Digital Commons Network^™

Linkage By Generically Gorenstein Cohen-Macaulay Ideals., Heath Mayall Martin

LSU Historical Dissertations and Theses

In a Gorenstein local ring R, two ideals A and B are said to be linked by an ideal I if the two relations A = (I: B) and B = (I: A) hold. In the case that I is a complete intersection, or a Gorenstein ideal, it is known that linkage preserves the Cohen-Macaulay property. That is, if A is a Cohen-Macaulay ideal, then so is B. However, if I is allowed to be a generically Gorenstein, Cohen-Macaulay ideal, easy examples show that this type of linkage does not preserve the Cohen-Macaulay property. The primary purpose of this work …

The Congruence Extension Property And Related Topics In Semigroups., Jill Ann Dumesnil

LSU Historical Dissertations and Theses

A semigroup has the congruence extension property (CEP) provided that each congruence on each subsemigroup can be extended to a congruence on the semi-group. This property, the ideal extension property (IEP), and other related concepts are studied from both an algebraic and a topological perspective in this work. A characterization of semigroups with CEP is given in terms of the lattice of congruences. A similar result is obtained for IEP. Semigroups in which the relation "is an ideal of" is transitive (t-semigroups) are explored. It is shown that each of CEP and IEP implies this condition and that these are …

Curriculum Based Measurement And Portfolio Assessment: An Effective Evaluation System, Johanna Roberts

All Graduate Projects

The researcher reviewed current literature regarding curriculum based assessment, curriculum based measurement (CBM) and portfolio assessment. The researcher developed a curriculum based measurement for kindergarten prereading and premath skills as a part of a portfolio system. A first grade math curriculum based measurement was designed collaboratively with two first grade teachers. A beginning reading assessment was also designed for the first grade. Results showed that a portfolio assessment with CBM's is an effective evaluation tool.

Only Problems, Not Solutions! (Fourth Edition), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

On The Number Of Independent Sets Of Nodes In A Tree, R. Dutton, N. Chandrasekharan, R. Brigham

Faculty Bibliography 1990s

No abstract provided.

Pashto And Math, Grade 1, Unknown

Books in Dari and Pashto

No abstract provided.

Practice Exercises-For The Georgia Teacher Certification Test In Mathematics, Beverly M. Davis

Theses and Dissertations

Since the Georgia Teacher Testing Program began in 1978, thousands of Georgia teachers and teacher candidates have taken the Georgia Teacher Certification Test (TCT) in mathematics. Although the mathematics test has been found to be valid, reliable, unbiased, and job-related, many test takers fail the test the first time the test is taken and consequently retake the test until a passing score is made or choose not to retake the test.

Multiple choice practice exercises were developed to assist those who are preparing to take this test. These practice exercises are based on objectives, assessment characteristics, and content components outlined …

A Study Of The Benefits Of Reflection By Journal Writing In Mathematical Learning And Attitudes In The Primary School, Sally Edmonds

Theses : Honours

This descriptive study examines journal writing for the purpose of identifying aspects of children's mathematical reflective ability. It was hypothesised that encouragement to engage with the process of mathematics by reflective writing would reveal and assist learning, and give children a vehicle through which they could express their attitudes about the mathematics they were learning. The aim of this study was to find answers to the following question: How does the keeping of a mathematical journal reveal children's understandings of the mathematics they are learning? Other questions related to the study were: -What evidence is there from the journals about …

The Congruence Extension Property, The Ideal Extension Property, And Ideal Semigroups., Karen Dommert Aucoin

LSU Historical Dissertations and Theses

A semigroup has the congruence extension property (CEP) provided that each congruence on each subsemigroup of S extends to a congruence on S. The ideal extension property (IEP) for semigroups is defined analogously. A characterization of commutative semigroups with IEP is given in terms of multiplicative conditions within and between the archimedean components of the semigroup. A similar characterization of commutative semigroups with CEP is sought. Toward this end, archimedean semigroups with CEP are characterized in terms of multiplicative structure and a number of necessary conditions on multiplication between the archimedean components of a commutative semigroup with CEP are established. …

