181 |
On Redfield's enumeration methods : application of group theory to combinatoricsHolton, D. A. (Derek Allan) January 1970 (has links)
No description available.
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182 |
On perfect and semi-perfect group ringsKaye, Sheila M. (Sheila Margaret) January 1969 (has links)
No description available.
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183 |
An embedding theorem for pro-p-groups, derivations of pro-p-groups and applications to fields and cohomology /Gildenhuys, D. (Dion) January 1966 (has links)
No description available.
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184 |
On the combinatorics of certain Garside semigroups /Cornwell, Christopher R., January 2006 (has links) (PDF)
Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2006. / Includes bibliographical references (p. 61-62).
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VARIATIONAL PRINCIPLES FOR FIELD VARIABLES SUBJECT TO GROUP ACTIONS (GAUGE).SADE, MARTIN CHARLES. January 1985 (has links)
This dissertation is concerned with variational problems whose field variables are functions on a product manifold M x G of two manifolds M and G. These field variables transform as type (0,1) tensor fields on M and are denoted by ψ(h)ᵅ (h = 1, ..., n = dim M, α = 1, ..., r = dim G). The dependence of ψ(h)ᵅ on the coordinates of G is given by a generalized gauge transformation that depends on a local map h:M → G. The requirement that a Lagrangian that is defined in terms of these field variables be independent of the coordinates of G and the choice of the map h endows G with a local Lie group structure. The class of Lagrangians that exhibits this type of invariance may be characterized by three invariance identities. These identities, together with an arbitrary solution of a system of partial differential equations, may be used to define field strengths associated with the ψ(h)ᵅ as well as connection and curvature forms on M. The former may be used to express the Euler-Lagrange equations in a particularly simple form. An energy-momentum tensor may also be defined in the usual manner; however additional conditions must be imposed in order to guarantee the existance of conservation laws resulting from this tensor. The above analysis may be repeated for the case that the field variables behave as type (0,2) tensor fields under coordinate transformations on M. For these field variables, the Euler-Lagrange expressions may be expressed as a product of a covariant divergence with the components λʰ of a type (1,0) vector field on M. An unexpected consequence of this construction is the fact that the Euler-Lagrange equations that result for the vector field λʰ are satisfied whenever the Euler-Lagrange equations associated with the field variables are satisfied.
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186 |
Computation in hyperbolic groupsMarshall, Joseph January 2001 (has links)
No description available.
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187 |
Combining lattices of soluble lie groupsHarkins, Andrew January 2000 (has links)
No description available.
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188 |
Growth series of certain groupsGill, C. P. January 1995 (has links)
No description available.
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189 |
Finite groups satisfying a certain 3-local conditionWilson, Steven S. January 1978 (has links)
No description available.
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Techniques in Lattice Basis ReductionUnknown Date (has links)
The mathematical theory of nding a basis of shortest possible vectors in a
given lattice L is known as reduction theory and goes back to the work of Lagrange,
Gauss, Hermite, Korkin, Zolotarev, and Minkowski. Modern reduction theory is voluminous
and includes the work of A. Lenstra, H. Lenstra and L. Lovasz who created
the well known LLL algorithm, and many other researchers such as L. Babai and C. P.
Schnorr who created signi cant new variants of basis reduction algorithms. The shortest
vector (SVP) and closest vector (CVP) problems, presently considered intractable,
are algorithmic tasks that lie at the core of many number theoretic problems, integer
programming, nding irreducible factors of polynomials, minimal polynomials of algebraic
numbers, and simultaneous diophantine approximation. Lattice basis reduction
also has deep and extensive connections with modern cryptography, and cryptanalysis
particularly in the post-quantum era. In this dissertation we study and compare
current systems LLL and BKZ, and point out their strengths and drawbacks. In
addition, we propose and investigate the e cacy of new optimization techniques, to
be used along with LLL, such as hill climbing, random walks in groups, our lattice
di usion-sub lattice fusion, and multistage hybrid LDSF-HC technique. The rst two methods rely on the sensitivity of LLL to permutations of the
input basis B, and optimization ideas over the symmetric group Sm viewed as a
metric space. The third technique relies on partitioning the lattice into sublattices,
performing basis reduction in the partition sublattice blocks, fusing the sublattices,
and repeating. We also point out places where parallel computation can reduce runtimes
achieving almost linear speedup. The multistage hybrid technique relies on the
lattice di usion and sublattice fusion and hill climbing algorithms. Unlike traditional
methods, our approach brings in better results in terms of basis reduction towards
nding shortest vectors and minimal weight bases. Using these techniques we have
published the competitive lattice vectors of ideal lattice challenge on the lattice hall of
fame. Toward the end of the dissertation we also discuss applications to the multidimensional
knapsack problem that resulted in the discovery of new large sets of
geometric designs still considered very rare. The research introduces innovative techniques
in lattice basis reduction theory and provides some space for future researchers
to contemplate lattices from a new viewpoint. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection
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