Relevant bibliographies by topics / Real conjugacy classes

Academic literature on the topic 'Real conjugacy classes'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Real conjugacy classes"

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Chan, Kai-Cheong, and Dragomir Ž. Đoković. "Conjugacy Classes of Subalgebras of the Real Sedenions." Canadian Mathematical Bulletin 49, no. 4 (December 1, 2006): 492–507. http://dx.doi.org/10.4153/cmb-2006-048-6.

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AbstractBy applying the Cayley–Dickson process to the division algebra of real octonions, one obtains a 16-dimensional real algebra known as (real) sedenions. We denote this algebra by A4. It is a flexible quadratic algebra (with unit element 1) but not a division algebra.We classify the subalgebras of A4 up to conjugacy (i.e., up to the action of the automorphismgroup G of A4) with one exception: we leave aside the more complicated case of classifying the quaternion subalgebras. Any nonzero subalgebra contains 1 and we show that there are no proper subalgebras of dimension 5, 7 or > 8. The proper non-division subalgebras have dimensions 3, 6 and 8. We show that in each of these dimensions there is exactly one conjugacy class of such subalgebras. There are infinitely many conjugacy classes of subalgebras in dimensions 2 and 4, but only 4 conjugacy classes in dimension 8.
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Beltrán, A., M. J. Felipe, and C. Melchor. "Squares of real conjugacy classes in finite groups." Annali di Matematica Pura ed Applicata (1923 -) 197, no. 2 (July 18, 2017): 317–28. http://dx.doi.org/10.1007/s10231-017-0681-0.

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Doković, Dragomir Ž., and Nguyêñ Quôć Thăńg. "Conjugacy Classes of Maximal Tori in Simple Real Algebraic Groups and Applications." Canadian Journal of Mathematics 46, no. 4 (August 1, 1994): 699–717. http://dx.doi.org/10.4153/cjm-1994-039-5.

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AbstractLet G be an almost simple complex algebraic group defined over R, and let G(R) be the group of real points of G. We enumerate the G(R)-conjugacy classes of maximal R-tori of G. Each of these conjugacy classes is also a single G(R)˚-conjugacy class, where G(R)˚ is the identity component of G(R), viewed as a real Lie group. As a consequence we also obtain a new and short proof of the Kostant-Sugiura's theorem on conjugacy classes of Cartan subalgebras in simple real Lie algebras.A connected real Lie group P is said to be weakly exponential (w.e.) if the image of its exponential map is dense in P. This concept was introduced in [HM] where also the question of identifying all w.e. almost simple real Lie groups was raised. By using a theorem of A. Borel and our classification of maximal R-tori we answer the above question when P is of the form G(R)˚.
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AMPARO, ELENA, and C. RYAN VINROOT. "ON THE NUMBER OF REAL CLASSES IN THE FINITE PROJECTIVE LINEAR AND UNITARY GROUPS." Glasgow Mathematical Journal 62, no. 1 (January 31, 2019): 93–107. http://dx.doi.org/10.1017/s0017089518000551.

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AbstractWe show that for any n and q, the number of real conjugacy classes in $ \rm{PGL}(\it{n},\mathbb{F}_q) $ is equal to the number of real conjugacy classes of $ \rm{GL}(\it{n},\mathbb{F}_q) $ which are contained in $ \rm{SL}(\it{n},\mathbb{F}_q) $, refining a result of Lehrer [J. Algebra36(2) (1975), 278–286] and extending the result of Gill and Singh [J. Group Theory14(3) (2011), 461–489] that this holds when n is odd or q is even. Further, we show that this quantity is equal to the number of real conjugacy classes in $ \rm{PGU}(\it{n},\mathbb{F}_q) $, and equal to the number of real conjugacy classes of $ \rm{U}(\it{n},\mathbb{F}_q) $ which are contained in $ \rm{SU}(\it{n},\mathbb{F}_q) $, refining results of Gow [Linear Algebra Appl.41 (1981), 175–181] and Macdonald [Bull. Austral. Math. Soc.23(1) (1981), 23–48]. We also give a generating function for this common quantity.
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Dolfi, Silvio, Emanuele Pacifici, and Lucia Sanus. "Finite groups with real conjugacy classes of prime size." Israel Journal of Mathematics 175, no. 1 (January 2010): 179–89. http://dx.doi.org/10.1007/s11856-010-0008-y.