Split Abelian Extensions Of Calgebras., Mark Andrew Curole

LSU Historical Dissertations and Theses

It is shown that the C* algebra of a groupoid with Haar system has a natural split abelian extension. For a split abelian extension of a C* algebra it is shown that all representations of the original algebra extend to the split abelian extension. Under a reasonable assumption it is shown that states extend to a split abelian extension. Definitions for quasi-invariant and ergodic measures are given for split abelian extension of C* algebras, and it is shown when the split abelian extension is the natural extension of the C* algebra of a groupoid with Haar system that these definitions …

Using Hypermedia To Improve The Dissemination And Accessibility Of Syllabus Documents With Particular Reference To Primary Mathematics, Alistair B. Campbell

Theses: Doctorates and Masters

The fundamental question that this study set out to investigate was: Can the advantages of hypermedia be extended to curriculum materials that are for the sole use of teachers? To consider this question, three areas needed to be investigated: hypermedia (the medium); teachers (the target) and curriculum documents (the content). Hypermedia has a long history dating back to Bush (1986) who in 1945 imagined his Memex system as building information trails between ideas. However, it was not until the mid 1980s that technology caught up with the theory and hypermedia came of age. The evaluation of hypermedia documents is still …

Restructuring For Mathematical Power: Techniques For Teaching Thinking In Algebra, Barbara D. Nelson

Critical and Creative Thinking Capstones Collection

Recent critiques of mathematics education have resulted in proposals to restructure learning and teaching for mathematical power. The new vision pictures the classroom as a community of learners where mathematics come alive as a useful tool in our technological society. However, many high school mathematics teachers are struggling to understand and implement the fundamental instructional change inherent in the vision. Written from the perspective of a high school teacher for experienced high school mathematics teachers, this thesis attempts to bridge vision and practice. To clarify the vision, current literature on reform in mathematics education is synthesized into a framework of …

Labeling Graphs With A Condition At Distance 2, Jerrold R. Griggs, Roger K. Yeh

Faculty Publications

No abstract provided.

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Logical "Paradox": A Response To Fallacies, Flaws, And Flimflam #36, Calvin Jongsma

Faculty Work Comprehensive List

Response to "Fallacies, Flaws, and Flimflam" by Ed Barbeau in The College Mathematics Journal, Vol. 23, No. 3 (May, 1992), pp. 203-206. Fallacies, Flaws, and Flimflam is a column in The College Mathematics Journal edited by Ed Barbeau of the Department of Mathematics at the University of Toronto.

Some Lesson About The Law From Self-Referential Problems In Mathematics, John M. Rogers, Robert E. Molzon

Michigan Law Review

We first describe briefly mathematician Kurt Gödel's brilliant Incompleteness Theorem of 1931, and explore some of its general implications. We then attempt to draw a parallel between axiomatic systems of number theory (or of logic in general) and systems of law, and defend the analogy against anticipated objections. Finally, we reach two types of conclusions. First, failure to distinguish between language and metalanguage in mathematical self-referential problems leads to fallacies that are highly analogous to certain legal fallacies. Second, and perhaps more significantly, Gödel's theorem strongly suggests that it is impossible to create a legal system that is "complete" in …

Some Aspects Of Multi Source Satellite Image Processing., L. Lalitha Dr.

Doctoral Theses

The observation of a target by a device plaoed at some distance from it is cal.led remote sensing as ngainst in situ sensing where the sensor is kept in contact with the target. Usually physical emanations such as the electr omagnetic radiation from the target s observed by the sensing device. Sensors mounted on aircraft or satallite platforms measure the amount of energy reflected from or emitted by the earth's surface. Sensors scan the ground below a nd to either side of the satellite platform and as the platform noves forward, an image of the earths surface is formed.A satellite …

Contributions To The Neyman-Scott And Mixture Problem., Joydeep Bhanja Dr.

