Relevant bibliographies by topics / Group theory and generalizations

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

Academic literature on the topic 'Group theory and generalizations'

Author: Grafiati
Published: 4 June 2021
Last updated: 29 July 2024

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Journal articles on the topic "Group theory and generalizations"

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Isaacs, I. M., and M. R. Pournaki. "Generalizations of Fermat's Little Theorem via Group Theory." American Mathematical Monthly 112, no. 8 (October 1, 2005): 734. http://dx.doi.org/10.2307/30037576.

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Isaacs, I. M., and M. R. Pournaki. "Generalizations of Fermat's Little Theorem via Group Theory." American Mathematical Monthly 112, no. 8 (October 2005): 734–40. http://dx.doi.org/10.1080/00029890.2005.11920246.

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Wang, Zichuan. "Proofs, Generalizations and Applications of Fermat’s Little Theorem." Highlights in Science, Engineering and Technology 47 (May 11, 2023): 32–36. http://dx.doi.org/10.54097/hset.v47i.8161.

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This paper introduces Fermat’s little theorem (FLT), which says that any integer raised to power is congruent to modulo . This paper will give several proofs of FLT, using methods including number theory and group theory, together with generalizations of FLT in different directions. FLT is an important result in number theory and group theory. It has multiple generalizations and corollaries, and one of its corollaries is the foundation of RSA cryptography. The effort made trying to prove FLT stimulated researches in many fields in mathematics, and FLT is crucial and fundamental in research of modern cryptography.
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MARCOLLI, MATILDE, and VARGHESE MATHAI. "TWISTED INDEX THEORY ON GOOD ORBIFOLDS, I: NONCOMMUTATIVE BLOCH THEORY." Communications in Contemporary Mathematics 01, no. 04 (November 1999): 553–87. http://dx.doi.org/10.1142/s0219199799000213.

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We study the twisted index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective action of the orbifold fundamental group. We apply these results to obtain qualitative results on real and complex hyperbolic spaces in two and four dimensions, related to generalizations of the Bethe–Sommerfeld conjecture and the Ten Martini Problem, on the spectrum of self adjoint elliptic operators which are invariant under a projective action of a discrete cocompact group.
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GRISHKOV, ALEXANDER, and EUGENE LOGINOV. "ON SOME GENERALIZATIONS OF GROUPS WITH TRIALITY." International Journal of Algebra and Computation 22, no. 02 (March 2012): 1250015. http://dx.doi.org/10.1142/s0218196711006820.

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In the present paper we generalize the concept of groups with triality and apply it to the theory of the Moufang, Bol and Bruck loops. Such generalizations allow us to reduce certain problems from the loop theory to problems in the theory of groups.
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Morato, Elisson. "GENERALIZAÇÃO DISCURSIVA E ENUNCIAÇÃO NAS CANTIGAS DE CONGADO EM MINAS GERAIS: UMA ABORDAGEM SEMIOLINGUÍSTICA." Entremeios, Revista de Estudos do Discurso 22, no. 22 (December 29, 2020): 236–54. http://dx.doi.org/10.20337/issn2179-3514revistaentremeiosvol22pagina236a254.

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This paper studies the discursive generalizations in the congado songs of the Brazilian state of Minas Gerais through the Discourse Analysis of French line. From the concept of discursive generalization, developed by Ali-Bouacha (1993, [2007] 2020) and by Moirand (1990), and throught the concepts of language competences, discursive strategies and enunciation, from the Semiolinguistic theory developed by Charaudeau (1983, [2000] 2020a, 2004a, 2004b, 2005a, 2005b, [2006] 2020b, 2008), we understand that discursive generalizations would be effects of meaning based on the assignation of this discourse to a meta-enunciator, building effects of universal truth. This procedure contributes for that a knowledge set forms the identity of a social group deeply identified with the Afro-Brazilian cultural traditions.
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Uuye, Otgonbayar. "The Baum-Connes conjecture for KK-theory." Journal of K-Theory 8, no. 1 (April 7, 2010): 3–29. http://dx.doi.org/10.1017/is010003012jkt114.

