Relevant bibliographies by topics / Algebra - Intermediate

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Algebra - Intermediate'

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Published: 4 June 2021
Last updated: 27 January 2023

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Journal articles on the topic "Algebra - Intermediate"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Algebra - Intermediate"

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Engstrom, Ronald W. Retzer Kenneth A. "The effects of logic on achievement in intermediate algebra." Normal, Ill. : Illinois State University, 1988. http://www.mlb.ilstu.edu/articles/dissertations/8818710.PDF.

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Thesis (D.A.)--Illinois State University, 1988.
Title from title page screen, viewed Oct. 13, 2004. Dissertation Committee: Kenneth A. Retzer (chair), Lynn H. Brown, John A. Dossey, Lotus D. Hershberger, Albert D. Otto, Walter D. Pierce. Includes bibliographical references (leaves 97-102) and abstract. Also available in print.
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Griffin, Melinda Rose. "Curricular pathways to Algebra I in eighth grade." W&M ScholarWorks, 2014. https://scholarworks.wm.edu/etd/1550154079.

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Pidgeon, Jennifer Virginie, and Katherine Anne Yule. "A unit on proportional relationships: A preparation for algebra." CSUSB ScholarWorks, 1998. https://scholarworks.lib.csusb.edu/etd-project/1556.

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Anderson, Dianne S. "The impact of writing and collaborative problem solving on student achievement and attitude in intermediate algebra /." ProQuest subscription required:, 1999. http://proquest.umi.com/pqdweb?did=990270451&sid=1&Fmt=2&clientId=8813&RQT=309&VName=PQD.

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Burnham, James N. Dossey John A. "The effects of extra study materials and notetaking instruction on success in intermediate algebra at the college level." Normal, Ill. Illinois State University, 1985. http://wwwlib.umi.com/cr/ilstu/fullcit?p8608947.

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Thesis (D.A.)--Illinois State University, 1985.
Title from title page screen, viewed June 30, 2005. Dissertation Committee: John Dossey (chair), Lawrence Eggan, Lotus Hershberger, Larry Kennedy, Albert Otto, Thomas Shilgalis. Includes bibliographical references (leaves 72-75) and abstract. Also available in print.
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Hoyte, Jennifer. "How the Use of Subjectivist Instructional Strategies in Teaching Multiple Sections of an Eighth Grade Algebra Class in Guyana Relates to Algebra Achievement and Attitude Changes toward Mathematics." FIU Digital Commons, 2017. http://digitalcommons.fiu.edu/etd/3380.

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In Guyana, South America, the Ministry of Education seeks to provide universal, inclusive education that prepares its citizens to take their productive places in society and to creatively solve complex, real-world problems. However, with frequent national assessments that are used to place students in high school, college or into jobs, teachers resort to using familiar strategies such as lecture, recitation and test drilling. Despite their efforts, over 56% of students are failing the Grade 6 assessments, 43% failing 10th grade Mathematics and over 60% failing college algebra courses. Such performance has been linked to students’ lower academic self-concept and their negative attitudes toward mathematics aggravated by an autocratic culture that continues to view the teacher as sole authority. Subjectivist instructional strategies integrate constructivism and affect by providing a learning experience that gives children more autonomy as they solve contextually relevant algebraic problems. In a quasi-experimental study involving a treatment and control group of eighth grade students at a high school in Guyana, a modified version of the Mathematics Value Inventory was used to measure students’ attitudes towards mathematics before and after the 10-week treatment. Scores on the final examination were used to determine achievement in algebra. Forty seven students in the treatment group were guided in exploring and discovering concepts for themselves. Formal definitions were delayed until after the students experimented with relatable scenarios. Forty two students in the control group were taught using multiple opportunities to practice. Analysis was done using General Linear Models to determine the variance in achievement and attitude scores accounted for by the instructional strategies while controlling for sex, challenge index, and, pretreatment scores for attitude and achievement. The challenge index was developed to identify outside influences on students’ performance such as: travel time; whether living at home; number in household; sleepiness; noisiness; and, resource availability. Results were not all as expected but some interesting relationships surfaced between the challenges, attitudes towards mathematics and achievement scores. Ultimately it was determined that the environment in which students had to study and the challenges they faced outweighed the small gains in attitude changes for the treatment group.
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Gardner, Mary Catherine. "Changing math anxiety and attitudes with the use of graphics calculators for college intermediate algebra classes : differences by gender, age of student and experience of instructor." Virtual Press, 1996. http://liblink.bsu.edu/uhtbin/catkey/1036817.

