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2007

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Articles 181 - 210 of 541

Full-Text Articles in Mathematics

Uniform Estimates For Eulerian-Lagrangian Methods For Singularly Perturbed Time-Dependent Problems, Hong Wang, Kaixin Wang Jun 2007

Uniform Estimates For Eulerian-Lagrangian Methods For Singularly Perturbed Time-Dependent Problems, Hong Wang, Kaixin Wang

Faculty Publications

We prove a priori optimal-order error estimates in a weighted energy norm for several Eulerian–Lagrangian methods for singularly perturbed, time-dependent convection-diffusion equations with full regularity. The estimates depend only on certain Sobolev norms of the initial and right-hand side data, but not on ε or any norm of the true solution, and so hold uniformly with respect to ε. We use the interpolation of spaces and stability estimates to derive an ε-uniform estimate for problems with minimal or intermediate regularity, where the convergence rates are proportional to certain Besov norms of the initial and right-hand side data.

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Mars Exploration Rover: Mathematics And People Behind The Mission, Uffe Thomas Jankvist, Bjørn Toldbod Jun 2007

Mars Exploration Rover: Mathematics And People Behind The Mission, Uffe Thomas Jankvist, Bjørn Toldbod

The Mathematics Enthusiast

This paper is a selective study of the mathematics and people involved with a specific space mission, namely the Mars Exploration Rover (MER) mission launched in 2003. The specific mathematics of the MER mission are sought uncovered through interviews with applied scientists who worked with different aspects of the mission at the Jet Propulsion Laboratory (JPL). Some of the more specific questions attempted answered through this article for instance concerns if the aerospace industry, exemplified by the MER mission, calls for new developments in mathematics or if it mostly relies on well established theories; how much independence the scientists have …

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On The Solution To Octic Equations, Raghavendra G. Kulkarni Jun 2007

On The Solution To Octic Equations, Raghavendra G. Kulkarni

The Mathematics Enthusiast

We present a novel decomposition method to decompose an eighth-degree polynomial equation, into its two constituent fourth-degree polynomials, as factors, leading to its solution. The salient feature of the octic equation solved here is that, the sum of its four roots being equal to the sum of the remaining four roots. We derive the condition to be satisfied by coefficients so that the given octic is solvable by the proposed method.

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Mathematics Education And Neurosciences: Relating Spatial Structures To The Development Of Spatial Sense And Number Sense, Fenna Van Nes, Jan De Lange Jun 2007

Mathematics Education And Neurosciences: Relating Spatial Structures To The Development Of Spatial Sense And Number Sense, Fenna Van Nes, Jan De Lange

The Mathematics Enthusiast

The Mathematics Education and Neurosciences (MENS) project is aimed at exploring the development of the mathematical abilities of young (four- to six-year old) children. It is initiated to integrate research from mathematics education with research from educational neuroscience in order to come to a better understanding of how the early skills of young children can best be fostered for supporting the development of mathematical abilities in an educational setting. This paper is specifically focused on the design research that is being conducted from the perspective of mathematics education in which we are investigating the relationship between young children’s insight into …

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Non-Linear Functions In Secondary School Of Lower Qualification Level (German Hauptschule), Astrid Beckmann Jun 2007

Non-Linear Functions In Secondary School Of Lower Qualification Level (German Hauptschule), Astrid Beckmann

The Mathematics Enthusiast

This article reports of the effectiveness of introducing non-linear functions in a German Hauptschule. Some research based recommendations are provided for practitioners with the goal of improving student competencies in lieu of PISA.

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Looking Back At The Beginning: Critical Thinking In Solving Unrealistic Problems, Mark Applebaum, Roza Leikin Jun 2007

Looking Back At The Beginning: Critical Thinking In Solving Unrealistic Problems, Mark Applebaum, Roza Leikin

The Mathematics Enthusiast

We believe that problem-solving skills engage critical thinking at every phase of problem solution. In this research a special attention is given to the fist phase - "understanding the problem". We consider this phase as a continuation of all the previous mathematical experience, in which understanding of new problems requires "looking back" at those solved in the past. Evaluation of the givens in the problem sometimes allows immediate solution whereas in other cases it shows that solution does not exist. We found that it is not easy for mathematics teachers to discover that a problem includes contradictory (i.e. unrealistic) conditions. …

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Gender Disparity In Mathematical Performance Revisited: Can Training In Problem Solving Bring Difference Between Boys And Girls?, M.A. Adeleke Jun 2007

