ-brackets [Lα(w)λ Lβ(w)]= (α∂+(α+β)λ) Lα+β(w). Finally, we give a classification of free intermediate series B-modules.
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20

Rech, Janice F., Sandra M. Juhler, and Harvey L. Johnson. "The effectiveness of videotapes in the individualized instruction of intermediate algebra and college algebra." International Journal of Mathematical Education in Science and Technology 26, no. 3 (May 1995): 463–72. http://dx.doi.org/10.1080/0020739950260314.

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21

Ayache, Ahmed. "The Set of Intermediate Rings as a Boolean Algebra." Communications in Algebra 43, no. 4 (December 31, 2014): 1377–86. http://dx.doi.org/10.1080/00927872.2013.865046.

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22

Petrogradsky, V. M. "Intermediate Growth in Lie Algebras and Their Enveloping Algebras." Journal of Algebra 179, no. 2 (January 1996): 459–82. http://dx.doi.org/10.1006/jabr.1996.0020.

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23

Yang, Hengyun, Ying Xu, and Jiancai Sun. "Harish-Chandra Modules of the Intermediate Series over the Topological N = 2 Superconformal Algebra." Algebra Colloquium 27, no. 02 (May 7, 2020): 343–60. http://dx.doi.org/10.1142/s1005386720000280.

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The topological N = 2 superconformal algebra was introduced by Dijkgraaf, Verlinde and Verlinde as the symmetry algebra of topological strings at d < 1. We give a classification of irreducible 𝕫 × 𝕫-graded modules of the intermediate series over this infinite-dimensional Lie superalgebra.
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24

SCIPIONI, R. "G-ALGEBRA AND CURVED SPACETIME." Modern Physics Letters A 10, no. 23 (July 30, 1995): 1705–9. http://dx.doi.org/10.1142/s0217732395001824.

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The recently proved nonexistence of generalized statistics in curved spacetime is reconsidered in the framework of g-algebra; we show in a rigorous way that for asymptotic states, a Fermi or Bose statistics in the “in” region always evolves a Bose or Fermi statistics in the “out” region; the new approach, however, permits one to infer that this fact might not be true when considering intermediate states.
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25

Eldersveld, Paul, and David Baughman. "ATTITUDES AND STUDENT PERCEPTIONS: THEIR MEASURE AND RELATIONSHIP TO PERFORMANCE IN ELEMENTARY ALGEBRA, INTERMEDIATE ALGEBRA, COLLEGE ALGEBRA, AND TECHNICAL MATHEMATICS." Community Junior College Research Quarterly of Research and Practice 10, no. 3 (January 1986): 203–17. http://dx.doi.org/10.1080/0361697860100305.

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26

Gilmer, Robert, and William Heinzer. "Finitely generated intermediate rings." Journal of Pure and Applied Algebra 37 (1985): 237–64. http://dx.doi.org/10.1016/0022-4049(85)90101-x.

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27

Zhu, Bin. "Cluster-Tilted Algebras and Their Intermediate Coverings." Communications in Algebra 39, no. 7 (July 2011): 2437–48. http://dx.doi.org/10.1080/00927872.2010.489082.

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28

Amrutam, Tattwamasi, and Dan Ursu. "A generalized Powers averaging property for commutative crossed products." Transactions of the American Mathematical Society 375, no. 3 (December 22, 2021): 2237–54. http://dx.doi.org/10.1090/tran/8567.

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We prove a generalized version of Powers’ averaging property that characterizes simplicity of reduced crossed products C ( X ) ⋊ λ G C(X) \rtimes _\lambda G , where G G is a countable discrete group, and X X is a compact Hausdorff space which G G acts on minimally by homeomorphisms. As a consequence, we generalize results of Hartman and Kalantar on unique stationarity to the state space of C ( X ) ⋊ λ G C(X) \rtimes _\lambda G and to Kawabe’s generalized space of amenable subgroups Sub a ⁡ ( X , G ) \operatorname {Sub}_a(X,G) . This further lets us generalize a result of the first named author and Kalantar on simplicity of intermediate C*-algebras. We prove that if C ( Y ) ⊆ C ( X ) C(Y) \subseteq C(X) is an inclusion of unital commutative G G -C*-algebras with X X minimal and C ( Y ) ⋊ λ G C(Y) \rtimes _\lambda G simple, then any intermediate C*-algebra A A satisfying C ( Y ) ⋊ λ G ⊆ A ⊆ C ( X ) ⋊ λ G C(Y) \rtimes _\lambda G \subseteq A \subseteq C(X) \rtimes _\lambda G is simple.
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29

Wink, Donald J., Sharon Fetzer Gislason, Barbara J. Zusman, Robert C. Mebane, and Sheila D. McNicholas. "The MATCH Program: A Preparatory Chemistry and Intermediate Algebra Curriculum." Journal of Chemical Education 77, no. 8 (August 2000): 999. http://dx.doi.org/10.1021/ed077p999.