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Graphics calculators have become an integral part of many introductory college mathematics courses. There has been little research to show the effects of introducing technology, along with an emphasis on the interrelationships of the numeric, symbolic, graphical, and verbal forms of functions, for courses that are traditionally considered pre-college mathematics. The major purpose of this study was to determine if changes in mathematics anxiety and attitudes occurred in Intermediate Algebra classes and to determine whether these changes were dependent on age, gender of student, and experience of instructor. The relationship between beginning levels of math anxiety and successful completion of the class were also examined.All sections of Intermediate Algebra taught at Grand Valley State University during the Winter semester of 1995 participated in the study. The first week of class, 479 students completed the initial survey. The final week of class, 264 of those students completed the survey again. In addition to gender and age of student, the survey instrumentcontained questions from seven of the Fennema-Sherman Mathematics Attitudes Scales. Each scale contained 12 questions, answered on a five point Likert type scale. High scores on the questionnaire indicated a positive attitude. Students in four sections were asked open ended questions every other week. At the end of the semester, instructors were given a questionnaire to determine their perceptions of how student's attitudes and anxieties changed.MANOVA for repeated measures using SPSS was used to perform the analyses with respect to age, gender, and teacher experience, over time. Faculty responses indicated they thought attitudes and levels of math anxiety improved over the semester. Although most groups did show some improvement, no significant change occurred. The only statistically significant differences detected were in math anxiety by gender and a combination of math anxiety and attitude by age. Females had higher levels of math anxiety (N = 166, initial M = 29.96, final M = 30.80) than males (N =.98, initial M = 33.87, final M = 34.79)and while older students appeared more math anxious, they also reflected a more positive attitude about mathematics.
Department of Educational Leadership
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Tonneson, Virginia Caine. "Teacher instructional practices designed to meet the individual learning needs of mathematically gifted/talented students in middle school Algebra I." W&M ScholarWorks, 2011. https://scholarworks.wm.edu/etd/1550154179.

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Rigdon, Misty B. "The impact of coteaching on regular education eighth grade student achievement on a basic skills algebra assessment." ScholarWorks, 2010. https://scholarworks.waldenu.edu/dissertations/783.

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Coteaching strategies have been implemented in many of the inclusion math classrooms in an attempt to improve the achievement of students. Math achievement continues to be a concern as reported by the National Mathematics Advisory Council in 2007. Educators and previous research reported that coteaching does not improve student achievement. The purpose of this study and the research question was designed to investigate, determine, and examine if coteaching has an impact on regular education students' achievement on an algebra assessment in the eighth grade. This concurrent mixed methods design used test data from a convenience sample of 70 eighth grade students and 6 math coteachers from a small rural middle school in a southern U.S state. The students were divided into a cotaught class (experimental) and a noncotaught class (control group). The teachers' perception and implementation of the coteaching model within the inclusive classroom was determined through interviews using a semi-structured interview guide. Students' achievement was measured based on math scores on a Basic Skills Algebra Assessment given at the beginning and end of 12 weeks. A two-way analysis of variance (ANOVA) was conducted to assess if differences exist on algebra achievement scores by group (control vs. treatment) and time (pretest vs. posttest). The results of the post hoc analysis, consisting of two independent sample t tests and two dependent sample t tests, revealed that significant mean differences did in fact exist on algebra achievement scores for only the experimental group suggesting that scores increased from pre to posttest. The interview data indicated that the teachers' perception of student learning was greater in the cotaught classroom. Evidence is provided to coteachers and administrators in support of implementing the coteaching model. It supports a change in students' attitudes and perceptions of other's differences as well as their ability to learn mathematics.
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Bhattacharya, Subhabrata. "Recognition of Complex Events in Open-source Web-scale Videos: Features, Intermediate Representations and their Temporal Interactions." Doctoral diss., University of Central Florida, 2013. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5768.