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AbstractWe define and compare two bivariant generalizations of the topological K - group Ktop(G). We consider the Baum-Connes conjecture in this context and study its relation to the usual Baum-Connes conjecture.
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Baytaş, Bekir, Martin Bojowald, and Sean Crowe. "Equivalence of Models in Loop Quantum Cosmology and Group Field Theory." Universe 5, no. 2 (January 23, 2019): 41. http://dx.doi.org/10.3390/universe5020041.

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The paradigmatic models often used to highlight cosmological features of loop quantum gravity and group field theory are shown to be equivalent, in the sense that they are different realizations of the same model given by harmonic cosmology. The loop version of harmonic cosmology is a canonical realization, while the group-field version is a bosonic realization. The existence of a large number of bosonic realizations suggests generalizations of models in group field cosmology.
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Dobrynina, Irina V., and Evgeny V. Manokhin. "ON THE SOLVABILITY OF GENERALIZATION OF THE CONJUGACY PROBLEM OF SUBGROUPS IN A CERTAIN CLASS OF ARTIN GROUPS." SOFT MEASUREMENTS AND COMPUTING 4, no. 65 (2023): 25–34. http://dx.doi.org/10.36871/2618-9976.2023.04.003.

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At the beginning of the twentieth century, the fundamental problems in group theory from the point of view of the existence of algorithms took shape. These include the problems of words, as well as the conjugacy of arbitrary words (formulated by M. Den). In addition, the problem of isomorphism for groups is posed (formulated by G. Titze). Russian algebraists P.S. Novikov and S.I. Adyan were able to obtain a proof of the unsolvability of these problems for all groups belonging to finitely defined groups. After the publication of these results, algorithmic problems, together with their various generalizations, are investigated already in fixed classes of groups. As one of the generalizations of the problem for conjugacy of arbitrary words, the question of conjugacy of arbitrary subgroups is posed, namely, the question of finding an algorithm that, by arbitrary subgroups given by a finite set of generating and defining words of some group, could determine whether they are conjugate in this group or not conjugate. As another generalization of the conjugacy of words, we can consider generalized conjugacy for words, which allows us to determine an algorithm capable of determining from arbitrary finite sets of words from a certain group whether they will be conjugated in it or not. If both of these generalizations are combined into one, then we get a generalization of the conjugacy problem of subgroups. Artin groups appeared a long time ago, they include wellknown braid groups that have been studied from an algebraic point of view since the twenties of the last century. The solution of the problems under consideration in Artin's groups caused great difficulties, which led to the allocation of various subclasses. The article proves the solvability of generalization of the conjugacy problem of subgroups in Artin groups on two generating ones.
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Guo, Xiao-Kan. "Thermofield double states in group field theory." International Journal of Modern Physics A 36, no. 02 (January 20, 2021): 2150008. http://dx.doi.org/10.1142/s0217751x21500081.

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Group field theories are higher-rank generalizations of matrix/tensor models, and encode the simplicial geometries of quantum gravity. In this paper, we study the thermofield double states in group field theories. The starting point is the equilibrium Gibbs states in group field theory recently found by Kotecha and Oriti, based on which we construct the thermofield double state as a “thermal” vacuum respecting the Kubo–Martin–Schwinger condition. We work with the Weyl [Formula: see text]-algebra of group fields, and a particular type of thermofield double states with single type of symmetry is obtained from the squeezed states on this Weyl algebra. The thermofield double states, when viewed as states on the group field theory Fock vacuum, are condensate states at finite flow parameter [Formula: see text]. We suggest that the equilibrium flow parameters [Formula: see text] of this type of thermofield double states in the group field theory condensate pictures of black hole horizon and quantum cosmology are related to the inverse temperatures in gravitational thermodynamics.
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Dissertations / Theses on the topic "Group theory and generalizations"

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Byler, Katherine S. "Generalizations of the bias invariant /." view abstract or download file of text, 2003. http://wwwlib.umi.com/cr/uoregon/fullcit?p3102156.