Gender Disparity In Mathematical Performance Revisited: Can Training In Problem Solving Bring Difference Between Boys And Girls?, M.A. Adeleke

Essays in Education

This study examined the problem solving performance of male and female students’ mathematical problem-solving performances using Conceptual Learning Strategy (CLS) and Procedural Learning Strategy PLS). A sample of 124 science students assigned into CLS, PLS and Conventional Method (CM) groups were involved in the study making use of pretest, post test control group design. The sample was drawn from three intact Senior Secondary School Two (SSII) classes from three local government Areas of Osun State in Nigeria and were taught for a period of eight weeks. Findings of the study showed a non significant difference in the performance of boys …

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Proof Without Words: A Graph Theoretic Decomposition Of Binomial Coefficients, Joseph Demaio Jun 2007

Proof Without Words: A Graph Theoretic Decomposition Of Binomial Coefficients, Joseph Demaio

Faculty Articles

No abstract provided.

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Mathematics: Always Important, Never Enough: A Christian Perspective On Mathematics And Mathematics Education, Calvin Jongsma Jun 2007

Mathematics: Always Important, Never Enough: A Christian Perspective On Mathematics And Mathematics Education, Calvin Jongsma

Pro Rege

This article is an edited version of the keynote address delivered by Dr. Jongsma at the B.J. Haan Education Conference on Teaching Math in the Christian School, held at Dordt College on March 9, 2006, for elementary and secondary school mathematics teachers, primarily in Christian schools. The article was earlier published online in the 2006 Journal of the ACMS (http://www.acmsonline.org/Jongsma.htm).

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Epsilon-Unfolding Orthogonal Polyhedra, Mirela Damian, Robin Flatland, Joseph O'Rourke Jun 2007

Epsilon-Unfolding Orthogonal Polyhedra, Mirela Damian, Robin Flatland, Joseph O'Rourke

Computer Science: Faculty Publications

An unfolding of a polyhedron is produced by cutting the surface and flattening to a single, connected, planar piece without overlap (except possibly at boundary points). It is a long unsolved problem to determine whether every polyhedron may be unfolded. Here we prove, via an algorithm, that every orthogonal polyhedron (one whose faces meet at right angles) of genus zero may be unfolded. Our cuts are not necessarily along edges of the polyhedron, but they are always parallel to polyhedron edges. For a polyhedron of n vertices, portions of the unfolding will be rectangular strips which, in the worst case, …

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Problems Related To Efficacy Measurement And Analyses, Sibabrata Banerjee May 2007

Problems Related To Efficacy Measurement And Analyses, Sibabrata Banerjee

Dissertations

In clinical research it is very common to compare two treatments on the basis of an efficacy variable. More specifically, if X and Y denote the responses of patients on the two treatments A and B, respectively, the quantity P(Y>X) (which can be called the probabilistic index for the Effect Size), is of interest in clinical statistics. The objective of this study is to derive an efficacy measure that would compare two treatments more informatively and objectively compared to the earlier approaches. Kernel density estimation is a useful non-parametric method that has not been well utilized as an applied …

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Prediction Of Mrna Polyadenylation Sites In The Human Genome And Mathematical Modeling Of Alternative Polyadenylation, Yiming Cheng May 2007

Prediction Of Mrna Polyadenylation Sites In The Human Genome And Mathematical Modeling Of Alternative Polyadenylation, Yiming Cheng

Dissertations

Messenger RNA (mRNA) polyadenylation plays many important roles in the cell, such as transcription termination, mRNA stability and transportation, and mRNA translation in eukaryotic cells. A large number of human and mouse genes have multiple polyadenylation sites (referred to as poly(A) sites) that lead to variable transcripts, some of which are translated into various protein products with different functions. However, the details about when and where the polyadenylation occurs, and how pre-mRNA switches from one poly(A) site to another are still unknown. This kind of 3 '-end processing can be regulated by the cell environment, cell cycle stage, and tissue …

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Domains Of Definition Of Monge-Ampère Operators On Compact Kähler Manifolds, Dan Coman, Vincent Guedj, Ahmed Zeriahi May 2007

Domains Of Definition Of Monge-Ampère Operators On Compact Kähler Manifolds, Dan Coman, Vincent Guedj, Ahmed Zeriahi

Mathematics - All Scholarship

Let (X, w) be a compact Kahler manifold. We introduce and study the largest set DMA(X, w) of w-plurisubharmonic (psh) functions on which the complex Monge-Ampere operator is well defined. It is much larger than the corresponding local domain of definition, though still a proper subset of the set PSH(X, w) of all w-psh functions. We prove that certain twisted Monge-Ampere operators are well defined for all w-psh functions. As a consequence, any w-psh function with slightly attenuated singularities has finite weighted Monge-Ampere energy.

