Digital Commons Network^™

Boolean Functions With Important Cryptographic Properties., Subhamoy Maitra Dr.

Doctoral Theses

In this thesis we concentrate on properties of cryptographically significant Boolean functions.The techniques are mainly combinstorial and provide new resulta on enumeration and construction of such functions. Initially we concentrate on a partieular subset of Boolean functions called the symmetric Boolean functions. A closed form expression for the Walsh transform of an arbitrary symmetric Boolean function is presented. We completely characterize the symmetric functions with maximum nonlinearity and show that the maximum nonlinearity of n-variable symmetrie function can be 2n-1-2[n-1l2], Moreover, new classes of symmetric balanced and symmetric correlation immune functions are considered.We provide a randomised heuristic to construct balanced …

Contributions To Random Interactions And Dynamical Systems., Santanu Chakraborty Dr.

Doctoral Theses

In recent years random iterations of maps on Polish spaces has gained prominence. They are. nice examples of Markov processes whose invariant measures can be used in Computer imaging (see Berger ( 1). They also arise as random perturabations of deterministic dynamical systems.Let S be a Polish space with its Borel a-field. Let r be a collection of Borel maps from S to S. Let P be a probability on r. Then starting with a point z in S, we choose a map yn er according to the law P and move to ya(x). Then we choose 2 € r …

Conjunction And Aggregation, Saul Levmore

Michigan Law Review

This Article begins with the puzzle of why the law avoids the issue of conjunctive probability. Mathematically inclined observers might, for example, employ the "product rule," multiplying the probabilities associated with several events or requirements in order to assess a combined likelihood, but judges and lawyers seem otherwise inclined. Courts and statutes might be explicit about the manner in which multiple requirements should be combined, but they are not. Thus, it is often unclear whether a factfinder should assess if condition A was more likely than not to be present - and then go on to see whether condition B …

Topological Conjugacy And Rigidity Of Affine Actions., Siddhartha Bhattacharya Dr.

Doctoral Theses

The main theme of this thesis is topological classiication of aline Hows on homogeneous spaces and rigidity of equivariant continuous maps between such dows. Both these aspects have been extensively studied in the literature for subgroup actions (cf. [Be), [B-Dj and [Wi) and for automorphism flows of the cyclic group (cf. [Ar]. [K-R] and [C-S). We will consider similar questions in more general situations. A detailed outline is given below. For a topological group T, by a r-flow we mean pair (X,p), where X is a opological space and p is a continuous action of I on X. For any …

Routing Algorithms For Channels, Switchboxes And Mcm's In Vlsi Layout Design., Sandip Das Dr.

Doctoral Theses

The term Very Large Scale Integration (VLSI) reflects the capability of semi- conductor industry to fabricate a complex electronic circuit consisting of millions of components on a single silicon substrate. The growth of semiconductor technol- ogy in recent years has been described by "Moore's law", enunciated in the late 1960s, which projected quadrupling of components in a chip in every three to four years. Several factors contributed to this tremendous growth : (i) reduction of line width of the basic device and interconnection wires due to the development of high- resolution lithographic techniques and improved processing capabilities, (ii) increase in …

An Ellam Scheme For Multidimensional Advection-Reaction Equations And Its Optimal-Order Error Estimate, Hong Wang, Xiquan Shi, Richard E. Ewing

Faculty Publications

We present an Eulerian-Lagrangian localized adjoint method (ELLAM) scheme for initial-boundary value problems for advection-reaction partial differential equations in multiple space dimensions. The derived numerical scheme is not subject to the Courant-Friedrichs-Lewy condition and generates accurate numerical solutions even if large time steps are used. Moreover, the scheme naturally incorporates boundary conditions into its formulation without any artificial outflow boundary conditions needed, and it conserves mass. An optimal-order error estimate is proved for the scheme. Numerical experiments are performed to verify the theoretical estimate.

Open To Reason, David L. Neuhouser

Books by Taylor faculty, staff, and administrators

Open to Reason is a comparison of the roles of reason, experience, imagination, intuition, faith, love, humility, and obedience in mathematics and religion.

Mathematics As Worship, David J. Stucki

Mathematics Faculty Scholarship

This paper treats worship in a broad, inclusive sense as the primary and necessary response of human beings to their creator. It provides a brief overview of the relationship between mathematics and theology from the Pythagoreans to the present. It argues that all knowledge is contingent upon faith and thus that contemplation of mathematical insights can lead to worship of God.