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Recognition of complex events in consumer uploaded Internet videos, captured under real-world settings, has emerged as a challenging area of research across both computer vision and multimedia community. In this dissertation, we present a systematic decomposition of complex events into hierarchical components and make an in-depth analysis of how existing research are being used to cater to various levels of this hierarchy and identify three key stages where we make novel contributions, keeping complex events in focus. These are listed as follows: (a) Extraction of novel semi-global features -- firstly, we introduce a Lie-algebra based representation of dominant camera motion present while capturing videos and show how this can be used as a complementary feature for video analysis. Secondly, we propose compact clip level descriptors of a video based on covariance of appearance and motion features which we further use in a sparse coding framework to recognize realistic actions and gestures. (b) Construction of intermediate representations -- We propose an efficient probabilistic representation from low-level features computed from videos, based on Maximum Likelihood Estimates which demonstrates state of the art performance in large scale visual concept detection, and finally, (c) Modeling temporal interactions between intermediate concepts -- Using block Hankel matrices and harmonic analysis of slowly evolving Linear Dynamical Systems, we propose two new discriminative feature spaces for complex event recognition and demonstrate significantly improved recognition rates over previously proposed approaches.
Ph.D.
Doctorate
Electrical Engineering and Computing
Engineering and Computer Science
Computer Engineering
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Books on the topic "Algebra - Intermediate"

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Gustafson, R. David. Intermediate algebra. 6th ed. Pacific Grove, CA: Brooks/Cole-Thomson Learning, 2001.

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Miller, Julie. Intermediate algebra. Dubuque, IA: McGraw-Hill, 2007.

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Willis, Alden T. Intermediate algebra. 2nd ed. Belmont, Calif: Wadsworth, 1987.

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Gustafson, R. David. Intermediate algebra. 4th ed. Pacific Grove, Calif: Brooks/Cole, 1995.

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Julie, Miller. Intermediate algebra. 2nd ed. Dubuque, IA: McGraw-Hill, 2008.

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Dugopolski, Mark. Intermediate algebra. 4th ed. Boston: McGraw-Hill Higher Education, 2004.

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Gustafson, R. David. Intermediate algebra. 5th ed. Pacific Grove, CA: Brooks/Cole Pub. Co., 1999.

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Burzynski, Denny. Intermediate algebra. Philadelphia, PA: Saunders College, 1989.

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Tobey, John. Intermediate algebra. 2nd ed. Englewood Cliffs, NJ: Prenctice Hall, 1995.

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Kerry, Bailey, ed. Intermediate algebra. 2nd ed. New York: McGraw-Hill, 2010.

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Book chapters on the topic "Algebra - Intermediate"

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Zarhin, Yuri. "Cubic Surfaces and Cubic Threefolds, Jacobians and Intermediate Jacobians." In Algebra, Arithmetic, and Geometry, 687–91. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4747-6_23.

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Karim, Driss. "On the Set of Intermediate Artinian Subrings." In Homological and Combinatorial Methods in Algebra, 139–49. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74195-6_14.

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Vrahatis, Michael N. "Survey on Generalizations of the Intermediate Value Theorem and Applications." In Computer Algebra in Scientific Computing, 1–17. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-14788-3_1.

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Tuma, M. "Intermediate Fill-In in Sparse QR Decomposition." In Linear Algebra for Large Scale and Real-Time Applications, 425–26. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-015-8196-7_56.

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Izelgue, Lahoucine, and Omar Ouzzaouit. "Pairs of Rings Whose All Intermediate Rings Are G–Rings." In Homological and Combinatorial Methods in Algebra, 111–15. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74195-6_11.

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Ravindra, Padmashree, HyeongSik Kim, and Kemafor Anyanwu. "An Intermediate Algebra for Optimizing RDF Graph Pattern Matching on MapReduce." In The Semanic Web: Research and Applications, 46–61. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21064-8_4.

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Xu, Runqing, Liming Li, and Bohua Zhan. "Verified Interactive Computation of Definite Integrals." In Automated Deduction – CADE 28, 485–503. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79876-5_28.