Doctoral Theses

Neyman and Scott (1948) were the first to point out that the method of maximum likelihood fails to provide elfficient estimates when the number of parameters grows with the sample size n. Consider the following examples introduced by them:Ezample 1.1 Let { Xi } be a sequence of independent random vectors in I", components Xij of Xi being independent normal with mean u, and variance o2 Ilere o2 is the parameter of interest. It is casy to sce that the maxinum likelihood estimate for o2 is not even consistent. It is also known (see Lindsay (1980), Pfanzagl (1982), van der …

The Mazur Intersection Property In Banach Spaces And Related Topics., Pradipta Bandyopadhyaya Dr.

Doctoral Theses

In the first part of this chapter we explain in general terms the main theme of this thesis and provide a chapter wise summary of its principal results. The second part recapitulates some of the known notions and results used in the subsequent chapters. The numbers given in parentheses correspond to those in the list of references on page 70.S. Mazur (40] was the first to consider the following smoothness property in normed linear spaces, called the Mazur Intersection Property (MIP), or, more briefly, the Property (1):Every closed bounded convex set is the intersection of closed balls containing it.He showed …

Hopf Algebras And Cohomology Operations, Zaiqing Li

Digitized Theses

The main purpose of this thesis is to study product structures of Hopf algebras, in particular for the cases of the Steenrod algebra and the Brown-Peterson algebra. In Chapter 1, we are given a Hopf algebra with basic operations {dollar}\{lcub}D\sp{lcub}R{rcub} \vert R :{dollar} exponential sequences{dollar}\{rcub}{dollar}, the coalgebra structure being the Cartan Formula. The main theorem is a formula expressing the products {dollar}D\sp{lcub}R{rcub}\cdot D\sp{lcub}S{rcub}{dollar} of basic operations using a star operation of scalar parameters. In Chapter 2, the Milnor Product Formula for the Steenrod algebra is shown to be a consequence of the main theorem in Chapter 1. The weighted symmetrical …

Pseudo Almost Periodic Functions And Their Applications, Chuanyi Zhang

Digitized Theses

The space of pseudo almost periodic functions on {dollar}{lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}{dollar} (denoted by {dollar}{lcub}\cal PAP{rcub}({lcub}\rm J\!I{rcub}\sb{lcub}a{rcub},X){dollar} when they are vector-valued and {dollar}{lcub}\cal PAP{rcub}({lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}){dollar} when they are scalar-valued, {dollar}{lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}=\lbrack a,\infty){dollar} for {dollar}a\in\IR{dollar} and {dollar}{lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}=\IR{dollar} for {dollar}a={lcub}-\infty{rcub}{dollar}, X is a Banach space) is defined and its properties are studied. A decomposition theorem is given showing that a function is in {dollar}{lcub}\cal PAP{rcub}({lcub}\rm J\!I{rcub}\sb{lcub}a{rcub},X){dollar} if and only if it is the sum of an almost periodic function and an ergodic perturbation. The relation between a pseudo almost periodic function and its almost periodic component is discussed. It is shown that {dollar}{lcub}\cal …

Lattice Statistics Of Polymer Adsorption, Dongming Zhao

Digitized Theses

The interaction of branched polymers with an adsorption surface is studied using rigorous and numerical methods. For a polymer network with a fixed topology and consisting of self-avoiding chains, we prove that the reduced free energy is the same as that for self-avoiding walks interacting with a surface. For a network modelled by a lattice animal, we prove that a phase transition exists when such an animal interacts with a surface. The transition points are numerically studied by one and two variable Pade approximants. A number of rigorous results for the statistics of lattice animals are also obtained.

Tournaments And Ideal Class Groups., Robert John Kingan

LSU Historical Dissertations and Theses

In a series of papers published in the 1930's, L. Redei and H. Reichardt established a method for determining the 4-rank of the narrow ideal class group of a quadratic number field, essentially by finding the rank over ${\bf F}\sb2$ of a $\{0,1\}$-matrix determined by applying the Kronecker symbol to the prime divisors of the field discriminant. When this field is of the form ${\bf Q}(m\sp{1\over2}),$ with $m={\pm}p\sb1{\cdots}p\sb{n},$ each $p\sb{i}\equiv3$ (mod 4) prime, this matrix takes a form similar to that of the adjacency matrix for a tournament graph. Also, in this case we can find the 4-rank of the …