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Robati, S. M. "Real-Imaginary Conjugacy Classes and Real-Imaginary Irreducible Characters in Finite Groups." Mathematical Notes 103, no. 1-2 (January 1, 2017): 251–58. http://dx.doi.org/10.1134/s0001434618010261.

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Sangroniz, Josu, and Joan Tent. "2-Groups with a fixed number of real conjugacy classes." Journal of Algebra 392 (October 2013): 42–51. http://dx.doi.org/10.1016/j.jalgebra.2013.05.031.

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Gongopadhyay, Krishnendu. "Algebraic Characterization of Isometries of the Hyperbolic 4-Space." ISRN Geometry 2012 (February 29, 2012): 1–12. http://dx.doi.org/10.5402/2012/757489.

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We classify isometries of the real hyperbolic 4-space by their conjugacy classes of centralizers. We use the representation of the isometries by quaternionic matrices to obtain this characterization. Another characterization in terms of conjugacy invariants is also given.
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Beltrán, A., and S. M. Robati. "Erratum to: Real-Imaginary Conjugacy Classes and Real-Imaginary Irreducible Characters in Finite Groups." Mathematical Notes 110, no. 3-4 (September 2021): 638–39. http://dx.doi.org/10.1134/s0001434621090352.

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Beltran, A., and Sajjad Mahmood Robati. "Erratum to: Real-Imaginary Conjugacy Classes and Real-Imaginary Irreducible Characters in Finite Groups." Matematicheskie Zametki 110, no. 4 (2021): 638–39. http://dx.doi.org/10.4213/mzm12922.

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Dissertations / Theses on the topic "Real conjugacy classes"

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BONAZZI, LORENZO. "Prime graphs of Finite Groups." Doctoral thesis, 2022. https://hdl.handle.net/2158/1294339.

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All the groups treated in the thesis are finite. Let X be a set of integers and consider the primes that divide some element of X as vertices, where two vertices are adjacent if their product divides some element of X. The graph obtained is called the prime graph on X. In this thesis we give an algebraic description of a group G in the following three cases. 1. When the Gruenberg-Kegel graph of G (that is the prime graph on the set of all group element orders) has a cut-set. 2. When the prime graph on the degrees of irreducible real characters of G has no edges. 3. When the prime graph on the lengths of real conjugacy classes has no edges. Is presented also a description of groups acting on a module in the case that the lengths of orbits are prime powers.
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Book chapters on the topic "Real conjugacy classes"

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Reutenauer, Christophe. "Words and Quadratic Numbers." In From Christoffel Words to Markoff Numbers, 43–48. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198827542.003.0007.

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This chapter offers an overview of words and quadratic numbers, and in particular ordering the conjugates of a Christoffel word. Within this topic the reader learns that the reversal of a Christoffel word is a conjugate, and that the lower and upper Christoffel words of the same slope are the smallest and the largest in their conjugation class. The chapter discusses computation in terms ofMarkoff numbers of the quadratic real number which has a periodic continued fraction with periodic pattern equal to a Christoffel word written on the alphabet 11, 22. It also reviews computation of theMarkoff supremum of a periodic biinfinite sequence, and of theLagrange number of a periodic sequence, both having a periodic pattern as above.
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Larson, Richard S., and Alexandre Chigaev. "Applications of Flow Cytometry to Cell Adhesion Biology: From Aggregates to Drug Discovery." In Flow Cytometry for Biotechnology. Oxford University Press, 2005. http://dx.doi.org/10.1093/oso/9780195183146.003.0023.

