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Showing 1 to 20 of 20 for “"linear group"”.
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Conjugacy Classes of the Piecewise Linear Group
The piecewise linear group is the set of all piecewise linear orientation preserving homeomorphisms from the interval to itself under the operation of composition. We present here a complete set of invariants to classify the conjugacy classes of this group. Our approach to this problem relies on …
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A linear group and state variable formulation of the electrical network analysis problem
… of a network analysis technique employing both a linear graph theory formulation of the topological relations and a state variable analysis of these relations. As a consequence of these investigations, a network analysis program, GENA, was developed. Special points of interest include the …
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The derived category of representations of the special linear group of degree two over a finite field
… study the modular representations of the special linear group of degree two over a finite field in defining characteristic. In particular, we study the automorphisms of derived category of representations. We have been able to obtain a new type of autoequivalence. This autoequivalence has some …
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Finite Solvable Subgroups of the General Linear Group of Prime Degree Over the Field of Complex Numbers
Made available in DSpace on 2014-12-09T22:17:37Z (GMT). No. of bitstreams: 1 6711875.pdf: 2000961 bytes, checksum: 9c6dc3b74bed4c4eae4cc4d170820180 (MD5) Previous issue date: 1967
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On the Subgroups of the Projective Four Dimensional Special Linear Group Over a Field Whose Order Is a Prime Greater Than Three
Made available in DSpace on 2014-12-11T18:23:48Z (GMT). No. of bitstreams: 1 7212231.pdf: 7014724 bytes, checksum: 4f9d073d63a5a9a276bdfd860277142c (MD5) Previous issue date: 1971
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A Characterization of the Four Dimensional Projective Special Linear Group Psl(5,3) Over the Field of Three Elements by the Centralizer of an Involution Contained in the Center of A Sylow 2-Subgroup
Made available in DSpace on 2014-12-11T18:23:50Z (GMT). No. of bitstreams: 1 7219870.pdf: 1808081 bytes, checksum: 0905db1d919380f22ad2998659d03da9 (MD5) Previous issue date: 1972
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Classifcation of Conics in the Tropical Projective Plane
… projective space, TP^n, and the tropical general linear group TPGL(n). After discussing some simple examples of tropical polynomials and their hypersurfaces, a strategy is given for finding all conics in the tropical projective plane. The classification of conics and an analysis of the coefficient …
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The ring of invariants of the orthogonal group over finite fields in odd characteristic
… dual of V we are concerned with the Orthogonal group $O(\xi_0)$, the subgroup of the General Linear Group $GL(V)$ that fixes $\xi_0$ and with invariants of this group. We have the Dickson Invariants which being invariants of the General Linear Group are then invariants of $O(\xi_0)$. Considering …
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Totally Real Galois Representations in Characteristic 2 and Arithmetic Cohomology
… taking Gal(Q bar/Q) to the general linear group of 3 x 3 matrices in characterisic 2, and our examples are where complex conjugation is mapped to the identity. Since this case has not yet been examined, the results of this paper are quite significant.
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Torsors over Simplicial Schemes
… Grothendieck site C, and let G be a sheaf of groups on C. We define a notion of G-torsor over X, generalizing a definition of Gillet, and prove that there is a bijection between the set of isomorphism classes of G-torsors over X, and the set of maps in the homotopy category of simplicial …
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Isotropic graphs with applications to parallel computation
… based on quotients of the projective linear group over a finite field, which was originally employed for constructing bounded concentrators of density q, for any prime power $q > 2$.
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The involution principle and h-positive symmetric functions
… that a polynomial representation of the general linear group of V is a sum of tensor products of symmetric powers of V. Expanding the iterated exponential function as a power series yields coefficients whose positivity implies the h-positivity of the characteristic of the symmetric group …
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New computational methods for analysing finitely-presented groups
… methods for the analysis of finitely-presented groups and show their usefulness in a variety of contexts. The first procedure creates a labelled coset graph which can be used for rewriting and also for finding expressions for subgroup elements in terms of given generators. We use this procedure …
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Finite Geometry and Computer Algebra, with Applications
… explore. Of particular interest is the area of groups and geometry. In this work we will examine various aspects of this interplay, in particular looking at geometric canonical forms of figures in various projective spaces under the action of the (projective) general linear group, and finding …
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The Effects of Locus of Control and Navigational Control on the Performance of Students in a Hypermedia Environment
… then randomly assigned to one of three treatment groups that differed in the way participants navigated through a hypermedia instructional program dealing with the human heart. In the Linear group, participants navigated through the program in a standard linear fashion. In the Branching group, …
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Structuring Representations in Deep Learning: Symmetries and Linear Models
… examine the implicit bias of gradient descent on linear group convolutional networks (G-CNNs), which provide a model for learning highly structured representations. For such architectures, we prove that gradient descent implicitly minimizes the net’s Schatten norm in Fourier space [Lawrence et …
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Geometric complexity theory and orbit closures of homogeneous forms
… and generality: Given the action of a general linear group on a space of homogeneous polynomials by variable substitution, we are interested in the closure of certain orbits, in particular the orbit of the determinant polynomial. Before we study the determinant, we first analyze the case where …
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On representations of quantum groups and Cherednik algebras
In the first part of the thesis, we study quantum groups associated to a semisimple Lie algebra g. The classical Chevalley theorem states that for [ a Cartan subalgebra and W the Weyl group of g, the restriction of g-invariant polynomials on g to [ is an isomorphism onto the W-invariant polynomials …
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Noncommutative rational functions and their finite-dimensional representations
… the complement of a free singularity locus of a linear matrix pencil. The inclusion problem for free loci, and thus for domains of noncommutative rational functions, is next solved in terms of epimorphisms between the coefficient algebras of the corresponding linear matrix pencils. This theorem, …
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Simple Groups and Related Topics
… symmetric presentations of several important groups. We have investigated permutation and monomial progenitors 2<sup>*8</sup>: (2<sup>3</sup>: 2<sup>2</sup>), 2*9: (3<sup>2</sup>: 2<sup>4</sup>), 2<sup>*10</sup>: (2<sup>4</sup>: (2 × 5)), 5<sup>*4</sup>:<sub>m</sub> (2<sup>3</sup>: …