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AbstractSymbolic computation is involved in many areas of mathematics, as well as in analysis of physical systems in science and engineering. Computer algebra systems present an easy-to-use interface for performing these calculations, but do not provide strong guarantees of correctness. In contrast, interactive theorem proving provides much stronger guarantees of correctness, but requires more time and expertise. In this paper, we propose a general framework for combining these two methods, and demonstrate it using computation of definite integrals. It allows the user to carry out step-by-step computations in a familiar user interface, while also verifying the computation by translating it to proofs in higher-order logic. The system consists of an intermediate language for recording computations, proof automation for simplification and inequality checking, and heuristic integration methods. A prototype is implemented in Python based on HolPy, and tested on a large collection of examples at the undergraduate level.
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Ljapin, E. S., and A. E. Evseev. "Intermediate Associativity." In The Theory of Partial Algebraic Operations, 89–102. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-017-3483-7_5.

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Mahajan, Meena, and Nitin Saurabh. "Some Complete and Intermediate Polynomials in Algebraic Complexity Theory." In Computer Science – Theory and Applications, 251–65. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-34171-2_18.

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Ahman, Danel, and Andrej Bauer. "Runners in Action." In Programming Languages and Systems, 29–55. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44914-8_2.

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AbstractRunners of algebraic effects, also known as comodels, provide a mathematical model of resource management. We show that they also give rise to a programming concept that models top-level external resources, as well as allows programmers to modularly define their own intermediate “virtual machines”. We capture the core ideas of programming with runners in an equational calculus $$\lambda _{\mathsf {coop}}$$ λ coop , which we equip with a sound and coherent denotational semantics that guarantees the linear use of resources and execution of finalisation code. We accompany $$\lambda _{\mathsf {coop}}$$ λ coop with examples of runners in action, provide a prototype language implementation in OCaml, as well as a Haskell library based on $$\lambda _{\mathsf {coop}}$$ λ coop .
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Conference papers on the topic "Algebra - Intermediate"

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Michaelsen, Eckart. "Intermediate grouping on remotely sensed data using Gestalt algebra." In SPIE Remote Sensing, edited by Lorenzo Bruzzone, Jon Atli Benediktsson, and Francesca Bovolo. SPIE, 2014. http://dx.doi.org/10.1117/12.2064396.

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Agrawal, O. P. "Quaternions, Hamilton Operators, and Kinematics of Mechanical Systems." In ASME 1987 Design Technology Conferences. American Society of Mechanical Engineers, 1987. http://dx.doi.org/10.1115/detc1987-0095.

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Abstract In this paper, quaternions are briefly reviewed and their associated matrix algebra is developed. Two Hamilton operators are defined and some of their properties are studied. The properties of these operators are then applied to find kinematic relations of a body undergoing spatial rotation and to find a recursive relation for intermediate-axes. The formulation presented provides an easy approach to kinematic analysis of spatial mechanical systems.
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Sun, Frederick, and Jonathan B. Hopkins. "Mobility Analysis of Interconnected Hybrid Flexure Systems Using Screw Algebra and Graph Theory." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59206.

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This paper introduces a general method for determining the mobility analysis of flexure systems of any complexity, including those that can’t be broken into parallel and serial flexure subsystems. Such systems are called interconnected hybrid flexure systems because they possess limbs with intermediate bodies that are connected by flexure systems or elements. The method in this paper utilizes screw algebra and graph theory to enable designers to determine the freedom spaces (i.e., the geometric shapes that represent all the ways a body is permitted to move) for all the bodies joined together by compliant flexure elements within interconnected hybrid flexure systems. Although many flexure-based precision motion stages, compliant mechanisms, and microarchitectured materials possess topologies that are highly interconnected, the theory for performing a mobility analysis of such interconnected flexure systems using traditional screw theory does not currently exist. The theory introduced here lays the foundation for an automated tool that can rapidly generate the freedom spaces of every rigid body within a general flexure system without having to perform traditional computationally expensive finite element analysis. Case studies are provided in the paper to demonstrate the utility of the proposed theory.
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Navaneethakrishnan, Ravisrinivas, Kristin L. Wood, and Richard H. Crawford. "An Object-Oriented Formalism for Geometric Reasoning in Engineering Design and Manufacture." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0403.