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Introduction (2007), Angela Hare May 2007

Introduction (2007), Angela Hare

ACMS Conference Proceedings 2007

Sixteenth Conference of the Association of Christians in the Mathematical Sciences

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Table Of Contents (2007), Association Of Christians In The Mathematical Sciences May 2007

Table Of Contents (2007), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2007

Sixteenth Conference of the Association of Christians in the Mathematical Sciences

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Schedule (2007), Association Of Christians In The Mathematical Sciences May 2007

Schedule (2007), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2007

Sixteenth Conference of the Association of Christians in the Mathematical Sciences

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On Connections Between Univalent Harmonic Functions, Symmetry Groups, And Minimal Surfaces, Stephen M. Taylor May 2007

On Connections Between Univalent Harmonic Functions, Symmetry Groups, And Minimal Surfaces, Stephen M. Taylor

Theses and Dissertations

We survey standard topics in elementary differential geometry and complex analysis to build up the necessary theory for studying applications of univalent harmonic function theory to minimal surfaces. We then proceed to consider convex combination harmonic mappings of the form f=sf_1+(1-s) f_2 and give conditions on when f lifts to a one-parameter family of minimal surfaces via the Weierstrauss-Enneper representation formula. Finally, we demand two minimal surfaces M and M' be locally isometric, formulate a system of partial differential equations modeling this constraint, and calculate their symmetry group. The group elements generate transformations that when applied to a prescribed harmonic …

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A Qualitative Analysis Of Hybrid Control Systems, Anca Georgeta Williams May 2007

A Qualitative Analysis Of Hybrid Control Systems, Anca Georgeta Williams

Dissertations and Theses

Hybrid Control Systems are increasingly investigated as models for control systems where the interaction between continuous and discrete processes is tightly integrated. As yet, there is no general agreement as to what constitutes a canonical hybrid system. Rather various subclasses of systems combining continuous evolution and discrete event characteristics are analyzed for each application. In this dissertation we first unify the presentation of hybrid systems with a rich model which encompasses most examples of interest. We classify the available results and show how they fit together within the different subcategories. In the main part of the dissertation we prove that …

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Which Chessboards Have A Closed Knight's Tour Within The Cube?, Joseph Demaio May 2007

Which Chessboards Have A Closed Knight's Tour Within The Cube?, Joseph Demaio

Faculty Articles

A closed knight's tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. When the chessboard is translated into graph theoretic terms the question is transformed into the existence of a Hamiltonian cycle. There are two common tours to consider on the cube. One is to tour the six exterior n x n boards that form the cube. The other is to tour within the n stacked copies of the n x n board that form the cube. This paper is concerned with the latter. In this paper …

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Some Results Of Backward Itô Formula, Guiseppe Da Prato, Jose-Luis Menaldi, Luciano Tubaro May 2007

Some Results Of Backward Itô Formula, Guiseppe Da Prato, Jose-Luis Menaldi, Luciano Tubaro

Mathematics Faculty Research Publications

We use the notion of backward integration, with respect to a general Lévy process, to treat, in a simpler and unifying way, various classical topics as: Girsanov theorem, rst order partial differential equations, the Liouville (or Lyapunov) equations and the stochastic characteristic method.

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Preprocessing Of Sar Interferometric Data Using Anisotropic Diffusion Filter, Kenneth Sartor, Josef Vaughn De Allen, Emile Ganthier, Gnana Bhaskar Tenali May 2007

Preprocessing Of Sar Interferometric Data Using Anisotropic Diffusion Filter, Kenneth Sartor, Josef Vaughn De Allen, Emile Ganthier, Gnana Bhaskar Tenali

Mathematics and System Engineering Faculty Publications

The most commonly used smoothing algorithms for complex data processing are blurring functions (i.e., Hanning, Taylor weighting, Gaussian, etc.). Unfortunately, the filters so designed blur the edges in a Synthetic Aperture Radar (SAR) scene, reduce the accuracy of features, and blur the fringe lines in an interferogram. For the Digital Surface Map (DSM) extraction, the blurring of these fringe lines causes inaccuracies in the height of the unwrapped terrain surface. Our goal here is to perform spatially non-uniform smoothing to overcome the above mentioned disadvantages. This is achieved by using a Complex Anisotropic Non-Linear Diffuser (CANDI) filter that is a …

