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Showing 1 to 20 of 68 for “"CAYLEY"”.
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Average Cayley genus for Cayley maps with dihedral groups
… and let Delta be a generating set for Gamma. A Cayley map associated with Gamma and Delta is an oriented 2-cell embedding of the Cayley graph GDelta (Gamma) such that the rotation of arcs emanating from each vertex is determined by a unique cyclic permutation of generators and their inverses. A …
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Cayley-Dickson Loops
<p>In this dissertation we study the Cayley-Dickson loops, multiplicative structures arising from the standard Cayley-Dickson doubling process. More precisely, the Cayley-Dickson loop <em>Q<sub>n</sub></em> is the multiplicative closure of basic elements of the algebra constructed by <em>n</em> …
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Automata on Cayley Graphs
… two properties of a tape must, in fact, be the Cayley graph of a suitable group. Recent investigations by various authors have begun to shed some light on what promises to be intimate connections between the geometry of a Cayley graph and the group-theoretic properties of the underlying group.
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Deformations of Cayley submanifolds
Cayley submanifolds of R^8 were introduced by Harvey and Lawson as an instance of calibrated submanifolds, extending the volume-minimising properties of complex submanifolds in Kähler manifolds. More generally, Cayley submanifolds are 4-dimensional submanifolds which may be defined in an 8-manifold …
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Deformation theory of Cayley submanifolds
Cayley submanifolds are naturally arising volume minimising submanifolds of $Spin(7)$- manifolds. In the special case that the ambient manifold is a four-dimensional Calabi--Yau manifold, a Cayley submanifold might be a complex surface, a special Lagrangian submanifold or neither. In this thesis, …
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Compact Symmetric Spaces, Triangular Factorization, and Cayley Coordinates
… the diagonal term d in classical cases, using Cayley coordinates (this choice of coordinate is motivated by considerations beyond sheer convenience). These formulas have several applications: 1) we can compute π₀(Φ(U/K) \ ∩ ∑(G/1) ) explicitly; 2) we can compute ʃ(Φ(U/K))ᵃΦ^-iλ (where ᵃΦ is the …
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Cayley maps for certain cyclic groups with odd generators
… work for both oral and written presentation; A Cayley graph provides us with a discrete model for a finite group with specified generating set. It is desirable to represent such structures in their simplest form and also so that certain symmetries are emphasized. By simplest form, we mean to …
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Nonnegative Polynomials, Sums of Squares and the Cayley-Bacharach Theorem
… that arise from linear relations known as the Cayley-Bacharach relations.
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Geometry, Kinematics, and Rigid Body Mechanics in Cayley-Klein Geometries
… vorgestellt, um darauf aufbauend eine Klasse von Cayley-Klein Räumen zu beschreiben. Diese Klasse enthält die drei klassischen Räume konstanter Krümmung (euklidisch, elliptisch und hyperbolisch). Die entsprechenden n-dimensionalen Cayley-Klein Geometrien werden dann als reelle Clifford-Algebren …
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A Dynamical Approach to the Potts Model on Cayley Tree
… h is varied for constant T on the binary rooted Cayley tree. Similarly to the Ising model, we show that for fixed T >0the 3-state Potts model for the ferromagnetic case exhibits a phase transition at one critical value of h or not at all, depending on T. However, an interesting new phenomenon …
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Universality of Cutoff for Random Walks on Random Cayley Graphs
Consider the random Cayley graph of a finite group G with respect to k generators chosen uniformly at random. This draws a Cayley graph uniformly amongst all degree-k Cayley graphs of G. A conjecture of Aldous and Diaconis (1985) from the '80s asserts, for k ≫ log |G|, the following: • the random …
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Extensions of the Cayley-Hamilton Theorem with Applications to Elliptic Operators and Frames.
<p>The Cayley-Hamilton Theorem is an important result in the study of linear transformations over finite dimensional vector spaces. In this thesis, we show that the Cayley-Hamilton Theorem can be extended to self-adjoint trace-class operators and to closed self-adjoint operators with trace-class …
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Particle Spreading in a Simple Majda Flow and Eigenvalue Estimation Through a Cayley Transform
… We consider a perturbation method based on a Cayley transform. We show that the change of basis V = (I + K/2)-1( I - K/2), where I is the identity operator and K is a skew-adjoint operator given by a formal perturbation argument, gives better error estimate.
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Extension of some theorems of complex functional analysis to linear spaces over the quaternions and Cayley numbers
… rings of the real Quaternions and the real Cayley algebra. The basic structure of Banach spaces over these division rings and the rings of bounded operators on these spaces is developed. Examples of finite and infinite dimensional spaces over these division rings are given. Questions …
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The Structure of the Cayley Complex and a Cubic-Time Algorithm for Solving the Conjugacy Problem for Groups of Prime Alternating Knots
This paper is as self-contained as possible, requiring only some familiarity with groups and with some concepts from first-year topology; some experience with graphs and/or geometric 2-complexes is helpful. The preface includes a history of knot theory and combinatorial group theory.
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A study of some rings of finite power
… number of nonisomorphic rings of that order. Cayley tables are presented for orders six and ten, and Bloom's results are amplified and Cayley tables are presented for order four in chapter 3. Incomplete results for orders eight and nine, together with their Cayley tables are presented in …
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