Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 9 of 9
Full-Text Articles in Entire DC Network
The Effects Of Analytic Reading Skills On Sixth Graders' Ability To Solve Mathematical Story Problems., Linda Hale Eilers
The Effects Of Analytic Reading Skills On Sixth Graders' Ability To Solve Mathematical Story Problems., Linda Hale Eilers
LSU Historical Dissertations and Theses
The purpose of the present study was to determine the effects of two levels of instructional treatment on sixth graders' ability to solve mathematical story problems. The two levels of instructional treatment were instruction in the use of graphic organizers in conjunction with specific analytic reading skills and instruction in specific analytic reading instruction alone. These were compared to the absence of either treatment. The steady decline in students' scores on measures of ability to read and solve story problems over the past decade prompted research in three sixth-grade public school classes in northeast Louisiana. The study employed an experimental/control, …
On The Homology Of Branched Cyclic Covers Of Knots., Wayne H. Stevens
On The Homology Of Branched Cyclic Covers Of Knots., Wayne H. Stevens
LSU Historical Dissertations and Theses
We consider the sequence of finite branched cyclic covers of $S\sp3$ branched along a tame knot $K : S\sp1\to S\sp3$ and prove several results about the homology of these manifolds. We show that the sequence of cyclic resultants of the Alexander polynomial of K satisfies a linear recursion formula with integral coefficients. This means that the orders of the first homology groups of the branched cyclic covers of K can be computed recursively. We further establish the existence of a recursion formula that generates sequences which contain the square roots of the orders of the odd-fold covers and that contain …
Existence And Uniqueness Theorems For Some White Noise Integral Equations., Dongya Zou
Existence And Uniqueness Theorems For Some White Noise Integral Equations., Dongya Zou
LSU Historical Dissertations and Theses
Let $({\cal S})\sbsp{\beta}{*},0\le\beta<1,$ be the Kondratiev-Streit spaces of generalized functions. Let $f:\lbrack 0,T\rbrack\times ({\cal S})\sbsp{\beta}{*}\to ({\cal S})\sbsp{\beta}{*},$ be weakly measurable, and satisfy a growth condition and a Lipschitz condition. Let $\theta :\lbrack 0, T\rbrack\to ({\cal S})\sbsp{\beta}{*},$ be weakly measurable and satisfy a growth condition. Then it is shown that the white noise integral equation $X\sb{t}=\theta\sb{t}+\int\sbsp{0}{t}f(s, X\sb{s})ds,0\le t\le T,$ has a unique solution in $({\cal S})\sbsp{\beta}{*}$, where the integral is a white noise integral in the Pettis or Bochner sense. This result is extended to ${\cal M}\sp*$, the Meyer-Yan distribution space. Some special equations are also solved explicitly. For $F\in L\sp2({\bf R}\sp+)$, let $A\sb{s}=\int\sbsp{-\infty}{s} F(s-u)\partial\sb{u}du,\ E\sb{s}= {\rm exp}(A\sb{s}),$ and $A\sbsp{s}{*},\ E\sbsp{s}{*}$ be their duals, respectively. The equation $X\sb{t}=\theta\sb{t}+\int\sbsp{0}{t} A\sbsp{s}{*}X\sb{s}ds, t\in\lbrack 0,T\rbrack,$ is solved in $({\cal S})\sp*$ or $(L\sp2)$, and the equation $X\sb{t}=\theta\sb{t}+\int\sbsp{0}{t} E\sbsp{s}{*}X\sb{s}ds, t\in\lbrack 0, T\rbrack,$ is solved in ${\cal M}\sp*,$ where $\theta$ is as above. Moreover, under certain conditions on $\theta,\Phi:\lbrack 0,T\rbrack\to ({\cal S})\sp*$ and $\sigma:\lbrack 0,T\rbrack\sp2\to{\bf R},$ the Volterra equation $X\sb{t}=\theta\sb{t}+\int\sbsp{0}{t}\sigma(t,s)\Phi\sb{s}\ {\rm o}\ X\sb{s}ds, t\in\lbrack 0,T\rbrack,$ is also solved, and its solution is in ${\cal M}\sp*, ({\cal S})\sbsp{\beta}{*},$ or $(L\sp2),$ depending on the growth conditions for $\theta$ and $\Phi.$ Finally, for a suitable deterministic function f, the white noise partial differential equation ${\partial u\over\partial t}=\Delta u+:e\sp{\dot B\sb{x}}: {\rm o}\thinspace u, u(0,x)=f(x),x\in{\bf R}\sp{n}, t\in\lbrack 0,\infty),$ is solved in ${\cal M}\sp*$.
