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Pure Framed Braids And 3-Manifolds., Jonathan Natov
Pure Framed Braids And 3-Manifolds., Jonathan Natov
LSU Historical Dissertations and Theses
This dissertation looks at representations of framed pure braids and compact orientable three manifolds. A representation, $\Phi:Z\sp{n}\oplus P\sb{n}\to \Gamma\sb{n},$ is constructed from the framed pure braid group on n strands to the mapping class group on a surface of genus n. The representation is used to obtain a presentation of the fundamental group. The representation, like that of (M-P), is compatible with Heegaard and Surgery descriptions. An algorithm is presented for transforming mapping class group elements to a stably equivalent pure framed braid, under the correspondence given by the representation. A geometric description, using the representation, is given for multiplication …
Lie Theory Of Differentiable Transformations On Banach-Type Manifolds., Amadou Belly Guisse
Lie Theory Of Differentiable Transformations On Banach-Type Manifolds., Amadou Belly Guisse
LSU Historical Dissertations and Theses
Let M be a manifold modeled on a Banach space B, and let U be an open subset of M containing the domain of some chart $\varphi$. The aim of this work is to set mathematical foundations (topological, algebraic geometrical) for the theory of pseudosemigroups of local transformations S on M and their infinitesimal generators $L\sp{r}(S,\ U).$ In the first part of this dissertation we define the topology of local uniform convergence, the most suitable in this case, similar to the compact open topology in the finite dimensional case, and show what relationship it has with different topologies. In the …
A Vector-Valued Operational Calculus And Abstract Cauchy Problems., Boris Baeumer
A Vector-Valued Operational Calculus And Abstract Cauchy Problems., Boris Baeumer
LSU Historical Dissertations and Theses
Initial and boundary value problems for linear differential and integro-differential equations are at the heart of mathematical analysis. About 100 years ago, Oliver Heaviside promoted a set of formal, algebraic rules which allow a complete analysis of a large class of such problems. Although Heaviside's operational calculus was entirely heuristic in nature, it almost always led to correct results. This encouraged many mathematicians to search for a solid mathematical foundation for Heaviside's method, resulting in two competing mathematical theories: (a) Laplace transform theory for functions, distributions and other generalized functions, (b) J. Mikusinski's field of convolution quotients of continuous functions. …
Unavoidable Minors Of Graphs Of Large Type., John Joseph Dittmann Jr
Unavoidable Minors Of Graphs Of Large Type., John Joseph Dittmann Jr
LSU Historical Dissertations and Theses
In this paper, we study one measure of complexity of a graph, namely its type. The type of a graph G is defined to be the minimum number n such that there is a sequence of graphs $G = G\sb0, G\sb1,\... , G\sb{n},$ where $G\sb{i}$ is obtained by contracting or deleting one edge from each block of $G\sb{i-1}$, and where $G\sb{n}$ is edgeless. We show that a 3-connected graph has large type if and only if it has a minor isomorphic to a large fan. Furthermore, we show that if a graph has large type, then it has a minor …
Graphs And Number Theory., Brian Heck
Graphs And Number Theory., Brian Heck
LSU Historical Dissertations and Theses
In the 1930's, L. Redei and H. Reichardt used certain matrices to aid in the determination of the structure of ideal class groups of quadratic number fields. This is a classical number theoretic problem which in general presents diffculties. Ideal class groups are finite abelian groups, and it is a result of Gauss that allows us to determine their 2-rank, in other words the number of cyclic factors of even order. Redei and Reichardt worked on determining the 4-rank, the number of factors of order divisible by 4. Later, the classical study of circulant graphs was utilized to further help …
Weak Convergence Of Interacting Stochastic Systems., George William Paslaski
Weak Convergence Of Interacting Stochastic Systems., George William Paslaski
LSU Historical Dissertations and Theses
The aim of the dissertation is to establish the weak convergence of mean-field interacting particle systems driven by Poisson random measures and semimartingales. The limit of the stochastic systems is identified by the use of martingale problems and Picard iteration schemes. The interacting systems driven by Poisson random measures are shown to be stable with respect to the coefficients of the system as well as the driving terms. The same results can be achieved when a random interaction term independent of the driving terms is introduced into the coefficients of the system. Equations driven by semimartingales do not neccesarily possess …