Statistics For Wildlifers: How Much And What Kind?, Douglas H. Johnson, Terry L. Shaffer, Wesley E. Newton

United States Geological Survey, Northern Prairie Wildlife Research Center: Publications

Quantitative methods are playing increasingly important roles in wildlife ecology and, ultimately, management. This change poses a challenge for wildlife practitioners and students who are not well educated in mathematics and statistics. Here we give our opinions on what wildlife biologists should know about statistics, while recognizing that not everyone is inclined mathematically. For those who are, we recommend that they take mathematics coursework at least through calculus and linear algebra. They should take statistics courses that are focused conceptually, stressing the "why" rather than the "how" of doing statistics. For less mathematically oriented wildlifers, introductory classes in statistical techniques …

A Coin Flipping Game With Non Transitive Odds, Stacy Jurgens

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

Making Connections: Compartmentalization In Pre -Calculus Students' Understanding Of Functions, Hope H. Gerson

Doctoral Dissertations

Students develop knowledge constructs that they build into concepts through their experiences. Students demonstrate compartmentalization when they understand a construct or concept within one representation, but not another, or when they do not connect mathematically related ideas. For instance, a student may understand f(x) to mean plug x into the function within a symbolic representation, but the same student may understand f(x) to mean f times x within a tabular representation. A student with these understandings has a compartmentalized understanding of function notation.

A two-month study was conducted with a class of pre-calculus students enrolled in a parochial high school. …

The Level Of Teacher Involvement In The Vermont Mathematics Portfolio Assessment Process And Instructional Practices In Grade 4 Classrooms, Carol Anne Fritz

Doctoral Dissertations

The comprehensive assessment system in Vermont includes student mathematics portfolios that are submitted to the state Department of Education for scoring. A student portfolio should include 5--7 pieces of best work selected by the student that can be scored. This alternative assessment process has been in place for ten years, but limited information has been available from classroom teachers about the instructional practices they use when teaching mathematics, or whether or not those practices have been influenced by the portfolio process.

The study was developed to answer questions about the instructional practices used by teachers. Teachers' responses were compared to …

Reflexivity, Elementary Operators And Cohomology, Jiankui Li

Doctoral Dissertations

Let H be a separable complex Hilbert space and let B(H) be the set of all bounded operators on H. In this dissertation, we show that if S is a n-dimensional subspace of B( H), then S is [ 2n ]-reflexive, where [t] denotes the largest integer that is less than or equal to t.

We obtain some lattice-theoretic conditions on a subspace lattice L which imply alg L , is strongly rank decomposable. Let S be either a reflexive subspace or a bimodule of a reflexive algebra. We find some conditions such that T has a rank one summand …

Physics Experiences And Calculus: How Students Use Physics To Construct Meaningful Conceptualizations Of Calculus Concepts In An Interdisciplinary Calculus /Physics Course, Karen Ann Marrongelle

Doctoral Dissertations

The purpose of this study was to investigate the manner by which students enrolled in an integrated Calculus/Physics course use their understanding of physics to inform their conceptualizations of calculus concepts. This study utilized a multiple case study design with analysis by and across cases. The cases represent eight first year students in the College of Engineering and Physical Sciences at the University of New Hampshire who enrolled in an integrated calculus/physics program. Data was gathered in a three-part process: (1) Semi-structured task-based interviews, (2) Participant-observation in the calculus/physics course, and (3) Obtaining copies of students' in-class notes, in-class activities, …

Are We Having Fun Yet? How Teachers Use Manipulatives To Teach Mathematics, Patricia S. Moyer-Packenham

Teacher Education and Leadership Faculty Publications

Teachers often comment that using manipulatives to teach mathematics is ‘fun!’ Embedded in the word ‘fun’ are important notions about how and why teachers use manipulatives in the teaching of mathematics. Over the course of one academic year, this study examined 10 middle grades teachers’ uses of manipulatives for teaching mathematics using interviews and observations to explore how and why the teachers used the manipulatives as they did. An examination of the participants’ statements and behaviors indicated that using manipulatives was little more than a diversion in classrooms where teachers were not able to represent mathematics concepts themselves. The teachers …

Densities Of 4-Ranks Of K(2) Of Rings Of Integers., Robert Burke Osburn

LSU Historical Dissertations and Theses

Conner and Hurrelbrink established a method of determining the structure of the 2-Sylow subgroup of the tame kernel K2( O ) for certain quadratic number fields. Specifically, the 4-rank for these fields was characterized in terms of positive definite binary quadratic forms. Numerical calculations led to questions concerning possible density results of the 4-rank of tame kernels. In this thesis, we succeed in giving affirmative answers to these questions.