Banach Space Valued Stochastic Differential Equations., Fariborz Asadian

LSU Historical Dissertations and Theses

Let $W(t,\omega)$ be a Brownian motion on an abstract Wiener space (i,H,B) corresponding to the canonical normal distribution on H. The well known theorem of Girsanov is proved for such a process with the perturbing term taking values in the Hilbert space H. Consider the stochastic integral equation $\xi(t) = x+\int\sbsp{0}{t}A(s,\xi(s))dW(s)+\int\sbsp{0}{t}\sigma(s,\xi(s))ds$ where x is in $B,\ A(\cdot,\cdot)$ and $\sigma(\cdot,\cdot)$ are bounded continuous functions from $\lbrack 0,\infty)\times B$ to $I+L\sb2(H)$ and H respectively. Here $L\sb2(H)$ denotes the collection of Hilbert Schmidt operators on H. Furthermore, suppose for every $s\ge 0$ the restriction of $A(s,\cdot)$ to H is invertible and $A(s,\cdot)$ and …

Beliefs, Autonomy, And Mathematical Knowledge, Judy Ann Rector

Doctoral Dissertations

The purpose of this study was to investigate the apparent effects of students' beliefs about mathematics and autonomy on their learning of mathematics. The study utilized a multiple-case study design with analysis by and across cases. The cases represented six high school students enrolled in either Algebra II or Algebra II/Trigonometry. Data was collected in three phases: (a) classroom observations and assessment of the teacher's perception of her role in the learning process, (b) an assessment of students' beliefs about mathematics and autonomy, and (c) an assessment of students' newly formed mathematical constructs on functions.

The beliefs' assessment included observing …

Finite Groups As A Generalization Of Vector Spaces Through The Use Of Splitting Systems, Joseph Kirtland

Doctoral Dissertations

The structure of a finite group is investigated through a geometry induced by the splitting systems of the group. The method is based on the one used to induce a geometry on a finite dimensional vector space over a finite field and as a result, concepts related to the special and projective linear group are extended to arbitrary groups. One major by-product is the classification of solvable multiprimitive groups of arbitrary derived length. This leads to a necessary and sufficient condition for a solvable nC-group to be multiprimitive.

Fourier Transform And Heat Equation In White Noise Analysis., Jung-Soon Kim Lee

LSU Historical Dissertations and Theses

In this dissertation, we study the Fourier transform and heat equation in the white noise set-up. It is known that the Fourier transform ${\cal F}$ can be defined on the space (${\cal S}$)* of generalized white noise functionals. We prove that ${\cal F}$ is the adjoint of a certain linear operator on the space (${\cal S}$) of test functionals. On the other hand, it is known that if f is a bounded Lip-1 function on an abstract Wiener space with Gaussian measures $P\sb{t},$ then $u(t)=P\sb{t}f$ solves the heat equation ${d\over dt}u(t)={1\over2}\Delta\sb{G}u(t)$ with initial condition u(0) = f where $\Delta\sb{G}$ is …

A Family Of Complexes Associated To An Almost Alternating Map, With Applications To Residual Intersections, Andrew R. Kustin, Bernd Ulrich

Faculty Publications

No abstract provided.

A Note On Orthogonal Polynomials, Xin Li

Faculty Bibliography 1990s

No abstract provided.

Sex-Related Differences In Autonomous Learning Behaviours And Mathematics Achievement, Laura Beahan

Theses : Honours

The autonomous learning behaviour model proposed by Fennema and Peterson (1985a, 1985b) hypothesises that sex- related differences in mathematics are a result of sex-related differences in autonomous learning behaviours. Autonomous learning behaviours include choosing to engage in high-level tasks, preferring to work independently on such tasks and persisting at them. The purpose of this study was to investigate sex-related differences in autonomous learning behaviours and to determine any relationship between the presence of these behaviours and achievement in mathematics. Twelve students studying the Year 1 unit "Foundations of Mathematics" were selected for the study, including two males and two females …