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Abstract Geometry is a language for representing and communicating mechanical design information. To enhance the integration of design and manufacturing tasks, a representation of product geometry at appropriate levels of abstraction for geometric reasoning is necessary. In addition, a mechanism to perform reasoning with the representation is needed. This paper describes a computational formalism for representing and manipulating geometry at different abstraction levels. Geometry is abstracted in terms of form features. Spatial relationships between features, which are important components for geometric reasoning, are represented using a modification of a previously developed technique — the intermediate geometry language (IGL). To enable geometric reasoning, information abstracted using features and the IGL is transformed into a data model based on object-oriented modeling technology. An object algebra is defined to query the data model for information.
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Liu, P., and J. N. Siddall. "Determination of the Minimum Evidence Set in Expert Systems Using Boolean Methods." In ASME 1989 Design Technical Conferences. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/detc1989-0055.

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Abstract A new method is proposed for rapidly solving expert system applications using Boolean algebra formulations. The method consists of two algorithms, applied after the conventional hierarchical type rules have been converted to Boolean expressions. The first algorithm automatically reduces the expressions to the equivalent of only two levels in a logic network, eliminating all intermediate conclusions, and also minimizes the number of inputs per rule. This algorithm has general application in the condensation of rule systems, and makes possible the use of high speed bit matching in specific solutions. The second algorithm operates on the reduced rule set so that, in a given application, a rapid solution is achieved using the fewest possible items of evidence, or user inputs. It is believed that these algorithms will be particularly useful in applications where high speed solutions are important.
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Ishihara, Yuki. "Modular Techniques for Intermediate Primary Decomposition." In ISSAC '22: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2022. http://dx.doi.org/10.1145/3476446.3535488.

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Haspel, Nurit, Dong Luo, and Eduardo Gonzalez. "Detecting intermediate protein conformations using algebraic topology." In 2016 IEEE 6th International Conference on Computational Advances in Bio and Medical Sciences (ICCABS). IEEE, 2016. http://dx.doi.org/10.1109/iccabs.2016.7802779.

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Wu Chengyong, Hu Weiping, Zhang Zhaoqing, and Qiao Ruliang. "Multi-view intermediate representation based on algebraic data type." In Proceedings Fourth International Conference/Exhibition on High Performance Computing in the Asia-Pacific Region. IEEE, 2000. http://dx.doi.org/10.1109/hpc.2000.846559.

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Sabrine Benreguig, Souheir, and Nassira Benhassine. "The Experience of Intermediate Housing in Algeria: Between Social And Spatial Arrangements (The Case Of Touggourt)." In 3rd International Conference of Contemporary Affairs in Architecture and Urbanism. Alanya Hamdullah Emin Paşa Üniversitesi, 2020. http://dx.doi.org/10.38027/n282020iccaua316270.

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Honda, Ryo, Hiroki Yamashita, and Hiroyuki Sugiyama. "Sliding Joint Constraints for the Analysis of Flexible Multibody Systems Using Intermediate Coordinates." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-65108.

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In this investigation, formulations of sliding joint constraints for flexible bodies modeled using the absolute nodal coordinate formulation are developed using intermediate coordinates. Since modeling of prismatic and cylindrical joints for flexible bodies requires solutions to moving boundary problems in which joint definition points are moving on flexible bodies, arc-length coordinates are introduced for defining time-variant constraint definition points on flexible bodies. While this leads to a systematic modeling procedure for sliding joints, specialized formulations and implementations are required in general multibody dynamics computer algorithms. For this reason, intermediate coordinates are introduced to derive a mapping between the generalized gradient coordinates used in the absolute nodal coordinate formulation and the intermediate rotational coordinates used for defining the orientation constraints with rigid bodies. With this mapping, existing joint constraint libraries formulated for rigid bodies can be employed for the absolute nodal coordinate formulation without significant modifications. It is also demonstrated that the intermediate coordinates and arc-length coordinates introduced for modeling sliding joint constraints can be systematically eliminated from the equations of motion and standard differential algebraic equations used in general multibody dynamics computer algorithms can be obtained. Several numerical examples are presented in order to demonstrate the use of the formulation developed in this investigation.
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