A Study Of Mathematics Course Sequence And Student Performance In Mathematics In A Block Scheduled High School, John Harvell Moody

Doctoral Dissertations

The 1983 study of the condition of American Education, A Nation at Risk, brought a significant amount of attention to the way in which schools provided students with the skills necessary to be productive citizens. Many of the recommendations contained in A Nation at Risk focused on the perceived poor performance of American students when compared to their counterparts worldwide. The year after publication of A Nation at Risk, the National Commission on Time and Learning published Prisoners of Time, a report that called for the establishment of high academic standards for students and a major restructuring of the school …

Learning And Understanding In Abstract Algebra, Bradford Reed Findell

Doctoral Dissertations

Students' learning and understanding in an undergraduate abstract algebra class were described using Tall and Vinner's notion of a concept image, which is the entire cognitive structure associated with a concept, including examples, nonexamples, definitions, representations, and results. Prominent features and components of students' concept images were identified for concepts of elementary group theory, including group, subgroup, isomorphism, coset, and quotient group.

Analysis of interviews and written work from five students provided insight into their concept images, revealing ways they understood the concepts. Because many issues were related to students' uses of language and notation, the analysis was essentially semiotic, …

Étude Numérique Et Expérimentale De L'Absorption Acoustique Et De La Transparence Acoustique Des Matériaux Poreux Hétérogènes En Basses Fréquences Dans Le But D'Identifier Des Solutions À Fort Potentiel D'Applicabilité, Noureddine Atalla, Celse K. Amédin, Raymond Panneton, Franck Sgard

Rapports de recherche scientifique

De par les niveaux élevés ainsi que le nombre de travailleurs concernés, les problèmes du bruit produit par les machines sont extrêmement importants et fort complexes. Tous les secteurs sont concernés : fabrication, forage, transport, bâtiment, manufacturier, etc. L'utilisation de dispositifs absorbants acoustiques constitue un moyen de réduire ces niveaux de bruit. Parmi ces dispositifs, on distingue les systèmes passifs dissipatifs qui consistent à placer un matériau absorbant sur le trajet de l'onde à absorber. Ces dispositifs passifs dissipatifs sont constitués essentiellement de matériaux poreux classiques (laines, mousses). Ils s’avèrent efficaces en hautes et moyennes fréquences mais très peu performants …

Logiciel D'Analyse Et De Gestion Du Bruit Ouie 2000 : Développement Et Intégration D'Un Modèle D'Acoustique Prévisionnelle, André L'Espérance

Rapports de recherche scientifique

Le bruit est un des principaux problèmes de santé et de sécurité au travail, mais le manque d’outils d’analyse rend la planification et la mise en œuvre de programmes d’intervention difficiles à réaliser. Pour répondre à ce besoin, le développement d’un logiciel d’analyse et de gestion du bruit a été entrepris. Pour être complet et efficace, un modèle d’acoustique prévisionnelle spécialement adapté devait cependant être mis au point. Le présent projet de recherche et développement visait à développer ce modèle et à développer les fonctionnalités graphiques et les fonctionnalités d’analyse en vue de réaliser un outil complet pouvant être accessible …

On K-Conjugacy Classes Of Maximal Tori In Semi-Simple Algebraic Groups., Uroyoan Ramon-Emeterio Walker

LSU Historical Dissertations and Theses

An attempt was made to make this a self-contained reading. The first three chapters are intended to provide the necessary background. Chapter one develops the tools needed from Galois Cohomology. Chapter two is a brief description of involutions, and in chapter three we define the notion of (linear) algebraic group, we give some examples and discuss some of their properties. In chapter four, we discuss some variants of the classical Skolem-Noether theorem, requiring only that the subalgebra have a unique faithful representation of full degree over a separable closure. We verify that we can extend every isomorphism to the whole …

Orientations Of Graphs Which Have Small Directed Graph Minors., Glenn Randolph Berman

LSU Historical Dissertations and Theses

Graphs are characterized by whether or not they have orientations to avoid one or more of the digraphs K&ar;3 , S&ar;3 , and P&ar;3 . K&ar;3 , S&ar;3 and P&ar;3 are created by starting with a triangle, a three point star, or a path of length three respectively, and replacing each edge with a pair of arcs in opposite directions. Conditions are described when all orientations of 3-connected and 4-connected graphs must have one or more of the above digraphs as a minor. It is shown that double wheels, and double wheels without an axle, are the only 4-connected graphs …

Vlsi Implementation Of A Massively Parallel Wavelet Based Zerotree Coder For The Intelligent Pixel Array, Geoffrey N. Alagoda