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Flow cytometry represents a powerful and evolving methodologic approach to cell adhesion biology. In its beginnings, flow cytometry was used solely to measure the expression of receptors on cellular surfaces and to correlate that expression with biologic function in non-flow-cytometry-based assays. From this primitive beginning, applications have proliferated and now include methodologies that measure real-time aggregation, receptor activity, and the downstream biologic consequences of cell adhesion. These biologic applications have led to platforms that are easily employed as drug screening and target validation tools. Functional assays that measure cell aggregation were initially developed to measure cell–cell interactions in the immune system, especially between cytotoxic cells and various cell types targeted as the focus of their cytotoxic activity. The cytotoxic “effector” cells and the “target” cells were stained with spectrally distinct fluorescent dyes, gently sedimented together into a cell pellet, and allowed to interact under static conditions for designated intervals of time. When resuspended and introduced into the flow cytometer, effector cells adherent to target cells were detected as “conjugate” particles emitting the fluorescence spectra of both dyes. Nonadherent effector and target cells were detected as monochromatically fluorescent particles. By using ion concentration–sensitive cytoplasmic fluorescent probes as the effector cell labels, it was also possible to detect physiological changes in intracellular ionized calcium and pH elicited by adhesion to target cells and to correlate these responses with cytotoxic function. Later, methods were developed for continuously measuring (“real-time”) cell adhesive interactions as they progressed over time in a fluid shear environment. A limitation of early adhesion kinetics analyses was that the fluid shear was generated with a magnetic stir bar and was thus neither homogeneous nor amenable to precise quantification. Subsequent refinement of these methods has enabled flow cytometric analysis of cell mixtures subjected to a more uniform and quantifiable fluid shear environment generated in a cone-plate viscometer. Cell mixtures are sampled periodically from the viscometer into a formalin fixative solution for subsequent off-line flow cytometric analysis. These experiments have been able to demonstrate a remarkable potentiation of adhesion efficiency through the combined action of two sets of adhesion molecules and a progression of adhesion molecule use from one class to another over time.
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Conference papers on the topic "Real conjugacy classes"

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Zhu, Xiaojin, Ji Liu, and Manuel Lopes. "No Learner Left Behind: On the Complexity of Teaching Multiple Learners Simultaneously." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/502.

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We present a theoretical study of algorithmic teaching in the setting where the teacher must use the same training set to teach multiple learners. This problem is a theoretical abstraction of the real-world classroom setting in which the teacher delivers the same lecture to academically diverse students. We define a minimax teaching criterion to guarantee the performance of the worst learner in the class. We prove that the teaching dimension increases with class diversity in general. For the classes of conjugate Bayesian learners and linear regression learners, respectively, we exhibit corresponding minimax teaching set. We then propose a method to enhance teaching by partitioning the class into sections. We present cases where the optimal partition minimizes overall teaching dimension while maintaining the guarantee on all learners. Interestingly, we show personalized education (one learner per section) is not necessarily the optimal partition. Our results generalize algorithmic teaching to multiple learners and offer insight on how to teach large classes.
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Nigmatullin, Raoul R. "The “Fractional” Kinetic Equations and General Theory of Dielectric Relaxation." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84647.

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Based on the Mori-Zwanzig formalism it becomes possible to suggest a general decoupling procedure, which reduces a wide set of various micromotions distributed over a self-similar structure to a few collective/reduced motions describing the relaxation/exchange behavior of a complex system in the mesoscale region. The frequency dependence of the reduced collective motion contains real and pair of complex-conjugate power-law exponents in the frequency domain and explains naturally the “universal response” (UR) phenomenon discovered by A. Jonscher in a wide class of heterogeneous materials. This strict mathematical result allows in developing a consistent and general theory of dielectric relaxation that can describe wide set of dielectric spectroscopy (DS) data measured in some frequency/temperature range in many heterogeneous materials. Based on this result it becomes possible also to suggest a new set of two-pole elements, which generalizes the conventional RLC-elements and can constitute the basis of new theory of the linear electric circuits.
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