The Lexington, Kentucky Civil Rights Movement

This thesis seeks to describe the regional differences between the northern and southern civil rights movements through the examination of the black freedom struggle in Lexington, Kentucky. The geographical location of Lexington offers a unique perspective in civil rights movement activity, as the local movement was not distinctly northern or southern in character. This thesis functions as an analysis of northern and southern civil rights movement activity and uses a narrative of the Lexington movement to place the city\u27s struggle in the context of each region. Oral interviews from white and black Lexingtonians that lived in the city before, during, and after the movement provide the basis for the narrative of the Lexington black freedom struggle. Through the examination of Lexington in different stages - segregation, the civil rights movement, and post-movement society - it is possible to obtain an understanding of the regional differences between the northern and southern movements, as well as Lexington\u27s placement among each region

Fischer decompositions for entire functions and the Dirichlet problem for parabolas

Let $P_{2k}$ be a homogeneous polynomial of degree $2k$ and assume that there exist $C>0$, $D>0$ and $\alpha \ge 0$ such that \begin{equation*} \left\langle P_{2k}f_{m},f_{m}\right\rangle_{L^2(\mathbb{S}^{d-1})}\geq \frac{1}{C\left( m+D\right) ^{\alpha }}\left\langle f_{m},f_{m}\right\rangle_{\mathbb{S}^{d-1}} \end{equation*} for all homogeneous polynomials $f_{m}$ of degree $m.$ Assume that $P_{j}$ for $j=0, \dots ,\beta <2k$ are homogeneous polynomials of degree $j$. The main result of the paper states that for any entire function $f$ of order there exist entire functions $q$ and $h$ of order bounded by $\rho$ such that \begin{equation*} f=\left( P_{2k}-P_{\beta }- \dots -P_{0}\right) q+h\text{ and }\Delta ^{h}r=0. \end{equation*} This result is used to establish the existence of entire harmonic solutions of the Dirichlet problem for parabola-shaped domains on the plane, with data given by entire functions of order smaller than $\frac{1}{2}$.Comment: 27 page

Bernstein operators for exponential polynomials

Let $L$ be a linear differential operator with constant coefficients of order $n$ and complex eigenvalues $\lambda_{0},...,\lambda_{n}$. Assume that the set $U_{n}$ of all solutions of the equation $Lf=0$ is closed under complex conjugation. If the length of the interval $[ a,b]$ is smaller than $\pi /M_{n}$, where M_{n}:=\max \left\{| \text{Im}% \lambda_{j}| :j=0,...,n\right\} , then there exists a basis $p_{n,k}$%, $k=0,...n$, of the space $U_{n}$ with the property that each $p_{n,k}$ has a zero of order $k$ at $a$ and a zero of order $n-k$ at $b,$ and each $$ is positive on the open interval $(a,b) .$ Under the additional assumption that $\lambda_{0}$ and $\lambda_{1}$ are real and distinct, our first main result states that there exist points $a=t_{0}<t_{1}<...<t_{n}=b$ and positive numbers $\alpha_{0},..,\alpha_{n}$%, such that the operator \begin{equation*} B_{n}f:=\sum_{k=0}^{n}\alpha_{k}f(t_{k}) p_{n,k}(x) \end{equation*} satisfies $B_{n}e^{\lambda_{j}x}=e^{\lambda_{j}x}$, for $j=0,1.$ The second main result gives a sufficient condition guaranteeing the uniform convergence of $B_{n}f$ to $f$ for each $f\in C[ a,b]$.Comment: A very similar version is to appear in Constructive Approximatio

SAGA: A project to automate the management of software production systems

The project to automate the management of software production systems is described. The SAGA system is a software environment that is designed to support most of the software development activities that occur in a software lifecycle. The system can be configured to support specific software development applications using given programming languages, tools, and methodologies. Meta-tools are provided to ease configuration. Several major components of the SAGA system are completed to prototype form. The construction methods are described

Silent Transitions in Automata with Storage

We consider the computational power of silent transitions in one-way automata with storage. Specifically, we ask which storage mechanisms admit a transformation of a given automaton into one that accepts the same language and reads at least one input symbol in each step. We study this question using the model of valence automata. Here, a finite automaton is equipped with a storage mechanism that is given by a monoid. This work presents generalizations of known results on silent transitions. For two classes of monoids, it provides characterizations of those monoids that allow the removal of \lambda-transitions. Both classes are defined by graph products of copies of the bicyclic monoid and the group of integers. The first class contains pushdown storages as well as the blind counters while the second class contains the blind and the partially blind counters.Comment: 32 pages, submitte

Knowledge-Based Collaborative Lean Manufacturing Management (KBCLMM) system

The objective of this research paper is to demonstrate the application of hybrid Knowledge-Based System, Gauging Absences of Pre-Requisites (GAP), and Analytic Hierarchy Process (AHP) approaches for selecting the improvement programs for Collaborative Lean Manufacturing Management (CLMM) System.In this research, a generic Knowledge-Based System is developed to measure the level of CLMM adoption in automotive manufacturers compared to the ideal system. Using the embedded GAP and AHP technique, the key lean manufacturing improvement programs can be prioritised by using both qualitative and quantitative criteria.The analysis covers the planning stage of the KBCLMM. The utilisation of the approach is demonstrated with an illustrative example