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Alliance Partitions In Graphs., Jason Lachniet May 2007

Alliance Partitions In Graphs., Jason Lachniet

Electronic Theses and Dissertations

For a graph G=(V,E), a nonempty subset S contained in V is called a defensive alliance if for each v in S, there are at least as many vertices from the closed neighborhood of v in S as in V-S. If there are strictly more vertices from the closed neighborhood of v in S as in V-S, then S is a strong defensive alliance. A (strong) defensive alliance is called global if it is also a dominating set of G. The alliance partition number (respectively, strong …

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Statistical Pronouncements V, Shlomo S. Sawilowsky May 2007

Statistical Pronouncements V, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

No abstract provided.

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Existence Of Minimizers And Necessary Conditions In Set-Valued Optimization With Equilibrium Constraints, Truong Q. Bao, Boris S. Mordukhovich May 2007

Existence Of Minimizers And Necessary Conditions In Set-Valued Optimization With Equilibrium Constraints, Truong Q. Bao, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we study set-valued optimization problems with equilibrium constraints (SOPEOs) described by parametric generalized equations in the form 0 is an element of the set G(x) + Q(x) where both G and Q are set-valued mappings between infinite-dimensional spaces. Such models particularly arise from certain optimization-related problems governed by set-valued variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish general results on the existence of optimal solutions under appropriate assumptions of the PalaisSmale type and then derive necessary conditions for optimality in the models under consideration by using advanced tools of variational analysis and generalized differentiation.

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Σary, Minnesota State University Moorhead, Mathematics Department May 2007

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

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On Distribution Of Integral Well-Rounded Lattices In Dimension Two, Lenny Fukshansky May 2007

On Distribution Of Integral Well-Rounded Lattices In Dimension Two, Lenny Fukshansky

CMC Faculty Publications and Research

Lecture given at the Illinois Number Theory Fest, May 2007.

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Bounds On K-Regular Ramanujan Graphs And Separator Theorems, James Skees May 2007

Bounds On K-Regular Ramanujan Graphs And Separator Theorems, James Skees

Masters Theses & Specialist Projects

Expander graphs are a family of graphs that are highly connected. Finding explicit examples of expander graphs which are also sparse is a difficult problem. The best type of expander graph in a. certain sense is a Ramanujan graph. Families of graphs that have separator theorems fail to be Ramanujan if the vertex set gets sufficiently large. Using separator theorems to get an estimate on the expanding constant of graphs, we get bounds 011 the number of vertices for such fc-regular graphs in order for them to be Ramanujan.

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Loop Edge Estimation In 4-Regular Hamiltonian Graphs, Yale Madden May 2007

Loop Edge Estimation In 4-Regular Hamiltonian Graphs, Yale Madden

Masters Theses & Specialist Projects

In knot theory, a knot is defined as a closed, non-self-intersecting curve embedded in three-dimensional space that cannot be untangled to produce a simple planar loop. A mathematical knot is essentially a conventional knot tied with rope where the ends of the rope have been glued together. One way to sample large knots is based on choosing a 4-regular Hamiltonian planar graph. A method for generating rooted 4-regular Hamiltonian planar graphs with n vertices is discussed in this thesis. In the generation process of these graphs, some vertices are introduced that can be easily eliminated from the resulting knot diagram. …

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Why? Why? Why?: Future Teachers Discover Mathematical Depth, Perla Myers Phd May 2007

Why? Why? Why?: Future Teachers Discover Mathematical Depth, Perla Myers Phd

Mathematics: Faculty Scholarship

In mathematics, it is not just the how, the procedures for solving problems, that is important, but the why, the underlying concepts, Perla Myers explains. When teachers regain the childlike wonder that leads them to seek the why of math, they will be better able to help their students learn.

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Sas Macro For Hierarchical Dependence In Meta Analysis, Matthew Wayne Maw May 2007

Sas Macro For Hierarchical Dependence In Meta Analysis, Matthew Wayne Maw

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This project implemented a simple and useful SAS (Statistical Analysis Software) macro for meta-analysis. The macro was specifically designed for hierarchically dependent meta-analysis but may also be used for independent meta-analysis. Two data files are necessary for this macro. One data file contains the study names, control and treatment group sizes with corresponding means and standard errors, covariates to be tested, an indicator variable noting hierarchically dependent study groups, and a variable providing the degrees of freedom for interdependent studies. The second file contains a variance/covariance matrix for the studies. The macro returns useful information such as study estimates and …

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