Szasz-Muntz Theorems For Nilpotent Lie Groups., Darwyn C. Cook
Szasz-Muntz Theorems For Nilpotent Lie Groups., Darwyn C. Cook
LSU Historical Dissertations and Theses
The classical Szasz-Muntz theorem says that for $f\ \in\ L\sp2(\lbrack 0, 1\rbrack )$ and $\{n\sb{k}\}\sbsp{k=1}{\infty}$ a strictly increasing sequence of positive integers,$$\int\limits\sbsp{0}{1}x\sp{n\sb{j}}f(x)dx=0\ \forall j\Rightarrow f=0\Leftrightarrow\sum\sbsp{j=1}{\infty}{{1}\over{n\sb{j}}}=\infty.$$We have generalized this theorem to compactly supported functions on $\Re\sp{n}$ and to an interesting class of nilpotent Lie groups. On $\Re\sp{n}$ we rephrased the condition above on an integral against a monomial as a condition on the derivative of the Fourier transform $\ f$. For compactly supported f this transform has an entire extension to complex n-space, and these derivatives are coefficients in a Taylor series expansion of $\ f$. In the nilpotent Lie groups …
Some Lifting Problems In Arithmetic Equivalence., Nancy C. Colwell
Some Lifting Problems In Arithmetic Equivalence., Nancy C. Colwell
LSU Historical Dissertations and Theses
The main theorem in this dissertation provides a partial answer to the following question: Given a $\doubz\sb{p}$-extension $F{\sb\infty} /F$ and a finite extension $K/F$, where F is a number field and p a prime number, to what extent does the K-splitting behavior the prime ideals of F determine the Iwasawa invariants of the $\doubz\sb{p}$-extension $K{\cdot}F{\sb\infty}/K$. The answer is that if two fields K and L are arithmetically equivalent over F, then $K{\cdot}F{\sb\infty} /K$ and $L{\cdot}F{\sb\infty} /L$ have exactly the same Iwasawa invariants for any $\doubz\sb{p}$-extension $F{\sb\infty} /F$, so long as p is not an exceptional divisor for K and L …
The Generalized Kompaneets Equation., Kunyang Wang
The Generalized Kompaneets Equation., Kunyang Wang
LSU Historical Dissertations and Theses
In the dissertation, the generalized Kompaneets equation$${\partial u\over\partial t}={1\over\beta(x)}\lbrack\alpha(x)(u\sb{x}+ku+F(x,u))\rbrack\sb{x}$$(for $x,t>0)$ is studied. For the linear case, when $F\equiv0,$ a complete theory is given. A brief discussion is carried for the nonlinear case when $F(x,u)=f(x)g(u).$. For the following equation,$$v\sb{t}=\varphi(y,v\sb{y})v\sb{yy}+\psi(y,v,v\sb{y}),$$Goldstein and Lin's result is extended to degenerate case. Also, for the following linear operator,$$Au=\alpha(x)u\prime\prime+\beta(x)u\prime$$(for $x\in \lbrack 0,$ 1)), Clement and Timmermans' result is extended to the case of discontinuous coefficients $\alpha$ and $\beta$.
A Polynomial Invariant Of Links In A Solid Torus., Jaehoo Park Kim
A Polynomial Invariant Of Links In A Solid Torus., Jaehoo Park Kim
LSU Historical Dissertations and Theses
A polynomial invariant of links in a solid torus is defined through an algebra $H\sb{n}({1\over2}$). $H\sb{n}({1\over2}$) modulo by an ideal is the type-B Hecke algebra. This invariant satisfies the $S\sb3$-skein relation as in the 1-trivial links case of dicromatic link invariant discovered by J. Hoste and M. Kidwell. A link in the solid torus is isotopic to a closed braid which is a braid in the braid group of the annulus. We find an invariant of links through a represention $\pi$ of the braid group of the annulus to the algebra $H\sb{n}({1\over2}$). A trace map X is defined on a …
Jordan Algebras And Lie Semigroups., Yongdo Lim
Jordan Algebras And Lie Semigroups., Yongdo Lim
LSU Historical Dissertations and Theses
For a Euclidean Jordan algebra V with the corresponding symmetric cone $\Omega$, we consider the semigroup $\Gamma\sb{\Omega}$ of elements in the automorphism group $G(T\sb{\Omega})$ of the tube domain $V$ + $i\Omega$ which can be extended to $\Omega$ and maps $\Omega$ into itself. A study of this semigroup was first worked out by Koufany in connection to Jordan algebra theory and Lie theory of semigroups. In this work we give a new proof of Koufany's results and generalize up to infinite dimensional Jordan algebras, so called $JB$-algebras. One of the nice examples of the semigroup $\Gamma\sb{\Omega}$ is from the Jordan algebra …
Matroid Connectivity., John Leo
Matroid Connectivity., John Leo
LSU Historical Dissertations and Theses
This dissertation has three parts. The first part, Chapter 1, considers the coefficient $b\sb{ij}(M)$ of $x\sp{i}y\sp{j}$ in the Tutte polynomial of a connected matroid M. The main result characterizes, for each i and j, the minor-minimal such matroids for which $b\sb{ij}(M)>0.$ One consequence of this characterization is that $b\sb{11}(M)>0$ if and only if the two-wheel is a minor of M. Similar results are obtained for other values of i and j. These results imply that if M is simple and representable over $GF(q),$ then there are coefficients of its Tutte polynomial which count the flats of M that …