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Thesis (Ph. D.)--University of Oregon, 2003.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 139-141). Also available for download via the World Wide Web; free to University of Oregon users.
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Zhang, Xiankun. "Generalizations of colorability and connectivity of graphs." Morgantown, W. Va. : [West Virginia University Libraries], 1998. http://etd.wvu.edu/templates/showETD.cfm?recnum=333.

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Thesis (Ph. D.)--West Virginia University, 1998.
Title from document title page. Document formatted into pages; contains vii, 97 p. : ill. Includes abstract. Includes bibliographical references (p. 93-96).
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Semeraro, Jason P. G. "Centralisers and amalgams of saturated fusion systems." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:43d7d6d0-363b-4bc7-b17f-5713cc586737.

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In this thesis, we mainly address two contrasting topics in the area of saturated fusion systems. The first concerns the notion of a centraliser of a subsystem E of a fusion system F, and we give new proofs of the existence of such an object in the case where E is normal in F. The second concerns the development of the theory of `trees of fusion systems', an analogue for fusion systems of Bass-Serre theory for finite groups. A major theorem finds conditions on a tree of fusion systems for there to exist a saturated completion, and this is applied to construct and classify certain fusion systems over p-groups with an abelian subgroup of index p. Results which do not fall into either of the above categories include a new proof of Thompson's normal p-complement Theorem for saturated fusion systems and characterisations of certain quotients of fusion systems which possess a normal subgroup.
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Kuckuck, Benno. "Finiteness properties of fibre products." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:a9624d17-9d11-4bd0-8c46-78cbba73469c.

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A group Γ is of type Fn for some n ≥ 1 if it has a classifying complex with finite n-skeleton. These properties generalise the classical notions of finite generation and finite presentability. We investigate the higher finiteness properties for fibre products of groups.
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Sale, Andrew W. "The length of conjugators in solvable groups and lattices of semisimple Lie groups." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:ea21dab2-2da1-406a-bd4f-5457ab02a011.

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The conjugacy length function of a group Γ determines, for a given a pair of conjugate elements u,v ∈ Γ, an upper bound for the shortest γ in Γ such that uγ = γv, relative to the lengths of u and v. This thesis focuses on estimating the conjugacy length function in certain finitely generated groups. We first look at a collection of solvable groups. We see how the lamplighter groups have a linear conjugacy length function; we find a cubic upper bound for free solvable groups; for solvable Baumslag--Solitar groups it is linear, while for a larger family of abelian-by-cyclic groups we get either a linear or exponential upper bound; also we show that for certain polycyclic metabelian groups it is at most exponential. We also investigate how taking a wreath product effects conjugacy length, as well as other group extensions. The Magnus embedding is an important tool in the study of free solvable groups. It embeds a free solvable group into a wreath product of a free abelian group and a free solvable group of shorter derived length. Within this thesis we show that the Magnus embedding is a quasi-isometric embedding. This result is not only used for obtaining an upper bound on the conjugacy length function of free solvable groups, but also for giving a lower bound for their Lp compression exponents. Conjugacy length is also studied between certain types of elements in lattices of higher-rank semisimple real Lie groups. In particular we obtain linear upper bounds for the length of a conjugator from the ambient Lie group within certain families of real hyperbolic elements and unipotent elements. For the former we use the geometry of the associated symmetric space, while for the latter algebraic techniques are employed.
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Wellen, George Arthur. "Branch groups and automata." Thesis, University of Oxford, 2008. http://ora.ox.ac.uk/objects/uuid:b0be5468-cce9-421b-85be-c386d7c3808a.