Theses: Doctorates and Masters

In the span of a few years, mobile multimedia communication has rapidly become a significant area of research and development constantly challenging boundaries on a variety of technologic fronts. Mobile video communications in particular encompasses a number of technical hurdles that generally steer technological advancements towards devices that are low in complexity, low in power usage yet perform the given task efficiently. Devices of this nature have been made available through the use of massively parallel processing arrays such as the Intelligent Pixel Processing Array. The Intelligent Pixel Processing array is a novel concept that integrates a parallel image capture …

Implementation Of Performance Assessment Tasks To Improve Third-Grade Achievement, Christine Gary-Johnson

Abraham S. Fischler College of Education ETD Archive

Performance assessment tasks are activities in which students demonstrate in a variety of ways their ability to think creatively and critically in producing a product. The research question that guided this. project was, Can the. implementation of performance assessment tasks improve 3rd-grade achievement as measured by the Baltimore Quarterly Assessment (Baltimore City Public School System, 1996a)? The participants in the program were 74 third-grade students, a cadre of 3 classroom teachers, 1 master teacher, 1 consultant teacher, 1 instructional support teacher, 1 Chapter I teacher, 1 parent liaison, and 2 administrators at Rosemont Elementary. School #63 in Baltimore, Maryland. Extensive …

Depth-First Search Embedded Wavelet Algorithm For Hardware Implementation, Li-Minn Ang

Theses: Doctorates and Masters

The emerging technology of image communication over wireless transmission channels requires several new challenges to be simultaneously met at the algorithm and architecture levels. At the algorithm level, desirable features include high coding performance, bit stream scalability, robustness to transmission errors and suitability for content-based coding schemes. At the architecture level, we require efficient architectures for construction of portable devices with small size and low power consumption. An important question is to ask if a single coding algorithm can be designed to meet the diverse requirements. Recently, researchers working on improving different features have converged on a set of coding …

Artin-Schreier Families And 2-D Cycle Codes, Cem Guneri

LSU Doctoral Dissertations

We start with the study of certain Artin-Schreier families. Using coding theory techniques, we determine a necessary and sufficient condition for such families to have a nontrivial curve with the maximum possible number of rational points over the finite field in consideration. This result produces several nice corollaries, including the existence of certain maximal curves; i.e., curves meeting the Hasse-Weil bound.We then present a way to represent two-dimensional (2-D) cyclic codes as trace codes starting from a basic zero set of its dual code. This representation enables us to relate the weight of a codeword to the number of rational …

Unit Sum Numbers Of Abelian Groups And Modules, Christopher Meehan

Doctoral

We discuss some open questions regarding the unit sum numbers of free modules of arbitrary infinite rank over commutative rings and, in particular, over principal ideal domains. The unit sum numbers of rational groups are then investigated: the importance of the rational prime 2 being an automorphism of the rational group is discussed and other results are achieved considering the number and distribution of rational primes which are, or are not, automorphisms of the group. We next prove the existence of rational groups with unit sum numbers greater than 2 but of finite value and we estimate an upper bound …

A Special Remedial Program To Improve The Skills Of Failing Eighth-Grade Students, John J. O'Malley Jr.

Abraham S. Fischler College of Education ETD Archive

This report describes an afterschool remedial program during the 2000-2001 school year at Forest Grove Middle School in Worcester, Massachusetts. The remedial program was an effort to improve the skills of 8th-grade students who fall short of the state norms on the mandatory 8th-grade Massachusetts Comprehensive Assessment Test (MCAS; Massachusetts Department of Education, 1999). An analysis of the 1999 test indicated that 480 8th-grade students in a 905-pupil enrollment at the school fell short of the passing grade, 51% in the mathematics section and 21% in the language arts section.

Planned solution strategies included (a) an afterschool and vacation remedial …

The Averaging Lemma, Ronald A. Devore, Guergana Petrova

Faculty Publications

No abstract provided.

On Logistic And Some New Discrimination Rules:Charecterizations,Inference And Application., Supratik Roy Dr.

Doctoral Theses

Introduction and Summary Consider the problem of classification of an observation into one of two specified populations. Fisher's classification rale, just as several other rules commonly used in practice, depends only on the ratio of the individual densities fi(x), i = 1,2. This led Cox (1966),/27) to model the "posterior odds" by a simple function. Specifically,Cox's logistic discrimination (LGD) rule is then based on the statistic a + 'ßx. This has the advantage that individual densities f.(x) need not be known and we only need to estimate the parameters a and B.Another advantage, which is claimed , is that the …