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30

Perrucci, Daniel, and Marie-Françoise Roy. "Quantitative fundamental theorem of algebra." Quarterly Journal of Mathematics 70, no. 3 (May 15, 2019): 1009–37. http://dx.doi.org/10.1093/qmath/haz008.

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Abstract Using subresultants, we modify a real-algebraic proof due to Eisermann of the fundamental theorem of Algebra (FTA) to obtain the following quantitative information: in order to prove the FTA for polynomials of degree d, the intermediate value theorem (IVT) is required to hold only for real polynomials of degree at most d2. We also explain that the classical proof due to Laplace requires IVT for real polynomials of exponential degree. These quantitative results highlight the difference in nature of these two proofs.
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31

Gwilliam, Owen, and Kasia Rejzner. "Relating Nets and Factorization Algebras of Observables: Free Field Theories." Communications in Mathematical Physics 373, no. 1 (January 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 constructions. In fact, both approaches encode equivalent information if one assumes the time-slice axiom. The key technical ingredient is to use time-ordered products as an intermediate step between a net of associative algebras and a factorization algebra.
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32

Wu, Yina, and Weiqiang Lin. "Classification of Z-Graded Modules of the Intermediate Series over the q-Analog Virasoro-like Algebra." Algebra Colloquium 17, no. 02 (June 2010): 247–56. http://dx.doi.org/10.1142/s100538671000026x.

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In this paper, we complete the classification of Z-graded modules of the intermediate series over a q-analog Virasoro-like algebra L. We first construct four classes of irreducible Z-graded L-modules of the intermediate series. Then we prove that any Z-graded L-module of the intermediate series must be one of the modules constructed by us, or a direct sum of some trivial L-modules.
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33

GUO, XIANGQIAN, XUEWEN LIU, and KAIMING ZHAO. "HARISH-CHANDRA MODULES OVER THE ℚ HEISENBERG–VIRASORO ALGEBRA." Journal of the Australian Mathematical Society 89, no. 1 (August 2010): 9–15. http://dx.doi.org/10.1017/s1446788710001436.

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34

Shneerson, L. M. "On Semigroups of Intermediate Growth." Communications in Algebra 32, no. 5 (December 31, 2004): 1793–803. http://dx.doi.org/10.1081/agb-120029902.

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35

Cox, Ben L., and Vyacheslav Futorny. "Structure of intermediate Wakimoto modules." Journal of Algebra 306, no. 2 (December 2006): 682–702. http://dx.doi.org/10.1016/j.jalgebra.2006.08.019.

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36

Shaikhha, Amir, Maximilian Schleich, and Dan Olteanu. "An intermediate representation for hybrid database and machine learning workloads." Proceedings of the VLDB Endowment 14, no. 12 (July 2021): 2831–34. http://dx.doi.org/10.14778/3476311.3476356.

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IFAQ is an intermediate representation and compilation framework for hybrid database and machine learning workloads expressible using iterative programs with functional aggregate queries. We demonstrate IFAQ for several OLAP queries, linear algebra expressions, and learning factorization machines over training datasets defined by feature extraction queries over relational databases.
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37

Zivkovic-Zlatanovic, Snezana, and Robin Harte. "On almost essentially Ruston elements of a Banach algebra." Filomat 24, no. 3 (2010): 149–55. http://dx.doi.org/10.2298/fil1003149z.

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38

Petrogradsky, Victor. "Nil restricted Lie algebras of oscillating intermediate growth." Journal of Algebra 588 (December 2021): 349–407. http://dx.doi.org/10.1016/j.jalgebra.2021.09.003.

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39

Nord, Gail D., and John Nord. "Applications: An Example of Algebra in Lake Roosevelt." Mathematics Teacher 88, no. 2 (February 1995): 116–20. http://dx.doi.org/10.5951/mt.88.2.0116.

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The NCTM's Standards documents (1989, 1991) encourage teachers to give students problems drawn from real-world contexts. This article demonstrates the mathematical nature of a marine environment-pollution problem. Examples discussed could be used to motivate students in a beginning-or intermediate-algebra classroom.
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40

Larson, Suzanne. "THE INTERMEDIATE VALUE THEOREM INf-RINGS." Communications in Algebra 30, no. 5 (May 31, 2002): 2469–504. http://dx.doi.org/10.1081/agb-120003479.

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41

Shneerson, L. M. "Relatively Free Semigroups of Intermediate Growth." Journal of Algebra 235, no. 2 (January 2001): 484–546. http://dx.doi.org/10.1006/jabr.2000.8503.

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42

Wu, Yadi, and Xiaoqing Yue. "Modules of the Intermediate Series over Not-finitely Graded Lie Algebras W(Γ)." Algebra Colloquium 28, no. 02 (May 11, 2021): 319–36. http://dx.doi.org/10.1142/s1005386721000250.

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Let [Formula: see text] be a class of not-finitely graded Lie algebras related to generalized Virasoro algebras with basis [Formula: see text], which satisfies relations [Formula: see text] and [Formula: see text]. In this paper, [Formula: see text]-modules of the intermediate series satisfying some conditions are constructed and classified. We also obtain modules of the intermediate series over the related Lie superalgebra.
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43

Bajorska, B., and O. Macedońska. "A Note on Groups of Intermediate Growth." Communications in Algebra 35, no. 12 (November 26, 2007): 4112–15. http://dx.doi.org/10.1080/00927870701544914.