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The focus of this thesis is finitely generated subgroups of the automorphism group of an infinite spherically homogeneous rooted tree (regular or irregular). The first chapter introduces the topic and outlines the main results. The second chapter provides definitions of the terminology used, and also some preliminary results. The third chapter introduces a group that appears to be a promising candidate for a finitely generated group of infinite upper rank with finite upper $p$-rank for all primes $p$. It goes on to demonstrate that in fact this group has infinite upper $p$-rank for all primes $p$. As a by-product of this construction, we obtain a finitely generated branch group with quotients that are virtually-(free abelian of rank $n$) for arbitrarily large $n$. The fourth chapter gives a complete classification of ternary automata with $C_2$-action at the root, and a partial classification of ternary automata with $C_3$-action at the root. The concept of a `windmill automaton' is introduced in this chapter, and a complete classification of binary windmill automata is given. The fifth chapter contains a detailed study of the non-abelian ternary automata with $C_3$-action at the root. It also contains some conjectures about possible isomorphisms between these groups.
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Kielak, Dawid. "Free and linear representations of outer automorphism groups of free groups." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:f2045fba-1546-4dd3-af9f-7d02c4fc505e.

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For various values of n and m we investigate homomorphisms from Out(F_n) to Out(F_m) and from Out(F_n) to GL_m(K), i.e. the free and linear representations of Out(F_n) respectively. By means of a series of arguments revolving around the representation theory of finite symmetric subgroups of Out(F_n) we prove that each homomorphism from Out(F_n) to GL_m(K) factors through the natural map p_n from Out(F_n) to GL(H_1(F_n,Z)) = GL_n(Z) whenever n=3, m < 7 and char(K) is not an element of {2,3}, and whenever n>5, m< n(n+1)/2 and char(K) is not an element of {2,3,...,n+1}. We also construct a new infinite family of linear representations of Out(F_n) (where n > 2), which do not factor through p_n. When n is odd these have the smallest dimension among all known representations of Out(F_n) with this property. Using the above results we establish that the image of every homomorphism from Out(F_n) to Out(F_m) is finite whenever n=3 and n < m < 6, and of cardinality at most 2 whenever n > 5 and n < m < n(n-1)/2. We further show that the image is finite when n(n-1)/2 -1 < m < n(n+1)/2. We also consider the structure of normal finite index subgroups of Out(F_n). If N is such then we prove that if the derived subgroup of the intersection of N with the Torelli subgroup T_n < Out(F_n) contains some term of the lower central series of T_n then the abelianisation of N is finite.
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Craven, David Andrew. "Algebraic modules for finite groups." Thesis, University of Oxford, 2007. http://ora.ox.ac.uk/objects/uuid:7f641b33-d301-4445-8269-a5a33f4b7e5e.

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The main focus of this thesis is algebraic modules---modules that satisfy a polynomial equation with integer co-efficients in the Green ring---in various finite groups, as well as their general theory. In particular, we ask the question `when are all the simple modules for a finite group G algebraic?' We call this the (p-)SMA property. The first chapter introduces the topic and deals with preliminary results, together with the trivial first results. The second chapter provides the general theory of algebraic modules, with particular attention to the relationship between algebraic modules and the composition factors of a group, and between algebraic modules and the Heller operator and Auslander--Reiten quiver. The third chapter concerns itself with indecomposable modules for dihedral and elementary abelian groups. The study of such groups is both interesting in its own right, and can be applied to studying simple modules for simple groups, such as the sporadic groups in the final chapter. The fourth chapter analyzes the groups PSL(2,q); here we determine, in characteristic 2, which simple modules for PSL(2,q) are algebraic, for any odd q. The fifth chapter generalizes this analysis to many groups of Lie type, although most results here are in defining characteristic only. Notable exceptions include the small Ree groups, which have the 2-SMA property for all q. The sixth and final chapter focuses on the sporadic groups: for most groups we provide results on some simple modules, and some of the groups are completely analyzed in all characteristics. This is normally carried out by restricting to the Sylow p-subgroup. This thesis develops the current state of knowledge concerning algebraic modules for finite groups, and particularly for which simple groups, and for which primes, all simple modules are algebraic.
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Wharton, Elizabeth. "The model theory of certain infinite soluble groups." Thesis, University of Oxford, 2006. http://ora.ox.ac.uk/objects/uuid:7bd8d05b-4ff6-4326-8463-f896e2862e25.

