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Articles 1 - 21 of 21
Full-Text Articles in Physical Sciences and Mathematics
Development Of Cfl-Free, Explicit Schemes For Multidimensional Advection-Reaction Equations, Hong Wang, Jiangguo Liu
Development Of Cfl-Free, Explicit Schemes For Multidimensional Advection-Reaction Equations, Hong Wang, Jiangguo Liu
Faculty Publications
We combine an Eulerian–Lagrangian approach and multiresolution analysis to develop unconditionally stable, explicit, multilevel methods for multidimensional linear hyperbolic equations. The derived schemes generate accurate numerical solutions even if large time steps are used. Furthermore, these schemes have the capability of carrying out adaptive compression without introducing mass balance error. Computational results are presented to show the strong potential of the numerical methods developed.
Helping At-Risk Students Add Up: Motivational Lessons For Students In High School Mathematics, Karen Beckner
Helping At-Risk Students Add Up: Motivational Lessons For Students In High School Mathematics, Karen Beckner
Mahurin Honors College Capstone Experience/Thesis Projects
No abstract provided.
Math Major, Math Major, Arthur T. Benjamin
Math Major, Math Major, Arthur T. Benjamin
All HMC Faculty Publications and Research
Sung to the tune of "Matchmaker" from Fiddler on the Roof:
Math major, math major, make me some math.
Find me a prime, sketch me a path.
Math major, math major look through your books,
And make me some perfect math.
Σary, Minnesota State University Moorhead, Mathematics Department
Σary, Minnesota State University Moorhead, Mathematics Department
Math Department Newsletters
No abstract provided.
Incorporating Technology In Mathematics Education: A Suite Of E-Activities For The Modem Mathematics Classroom, Jennifer E. Youngberg
Incorporating Technology In Mathematics Education: A Suite Of E-Activities For The Modem Mathematics Classroom, Jennifer E. Youngberg
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
National studies indicate major deficiencies in students' understanding of mathematics. Research suggests that students tend to view mathematics as a set of computational rules rather than a process of discovery and a tool for problem-solving. Most students fail to grasp the concepts behind the computations.
Technology provides a partial solution to this problem. Over the past decade, computers have emerged as a powerful tool in education. Computers place the control of action in the learning process with the student. They allow students to experiment with, explore, and discover mathematics at their own pace. With computers, students can consider more examples …
Mathematical Constance (A Poem Dedicated To Constance Reid), Arthur T. Benjamin
Mathematical Constance (A Poem Dedicated To Constance Reid), Arthur T. Benjamin
All HMC Faculty Publications and Research
Mathematical Constance (A Poem Dedicated to Constance Reid)
I think that I shall never see
A constant lovelier than e,
Whose digits are too great too state,
They're 2.71828…
And e has such amazing features
It's loved by all (but mostly teachers).
With all of e's great properties
Most integrals are done with … ease.
Theorems are proved by fools like me
But only Euler could make an e.
I suppose, though, if I had to try
To choose another constant, I
Might offer i or phi or pi.
But none of those would satisfy.
Of all the …
There Really Are No Contradictions: A Response, Calvin Jongsma
There Really Are No Contradictions: A Response, Calvin Jongsma
Faculty Work Comprehensive List
Response to "There are no Contradictions" by T.G. Ammon in The College Mathematics Journal, Vol. 31, No. 1 (Jan., 2000), pp. 48-49 which was part of the "Fallacies, Flaws, and Flimflam" column edited by Ed Barbeau of the Department of Mathematics at the University of Toronto.
Some Problem In Homogenization., M. Rajesh Dr.
Abstracting Aristotle’S Philosophy Of Mathematics, John J. Cleary
Abstracting Aristotle’S Philosophy Of Mathematics, John J. Cleary
Research Resources
In the history of science perhaps the most influential Aristotelian division was that
between mathematics and physics. From our modern perspective this seems like an unfortunate deviation from the Platonic unification of the two disciplines, which guided Kepler and Galileo towards the modern scientific revolution. By contrast, Aristotle’s sharp distinction between the disciplines seems to have led to a barren scholasticism in physics, together with an arid instrumentalism in Ptolemaic astronomy. On the positive side, however, astronomy was liberated from commonsense realism for the conceptual experiments of Aristarchus of Samos, whose heliocentric hypothesis was not adopted by later astronomers because …
Stochastic Comparision And Dependence Among Order Statistics,Spacing And Concomitants Of Order Statistics., Baha-Eldin Khaledi Dr.
Stochastic Comparision And Dependence Among Order Statistics,Spacing And Concomitants Of Order Statistics., Baha-Eldin Khaledi Dr.
Doctoral Theses
The simplest and the most common way of comparing two random variables is through their means and variances. It may happen that in some cases the median of X is larger than the median of Y, while the mean of X is smaller than the mean of Y. However, this confusion will not arise if the random variables are stochastically ordered. Similarly, the same may happen if one would like to compare the variability of X with that of Y based only on numerical measures of variability. Besides, these characteristics of distributions might not exist in some cases. In most …
Mapping Quantitative Trait Loci In Humans: Some Statistical Contributions., Saurabh Ghosh Dr.
Mapping Quantitative Trait Loci In Humans: Some Statistical Contributions., Saurabh Ghosh Dr.
Doctoral Theses
Maty qualitative tralts - such an, milk yield la cows, blood pressure in lumans --are known to be determined primarly, though zot exclusively, by inherited genetic luctora. It ls the of coasklerable impartance to identify chromosontal locations of tho genes that control a quantitative character. Linkage analysis (Ou 1990), which deals with the deduction of linkagn and estimation of recombination fractions among the loci controlling a qualitative/quantitative character and major loci wkoo poertions are knows aprfori, is widely used for localisation of gens. Although statistical methodologies for magplag gemen determining dichotomos qualitative charactes in humans aro well-developed, the demicrant of …
Boolean Functions With Important Cryptographic Properties., Subhamoy Maitra Dr.
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.
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 …
Topological Conjugacy And Rigidity Of Affine Actions., Siddhartha Bhattacharya Dr.
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.
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
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.
Mathematics As Worship, David J. Stucki
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.
Open To Reason, David L. Neuhouser
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.
Depth-First Search Embedded Wavelet Algorithm For Hardware Implementation, Li-Minn Ang
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 …
Unit Sum Numbers Of Abelian Groups And Modules, Christopher Meehan
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 …
Artin-Schreier Families And 2-D Cycle Codes, Cem Guneri
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 …