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44

Bartholdi, L., I. I. Reznykov, and V. I. Sushchansky. "The smallest Mealy automaton of intermediate growth." Journal of Algebra 295, no. 2 (January 2006): 387–414. http://dx.doi.org/10.1016/j.jalgebra.2004.08.040.

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45

NARAYANA SWAMY, P. "INTERPOLATING STATISTICS AND q-DEFORMED OSCILLATOR ALGEBRAS." International Journal of Modern Physics B 20, no. 06 (March 10, 2006): 697–713. http://dx.doi.org/10.1142/s0217979206033498.

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The idea that a system obeying interpolating statistics can be described by a deformed oscillator algebra, or quantum groups, has been an outstanding issue. We are able to demonstrate that a q-deformed oscillator algebra can be used to describe the statistics of particles which provide a continuous interpolation between Bose and Fermi statistics. We show that the generalized intermediate statistics splits into Boson-like and Fermion-like regimes, each described by a unique oscillator algebra. The thermostatistics of Boson-like particles is described by employing q-calculus based on the Jackson derivative while the Fermion-like particles are described by ordinary derivatives of thermodynamics. Thermodynamic functions for systems of both types are determined and examined.
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46

Guo, Xiangqian, Rencai Lu, and Kaiming Zhao. "Classification of irreducible Harish-Chandra modules over generalized Virasoro algebras." Proceedings of the Edinburgh Mathematical Society 55, no. 3 (April 12, 2012): 697–709. http://dx.doi.org/10.1017/s0013091510001604.

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AbstractLet G be an arbitrary non-zero additive subgroup of the complex number field ℂ, and let Vir[G] be the corresponding generalized Virasoro algebra over ℂ. In this paper we determine all irreducible weight modules with finite-dimensional weight spaces over Vir[G]. The classification strongly depends on the index group G. If G does not have a direct summand isomorphic to ℤ (the integers), then such irreducible modules over Vir[G] are only modules of intermediate series whose weight spaces are all one dimensional. Otherwise, there is one further class of modules that are constructed by using intermediate series modules over a generalized Virasoro subalgebra Vir[G0] of Vir[G] for a direct summand G0 of G with G = G0 ⊕ ℤb, where b ∈ G \ G0. This class of irreducible weight modules do not have corresponding weight modules for the classical Virasoro algebra.
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47

Smith, Joseph G., and William B. Michael. "Validity of Scores on Alternative Predictors of Success in a College Algebra Course." Psychological Reports 82, no. 2 (April 1998): 379–86. http://dx.doi.org/10.2466/pr0.1998.82.2.379.

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For a sample of 59 male and 26 female students in continuing education at a private university, analyses indicated that (a) scores on a basic algebra test (either in a traditional multiple-choice format in which each item is accompanied by a reinforcing illustrative example) employed for placement of students in an intermediate algebra course were promising predictors of success in this course ( rs = .67 and .66, respectively, p < .05) and (b) affective measures representing the constructs of mathematics anxiety and locus of control appeared to have little, if any, predictive validity.
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48

Chisko, Ann M. "Developmental Math: Problem Solving and Survival." Mathematics Teacher 78, no. 8 (November 1985): 592–96. http://dx.doi.org/10.5951/mt.78.8.0592.

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Before students enroll in such college- level mathematics classes as calculus, statistics, or precalculus algebra and trigonometry, they may need to take preliminary courses. These courses cover prealgebra arithmetic or beginning and intermediate algebraic topics commonly offered at the middle and secondary school levels.
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49

LÜ, RENCAI, and KAIMING ZHAO. "CLASSIFICATION OF IRREDUCIBLE WEIGHT MODULES OVER THE TWISTED HEISENBERG–VIRASORO ALGEBRA." Communications in Contemporary Mathematics 12, no. 02 (April 2010): 183–205. http://dx.doi.org/10.1142/s0219199710003786.

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In this paper, all irreducible weight modules with finite dimensional weight spaces over the twisted Heisenberg–Virasoro algebra are determined. There are two different classes of them. One class is formed by simple modules of intermediate series, whose nonzero weight spaces are all 1-dimensional; the other class consists of the irreducible highest weight modules and lowest weight modules.
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50

WANG, XIAO-GUANG, and HONGCHEN FU. "SUPERPOSITION OF THE λ-PARAMETERIZED SQUEEZED STATES." Modern Physics Letters B 14, no. 07n08 (April 10, 2000): 243–50. http://dx.doi.org/10.1142/s0217984900000367.

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The superposition states of the λ-parameterized squeezed states are introduced and investigated. These states are intermediate states interpolating between the number and Schrödinger cat states and admit algebraic characterization in terms of su(1, 1) algebra. It is shown that these states exhibit remarkable nonclassical properties.
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