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This thesis is concerned with aspects of the model theory of infinite soluble groups. The results proved lie on the border between group theory and model theory: the questions asked are of a model-theoretic nature but the techniques used are mainly group-theoretic in character. We present a characterization of those groups contained in the universal closure of a restricted wreath product U wr G, where U is an abelian group of zero or finite square-free exponent and G is a torsion-free soluble group with a bound on the class of its nilpotent subgroups. For certain choices of G we are able to use this characterization to prove further results about these groups; in particular, results related to the decidability of their universal theories. The latter part of this work consists of a number of independent but related topics. We show that if G is a finitely generated abelian-by-metanilpotent group and H is elementarily equivalent to G then the subgroups gamma_n(G) and gamma_n(H) are elementarily equivalent, as are the quotient groups G/gamma_n(G) and G/gamma_n(H). We go on to consider those groups universally equivalent to F_2(VN_c), where the free groups of the variety V are residually finite p-groups for infinitely many primes p, distinguishing between the cases when c = 1 and when c > 2. Finally, we address some important questions concerning the theories of free groups in product varieties V_k · · ·V_1, where V_i is a nilpotent variety whose free groups are torsion-free; in particular we address questions about the decidability of the elementary and universal theories of such groups. Results mentioned in both of the previous two paragraphs have applications here.
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Riley, Timothy Rupert. "Asymptotic invariants of infinite discrete groups." Thesis, University of Oxford, 2002. http://ora.ox.ac.uk/objects/uuid:30f42f4c-e592-44c2-9954-7d9e8c1f3d13.

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Asymptotic cones. A finitely generated group has a word metric, which one can scale and thereby view the group from increasingly distant vantage points. The group coalesces to an "asymptotic cone" in the limit (this is made precise using techniques of non-standard analysis). The reward is that in place of the discrete group one has a continuous object "that is amenable to attack by geometric (e.g. topological, infinitesimal) machinery" (to quote Gromov). We give coarse geometric conditions for a metric space X to have N-connected asymptotic cones. These conditions are expressed in terms of certain filling functions concerning filling N-spheres in an appropriately coarse sense. We interpret the criteria in the case where X is a finitely generated group Γ with a word metric. This leads to upper bounds on filling functions for groups with simply connected cones -- in particular they have linearly bounded filling length functions. We prove that if all the asymptotic cones of Γ are N-connected then Γ is of type FN+1 and we provide N-th order isoperimetric and isodiametric functions. Also we show that the asymptotic cones of a virtually polycyclic group Γ are all contractible if and only if Γ is virtually nilpotent. Combable groups and almost-convex groups. A combing of a finitely generated group Γ is a normal form; that is a choice of word (a combing line) for each group element that satisfies a geometric constraint: nearby group elements have combing lines that fellow travel. An almost-convexity condition concerns the geometry of closed balls in the Cayley graph for Γ. We show that even the most mild combability or almost-convexity restrictions on a finitely presented group already force surprisingly strong constraints on the geometry of its word problem. In both cases we obtain an n! isoperimetric function, and upper bounds of ~ n2 on both the minimal isodiametric function and the filling length function.
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Books on the topic "Group theory and generalizations"

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Bestvina, Mladen, Michah Sageev, and Karen Vogtmann. Geometric group theory. Providence, RI: American Mathematical Society, 2014.

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Benjamin, Fine. Algebraic generalizations of discrete groups: A path to combinatorial group theory through one-relator products. New York: Marcel Dekker, 1999.

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Volodymyr, Mazorchuk, ed. Classical finite transformation semigroups: An introduction. London: Springer, 2009.

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J, Collins D., ed. Combinatorial group theory and applications to geometry. Berlin: Springer, 1998.

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M, Lazard, and Cartier Pierre, eds. Classification des Groupes Algébriques Semi-simples: The Classification of Semi-simple Algebraic Groups Collected Works. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005.

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Schneider, Peter. Modular Representation Theory of Finite Groups. London: Springer London, 2013.

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Pavel, Zalesskii, ed. Profinite groups. 2nd ed. Berlin: Springer, 2010.

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Machì, Antonio. Groups: An Introduction to Ideas and Methods of the Theory of Groups. Milano: Springer Milan, 2012.

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Herbert, Heyer, and Oberwolfach Conference on Probability Measures on Groups (10th : 1990), eds. Probability measures on groups, X. New York: Plenum Press, 1991.

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Morse, Robert Fitzgerald, editor of compilation, Nikolova-Popova, Daniela, 1952- editor of compilation, and Witherspoon, Sarah J., 1966- editor of compilation, eds. Group theory, combinatorics and computing: International Conference in honor of Daniela Nikolova-Popova's 60th birthday on Group Theory, Combinatorics and Computing, October 3-8, 2012, Florida Atlantic University, Boca Raton, Florida. Providence, Rhode Island: American Mathematical Society, 2013.

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Book chapters on the topic "Group theory and generalizations"

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Lewis, Mark L. "Camina Groups, Camina Pairs, and Generalizations." In Group Theory and Computation, 141–73. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-2047-7_8.

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Robinson, Derek J. S. "Generalizations of Nilpotent and Soluble Groups." In A Course in the Theory of Groups, 356–84. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4419-8594-1_12.

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Robinson, Derek J. S. "Generalizations of Nilpotent and Soluble Groups." In A Course in the Theory of Groups, 342–70. New York, NY: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4684-0128-8_12.

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Bubboloni, Daniela, Pablo Spiga, and Thomas Stefan Weigel. "Almost Simple Groups Having Socle a Sporadic Simple Group." In Normal 2-Coverings of the Finite Simple Groups and their Generalizations, 129–33. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-62348-6_10.

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Guo, Wenbin. "The $\mathfrak{F}$ -Hypercenter and Its Generalizations." In Structure Theory for Canonical Classes of Finite Groups, 1–61. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-45747-4_1.

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Kimoto, Kazufumi. "Generalized Group–Subgroup Pair Graphs." In International Symposium on Mathematics, Quantum Theory, and Cryptography, 169–85. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5191-8_14.

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Abstract A regular finite graph is called a Ramanujan graph if its zeta function satisfies an analog of the Riemann Hypothesis. Such a graph has a small second eigenvalue so that it is used to construct cryptographic hash functions. Typically, explicit family of Ramanujan graphs are constructed by using Cayley graphs. In the paper, we introduce a generalization of Cayley graphs called generalized group–subgroup pair graphs, which are a generalization of group–subgroup pair graphs defined by Reyes-Bustos. We study basic properties, especially spectra of them.
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Ustimenko, V. A. "On Some Properties of Geometries of Chevalley Groups and Their Generalizations." In Investigations in Algebraic Theory of Combinatorial Objects, 473–505. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-017-1972-8_17.

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Fulton, William. "Generalizations." In Intersection Theory, 393–405. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1700-8_21.

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Arov, Damir Z., and Harry Dym. "Generalizations." In Operator Theory: Advances and Applications, 225–54. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-70262-9_7.

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Korostelev, A. P., and A. B. Tsybakov. "Generalizations and Extensions." In Minimax Theory of Image Reconstruction, 128–62. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-2712-0_5.

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Conference papers on the topic "Group theory and generalizations"

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Hecht, K. T. "Generalizations of the vector coherent state method." In Group Theory in Physics: Proceedings of the international symposium held in honor of Professor Marcos Moshinsky. AIP, 1992. http://dx.doi.org/10.1063/1.42843.

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Hamm, Keaton, Benjamin Hayes, and Armenak Petrosyan. "Rearranged Fourier Series and Generalizations to Non-Commutative Groups." In 2019 13th International conference on Sampling Theory and Applications (SampTA). IEEE, 2019. http://dx.doi.org/10.1109/sampta45681.2019.9030904.

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Kharinov, Mikhail. "Natural non‐group symmetry in modern applications." In V International Scientific Workshop on Modeling, Information Processing and Computing. CEUR-WS.org, 2022. http://dx.doi.org/10.47813/dnit-mip5/2022-3091-38-45.

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Intuitively perceived symmetry is formalized for effective application in physics, mathematics, and engineering. In this regard, several scientific research directions are indicated, which are expressed by three generalizations: a) the concept of symmetry using the example of normalized Hadamard matrices; b) cross vector product for the cases of three arguments and seven-dimensional space, c) Lorentz transformations for doubling the spacetime dimension. To generalize and formalize the concept of symmetry, the preservation of the symmetry of matrices under permutations of rows (columns) is studied. It is shown that the set of symmetrypreserving permutations does not constitute a group. For the development of the octonion toolkit and the best generalization of the vector product, based on symmetry considerations, the decomposition of the triple product of octonions into the sum of a triple anticommutator, a triple commutator (generalized vector product) and an associator is deduced. To begin the generalization of Lorentz transformations Lorentz boost is recorded in terms of quaternions so that the treated expressions retain their meaning in the octonionic space. To speed up the assimilation of the research results, the paper proposes some elementary information on the three listed topics, which it is desirable to place in reference books, as well as bring to the attention of students in general education courses at technical universities.
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Rodríguez Carrión, Awilda. "The Hidden Ground: Native American Intercultural Relations." In Schools of Thought Conference. University of Oklahoma, 2020. http://dx.doi.org/10.15763/11244/335070.

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Over the last two decades, a trend has been developing in the design community to promote social equity and emphasize the ethical responsibility of design. Community participation, programming, and post-occupancy evaluations have cemented a more democratic design process in which users, clients, and community members are given a voice to affect the final architecture product through a process called participatory design. This modus operandi becomes more vital when dealing with subcultures that historically have felt marginalized from the dominant culture. In the United States, there is great diversity among Native Americans, but our mainstream culture tends to see them as a homogeneous group, focusing on their commonalities rather than discovering and understanding individual tribal values. With the blind acceptance of generalizations about any subculture, we may miss the critical details that shape the opportunity to showcase their uniqueness and celebrate their differences. Within the studio context, what learning modalities are best to implement a participatory and constructivist learning experience? Traditionally, studio teaching with project-based design focuses on students learning formal considerations of design such as theory, environmental/structural performance, and implementation of regulatory measures. The participatory design methodology (PDM) differs in its approach by focusing on a process that emerges from all players. It does not dictate design but creates an environment that allows it to emerge through the process and interactions. The PDM process prioritizes collective synergy and creativity using participation techniques to allow for alternative solutions. In response to an inquiry by the Pawnee Native American Tribe, which invited us to investigate a proper approach to conduct design propositions within their land, this paper will report the lessons learned from the process and will exhibit alternate ways of implementing design ideas, using methodologies that expand the boundaries of academia while reaching out to native communities.
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Khrennikov, Andrei. "p-Adic Probability Theory and Its Generalizations." In p-ADIC MATHEMATICAL PHYSICS: 2nd International Conference. AIP, 2006. http://dx.doi.org/10.1063/1.2193115.

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Fletcher, Alyson, Mojtaba Sahraee-Ardakan, Sundeep Rangan, and Philip Schniter. "Expectation consistent approximate inference: Generalizations and convergence." In 2016 IEEE International Symposium on Information Theory (ISIT). IEEE, 2016. http://dx.doi.org/10.1109/isit.2016.7541287.

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Kurkoski, Brian M., and Ricardo Antonio Parrao Hernandez. "Message variance convergence condition for generalizations of LDLC lattices." In 2014 IEEE Information Theory Workshop (ITW). IEEE, 2014. http://dx.doi.org/10.1109/itw.2014.6970784.

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Courtade, Thomas A. "Concavity of entropy power: Equivalent formulations and generalizations." In 2017 IEEE International Symposium on Information Theory (ISIT). IEEE, 2017. http://dx.doi.org/10.1109/isit.2017.8006489.

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Andreev, V. K. "On Nusselt’s solution and its generalizations." In NUMERICAL METHODS FOR SOLVING PROBLEMS IN THE THEORY OF ELASTICITY AND PLASTICITY (EPPS 2021). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0073944.

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GOLDIN, GERALD A., and VLADIMIR SHTELEN. "GENERALIZATIONS OF YANG-MILLS THEORY WITH NONLINEAR CONSTITUTIVE EQUATIONS." In Proceedings of the 3rd International Symposium. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702340_0039.

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Reports on the topic "Group theory and generalizations"

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Tercek, Michael. Climate monitoring in the Mediterranean Coast Network 2020: Santa Monica Mountains National Recreation Area. National Park Service, September 2022. http://dx.doi.org/10.36967/2294435.

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This report details the climate (temperature, precipitation, drought, and streamflow) of Santa Monica Mountains National Recreation Area (NRA) during 2020. Gridded GIS maps are used to present broad-brush conditions across the region for each month. This regional presentation is compared to detailed data from Remote Automated Weather Stations (RAWS), weather stations in Global Historical Climatology Network (GHCN), and data from USGS stream gages. Prior to analysis, a set of data quality control checks were performed by the authors in accordance with an established National Park Service protocol (Rocky Mountain Climate Working Group 2010). Key points summarizing calendar year 2020 are presented as bullets in the Conclusion section at the end of the report. There was significant spatial and month to month variability in the data that provided exceptions to these generalizations, so an examination of the regional maps is key to understanding the climatic patterns for 2020. Readers can download the data used in this report and make custom climate graphs and tables of their own by visiting www.ClimateAnalyzer.org.
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Ilfen, Daniel R., Jillian Shairo, Eduardo Salas, and Howard Weiss. Functions of Group Goals: Possible Generalizations from Individuals to Groups. Fort Belvoir, VA: Defense Technical Information Center, December 1987. http://dx.doi.org/10.21236/ada203654.

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Herald, Christopher. SU(3) Generalizations of the Casson Invariant from Gauge Theory. GIQ, 2012. http://dx.doi.org/10.7546/giq-3-2002-278-289.

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Keane, Michael K., and David W. Jensen. Computer Programming and Group Theory. Fort Belvoir, VA: Defense Technical Information Center, May 1990. http://dx.doi.org/10.21236/ada225155.

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Cho, Yong Seung. Finite Group Actions in Seiberg–Witten Theory. GIQ, 2012. http://dx.doi.org/10.7546/giq-8-2007-135-143.

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Goldin, Gerald A., and David H. Sharp. Diffeomorphism Group Representations in Relativistic Quantum Field Theory. Office of Scientific and Technical Information (OSTI), December 2017. http://dx.doi.org/10.2172/1415360.

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Chevassut, Olivier. Authenticated group Diffie-Hellman key exchange: theory and practice. Office of Scientific and Technical Information (OSTI), October 2002. http://dx.doi.org/10.2172/805133.

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Melhuish, Kathleen. The Design and Validation of a Group Theory Concept Inventory. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.2487.

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Birdsall, C. K. Plasma Theory and Simulation Group Annual Progress Report for 1989. Fort Belvoir, VA: Defense Technical Information Center, December 1989. http://dx.doi.org/10.21236/ada231967.

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Birdsall, Charles K. Plasma Theory and Simulation Group Annual Progress Report, for 1990. Fort Belvoir, VA: Defense Technical Information Center, December 1990. http://dx.doi.org/10.21236/ada233037.

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